Arduino Factory Automation

arXiv:physics/0411123v2 [physics.acc-ph] 23 Nov 2004

Bnl-72369-2004, Fnal-Tm-2259, Lbnl-55478

Neutrino Factory and Beta Beam Experiments and Development C. Albright,1 V. Barger,2 J. Beacom,1 J.S. Berg,3 E. Black,4 A. Blondel,5 S. Bogacz,6 S. Brice,1 S. Caspi,7 W. Chou,1 M. Cummings,8 R. Fernow,3 D. Finley,1 J. Gallardo,3 S. Geer,1 J.J. Gomez-Cadenas,9 M. Goodman,10 D. Harris,1 P. Huber,11 A. Jansson,1 C. Johnstone,1 S. Kahn,3 D. Kaplan,4 H. Kirk,3 T. Kobilarcik,1 M. Lindner,11 K. McDonald,12 O. Mena,1 D. Neuffer,1 V. Palladino,13 R. Palmer,3 K. Paul,14 P. Rapidis,1 N. Solomey,4 P. Spampinato,15 D. Summers,16 Y. Torun,4 K. Whisnant,17 W. Winter,11 M. Zisman,7 and The Neutrino Factory and Muon Collider Collaboration 1Fermi National Accelerator Laboratory, Batavia, IL 60510, USA 3Brookhaven National Laboratory, Upton, NY 11973, USA 5DPNC, Section de Physique, Universit´e de Gen`eve, Switzerland 6Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606, USA 7Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

Universidad De Valencia, E-46100 Burjassot, Spain

10Argonne National Laboratory, Argonne, IL 60439, USA 11Technischen Universit¨at M¨unchen, Garching, Germany 13INFN Napoli e Universit`a Federico II, Napoli, Italy

Urbana-Champaign, Il 60115, Usa

15Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Abstract

The long-term prospects for fully exploring three-flavor mixing in the neutrino sector depend upon an ongoing and increased investment in the appropriate accelerator R&D. Two new concepts have been proposed that would revolutionize neutrino experiments, namely the Neutrino Factory and the Beta Beam facility. These new facilities would dramatically improve our ability to test the three-flavor mixing framework, measure CP violation in the lepton sector, and perhaps determine the neutrino mass hierarchy, and, if necessary, probe extremely small values of the mixing angle θ13. The stunning sensitivity that could be achieved with a Neutrino Factory is described, together with our present understanding of the corresponding sensitivity that might be achieved with a Beta Beam facility.

In the Beta Beam case, additional study is required to better understand the optimum Beta Beam energy, and the achievable sensitivity. Neither a Neutrino Factory nor a Beta Beam facility could be built without significant R&D. An impressive Neutrino Factory R&D effort has been ongoing in the U.S. and elsewhere over the last few years and significant progress has been made towards optimizing the design, developing and testing the required accelerator components, and significantly reducing the cost. The recent progress is described here. There has been no corresponding activity in the U.S. on Beta Beam facility design and, given the very limited resources, there is little prospect of starting a significant U.S. Beta Beam R&D effort in the near future. However, the Beta Beam concept is interesting, and progress on its development in Europe should be followed. The Neutrino Factory R&D program has reached a critical stage in which support is required for two crucial international experiments and a third-generation international design study. If this support is forthcoming, a Neutrino Factory could be added to the Neutrino Community’s road map in about a decade.

Preface

In response to the remarkable recent discoveries in neutrino physics, the APS Divisions of Particles and Fields, and of Nuclear Physics, together with the APS Divisions of Astrophysics and the Physics of Beams, have organized a year long Study on the Physics of Neutrinos that began in the fall of 2003. Within the context of this study, the Neutrino Factory and Beta Beam Experiments and Development Working Group was charged with reviewing, and if possible advancing, our understanding of the physics capabilities and design issues for these two new types of future neutrino facilities. To fulfill this charge, the working group conducted a Workshop at ANL March 3–4, 2004. The presentations and discussion at this Neutrino Factory and Beta Beams Workshop, together with the Neutrino Factory Design work of the Neutrino Factory and Muon Collider Collaboration , form the basis for this report.

Over the last few years, there have been a series of workshops that have explored the design and physics capabilities of Neutrino Factories. These meetings include the international NUFACT Workshop series [3, 4, 5, 6, 7], many smaller, more specialized, workshops focused on specific parts of Neutrino Factory design and technology, and two more detailed Feasibility Studies [8, 9]. In addition, a large body of literature documents the physics motivation for Neutrino Factories and the progress that has been made towards realizing this new type of neutrino facility. The Neutrino Factory related goals for the working group were therefore to (i) review and summarize the results of the extensive work already done, and (ii) to update the picture utilizing the design study resources of the Neutrino Factory and Muon Collider Collaboration, and the latest results from those making detailed studies of the physics capabilities of Neutrino Factories.

The Beta Beam Concept Is Several Years

younger than the Neutrino Factory concept, and the community’s understanding of both the physics capabilities and the required design parameters (particularly the beam energy)

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is still evolving. Beta Beam R&D is being pursued in Europe, but there is no significant Beta Beam R&D activity in the U.S. Hence, Beta Beam related goals of the working group were necessarily more modest than the equivalent Neutrino Factory related goals. We restricted our ambitions to reviewing the evolving understanding of the physics reach coming out of work from Beta Beam proponents in Europe, and the R&D challenges that must be met before a Beta Beam facility could be built. Possibilities for Neutrino Factory and Beta Beam facilities seem to have caught the imagination of the community. We hope that this report goes some way towards documenting why, and what is required to make these new and very promising neutrino tools a reality.

Introduction

Neutrino Factory [10, 11, 12] and Beta Beam facilities offer two exciting options for the long-term neutrino physics program. In the U.S. there has been a significant investment in developing the concepts and technologies required for a Neutrino Factory, but no equiv- alent investment in developing Beta Beams. In the following we consider first the Neutrino Factory, and then the Beta Beam case.

New accelerator technologies offer the possibility of building, in the not-too-distant future, an accelerator complex to produce and capture more than 1020 muons per year . It has been proposed to build a Neutrino Factory by accelerating the muons from this intense source to energies of several tens of GeV, injecting them into a storage ring having long straight sections, and exploiting the intense neutrino beams that are produced by muons

(1)

offer exciting possibilities to pursue the study of neutrino oscillations and neutrino interac- tions with exquisite precision. To create a sufficiently intense muon source, a Neutrino Factory requires an intense multi-GeV proton source capable of producing a primary proton beam with a beam power of 1 MW or more on target. This is just the proton source required in the medium term for Neutrino Superbeams. Hence, there is a natural evolution from Superbeam experiments in the medium term to Neutrino Factory experiments in the longer term.

The physics case for a Neutrino Factory will depend upon results from the next round of planned neutrino oscillation experiments. If the unknown mixing angle θ13 is small, such that sin2 2θ13 < O(10−2), or if there is a surprise and three-flavor mixing does not completely describe the observed phenomenology, then answers to some or all of the most important neutrino oscillation questions will require a Neutrino Factory. If sin2 2θ13 is large, just below the present upper limit, and if there are no experimental surprises, the physics case for a Neutrino Factory will depend on the values of the oscillation parameters, the achievable sensitivity that will be demonstrated by the first generation of νe appearance experiments, and the nature of the second generation of basic physics questions that will emerge from the first round of results. In either case (large or small θ13), in about a decade the neutrino

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community may need to insert a Neutrino Factory into the global neutrino plan. The option to do this in the next 10–15 years will depend upon the accelerator R&D that is done during the intervening period.

In the U.S., the Neutrino Factory and Muon Collider Collaboration (referred to herein as the Muon Collaboration, or MC) is a collaboration of 130 scientists and engineers devoted to carrying out the accelerator R&D that is needed before a Neutrino Factory could be inserted into the global plan. Much technical progress has been made over the last few years, and the required key accelerator experiments are now in the process of being proposed and approved.

The 2001 Hepap Subpanel Recommended A Level Of

support that is sufficient to perform the critical accelerator R&D during the next 10–15 years. This support level significantly exceeds the present investment in Neutrino Factory R&D. In addition to the U.S. effort, there are active Neutrino Factory R&D groups in Europe , and Japan , and much of the R&D is performed and organized as an international endeavor. Thus, because a Neutrino Factory is potentially the key facility for the long-term neutrino program, Neutrino Factory R&D is an important part of the present global neutrino program. Indeed, the key R&D experiments are seeking funding now, and will need to be supported if Neutrino Factories are to be an option for the future.

Consider next Beta Beam facilities , . It has been proposed to modify the Neu- trino Factory concept by injecting beta-unstable radioactive ions, rather than muons, into a storage ring with long straight sections. This would produce a pure νe or ¯νe beam, depend- ing on the stored ion species. The very low Q value for the decay means that the resulting neutrino beam will have a very small divergence, but it also means that the parent ions must be accelerated to high energies to produce neutrinos with even modest energies. The baseline Beta Beam concept involves accelerating the radioactive ions in the CERN SPS, which yields neutrino beams with energies of a few hundred MeV. The sensitivity of these Beta Beams to small values of θ13 appears to be comparable with the ultimate sensitivity of Superbeam experiments. Better performance might be achieved with higher energy Beta Beams, requiring the ions to be accelerated to at least TeV energies. This requires further study. This R&D is currently being pursued in Europe, where the proponents hope that a Beta Beam facility together with a Superbeam at CERN and a very massive water Cerenkov detector in the Fr´ejus tunnel, would yield a very exciting neutrino program.

In this report, we summarize the expected sensitivities of Neutrino Factory and Beta

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Beam neutrino oscillation experiments, and the status of the R&D required before these exciting facilities could become a part of the neutrino community’s global plan. Exploiting the enthusiastic involvement of the Muon Collaboration in the study, we also describe an up- dated Neutrino Factory design that demonstrates significant progress toward cost reduction for this ambitious facility. The report is organized as follows. Section II describes in some de- tail the Neutrino Factory and Beta Beam design concepts. In Section III, Neutrino Factory and Beta Beam properties are described and compared with conventional neutrino beams.

The neutrino oscillation physics reach is presented in Section IV. Progress on Neutrino Factory designs along with some comments on the possibility of a U.S.-based Beta Beam facility are discussed in Section V. The Neutrino Factory and Beta Beam R&D programs are described in Section VI. A summary is given in Section VII and some recommendations are presented in Section VIII. Finally, in Appendix A a cost scaling with respect to the Feasibility Study-II cost numbers is presented.

Machine Concepts

In this Section we describe the basic concepts that are used to create a Neutrino Factory or a Beta Beam facility. Though the details of the two facilities are quite different, many of the required features have common origins. Both facilities are “secondary beam” machines, that is, a production beam is used to create the secondary beam that eventually provides the neutrino flux for the detector.

For a Neutrino Factory, the production beam is a high intensity proton beam of moderate energy (beams of 2–50 GeV have been considered by various groups) that impinges on a target, typically a high-Z material. The collisions between the proton beam and the target nuclei produce a secondary pion beam that quickly decays into a longer-lived (2.2 µs) muon beam. The remainder of the Neutrino Factory is used to condition the muon beam (see Section II A), accelerate it rapidly to the desired final energy of a few tens of GeV, and store it in a decay ring having a long straight section oriented such that decay neutrinos produced there will hit a detector located thousands of kilometers from the source.

A Beta Beam facility is one in which a pure electron neutrino (from β+) or antineutrino (from β−) beam is produced from the decay of beta unstable radioactive ions circulating in a storage ring. As was the case for the Neutrino Factory, current Beta Beam facility

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concepts are based on using a proton beam to hit a layered production target.

In This

case, nuclear reactions are used to produce secondary particles of a beta-unstable nuclide. The proposed approach uses either spallation neutrons from a high-Z target material or the incident protons themselves to generate the required reactions in a low-Z material. The nuclide of interest is then collected, ionized, accumulated, and accelerated to its final energy.

The process is relatively slow, but this is acceptable as the lifetimes of the required nuclides, of order 1 s, are sufficiently long.

Neutrino Factory

The various components of a Neutrino Factory, based in part on the most recent Feasibil- ity Study (Study-II, referred to herein as FS2) that was carried out jointly by BNL and the U.S. Neutrino Factory and Muon Collider Collaboration, are described briefly below.

Details of the design discussed here are based on the specific scenario of sending a neutrino beam from BNL to a detector in Carlsbad, New Mexico. More generally, however, the design exemplifies a Neutrino Factory for which two Feasibility Studies [8, 9] have demonstrated technical feasibility (provided the challenging component specifications are met), established a cost baseline, and established the expected range of physics performance. It is worth not- ing that the Neutrino Factory design we envision could fit comfortably on the site of an existing laboratory, such as BNL or FNAL. As part of the current Study, we have devel- oped improved methods for accomplishing some of the needed beam manipulations. These improvements are included in the description below.

The main ingredients of a Neutrino Factory include: • Proton Driver: Provides 1–4 MW of protons on target from an upgraded AGS; a new booster at Fermilab would perform equivalently.

• Target and Capture: A high-power target immersed in a 20 T superconducting solenoidal field to capture pions produced in proton-nucleus interactions. The high magnetic field at the target is smoothly tapered down to a much lower value, 1.75 T, which is then maintained through the bunching and phase rotation sections of the Neutrino Factory.

• Bunching and Phase Rotation: We first accomplish the bunching with rf cavities

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of modest gradient, whose frequencies change as we proceed down the beam line. After bunching the beam, another set of rf cavities, with higher gradients and again having decreasing frequencies as we proceed down the beam line, is used to rotate the beam in longitudinal phase space to reduce its energy spread.

• Cooling: A solenoidal focusing channel, with high-gradient 201.25 MHz rf cavities and LiH absorbers, cools the transverse normalized rms emittance from 17 mm·rad to about 7 mm·rad. This takes place at a central muon momentum of 220 MeV/c.

• Acceleration: A superconducting linac with solenoidal focusing is used to raise the muon beam energy to 1.5 GeV, followed by a Recirculating Linear Accelerator (RLA), arranged in a “dogbone” geometry, to provide a 5 GeV muon beam. Thereafter, a pair of cascaded Fixed-Field, Alternating Gradient (FFAG) rings, having quadrupole triplet focusing, is used to reach 20 GeV. Additional FFAG stages could be added to reach a higher beam energy, if the physics requires this.

• Storage Ring: We employ a compact racetrack-shaped superconducting storage ring in which ≈35% of the stored muons decay toward a detector located some 3000 km from the ring. Muons survive for roughly 500 turns.

1.

Proton Driver

The proton driver considered in FS2, and taken here as well, is an upgrade of the BNL Alternating Gradient Synchrotron (AGS) and uses most of the existing components and facilities; parameters are listed in Table I. To serve as the proton driver for a Neutrino Factory, the existing booster would be replaced by a 1.2 GeV superconducting proton linac.

The modified layout is shown in Fig. 1. The AGS repetition rate would be increased from 0.5 Hz to 2.5 Hz by adding power supplies to permit ramping the ring more quickly. No new technology is required for this—the existing supplies would be replicated and the magnet strings would be split into six sectors rather than the two used presently. The total proton charge (1014 ppp in six bunches) is only 40% higher than the current performance of the AGS. However, the bunches required for a Neutrino Factory are shorter than those used in the AGS at present, so there is a large increase in peak current and concomitant need for an improved vacuum chamber; this is included in the upgrade. The six bunches are extracted

To Target Station

FIG. 1: (Color) AGS proton driver layout. separately, spaced by 20 ms, so that the target and rf systems that follow need only deal with single bunches at an instantaneous repetition rate of 50 Hz (average rate of 15 Hz).

The average proton beam power is 1 MW. A possible future upgrade to 2 × 1014 ppp and 5 Hz could give an average beam power of 4 MW. At this higher intensity, a superconducting bunch compressor ring would be needed to maintain the rms bunch length at 3 ns.

If the facility were built at Fermilab, the proton driver would be newly constructed. A number of technical options are presently being explored ,. TABLE I: Proton driver parameters for BNL design.

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2.

Target And Capture

A mercury-jet target is chosen to give a high yield of pions per MW of incident proton power. The 1-cm-diameter jet is continuous, and is tilted with respect to the beam axis. The target layout is shown in Fig. 2. We assume that the thermal shock from the interacting FIG. 2: (Color) Target, capture solenoids and mercury containment.

proton bunch fully disperses the mercury, so the jet must have a velocity of 20–30 m/s to allow the target material to be renewed before the next proton bunch arrives. Calculations of pion yields that reflect the detailed magnetic geometry of the target area have been performed with the MARS code and are reported in Section V. The FS2 design was updated for the present study to improve muon throughput. To avoid mechanical fatigue problems, a mercury pool serves as the beam dump. This pool is part of the overall target system—its mercury is circulated through the mercury jet nozzle after passing through a heat exchanger. Pions emerging from the target are captured and focused down the decay channel by a solenoidal field that is 20 T at the target center, and tapers down, over 12 m, to 1.75 T. The 20 T solenoid, with a resistive magnet insert and superconducting outer coil, is similar in character to higher field (up to 45 T), but smaller bore, magnets existing at

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several laboratories . The magnet insert is made with hollow copper conductor having ceramic insulation to withstand radiation. MARS simulations of radiation levels show that, with the shielding provided, both the copper and superconducting magnets will have reasonable lifetime.

3.

Buncher And Phase Rotation

Pions, and the muons into which they decay, are generated in the target over a very wide range of energies, but in a short time pulse (≈3 ns rms). To prepare the muon beam for acceleration thus requires significant “conditioning.” First, the bunch is drifted to develop an energy correlation, with higher energy particles at the head and lower energy particles at the tail of the bunch. Next, the long bunch is separated into a number of shorter bunches suitable for capture and acceleration in a 201-MHz rf system. This is done with a series of rf cavities having frequencies that decrease along the beam line, separated by suitably chosen drift spaces. The resultant bunch train still has a substantial energy correlation, with the higher energy bunches first and progressively lower energy bunches coming behind.

The large energy tilt is then “phase rotated”, using additional rf cavities and drifts, into a bunch train with a longer time duration and a lower energy spread. The beam at the end of the buncher and phase rotation section has an average momentum of about 220 MeV/c.

The proposed system is based on standard rf technology, and is expected to be much more cost effective than the induction-linac-based system considered in Ref. . A fringe benefit of the rf-based system is the ability to transport both signs of muon simultaneously.

4.

Cooling

Transverse emittance cooling is achieved by lowering the beam energy in LiH absorbers, interspersed with rf acceleration to keep the average energy constant. Both transverse and longitudinal momenta are lowered in the absorbers, but only the longitudinal momentum is restored by the rf system. The emittance increase from Coulomb scattering is controlled by maintaining the focusing strength such that the angular spread of the beam at the absorber locations is reasonably large. In the present cooling lattice, the energy absorbers are attached directly to the apertures of the rf cavity, thus serving the dual purposes of closing the

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cavity apertures electromagnetically (increasing the cavity shunt impedance) and providing energy loss. Compared with the approach used in FS2, the absorbers are more distributed, and do not lend themselves to being located at an optical focus. Therefore, the focusing is kept essentially constant along the cooling channel, but at a beta function somewhat higher than the minimum value achieved in FS2. A straightforward Focus-Focus (FOFO) lattice is employed. The solenoidal fields in each half-cell alternate in sign, giving rise to a sinusoidal field variation along the channel. Use of solid absorbers instead of the liquid- hydrogen absorbers assumed in FS2 will considerably simplify the cooling channel, and the new magnet requirements are also more modest, since fewer and weaker components are needed compared with FS2. Together, these features reduce the cost of the cooling channel with respect to the FS2 design. Although the cooling performance is reduced, the overall throughput is comparable to that in FS2 due to the increased acceptance built into the downstream acceleration system.

Here too, the ability to utilize both signs of muon is available. 5.

Acceleration

Parameters of the acceleration system are listed in Table II. A matching section, using normal conducting rf systems, matches the cooling channel optics to the requirements of a superconducting rf linac with solenoidal focusing which raises the energy to 1.5 GeV. The linac is in three parts (see Section V B). The first part has only a single-cell 201 MHz cavity per period. The second part, with longer period, has a 2-cell rf cavity unit per period. The third part, as a still longer period becomes possible, accommodates two 2-cell cavity units per period. Figure 3 shows the three cryomodule types that make up the pre-accelerator linac.

This linac is followed by a 3.5-pass dogbone RLA (see Fig. 4) that raises the energy from 1.5 to 5 GeV. The RLA uses four 2-cell superconducting rf cavity structures per cell, and utilizes quadrupole triplet (as opposed to solenoidal) focusing.

Following the RLA are two cascaded FFAG rings that increase the beam energy from 5– 10 GeV, and 10–20 GeV, respectively. Each ring uses combined-function magnets arranged in a triplet (F-D-F) focusing arrangement. The lower energy FFAG ring has a circumference of about 400 m; the higher energy ring is about 500 m in circumference. As discussed in

6.75 M

FIG. 3: (Color) Layouts of superconducting linac pre-accelerator cryomodules. Blue lines are the SC walls of the cavities and solenoid coils are indicated in red. The dimension of the cryomodules are shown in Table X and Table XI summarizes parameters for the linac.

FIG. 4: (Color) Layout of the RLA. Section V B, an effort was made to achieve a reasonably cost-optimized design. Without detailed engineering, it is not possible to fully optimize costs, but we have employed general formulae that properly represent the cost trends and that were considered adequate to make choices at the present stage of the design. As the acceleration system was one of the dominant cost items in FS2, we are confident that the approach adopted here will result in a less expensive Neutrino Factory facility with essentially the same performance as calculated for the FS2 design. Achieving a higher beam energy would require additional FFAG acceleration stages.

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TABLE II: Main parameters of the muon accelerator driver.

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6.

Storage Ring

After acceleration in the final FFAG ring, the muons are injected into the upward-going straight section of a racetrack-shaped storage ring with a circumference of 358 m. Parameters of the ring are summarized in Table III. High-field superconducting arc magnets are used to minimize the arc length and maximize the fraction (35%) of muons that decay in the downward-going straight, generating neutrinos headed toward the detector located some 3000 km away.

All muons are allowed to decay; the maximum heat load from their decay electrons is 42 kW (126 W/m). This load is too high to be dissipated in the superconducting coils. For FS2, a magnet design was chosen that allows the majority of these electrons to exit between separate upper and lower cryostats, and be dissipated in a dump at room temperature.

To maintain the vertical cryostat separation in focusing elements, skew quadrupoles are employed in place of standard quadrupoles. In order to maximize the average bending field,

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TABLE III: Muon storage ring parameters.

200

Nb3Sn pancake coils are employed. One coil of the bending magnet is extended and used as one half of the previous (or following) skew quadrupole to minimize unused space. For site-specific reasons, the ring is kept above the local water table and is placed on a roughly 30-m-high berm. This requirement places a premium on a compact storage ring. In the present study, no attempt was made to revisit the design of the FS2 storage ring.

For

further technical details on this component, see FS2, Ref. . The footprint of a Neutrino Factory is reasonably small, and such a machine would fit easily on the site of an existing laboratory.

Beta Beam Facility

The idea of a Beta Beam facility was first proposed by P. Zucchelli in 2002 . As the name suggests, it employs beams of beta-unstable nuclides. By accelerating these ions to high energy and storing them in a decay ring (analogous to that used for a muon-based Neutrino Factory) a very pure beam of electron neutrinos (or antineutrinos) can be produced. As the kinematics of the beta decay is well understood, the energy distribution of the neutrinos can be predicted to a very high accuracy. Furthermore, as the energy of the beta decay is low compared with that for muon decay, the resulting neutrino beam has a small divergence.

For low-Z beta-unstable nuclides, typical decay times are measured in seconds. Thus, there is not so high a premium on rapid acceleration as is true for a Neutrino Factory, and conventional (or even existing) accelerators could be used for acceleration in a Beta Beam facility. Two ion species, both having lifetimes on the order of 1 s, have been identified as optimal candidates: 6He for producing antineutrinos and 18Ne for neutrinos.

Following the initial proposal, a study group was formed at CERN to investigate the feasibility of the idea, and, in particular, to evaluate the possibility of using existing CERN machines to accelerate the radioactive ions. Their study took an energy of γ = 150 for 6He, which corresponds to the top energy of the SPS for this species and also matches the distance to the proposed neutrino laboratory in the Fr´ejus tunnel rather well.

In the spring of 2003, a European collaboration, the Beta Beam Study Group, was formed. Eventually, they obtained funding from the European Union to produce a conceptual design study. Here, we take our information from recent presentations made by members of this group .

The EU Beta Beam Study Group has undertaken the study of a Beta Beam facility with the goal of presenting a coherent and realistic scenario for such a device. Their present “boundary conditions” are to re-use a maximum of existing (CERN) infrastructure and to base the design on known technology—or reasonable extrapolations thereof. In this sense, the approach taken is similar to that of the Neutrino Factory feasibility studies.

For practical reasons, the Beta Beam study was included in the larger context of the EURISOL study, due to the large synergies between the two at the low energy end. (The EURISOL study aims to build a next-generation facility for on-line production of radioactive isotopes, including those needed for the Beta Beam facility.)

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FIG. 5: (Color) Proposed ion source system for production of 6He beam. The basic ingredients of a Beta Beam facility are: • Proton Driver: A 2.2 GeV proton beam from the proposed Super Proton Linac (SPL) at CERN would be used to initiate the nuclear reactions that ultimately generate the required beta-unstable nuclides (6He is used as the antineutrino source and 18Ne is used as the neutrino source).

• ISOL Target and Ion Source: The target system is patterned after that of the EURISOL facility . For 6He production, the target core would be a heavy metal (mercury ) that converts the incoming proton beam into a neutron flux. Surround- ing the core is a cylinder of BeO that produces 6He via the 9Be(n,α) reaction. 18Ne would be produced via direct proton spallation on a MgO target . The nuclides of interest will be extracted from the target as neutral species, and so must be ionized to produce the beam to be accelerated. The proposed ion source technology, shown in

Fig. 5, Is Based On A Pulsed “Ecr-Duoplasmatron.”

• Acceleration: Low energy acceleration would make use of a linac to accelerate the nuclide of interest to 20–100 MeV/u, followed by a Rapid Cycling Synchrotron (RCS) with multi-turn injection that would accelerate the ion beam to 300 MeV/u. This system would feed the CERN PS with 16 bunches (2.5 × 1012 ions per bunch), which

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would be merged to 8 bunches during the acceleration cycle to γ = 9. Finally, the bunches would be transferred to the SPS and accelerated to γ ≈150, which corre- sponds to the maximum magnetic rigidity of that accelerator.

• Decay Ring: The racetrack decay ring would have the same circumference as the SPS (6880 m), with a long straight section, some 2500 m, aimed at the detector. At the final energy, the lifetime of the beam becomes minutes rather than seconds. Stacking is required to load the ring with enough ions to get an acceptable neutrino flux.

The parallels with the Neutrino Factory are obvious. The main difference between the two types of facility is in the initial capture and beam preparation. In the Neutrino Factory, the beam must be bunched, phase rotated, and ionization cooled. In the Beta Beam facility, the beam must be collected, ionized, and bunched.

1.

Proton Driver

The proposed proton driver for the Beta Beam facility is the SPL, a 2.2 GeV Supercon- ducting Proton Linac presently being designed at CERN to serve both the LHC and the EURISOL facility. The machine will operate at 50 Hz and will be designed to provide up to 4 MW of proton beam power. The present scenario is illustrated in Fig. 6. It is anticipated that the ISOL target will require only about 5% of the proton beam power, i.e., about 200 kW.

FIG. 6: (Color) Baseline layout of the SPL facility at CERN.

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2.

Isol Target And Ion Source

As noted earlier, the target for 6He will use a water-cooled tungsten or a liquid-lead core to serve as a proton-to-neutron converter. Surrounding this core will be a cylinder of BeO, as shown in Fig. 7. In the case of 18Ne, a more straightforward approach will suffice.

The proton beam will impinge directly on a MgO target, producing the required nuclide via spallation. An ion source capable of producing the required intense pulses is proposed; development work on this device (see Fig. 5) is under way at Grenoble . The device uses a very high density plasma (ne ∼1014 cm−3) in a 2–3 T solenoidal field and operates at 60–90 GHz. It is expected to provide pulses of 1012–1013 ions per bunch.

FIG. 7: (Color) Proposed ISOL-type target for production of 6He beam. 3.

Acceleration

The proposed acceleration scheme is based on the existing CERN machines (PS and SPS). Initial acceleration would be via a linac, followed by a rapid cycling synchrotron that would be filled by multiturn injection. The RCS would provide a single bunch, 150 ns long, at 300 MeV/u. The PS is a relatively slow machine, and this results in substantial radiation levels due to decays while the beam energy, and hence the lifetime, is low. A rapid-cycling PS replacement would be of considerable benefit in this regard, though it is not part of the baseline scenario. Another idea that merit consideration is the use of a FFAG, which perhaps could be used to accelerate muons at a latter time.

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The SPS space-charge limit at injection is another issue to deal with, and will likely require a transverse emittance blowup to manage it. A new 40 MHz rf system will be added to the existing 200 MHz system in the SPS to accelerate the beam to γ = 150.

4.

Decay Ring

The beam is transferred at full energy to a racetrack-shaped Decay Ring having the same circumference as the SPS. The length of the decay straight section (the one aimed at the detector) is chosen to permit about 35% of the decays to occur there. At full energy, the lifetime is minutes rather than seconds. This allows—and also requires—the beam to be stacked in the Decay Ring to provide the required decay intensity. The proposed stacking technique, asymmetric bunch merging, is based on somewhat complicated rf gymnastics, but has already been shown to work experimentally in tests . An interesting possibility that has arisen only recently is the idea of storing both 6He and 18Ne in the ring simultane- ously. This requires that the neon beam have the same rigidity as the helium beam, which corresponds to γNe = 250. For a detector at Fr´ejus, the optimum energies are γHe = 60 and γNe = 100.

Beam Properties

The most important neutrino oscillation physics questions that we wish to address in the coming decades require the study of νe ↔νµ transitions in long baseline experiments. Conventional neutrino beams are almost pure νµ beams, which therefore permit the study of νµ →νe oscillations. The experiments must look for νe CC interactions in a distant detector. Backgrounds that fake νe CC interactions, together with a small νe component in the initial beam, account for O(1%) of the total interaction rate. This makes it difficult for experiments using conventional neutrino beams to probe very small oscillation amplitudes, below the 0.01 −0.001 range. This limitation motivates new types of neutrino facilities that provide νe beams, permitting the search for νe →νµ oscillations, and if the beam energy is above the ντ CC interaction threshold, the search for νe →ντ oscillations. Neutrino Factory and Beta Beam facilities both provide νe (and ¯νe) beams, but with somewhat different beam properties. We will begin by describing Neutrino Factory beams, and then describe Beta

21

Beam facility beams.

Neutrino Factory Beams

Neutrino Factory beams are produced from muons decaying in a storage ring with long straight sections. Consider an ensemble of polarized negatively-charged muons. When the muons decay they produce muon neutrinos with a distribution of energies and angles in the

D2Nνµ

dxdΩc.m.

(2)

where x ≡2Eν/mµ, θc.m. is the angle between the neutrino momentum vector and the muon spin direction, and Pµ is the average muon polarization along the beam direction.

D2N¯Νe

dxdΩc.m.

(3)

and the corresponding distributions for ¯νµ and νe from µ+ decay are obtained by the re- placement Pµ →−Pµ. Only neutrinos and antineutrinos emitted in the forward direction (cos θlab ≃1) are relevant to the neutrino flux for long-baseline experiments; in this limit Eν = xEmax and at high energies the maximum Eν in the laboratory frame is given by Emax = γ(1 + β cos θc.m.)mµ/2, where β and γ are the usual relativistic factors. The νµ and ¯νe distributions as a function of the laboratory frame variables are then given by:

12X2

4π [(1 −x) + (1 −x)Pµ cos θc.m.] .

(5)

Thus, for a high energy muon beam with no beam divergence, the neutrino and antineutrino energy and angular distributions depend upon the parent muon energy, the decay angle, and the direction of the muon spin vector.

With The Muon Beam Intensities That Could

be provided by a muon–collider type muon source the resulting neutrino fluxes at a distant site would be large. For example, Fig. 8 shows as a function of muon energy and polarization, the computed fluxes per 2×1020 muon decays at a site on the other side of the

22

Earth (L = 10000 km). Note that the νe (¯νe) fluxes are suppressed when the muons have P = +1 (−1). This can be understood by examining Eq. (5) and noting that for P = −1 the two terms cancel in the forward direction for all x. At low energies, the neutrino CC FIG. 8: Calculated ν and ¯ν fluxes in the absence of oscillations at a far site located 10000 km from a Neutrino Factory in which 2 × 1020 muons have decayed in the storage ring straight section pointing at the detector. The fluxes are shown as a function of the energy of the stored muons for negative muons (top two plots) and positive muons (bottom two plots), and for three muon polarizations as indicated. The calculated fluxes are averaged over a circular area of radius 1 km at the far site. Calculation from Ref. .

interaction cross section is dominated by quasi-elastic scattering and resonance production. However, if Eν is greater than ∼10 GeV, the total cross section is dominated by deep

(6)

σ(ν + N →ℓ+ + X) ≈0.34 × 10−38 × Eν(GeV) cm2 .

23

The number of ν and ¯ν CC events per incident neutrino observed in an isoscalar target is

Given By:

N(ν + N →ℓ−+ X) = 4.0 × 10−15 × Eν(GeV) events per g/cm2,

(8)

N(ν + N →ℓ+ + X) = 2.0 × 10−15 × Eν(GeV) events per g/cm2.

(9)

Using this simple form for the energy dependence of the cross section, the predicted energy distributions for νe and νµ interacting in a far detector (cos θ = 1) at a Neutrino Factory are shown in Fig. 9. The interacting νµ energy distribution is compared in Fig. 10 with the corresponding distribution arising from the high–energy NUMI wide-band beam. Note that neutrino beams from a Neutrino Factory have no high energy tail, and in that sense can be considered narrow-band beams.

Number Of Charged Current Interactions

FIG. 9: Charged current event spectra at a far detector. The solid lines indicate zero polarization, the dotted lines indicate polarization of ±0.3 and the dashed lines indicate full polarization. The P = 1 case for electron neutrinos results in no events and is hidden by the x axis.

identified when the final state lepton exceeds a threshold energy. The calculated final state lepton distributions are shown in Fig. 11. Integrating over the energy distribution, the total

24

FIG. 10: (Color) Comparison of interacting νµ energy distributions for the NUMI high energy wide-band beam (Ref. ) with a 20 GeV Neutrino Factory beam (Ref. ) at L = 730 km and a 30 GeV Neutrino Factory beam at L = 2900 km. The Neutrino Factory distributions have been calculated based on Eq. (2) (no approximations), and include realistic muon beam divergences and energy spreads.

ν and ¯ν interaction rates per muon decay are given by:

6

10.

(12)

The calculated νe and νµ CC interaction rates resulting from 1020 muon decays in the storage ring straight section of a Neutrino Factory are compared in Table IV with expectations for the corresponding rates at the next generation of accelerator–based neutrino experiments.

Note that event rates at a Neutrino Factory increase as E3

Μ, And Are Significantly Larger

than expected for the next generation of approved experiments if Eµ > 20 GeV. The radial dependence of the event rate is shown in Fig. 12 for a 20 GeV Neutrino Factory and three baselines.

25

FIG. 11: Lepton energy spectra for CC ¯νµ (top left), νµ (top right), νe (bottom left), and ¯νe (bottom right) interactions. Note that z is the energy normalized to the primary muon energy z = Eℓ/Eµ. Calculation from Ref. .

0

20 40 60 80 100

Νµ Cc Events Per Kton Of Detector

FIG. 12: (Color) Events per kton of detector as a function of distance from the beam center for a 20 GeV muon beam.

Table Iv:

Muon neutrino and electron antineutrino CC interaction rates in the absence of oscillations, calculated for baseline length L = 732 km (FNAL →Soudan), for MINOS using the wide-band beam and a muon storage ring delivering 1020 decays with Eµ = 10, 20, and 50 GeV at three baselines. The Neutrino Factory calculation includes a realistic muon beam divergence and energy spread.

770

We next consider the systematic uncertainties on the neutrino flux. Since muon decay kinematics is very well understood, and the beam properties of the muons in the storage ring can be well determined, we expect the systematic uncertainties on the neutrino beam intensity and spectrum to be small compared to the corresponding uncertainties on the properties of conventional neutrino beams. In the muon decay straight section of a Neutrino Factory, the muon beam is designed to have an average divergence given by σθ = O( 0.1 γ ).

The neutrino beam divergence will therefore be dominated by muon decay kinematics, and

27

TABLE V: Dependence of predicted charged current event rates on muon beam properties at a Neutrino Factory. The last column lists the required precisions with which each beam property must be determined if the uncertainty on the neutrino flux at the far site is to be less than ∼1%.

Here ∆denotes uncertainty while σ denotes the spread in a variable. Table from Ref. .

∆Pµ < 0.025

uncertainties on the beam direction and divergence will yield only small uncertainties in the neutrino flux at a far site. However, if precise knowledge of the flux is required, the uncertainties on θ and σθ must be taken into account, along with uncertainties on the flux arising from uncertainties on the muon energy distribution and polarization. The relation- ships between the uncertainties on the muon beam properties and the resulting uncertainties on the neutrino flux are summarized in Table V. If, for example, we wish to know the νe and νµ fluxes at a far site with a precision of 1%, we must determine the beam divergence, σθ, to 20% (see, Fig. 13), and ensure that the beam direction is within 0.6 × σθ of the nominal direction (see, Fig. 14). We point out that it should be possible to do much better than this, and consequently, to know the fluxes at the far site with a precision much better than 1%.

We now consider the event distributions in a detector at a near site, close to the Neutrino Factory, which will be quite different from the corresponding distributions at a far site. There are two main reasons for this difference. First, the near detector accepts neutrinos over a large range of muon decay angles θ, not just those neutrinos traveling in the extreme

28

FIG. 13: (Color) Dependence of CC interaction rates on the muon beam divergence for a detector located at L = 2800 km from a muon storage ring containing 30 GeV unpolarized muons. Rates are shown for νe (boxes) and νµ (circles) beams in the absence of oscillations, and for νe →νµ oscillations (triangles) with the three–flavor oscillation parameters, δm2

32 =

3.5 × 10−3 eV2/c4, s13 = 0.10, s23 = 0.71, s12 = 0.53, δ = 0. The calculation is from Ref. . forward direction. This results in a broader neutrino energy distribution that is sensitive to the radial size of the detector (Fig. 15).

Second, if the distance of the near detector from the end of the decay straight section is of the order of the straight section length, then the θ acceptance of the detector varies with the position of the muon decay along the straight section.

This Results In A More

complicated radial flux distribution than expected for a far detector. However, since the dominant effects are decay length and muon decay kinematics, it should be modeled quite accurately (Fig. 16). Note that, even in a limited angular range, the event rates in a near detector are very high. Figure 17 illustrates the event rates per g/cm2 as a function of energy.

Because most of the neutrinos produced forward in the center of mass traverse the detector fiducial volume, the factor of γ2 present in the flux for θ ∼0 is canceled and the event rate increases linearly with Eµ. For a 50 GeV muon storage ring, the interaction rate per 1020 muon decays is 7 × 106 events per g/cm2. Finally, in the absence of special magnetized shielding, the high neutrino event rates in any material upstream of the detector will cause

29

FIG. 14: (Color) Dependence of CC interaction rates on the neutrino beam direction. Relative rates are shown for a detector at a far site located downstream of a storage ring containing 30 GeV unpolarized muons, and a muon beam divergence of 0.33 mrad. Rates are shown for νe (triangles) and νµ (circles) beams in the absence of oscillations, and for νe →νµ oscillations (boxes) with the three–flavor oscillation parameters shown in Fig. 13. The calculation is from Ref. .

substantial backgrounds. The event rate in the last three interaction lengths (300 g/cm2) of the shielding between the detector and the storage ring would be 30 interactions per beam spill at a 15 Hz machine delivering 2 × 1020 muon decays per year. These high background rates will require clever magnetized shielding designs and fast detector readout to avoid overly high accidental rates in low mass experiments.

Beta Beams

We now consider the beam properties at a Beta Beam facility. In a Beta Beam facility the neutrinos are generated by the decay of radioactive nuclei rather than muons. The two ions deemed optimal are 18Ne for νe and 6He for ¯νe production. The resulting initial neutrino beam consists of a single flavor. In addition, since the decay kinematics is well known, the uncertainties on the neutrino energy spectrum are expected to be small. The electron energy

R<20 Cm

FIG. 15: Events per g/cm2 per GeV for a detector 40 m from a muon storage ring with a 600 m straight section. The three curves show all events and those falling within 50 and 20 cm of the beam center.

2000

FIG. 16: (Color) Events per g/cm2 as a function of the transverse coordinate, x, 50 m downstream of a 50 GeV neutrino factory providing 1020 muon decays. The central peak is mainly due to decays in the last hundred meters of the decay pipe while the large tails are due to upstream decays.

Eµ(Gev)

FIG. 17: (Color) Events per year and per g/cm2 at a near detector as a function of muon beam energy in GeV. The solid curves indicate all events, the dashed and dotted curves show the effects of radial position cuts.

(13)

where E0 is the electron end-point energy, which is 3.5 MeV for 6He and 3.4 MeV for 18Ne. In the rest frame of the ion, the spectrum of the neutrinos is

(E0 −Eν)2 −M2

e.

(14)

After performing a boost and normalizing to the total decays (in the straight section) Nβ, the neutrino flux per solid angle in a detector located at a distance L and aligned with the



.

32

The neutrino flux and energy distribution depend upon the boost γ, and hence upon the energies of the stored radioactive ions. The original Beta Beam proposal was to use the CERN SPS to accelerate the ions. The desire to simultaneously store ions of both species in the storage ring, and build a large detector in the Fr´ejus tunnel in France (which fixes the baseline), has led to proposed Beta Beam energies corresponding to γ ∼60 and 100 for the two ion species, yielding mean neutrino energies of 0.2 GeV and 0.3 GeV. Recently it has been suggested that these energies are too low for optimal sensitivity to the interesting physics, and hence higher energy scenarios are being considered, using the Fermilab Tevatron, or the CERN LHC to accelerate the ions. Figure 18 shows the expected fluxes for the three scenarios, “low” energy (e.g., SPS), “medium” energy (e.g., Tevatron), and “high” energy (e.g., LHC). Although the integrated fluxes are similar, the cross section grows with energy, yielding more events for the higher energies. Table VI shows the expected charged current event rates for the three setups. However, it should be noted that the higher energy options TABLE VI: Number of charged current events without oscillations per kton-year for the three reference setups described in the text. Also is shown the average neutrino energy. Table from Ref. .

5.01/7.55

require both a TeV (or multi-TeV) accelerator and storage ring, which are expensive and introduce additional technical challenges. Finally, further study is needed to fully explore the systematic uncertainties on the beam properties of a Beta Beam facility. Note however, that the neutrino beam divergence is controlled by the Q value of the beta decay, and the beam divergence in the straight section. In the CERN (low energy) case, the typical decay angle is 7 mrad. By contrast, the parent beam divergence would be O(100) µrad, assuming a 200 m beta function in the decay section. For higher energies, both inherent neutrino divergence, and the parent beam divergence scale like 1/γ. Hence the decay kinematics is expected to dominate the beam divergence for all the Beta Beam scenarios. A more detailed understanding of the systematics must await a detailed design for the storage ring and an

33

understanding of the beam halo, etc. Background conditions for near detectors also deserve study.

E Ν (Gev)

FIG. 18: (Color) Comparison of Beta Beam neutrino fluxes for the three setups described in the text, shown as a function of the neutrino energy for ¯νe (solid) and νe (dashed).

Figures From

Ref. .

And Beta Beam

Ultimately, to fully test the three-flavor mixing framework, determine all of the relevant neutrino oscillation parameters, and answer the most important neutrino-oscillation related physics questions, we would like to measure the oscillation probabilities P(να →νβ) as a function of the baseline L and neutrino energy E (and hence L/E) for all possible initial and final flavors α and β. This requires a beam with a well known initial flavor content, and the detector via charged current (CC) and neutral current (NC) interactions to produce a lepton accompanied by a hadronic shower arising from the remnants of the struck nucleon.

accomplish our ultimate goal, we will need νe in addition to νµ beams, and detectors that can distinguish between NC, νe CC, νµ CC, and ντ CC interactions. Conventional neutrino beams are νµ beams, Beta Beams provide νe beams, and Neutrino Factories provide νe and νµ beams. The sensitivities of experiments at the different facilities will depend on their statistical precision, the background rates, the ability of the experiments to discriminate between true and false solutions within the three-flavor mixing parameter space, and the ability of the experimental setups to detect as many of the oscillation modes as possible.

In the following, we will first consider the experimental signatures and sensitivities at a Neutrino Factory, and then the corresponding signatures and sensitivities at a Beta Beam facility.

Neutrino Factory Sensitivity

1.

Wrong-Sign Muons

At a Neutrino Factory in which, for example, positive muons are stored, the initial beam consists of 50% νe and 50% ¯νµ. In the absence of oscillations, the νe CC interactions produce electrons and the ¯νµ CC interactions produce positive muons. Note that the charge of the of νe →νµ oscillations, the νµ CC interactions produce negative muons (i.e., wrong–sign muons). This is a very clean experimental signature since, with a segmented magnetized

35

iron-scintillator sampling calorimeter for example, it is straightforward to suppress back- grounds to 1 part in 104 of the total CC interaction rate, or better. This means that at a Neutrino Factory backgrounds to the νe →νµ oscillation signal are extremely small. The full statistical sensitivity can therefore be exploited down to values of sin2 2θ13 approaching 10−4 before backgrounds must be subtracted and further advances in sensitivity scale like

N

rather than N. This enables Neutrino Factories to go beyond the sensitivities achievable by conventional neutrino Superbeams, by about two orders of magnitude. A more complete discussion of backgrounds at a Neutrino Factory can be found in Refs. [39, 40, 41, 42].

|∆M221| = 5 X 10−5 Ev 2

FIG. 19: (Color) Predicted ratios of wrong–sign muon event rates when positive and negative muons are stored in a 20 GeV Neutrino Factory, shown as a function of baseline. A muon measurement threshold of 4 GeV is assumed. The lower and upper bands correspond, respectively, to the two possible neutrino mass eigenstate orderings, as labeled. The widths of the bands show how the predictions vary as the CP violating phase δ is varied from −π

2 , With The Thick Lines Showing

the predictions for δ = 0. The statistical error bars correspond to a Neutrino Factory yielding a data sample of 1021 decays with a 50 kton detector. Figure from Ref. .

36

We now consider how wrong-sign muon measurements at a Neutrino Factory are used to answer the most important neutrino oscillation physics questions. Suppose we store positive muons in the Neutrino Factory, and measure the number of events tagged by a negative muon in a distant detector, and then store negative muons and measure the rate of events tagged by a positive muon. To illustrate the dependence of the expected measured rates on the chosen baseline, the neutrino mass hierarchy, and the complex phase δ, we will fix the other oscillation parameters and consider an experiment downstream of a 20 GeV Neutrino Factory. Let half of the data taking be with µ+ stored, and the other half with µ−stored. In Fig. 19, the predicted ratio of wrong-sign muon events R ≡N(¯νe →¯νµ)/N(νe →νµ) is shown

As A Function Of Baseline For ∆M2

32 = +0.0035 eV2 and −0.0035 eV2, with sin2 2θ13 set to the small value 0.004. (Although these ∆m2 values are now a little different from those emerging from global analyses of the atmospheric and solar neutrino data, they are the ones used for the figure, which comes from Ref. , and are still useful to illustrate how the measurements can be used to determine the oscillation parameters.) Figure 19 shows two bands. The upper

(Lower) Band Corresponds To ∆M2

32 < 0 (> 0). Within the bands, the CP phase δ is varying. At short baselines the bands converge, and the ratio R = 0.5 since the antineutrino CC cross section is half of the neutrino CC cross section. At large distances, matter effects enhance

32 < 0 And Reduce R If ∆M2

32 > 0, and the bands diverge. Matter effects become significant for baselines exceeding about 2000 km. The error bars indicate the expected statistical uncertainty on the measured R with a data sample of 5 × 1022 kton-decays. With

These Statistics, The Sign Of ∆M2

32 is determined with very high statistical significance. With an order of magnitude smaller data sample (entry level scenario ) or with an order of magnitude smaller sin2 2θ13 the statistical uncertainties would be

Of ∆M2

32 could still be determined with convincing precision.

In Addition To The Ratio Of

wrong–sign muon signal rates R, the two energy-dependent wrong-sign muon event energy distributions can be separately measured. To show how this additional information can help, the predicted measured energy distributions 2800 km downstream of a 30 GeV Neutrino Factory are shown in Figs. 20 and 21 for, respectively, νe →νµ and ¯νe →¯νµ wrong–sign muon events. The distributions are shown for a range of positive and negative values of

Δm2

32. Note that, after allowing for the factor of two difference between the neutrino and

32 > 0 We Would Expect To Observe A

lower wrong–sign muon event rate and a harder associated spectrum when positive muons

37

FIG. 20: (Color) Predicted measured energy distributions for CC events tagged by a wrong-sign (negative) muon from νe →νµ oscillations (no cuts or backgrounds), shown for various δm2

32,

as labeled. The predictions correspond to 2 × 1020 decays, Eµ = 30 GeV, L = 2800 km, and a

Representative Set Of Values For Δm2

12, sin2 2θ13, sin2 2θ23, sin2 2θ12, and δ. Results are from Ref. . are stored in the Neutrino Factory than when negative muons are stored. On the other

Hand, If Δm2

32 < 0 we would expect to observe a higher wrong–sign muon event rate and a softer associated spectrum when positive muons are stored in the Neutrino Factory than when negative muons are stored. Hence, measuring the differential spectra when positive and negative muons are alternately stored in the Neutrino Factory can both enable the sign

Of Δm2

32 to be unambiguously determined , and also provide a measurement of δm2

32 And

a consistency check between the behavior of the rates and energy distributions. 2.

Other Channels

In practice, to measure θ13, determine the mass hierarchy, and search for CP violation, the analysis of the wrong-sign muon rates must be performed allowing all of the oscillation parameters to simultaneously vary within their uncertainties. Since the relationship between the measured quantities and the underlying mixing parameters is complicated, with a min-

38

FIG. 21: (Color) Same as in Fig. 20, for CC events tagged by a wrong-sign (positive) muon from ¯νe →¯νµ oscillations. imal set of measurements it may not be possible to identify a unique region of parameter space consistent with the data. For Superbeams a detailed discussion of this problem can be found in Refs. [46, 47, 48, 49, 50, 51]. To understand the nature of the challenge, Fig. 22 shows, as a function of θ13, θ23, δ and the assumed mass hierarchy, the predicted number of wrong–sign muon events when negative muons are stored in the Neutrino Factory, versus the corresponding rate when positive muons are stored. The example is for a 16 GeV Neutrino Factory with a baseline of 2000 km, and 10 years of data taking with a 100 kton detector and 2 × 1020 µ+ and 2 × 1020 µ−decays in the beam-forming straight section per year.

The ellipses show how the predicted rates vary as the CP phase δ varies. All of the CP conserving points (δ = 0 and π) lie on the diagonal lines. Varying the mixing angles moves the ellipses up and down the lines. Varying the mass hierarchy moves the family of ellipses from one diagonal line to the other. Note that the statistics are large, and the statistical errors would be barely visible if plotted on this figure. Given these statistical errors, for the parameter region illustrated by the figure, determining the mass hierarchy (which diagonal line is the measured point closest to) will be straightforward. Determining whether there is CP violation in the lepton sector will amount to determining whether the measured point

39

FIG. 22: (Color) The predicted number of wrong–sign muon events when negative muons are stored in the Neutrino Factory, versus the corresponding rate when positive muons are stored, shown as a function of θ13, θ23, δ and the assumed mass hierarchy, as labeled. The calculation corresponds to a 16 GeV Neutrino Factory with a baseline of 2000 km, and 10 years of data taking with a 100 kton detector and 2 × 1020 µ+ and 2 × 1020 µ−decays in the beam-forming straight section per year.

The ellipses show how the predicted rates vary as the CP phase δ varies. is consistent with being on the CP conserving line. Determining the exact values for the mixing angles and δ is more complicated, since various combinations can result in the same predicted values for the two measured rates. This is the origin of possible false solutions in the three–flavor mixing parameter space. To eliminate those false solutions, event samples other than νe →νµ transitions tagged by wrong-sign muons will be important. We have seen that, in the presence of νe →νµ oscillations, the νµ CC interactions produce nega- tive muons (i.e., wrong–sign muons). Similarly, ¯νµ →¯νe oscillations produce wrong–sign electrons, ¯νµ →¯ντ oscillations produce events tagged by a τ +, and νe →ντ oscillations produce events tagged by a τ −. Hence, there is a variety of information that can be used to measure or constrain neutrino oscillations at a Neutrino Factory, namely the rates and

(B) Wrong–Sign Muons

(c) electrons or positrons (their charge is difficult to determine in a massive detector)

(E) Negative Τ–Leptons

(f) no charged lepton. If these measurements are made when there are alternately positive and negative muons decaying in the storage ring, there are a total of 12 spectra that can be used to extract infor- mation about the oscillations. Some examples of the predicted measured spectra are shown as a function of the oscillation parameters in Figs. 23 and 24 for a 10 kton detector sited 7400 km downstream of a 30 GeV Neutrino Factory. These distributions are sensitive to the oscillation parameters, and can be fit simultaneously to extract the maximum information.

Clearly, the high intensity νe, ¯νe, νµ, and ¯νµ beams at a Neutrino Factory would provide a wealth of precision oscillation data. The full value of this wealth of information has not been fully explored, but some specific things to be noted are: 1. It has been shown [52, 53, 54, 55] that the various measurements at a Neutrino Fac- tory provide sufficient information to eliminate false solutions within the three–flavor parameter space. Indeed the wealth of information in the Neutrino Factory data is essential for this purpose.

2. If sin2 2θ13 exceeds ∼0.001 the νe →ντ channel is particularly important, both as a means to suppress the false solutions [52, 53, 56], and also as the only direct ex- perimental probe of νe ↔ντ transitions. The ability of the νe →ντ measurements to eliminate false solutions is illustrated in Fig. 25, which, for a representative set of oscillation parameters, shows as a function of the CP phase δ the location of the false solution with respect to the correct solution in θ13–space (or more precisely, the distance between the two solutions ∆θ). Note that, when compared to the ¯νe →¯νµ case, ∆θ has the opposite sign for ¯νe →¯ντ. In practice, this means that together the two measurements enable the false solution to be effectively eliminated.

3. Within the three–flavor framework, the relationship between the measured oscillation probabilities and the associated oscillation parameters is complicated. Experimental

41

redundancy, permitting the over-determination of the oscillation parameters, is likely to prove essential, both to weed out misleading measurements and to ensure that the three-flavor framework is correct.

E Vis (Gev)

FIG. 23: (Color) Visible energy spectra for four event classes when 1021 µ−decay in a 30 GeV Neutrino Factory at L = 7400 km. Black solid histogram: no oscillations. Blue dotted histogram:

Δm2

32 = 3.5 × 10−3 eV2/c4, sin2 θ23 = 1.

32 = 7 × 10−3 Ev2/C4,

sin2 θ23 = 1. The distributions in this figure and the following figure are for an ICANOE-type detector, and are from Ref. . 3.

Neutrino Factory Calculations

To understand how sensitive Neutrino Factory measurements will be in determining θ13 and the neutrino mass hierarchy, and the sensitivity to CP violation in the lepton sector, we must consider the impact of statistical and systematic uncertainties, correlations between

E Vis (Gev)

FIG. 24: (Color) Same as in Fig. 23, but with positive muons circulating in the storage ring. The difference between the two figures is due to the different cross section for neutrinos and antineutrinos, and to matter effects.

the parameters that vary within fits to the measured distributions, and the presence or absence of false solutions in the three-flavor mixing parameter space. To take account of these effects, and to see which different neutrino oscillation experiments best complement one another, a global fitting program has been created [55, 58] that uses simulated right-sign

Muon And Wrong-Sign Muon Data Sets, And Includes:

1. Beam spectral and normalization uncertainties. 2. Matter density variations of 5% about the average value. 3. Constraint of solar neutrino oscillation parameters within the post-KamLAND LMA region.

4. Simulation of νµ CC QE, νµ and νe CC inelastic, and NC events for all flavors. Note

Μ

FIG. 25: (Color) Equiprobability curves in the (∆θ, δ) plane, for ¯θ13 = 5◦, ¯δ = 60◦, Eν ∈[5, 50] GeV and L = 732 km for the νe →νµ and νe →ντ oscillation (neutrinos on the left, antineutrinos on the right). ∆θ is defined as the difference between the reconstructed parameter θ13 and the input parameter ¯θ13, i.e., ∆θ = θ13 −¯θ13. From Ref. .

that the NC events are included in the analysis as a source of background. The NC signal is not yet exploited as an additional constraint. 5. A check of the influence of cross section uncertainties (this mostly affects energies lower than those of interest for Neutrino Factories).

6. Energy-dependent detection efficiencies, enabling energy threshold effects to be taken into account. 7. Gaussian energy resolutions.

8. Flavor, charge, and event misidentification. 9. Overall energy-scale and normalization errors. 10. An analysis of statistical and systematic precisions, and the ability to eliminate false solutions.

The calculated signal and background rates are listed in Table VII. The roughly two orders of magnitude improvement in the signal/background ratio at a Neutrino Factory, compared

44

TABLE VII: Signal and background rates for a CERN SPS Beta beam, a high performance Super- beam (a 4 MW JHF beam with a 1 Mton water Cerenkov detector), and a Neutrino Factory. The numbers correspond to sin2 2θ13 = 0.1 and δ = 0. The rates have been calculated by the authors of Ref. .

85.2

with the corresponding ratio at a high performance Superbeam, is evident. The results from the full calculations are shown in Fig. 26. The calculation is more fully described in Ref. . The figure shows the minimum value of sin2 2θ13 for which three experimental goals could be achieved (with 3σ significance). First, the observation of a finite value of θ13. Second, the determination of the neutrino mass hierarchy. Third, the observation of non-zero CP violation in the lepton sector if the underlying δ corresponds to maximal CP violation.

The three groups of bars correspond to three different experimental scenarios, with different baselines. The favored scenario is the one illustrated by the bottom group of three bars, for which there are two detectors, one at L = 7500 km and the other at L = 3000 km. Note

That:

At a Neutrino Factory sin2 2θ13 can be measured, the neutrino mass hierarchy determined, and a search for CP violation in the lepton sector made for all values of sin2 2θ13 down to O(10−4), or even a little less.

If sin2 2θ13 is fairly large, Superbeam experiments may also establish its value, and perhaps determine the mass hierarchy and begin the search for CP violation. Figure 27 illustrates the role of a Neutrino Factory over a broad range of sin2 2θ13 values. The figure shows, as a function of the underlying value of sin2 2θ13, the 1σ precision on the determination of

Sensitivity Reach In Sin22Θ13

CP viol.

Sin22Θ13

CP viol.

Sin22Θ13

CP viol.

No Sensitivity!

FIG. 26: (Color) The sensitivity reaches as functions of sin2 2θ13 for sin2 2θ13 itself, the sign of

∆M2

31 > 0, and (maximal) CP violation δCP = π/2 for each of the indicated baseline combinations. The bars show the ranges in sin2 2θ13 where sensitivity to the corresponding quantity can be achieved at the 3σ confidence level. The dark bars mark the variations in the sensitivity limits by

Allowing The True Value Of ∆M2

21 to vary in the 3σ LMA-allowed range given in Ref. and others

(∆M2

21 ∼4 × 10−5 eV2 −3 × 10−4 eV2). The arrows/lines correspond to the LMA best-fit value. Figure from Ref. . the phase δ at a Neutrino Factory, and at a representative high-performance Superbeam, together with the combined Neutrino Factory plus Superbeam sensitivity. Below values of sin2 2θ13 ∼10−2 the Neutrino Factory sensitivity is significantly better than the sensitivity that can be achieved with Superbeams, and indeed provides the only sensitivity to the CP phase if sin2 2θ13 is significantly smaller than 10−2. Above sin2 2θ13 ∼10−2 the Neutrino Factory measurements still enable a modest improvement to the CP violation measurement sensitivity, but the exact impact that a Neutrino Factory might have in this case is less clear. The uncertainty on the matter density, which is believed to be O(5%), is likely to be a limiting uncertainty for CP violation measurements . Improved knowledge of the

Reactor-Ii

FIG. 27: (Color) The 1σ precision on the determination of the phase δ at a Neutrino Factory, and at a representative high-performance Superbeam, together with the combined Neutrino Factory plus Superbeam sensitivity. The sensitivities are shown as a function of the underlying value of sin2 2θ13. The thin curves correspond to cases where the the sign-degeneracy is not taken into account. Calculation from the authors of Ref. .

matter density along the neutrino flight-path would improve the expected Neutrino Factory sensitivity. In addition, Bueno et al. have shown that the energy dependencies of matter and CP violating effects are different, and can be exploited to further separate the two effects. For sin2 2θ13 > 0.01, the case for a Neutrino Factory will depend upon just how well Superbeam experiments will ultimately be able to do, whether any new discoveries are made along the way that complicate the analysis, whether any theoretical progress is made along the way that leads to an emphasis on the type of measurements that a Neutrino Factory excels at, how important further tests of the oscillation formalism is in general, and the importance of observing and measuring νe →ντ oscillations in particular.

We conclude there is a strong physics case for a Neutrino Factory if sin2 2θ13 is less than ∼0.01. There may also be a strong case if sin2 2θ13 is larger than this,

47

but it is too early to tell. 4.

Special Case: Θ13 = 0

The case θ13 = 0 is very special. The number of mixing angles needed to describe the 3 × 3 unitary neutrino mixing matrix would be reduced from three to two, suggesting the existence of a new conservation law resulting in an additional constraint on the elements of the mixing matrix. The discovery of a new conservation law happens rarely in physics, and almost always leads to revolutionary insights in our understanding of how the physical universe works. Hence, if it were possible to establish that θ13 = 0, it would be a major discovery. Note that in the limit θ13 →0, the oscillation probability for νe ↔νµ transitions

(17)

where the matter parameter A = 1 if the neutrino energy corresponds to the matter reso- nance, which for a long-baseline terrestrial experiment means neutrino energies E ∼12 GeV. In addition, if the baseline L is chosen such that L/E corresponds to the oscillation maxi-

31

.

(18)

Substituting into this expression values for the oscillation parameters that are consistent with the present solar and atmospheric neutrino data, we are led to conclude that even if θ13 = 0, provided the neutrino energy and baseline are chosen appropriately, νe ↔νµ transitions are still directly observable in an appearance experiment if oscillation probabilities of O(10−4) are observable. Hence, if θ13 is very small, the ideal neutrino oscillation experiment will be a long baseline experiment that uses neutrinos with energies close to 12 GeV, i.e., uses a baseline such that L/E corresponds to the oscillation maximum, and is sensitive to values of P(νe ↔νµ) ∼10−4 or smaller. Neutrino Factories provide the only way we know to satisfy these experimental requirements.

If θ13 = 0 a Neutrino Factory experiment would enable (i) the first observation of νe ↔νµ transitions in an appearance experiment, and (ii) an upper limit on sin2 2θ13 of O(10−4) or smaller.

48

These are major experimental results that would simultaneously provide a final confirma- tion the three-flavor mixing framework (by establishing νe ↔νµ transitions in an appearance experiment) while strongly suggesting the existence of a new conservation law. In consid- ering the case θ13 = 0, it should be noted that within the framework of GUT theories, radiative corrections will change the value of sin2 2θ13 measured in the laboratory from the underlying value of sin2 2θ13 at the GUT scale.

Recent Calculations Have Suggested

that these radiative corrections to sin2 2θ13 will be O(10−4). If this is the case, the ultimate Neutrino Factory experiment would not only provide the first direct observation of νe →νµ

Transitions, But Would Also

• establish a finite value for θ13 at laboratory scales consistent with being zero at the

• Determine The Sign Of ∆M2

31, and hence determine whether the neutrino mass hierarchy

Is Normal Or Inverted, And

• detect maximal CP violation in the lepton sector. These would be tremendously important results.

Beta Beam Calculations And Results

The Beta Beam concept is more recent than the Neutrino Factory idea, and the perfor- mance of Beta Beam experiments is less well established. Recent calculations of the sin2 2θ13 sensitivity for low energy Beta Beam scenarios [62, 63] have included the effects of system- atic uncertainties, correlations, and false solutions in parameter space. Expected signal and background rates are summarized in Table VII. The expected signal rates are relatively modest. The neutrino Beta Beam signal would be a factor of 2–3 less than expected at a high–performance Superbeam, and a factor of 14 less than at a Neutrino Factory. The rates are even lower for an antineutrino Beta Beam; a factor of 20 less than the rates at a high– performance Superbeam, and a factor of 32 less than at a Neutrino Factory. In addition, it has been pointed out that the neutrino energies are comparable to the target nucleon kinetic energies due to Fermi motion, and therefore there is no useful spectral information in the low energy Beta Beam measurements. Hence, the useful information is restricted to

49

the measured muon neutrino (and antineutrino) appearance rates. Nevertheless, the sig- nal/background ratios are good: 12.5 for the neutrino Beta Beam (compared with 6.2 for the Superbeam and 735 for the Neutrino Factory), and an impressive 478 for the antineu- trino Beta Beam (compared with 2.8 for the Superbeam and 85 for the Neutrino Factory).

Hence the interest in Beta Beams. The ability of a low-energy Beta Beam to discover a

1

FIG. 28: (Color) CERN SPS Beta Beam sensitivity. finite value for sin2 2θ13 is compared in Fig. 28 with the corresponding 3σ sensitivities at a Neutrino Factory and high performance Superbeam. The leftmost limits of each of the bars in Fig. 28 show the statistical sensitivities, and the shaded regions within the bars show the degradation of the sensitivities due to irreducible experimental systematics, the effects of correlations, and the effects of false solutions in the three-flavor mixing parameter space.

The rightmost limit of the bars therefore gives the expected sensitivities for each experiment. The sensitivity of the low–energy Beta Beam experiment is expected to be comparable to the corresponding Superbeam sensitivity. A Neutrino Factory would improve on the Beta Beam sensitivity by about a factor of 40. Combining low-energy Beta Beam results (the two measured rates) with Superbeam results would enable the impact of correlations and ambiguities to be reduced, which would potentially enable an improvement in the sin2 2θ13 sensitivity by a factor of 2–3 over the standalone results. Hence, low energy Beta Beams offer only a modest improvement in the sin2 2θ13 sensitivity beyond that achievable with a high–performance Superbeam, and this realization has led to the consideration of higher en-

50

ergy Beta Beams [38, 64]. In particular, it has been proposed that the energies be increased by at least a factor of a few so that the neutrino and antineutrino energies are well above the Fermi motion region, which would enable useful spectral information to be extracted from the Beta Beam measurements. In addition, this would increase the signal rates (Table VI), and if the energy were sufficiently high to result in significant matter effects, then it would be possible (if θ13 is sufficiently large) to use Beta Beams to determine the neutrino mass hierarchy. The particular scenarios that have been considered are: Low Energy Beta Beam: This is the standard CERN scenario using the SPS for acceler- ation, and a 1 megaton water Cerenkov detector in the Fr´ejus tunnel (γ = 60, L = 130 km).

Medium Energy Beta Beam: This would require the Fermilab Tevatron (or equivalent) for acceleration, and a 1 megaton water Cerenkov detector in the Soudan mine (γ = 350, L = 730 km).

High Energy Beta Beam: This would require the LHC for acceleration, with γ = 1500, L = 3000 km. In all three cases, the running time is assumed to be 10 years. The improvement in statistical precision enabled by the higher energy Beta Beam scenarios is illustrated in Table VI and Fig. 29. The figure shows, for the three scenarios, the 1σ, 2σ, and 3σ contours in the (θ13, δ)– plane. Note that the expected sensitivity for the medium energy case with a “small” water Cerenkov detector is comparable to the low energy case with the megaton water Cerenkov detector. However, the medium energy sensitivity is dramatically improved with the much bigger detector.

The further improvement obtained by going to LHC energies seems to be marginal. Given the likelihood that the LHC would not be available as a Beta Beam accelerator for a very long time, perhaps the most interesting scenario is the medium energy one. To understand the ability of medium energy Beta Beams to establish a finite value for θ13, determine the neutrino mass hierarchy, and search for CP violation in the lepton sector, the full analysis must be performed, taking care of all known systematic effects, and the impact of correlations and degeneracies. Although this full analysis has not yet been done, a step towards it has been made, and the results are encouraging. Figure 30 shows the region of the (θ13, δ)–plane within which sin δ = 1 (maximal CP violation) can be separated

51

FIG. 29: (Color) Low-, Medium-, and High-Energy Beta Beam sensitivities. The estimated 1σ, 2 σ and 3 σ contours are shown for the setups described in the text. See Ref. . 30: Region where δ can be distinguished from δ = 0◦or δ = 180◦with a 99% CL for the low en- ergy Beta Beam(solid), medium energy Beta Beam with an UNO-type detector of 400 kton(dashed) and with the same detector with a factor 10 smaller mass (dashed-dotted), and finally for the high energy Beta Beam (dotted) with a 40 kton tracking calorimeter. Figure from Ref.

52

from sin δ = 0 (no CP violation) at the 99% C.L. The medium energy setup is sensitive to maximal CP violation for values of θ13 exceeding ∼0.5 degrees (sin2 2θ13 ∼3 × 10−4). This is within a factor of a few of the expected sensitivity that can be achieved at a Neutrino Factory. It will be interesting to see if this calculated medium energy Beta Beam sensitivity is significantly degraded when the uncertainties on all the oscillation parameters and the systematic uncertainties on the neutrino cross sections, etc., are included in the calculation.

Finally, Fig. 31 shows, for the medium energy Beta Beam scenario, the region of the (θ13, δ)–

Fig. 31: Regions Where The True Sign(∆M2

23) = +1 can be measured at 99% C.L. (i.e., no solution at this level of confidence exists for the opposite sign). The lines correspond to the medium energy Beta Beam with a 400 kton water Cerenkov (solid), a 40 kton detector (dashed), and to the high energy Beta Beam(dotted). Figure from Ref. .

plane within which the neutrino mass hierarchy can be determined. The smallest value of θ13 for which this can be accomplished is seen to be 2−3 degrees (sin2 2θ13 = 0.005−0.01), which is perhaps a little better than with a Superbeam, but is not competitive with a Neutrino Factory.

Sign

In this Section we describe the technical work accomplished as part of the present Study. For the Neutrino Factory (Sections V A and V B) our focus was to update the FS2 design with some of the more cost-effective approaches we have studied. In particular, a more optimized capture section was designed, a shorter and less expensive bunching and phase rotation scheme was developed, and a more optimized acceleration scheme based on a combination of RLA and FFAG rings was worked out. Based on the improved designs presented here, we worked out approximately what the savings with respect to FS2 costs were. This is described in the Appendix.

For the Beta Beam facility, we have taken a brief look in Section V C at the implications of using existing U.S. accelerator facilities at BNL and Fermilab to provide the required beams. There is a real motivation to explore this idea, because it appears that there are significant scientific benefits associated with producing the neutrino beams from a Beta Beam facility at higher energy than would be possible at CERN in the foreseeable future.

Neutrino Factory Front End

The front end of the neutrino factory (the part of the facility between the target and the first linear accelerator) represented a large fraction of the total facility costs in FS2 . However, several recent developments have given hope that a new design for the front end may be possible that is significantly less expensive: • A new approach to bunching and phase rotation using the concept of adiabatic rf bunching [65, 66, 67, 68, 69] eliminates the very expensive induction linacs used in

Fs2.

• For a moderate cost, the transverse acceptance of the accelerator chain could be dou- bled from its FS2 value. • This diminished the demands on the transverse ionization cooling section and allowed the design of a simplified cooler with fewer components and reduced magnetic field strength.

54

We denote as “Study 2a” the simulations that have been made of the performance of this new front end, together with the new scheme for acceleration. The Monte Carlo simulations were performed with the code ICOOL . The concept of the adiabatic buncher is compared with

Rf-Rotation

FIG. 32: (Color) Comparison of the buncher concept used here with the bunching system used in

Fs2.

the system used in FS2 in Fig. 32. The longitudinal phase space after the target is the same in both cases. Initially, there is a small spread in time, but a very large spread in energy. The target is followed by a drift space in both cases, where a strong correlation develops between time and energy. In FS2, the energy spread in the correlated beam was first flattened using a series of induction linacs. The induction linacs did an excellent job, reducing the final rms energy spread to 4.4%. The beam was then sent through a series of rf cavities for bunching,

55

which increased the energy spread to ≈8%. In the new scheme, the correlated beam is first adiabatically bunched using a series of rf cavities with decreasing frequencies and increasing gradients. The beam is then phase rotated with a second string of rf cavities with decreasing frequencies and constant gradient. The final rms energy spread in the new design is 10.5%.

This spread is adequate for the new cooling channel. The overall layout of the new front–end

295

FIG. 33: (Color) Overall layout of the front-end. design is shown in Fig. 33. The first ≈12 m is used to capture pions produced in the target. The field here drops adiabatically from 20 T over the target down to 1.75 T. At the same time, the radial aperture of the beam pipe increases from 7.5 cm at the target up to 25 cm.

Next comes ≈100 m for the pions to decay into muons and for the energy-time correlation to develop. The adiabatic bunching occupies the next ≈50 m and the phase rotation ≈50 m following that. Lastly, the channel has ≈80 m of ionization cooling. The total length of the new front end is 295 m. The longitudinal field component on-axis is shown for the full front-end in Fig. 34. The field falls very rapidly in the collection region to a value of 1.75 T.

It keeps this value with very little ripple over the decay, buncher and rotator regions. After a short matching section, the 1.75 T field is changed adiabatically to the alternating field used in the cooler. The beam distributions used in the simulations were generated using MARS . The distribution is calculated for a 24 GeV proton beam interacting with a Hg jet . The jet is incident at an angle of 100 mrad to the solenoid axis, while the beam is incident at an angle of 67 mrad to the solenoid axis. An independent study showed that the resulting 33 mrad crossing angle gives near-peak acceptance for the produced pions. An examination of particles that were propagated to the end of the front-end channel shows that they have a peak initial longitudinal momentum of ≈300 MeV/c with a long high-energy tail, and a peak initial transverse momentum ≈180 MeV/c. We used an improved axial field profile in the capture region that increased the final number of muons per proton in

56

FIG. 34: Longitudinal field component Bz on-axis along the Study2a front-end. the accelerator acceptance by ≈10%. The new axial field profile (marked KP) is compared in Fig. 35 with the profile used in FS2. Figure 36 shows the actual coil configuration in the collection region. The end of the 60 cm long target region is defined as z = 0. The three small radius coils near z = 0 are Cu coils, while the others are superconducting. The left axis shows the error field on-axis compared with the desired field profile. We see that the peak error field is ≈0.07 T. Figure 37 shows a MARS calculation of the absorbed radiation dose in the collection region. The peak deposition in the superconducting coils is ≈1 Mgy/yr for a 1 MW beam running for 1 Snowmass year of 107 s. Assuming a lifetime dose for the insulation of 100 Mgy, there should be no problem with radiation damage in the coils.

Two cells of the buncher lattice are shown schematically in Fig. 38. Most of the 75 cm cell length is occupied by the 50-cm-long rf cavity. The cavity iris is covered with a Be window. The limiting radial aperture in the cell is determined by the 25 cm radius of the window. The 50-cm-long solenoid was placed outside the rf cavity in order to decrease the magnetic field ripple on the axis and minimize beam losses from momentum stop bands.

The buncher section contains 27 cavities with 13 discrete frequencies and gradients varying from 5–10 MV/m.

Authors:

Peder EZ Larson 1, 2,* , Jenna ML Bernard1, James A Bankson 3, Nikolaj Bøgh 4, Robert A Bok1, Albert P. Chen 5, Charles H Cunningham 6,7, Jeremy Gordon1, Jan-Bernd Hövener 8, Christoffer Laustsen 4, Dirk Mayer 9,10, Mary A McLean11 12, Franz Schilling13, James Slater1, Jean-Luc Vanderheyden5, 14, Cornelius von Morze 15, Daniel B Vigneron1, 2, Duan Xu1, 2, and the HP 13C

94143, Usa.

Denmark. 5 GE Healthcare, Menlo Park, California, USA. 6 Physical Sciences, Sunnybrook Research Institute, Toronto, Ontario, Canada.

8 Section Biomedical Imaging, Molecular Imaging North Competence Center (MOIN CC), Medicine, Baltimore, MD, USA. Cambridge, United Kingdom.

14Jlvmi Consulting Llc, Dousman, Wi, Usa

#See Acknowledgements for a list of all HP 13C MRI Consensus Group Members This work was supported by the ISMRM Hyperpolarized Media MR Study Group, the ISMRM Hyperpolarization Methods & Equipment Study Group, and the Hyperpolarized MRI Technology Resource Center (NIH/NIBIB grant P41EB013598).

Abstract

MRI with hyperpolarized (HP) 13C agents, also known as HP 13C MRI, can measure processes such as localized metabolism that is altered in numerous cancers, liver, heart, kidney diseases, and more. It has been translated into human studies during the past 10 years, with recent rapid growth in studies largely based on increasing availability of hyperpolarized agent preparation methods suitable for use in humans. This paper aims to capture the current successful practices for HP MRI human studies with [1-13C]pyruvate - by far the most commonly used agent, which sits at a key metabolic junction in glycolysis. The paper is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification. In each area, we identified the key components for a successful study, summarized both published studies and current practices, and discuss evidence gaps, strengths, and limitations. This paper is the output of the “HP 13C MRI Consensus Group” as well as the ISMRM Hyperpolarized Media MR and Hyperpolarized Methods & Equipment study groups. It further aims to provide a comprehensive reference for future consensus building as the field continues to advance human studies with this metabolic imaging modality.

Keywords: Hyperpolarized MRI, metabolic imaging, carbon-13, pyruvate, dissolution dynamic

Introduction

MRI with hyperpolarized 13C agents, also known as hyperpolarized (HP) 13C MRI, has shown great potential as a novel imaging modality, particularly for its ability to probe metabolic processes in real time. The first human studies with HP [1-13C]pyruvate were performed in 2011 in prostate cancer patients (1).

Since then, there have been over 60 papers published with imaging results of human subjects from 13 different sites, with applications including prostate cancer, brain tumors, breast cancer, kidney cancer, pancreatic cancer, metastatic disease, liver disease, ischemic heart disease, diabetes and cardiomyopathies. The vast majority of these studies used [1-13C]pyruvate (1–63), where [2-13C]pyruvate (64) and 13C-urea (56) have been demonstrated too.

As clinical HP 13C MRI advances, there is a growing need to build consensus for best practices, which are critical for comparing data across sites, performing multi-site trials,deploying methods to new sites, partnering with vendors, and potentially for obtaining broader regulatory approvals.

In March 2022, we initiated an effort to build consensus within the HP 13C MRI community with this opportunity in mind, and it was greeted with strong enthusiasm. The “HP 13C MRI Consensus Group”, containing over 55 members from 27 sites, identified the area of greatest need and opportunity for consensus building to be HP [1-13C]pyruvate human

●

Pyruvate is the most mature and widely used HP agent and has the most significant translational evidence emphasizing the potential clinical impact.

●

Clinical trials, particularly multi-site trials, have the strongest need for consensus methods to ensure that data can be combined across sites. This work is a Position Paper for which the goal is to describe current successful practices and study methods for HP [1-13C]pyruvate human studies along with justification to support those practices. This is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification (Fig. 1). The current successful practices and study methods include a literature review of published peer-reviewed journal papers showing human HP [1-13C]pyruvate study data, up to September 2022 (1–63), as well as new unpublished information from surveys of HP 13C study sites. Based on this information, we also highlight the evidence gaps, strengths, and limitations of current practices which are summarized at the end of each section.

Figure 1: Illustration of the HP 13C MRI human study process, including the 4 major areas covered in this paper: Hyperpolarized 13C-pyruvate preparation, MRI system setup and calibration, Acquisition and Reconstruction, and Data Analysis and Quantification.

Figure 2: Anatomical targets of HP [1-13C]pyruvate MRI human studies published up to September 2022.

Hyperpolarized 13C-Pyruvate Preparation

This section covers the processes for creating the HP agent, 13C pyruvate, and will include many aspects and considerations that are needed to safely and effectively prepare doses for metabolic imaging studies in human subjects. These include material, personnel, equipment and facility, fluid path preparation, quality control, and release.

It is helpful to understand that the specifications of a dose of 13C pyruvate suitable for in vivo MR HP metabolic imaging were shaped in part by early preclinical studies performed by GE HealthCare summarized in Ref. (65). In short, the safety of the two novel drug components, 13C pyruvate and the electron paramagnetic agent (EPA) AH111501, were demonstrated in those studies. The more precise formulation of the dose suitable for human use was then determined from clinical studies (66) that included two Phase 1 clinical trials in young and elderly healthy volunteers without hyperpolarization of the 13C nuclei and another Phase 1/2a dose escalation and imaging feasibility study with HP 13C pyruvate in 31 prostate cancer patients at the With the exception of the first HP 13C imaging clinical trial, which utilized a prototype device in a cleanroom (1), all HP 13C studies performed in humans to date have utilized the SPINlab polarizer (manufactured by GE HealthCare). Consequently all doses of the HP 13C pyruvate delivered by SPINlab have been produced using the “SPINlab Pharmacy Kit” that serves as the container-closure system for the various drug components (13C pyruvic acid and EPA mixture, dissolution medium, and neutralization and dilution medium) during sample polarization, dissolution and quality control (QC) processes. Thus many aspects of the HP sample preparation considerations discussed below are related to the SPINlab instrument and the consumables designed to be used with it (67).

General Considerations

While more than 860 patients or healthy subjects having been injected with HP 13C pyruvate as of January 2022 without reports of any serious adverse events (68), HP 13C pyruvate injection remains an investigational MR contrast agent and can only be administered by those with Investigational New Drug (IND) exemption from the Food and Drug Administration (FDA) in the USA, a Clinical Trial Application (CTA) in Canada, approval from National Research Ethics Committee Services in the UK, or approval from the relevant local regulatory body. Thus, methods and processes involved to produce a dose should have patient safety as the first priority. Since utilizing dissolution dynamic nuclear polarization (dissolution-DNP) for human use is still a relatively new development, there are no existing published regulatory guidelines specifically for this method.

There are two major production styles that determine how various sites approach the agent preparation. In the US, the most common approach is to rely on a sterilizing filter (“Terminal Sterilization”) to ensure sterility of the final product, akin to PET tracer production, where a starting molecule with a radioisotope is processed using various other ingredients to make the final, desired and injectable contrast agent within a necessarily short amount of time (69). For these sites, sterilization of the components and accessories upstream of this filter are not required, although many of them were manufactured and tested following Good Manufacturing Practice (GMP) or Good Laboratory Practice (GLP) requirements. The filling process is usually performed under an ISO 5 laminar flow hood, but a clean room or an isolator is not required.

This approach is typically accompanied by testing the integrity of the sterilizing filter prior to release of the dose for injection. Typically, post release endotoxin and sterility tests are performed using an aliquot reserved from each released dose.

In the UK and EU, the most common approach is to more-closely follow sterile pharmaceutical compounding guidelines (70), where all components and ingredients are required to be sterile or manufactured under GMP guidelines and are assembled and filled within a clean room environment or an isolator system (“Sterile Preparation”). Typically a batch of Pharmacy Kits for HP 13C pyruvate injection are prepared together. The sterility of the final dose is also ensured by batch validation testing, in addition to the sterility of the ingredients and the sterile compounding process. The endotoxin and sterility testing are performed for the process validation but are not performed for each injected dose.

Some institutions fill and assemble the Pharmacy Kit required for a specific study on the same day or the day prior to polarization, dissolution, and patient administration, but others have also demonstrated the feasibility of preparing a batch of kits, keeping them in a -20ºC freezer and using them over a period of a few months.

Beyond the obvious requirements that the process and the facility has to ultimately produce a dose that is safe to inject into a human, regulatory authorities will also focus on the question “Are you in control of your processes?”. To be in control of your process requires an in-depth and broad understanding of all processes involved in pre, post, and during the production process.

Personnel

It is typical and may be required to have licensed personnel involved in the production process depending on local regulations.Typically a pharmacist, radiopharmacist or other similarly qualified person (QP), in charge of the facility where the Pharmacy Kit filling and preparation is taking place, is responsible for the overall process and the release of the injectable dose.

Qualified cleanroom technicians are often involved in the Pharmacy Kit filling under the supervision of the pharmacist or QP. As is required for pharmaceutical compounding or PET tracer production, training requirements and training records for all personnel need to be maintained and available for audit by the FDA or equivalent.

Equipment And Facility

The facility and all equipment need to have standard operating procedures (SOPs) that describe how equipment is used, maintained, and calibrated to comply with relevant legislation. Currently, almost all the filling of the Pharmacy Kit takes place within a compounding laminar flow hood or isolator (typically ISO 5). At some sites, the filling is conducted within a cleanroom, while at others, it is conducted in a dedicated non-cleanroom space, reflecting differences in cleanroom approach and specifications between regulators worldwide (71). Some equipment or facilities, such as the compounding hood or cleanroom, may require external certified laboratories for testing.

Material Handling

Material handling guidelines (69,70) require SOPs detailing a system to track all of the materials involved in the HP production process for a particular patient dose, similar to current good manufacturing practice (cGMP) requirements for material handling for drug compounding. This includes acceptance standards, storage conditions, amount used in the patient dose for each ingredient and materials used in the assembly of the fluid path and Pharmacy Kit. Currently some users choose to open and inspect and sometimes modify the Pharmacy Kits upon arrival, but some users keep them in the sealed packaging until they are required for dose preparation.

Pharmacy Kit Filling And Assembling

As required by an IND or its equivalent, the preparation of the doses of HP 13C agent are detailed in the Chemistry, Manufacturing, and Control (CMC) section of an applicable regulatory submission; an example of this has been made available (72). It describes the processes of filling the Pharmacy Kit with the different components that make up the final drug product, and of assembling the final kit for either storage or immediate use in the polarizer. Special attention should be given to the laser welding process in order to satisfy installation qualification (IQ) and operational qualification (OQ). Typically, the final developed process is validated by process qualification (PQ) runs, during which 3 or more Pharmacy Kits are filled and used and the final HP 13C products are tested for endotoxin and sterility and to confirm that they meet the dose specifications for injections (usually including pyruvate concentration, residual EPA concentration, pH, liquid state polarization level and dose temperature). The data from 3 consecutive PQ runs are submitted as part of the IND submission (or its equivalent), and are often also reviewed by the Institutional Review Board (IRB) where the studies are conducted.

Quality Control And Dose Release

The quality control (QC) and dose release can be separated into two aspects: one is the QC and release of the filled Pharmacy Kit, and second is the QC and release of the HP 13C agent for injection, after polarization and dissolution. For institutions filling a batch of kits and storing them to use over a period of time, typically the batch can be released based on initial validation, environmental monitoring data from the day of kit production, and if filters are used during preparation of any of the components, filter integrity testing. But in some cases one or more kits are used for validation before the batch of kits are released for future use. For institutions that fill only the kits required for specific studies shortly before the experiment, the filled kits often do not go through separate release tests before they are used.

The quality control of the HP 13C pyruvate solution post dissolution is primarily performed to ensure that the agent meets the dose specifications (Table 1) before it is administered to the subject. These specifications target both safety (pH, residual EPA, temperature) and efficacy (pyruvate concentration, polarization, volume). Typically, the pyruvate concentration, residual EPA concentration, pH, dose temperature, dose volume, and liquid state polarization are measured by the QC accessory associated with the SPINlab polarizer. Some users perform a secondary measurement for one of the parameters, such as pH, using a different instrument or pH paper. For sites that do not go through a separate release testing process for batch filled kits, the integrity of the sterilization assurance filter, a part of the Pharmacy Kit, is typically tested as a part of the dose release. It is also common for these users to preserve an aliquot of the final HP 13C pyruvate solution for post-release endotoxin and sterility testing. This testing cannot be completed fast enough to test an individual dose prior to injection, but this is why other processes such as PQ runs and validation testing are done to minimize the chance a subject could be injected with a contaminated dose.

The Final Dose Release And Injection

should be done under the supervision of a licensed professional, based on local regulations.

Some Key Challenges

Many of the challenges associated with HP 13C pyruvate preparation can be attributed to the conditions required for the dissolution-DNP method of high magnetic field (~3-7 T) and very low temperature (~1 K) during polarization, with pressurized and superheated water necessary for the rapid dissolution event. These extreme conditions are quite challenging for the design of the container-closure and fluid path system. In particular, the cryogenic temperature in the polarizer requires special attention to any moisture or ambient (moist) air introduced into that portion of the fluid path, which can form an ice block at ~1 K. This ice can lead to flow restriction during the dissolution event and reduce the strength of the laser welded bond between the cryovial and its cap. This can ultimately produce failures in the dissolution step, including variations in final pyruvate concentration and pH that may fail to meet QC release criteria as well as fluid path ruptures that provide no available dose and result in polarizer down-time.

The polarization of the HP 13C pyruvate sample decays quickly over the span of a few minutes after dissolution, and thus the process of dissolution, QC for release, and injection should be completed as fast as possible to preserve the high polarization level achieved. Any delays in the preparation process, such as transportation time or equipment malfunction, can significantly reduce the final polarization and result in lower quality imaging data.

Current Practices

A summary of data collected from all sites performing clinical trials with HP 13C-pyruvate is shown in Fig. 3 and Table 1, including the specification of the final dose and how the quality control and release of the final dose are performed. There is a split in the Production Style, described in the General Considerations section above, with 8/13 sites using Sterile Preparation versus 5/13 using Terminal Sterilization. While many of the dose specifications show notable differences in acceptable ranges, all of these variations listed in tables have been successfully and safely been used to perform HP 13C pyruvate studies in humans. Their differences depend on the institutions’ preferences, resources and their particular regulatory situation. There is high similarity in pyruvate ranges, temperature ranges, EPA limits, and volume limits. There is modest variability in pH ranges and large variability in the endotoxin test limit. There is a 3-fold difference in acceptable polarization levels, which are measured to ensure a futile dose is not injected since the polarization is directly proportional to SNR. This reflects the decision by several sites to believe that useful data can be still be obtained with suboptimal polarizations.

Figure 3: Hyperpolarized agent preparation methods reported by sites currently performing HP

In House

Table 1: HP 13C-pyruvate preparation parameters, methods, and dose specifications used for quality control testing and release as well as validation. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. The parameters used for product release are noted in bold text, otherwise these parameters are measured for batch validation or other QC measurements. The endotoxin and sterility testing are performed during process validation of the batch and/or post-injection, and largely depends on the agent production approach.

Summary

The overall safety record of HP 13C-pyruvate has been very strong, and the SPINlab hyperpolarizer has proven to provide high polarizations at human sized doses while meeting numerous QC and release criteria. A weakness remains the failure modes of the SPINlab Phamacy Kits (e.g. ice blocks, path ruptures), which are placed under extreme requirements particularly during dissolution. The preparation process still requires a high degree of expertise.

Therefore, there is a significant need to improve the reliability, robustness, and ease of operation for generating HP 13C-pyruvate doses for human studies. Furthermore, there is a divide between manufacturing and sterile compounding style preparation as well as other site-specific practices, resulting in variations in SOPs and justification required to relevant regulatory bodies. There have also been no comparisons between these approaches. It is also unclear what release criteria and QC parameters are truly required to ensure patient safety.

However, all of the reported methods are acceptable and approved by the appropriate regulatory authorities, and have led to the rapid expansion of successful human studies in recent years.

Mri System Setup And Calibrations

This section covers the MRI system setup, including the imaging system, RF coils, phantoms, and prescan calibration methods.

Imaging System

The main prerequisite for a given MRI scanner to be capable of supporting studies with HP 13C is its “broadband” capability to transmit and receive radiofrequency (RF) signal at the frequency of 13C, which is around 4 times lower than 1H. This does not come as a default on clinical MR devices. The transmit power of the broadband amplifier should also be sufficient to support the intended flip angle and RF pulse shape with the employed transmission RF coil(s) for 13C. Most studies to date use relatively low flip angles (< 90 degrees) for HP 13C in order to preserve polarization for time-resolved imaging. The capability to receive 13C signal on multiple channels is also desirable to increase SNR, as discussed further in the “RF coils” section.

The choice of magnetic field strength is primarily dependent on the metabolites’ frequency separation due to chemical shift dispersion and 1H imaging. High field strengths do not enhance hyperpolarized 13C signal as they do for 1H because the signal strength in a HP experiment relies on manipulating the population of quantum energy states outside of the MRI scanner.

However, the injected HP 13C-pyruvate and its metabolic products have greater frequency separation at higher fields, and it may thus be easier to separate and quantify these resonances at higher fields. This comes at the cost of a reduction in the achievable T2* and often reduced T1. As the initial polarization is independent of the imaging field strength it has been proposed that the increased T2* at 1.5T can potentially be exploited to increase SNR by adapting the acquisition bandwidth or reduce off-resonance imaging effects in cases when the decay of the transverse magnetization is dominated by T2* (73). In practice, 3T has been used in all published human 13C-pyruvate studies surveyed (Supporting Table S1), and comprises the majority of scanners currently in use for human studies (Table 3). A field strength of 3T is well-suited for 1H MRI anatomical reference and correlative imaging.

Stronger and more rapidly slewing magnetic field gradients support more rapid spatial encoding, particularly for metabolite-specific single-shot imaging using echo-planar imaging (EPI) or spiral imaging (See “Acquisition and Reconstruction”). Although the spatial resolution acquired for HP 13C imaging is typically much coarser than for 1H MRI, the factor of ~4 in gyromagnetic ratio leads to the same reduction factor in performance of the gradient system, so 13C experiments are potentially more limited by gradient hardware performance. To date, all human studies have used the commercially-available integrated gradient systems provided in clinical MRI scanners.

Optimization of scanner design has understandably focused on minimization of artifacts in 1H MRI, where devices such as room lights, the gradient amplifiers, and the motors driving the patient bed are checked to ensure that they do not produce RF interference at the 1H frequency, but artifacts may arise at other frequencies. Eddy current compensation is also not always appropriately adjusted for nuclei at other frequencies (74). In order to optimize for 13C, many sites have performed checks on phantoms for RF interference, gradient artifacts, and eddy currents (74), including the use of post-hoc gradient impulse response function characterisation and correction, and some vendors have fixed these issues as well.

Rf Coils

For HP 13C imaging studies in humans, RF coils for both 1H and 13C nuclei are needed, with 1H MRI providing an anatomical reference for registration and optional additional multiparametric MRI readouts. At the Larmor frequency of 13C nuclei, the relative contributions from coil noise compared to sample noise increase compared to 1H (73,75), although sample noise still is likely the dominant contributor for human-sized coils at 32.1MHz - the resonance frequency of 13C nuclei at 3T.

The key requirement for human 13C-pyruvate RF coils are that the coil geometry and sensitive volume must cover the volume of interest in the subject. Table 2 and Figure 4 shows coil configurations that have been used and optimized for applications in different anatomic regions.

Volume resonators are most commonly used for transmit, as they surround the subject to

Provide B1 Transmit Across The Fov (B1

+). While 1H relies on a large birdcage (“body”) coil built into the scanner, 13C transmit coils must be placed inside the bore. This takes up valuable space within the magnet, and also has led to the use of designs with relatively inhomogeneous

B1

+. Many human studies have used Helmholz pair resonators for transmit, including the “clamshell coil”, which has a notably inhomogeneous B1

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

angles that control the use of the hyperpolarized magnetization and creates errors in common HP metrics (9,76). The exception are head coils, where birdcage designs with highly

Homogeneous B1

+ can be placed around the head while easily fitting inside the bore. As with 1H MRI, higher SNR can typically be achieved by smaller receive coil elements, such as surface coils or phased arrays, and the majority of 13C receive coils used have layouts similar to 1H phased arrays.

RF coil quality control is important to ensure proper functioning of the coils to provide consistent imaging quality, especially with limited natural abundance 13C signal in vivo. It typically involves 1) a physical integrity check of the coil cables and connectors and 2) phantom SNR tests to check the coil’s performance and to monitor it over time (see Phantoms below). An useful reference for RF coil quality control is outlined in the MRI accreditation program of the American College of Radiology (77) and can be adapted for 13C coils.

Notably, configurations for brain and prostate studies used dual-tuned 1H/13C coil designs, which greatly simplify workflow and registration of 1H and 13C images, as no switching of coils is needed.

(1)

Table 2: RF coil configurations reported for human HP [1-13C]pyruvate studies.

Tx = Transmit

coil, RX = receive coil. The commonly used “clamshell” TX coil is a Helmholz pair design. For 1H RF configurations, all used the Body coil for TX unless otherwise noted, and “repositioned” indicates the 13C coil was removed for 1H imaging. One representative reference is listed for each configuration. The RF coil configurations reported in the reviewed papers are shown in Supporting Table S1.

Figure 4: Examples of RF coil configurations used for human HP [1-13C]pyruvate brain studies. (A,B) 13C Clamshell TX (Helmholz pair) and 2× 4-channel paddle RX arrays. (C) 13C Birdcage volume TX and 32-channel RX array (RX array slides into TX coil). (D) 13C Birdcage volume TX and 24-channel RX array, combined with a 1H 8-channel RX array. Image reproduced with permission from Ref (16).

Phantoms

Since hyperpolarized magnetization is non-renewable, phantoms containing 13C nuclei are important to: 1) test the multi-nuclear capabilities of the imaging system, including all parts of the signal excitation and receive chain; 2) perform calibration measurements before a scan with hyperpolarized nuclei; and 3) perform necessary pre-scan adjustments (see “Prescan Calibration” section). The phantoms currently in use are listed in Table 3. Their composition must provide sufficient 13C signal, with additional considerations of conductivity, stability, chemical shift(s) present, potential for dynamic imaging, and cost. The phantom geometries are typically either compact, in order to be used alongside the subject during a HP scan, or large enough to mimic the inner volume of a RF coil for system testing.

One popular compact design contains enriched 13C-urea at high concentration, typically 8 M, which provides a single resonance, placed inside a small container ~1 mL. The most common recipe mixes 13C-urea in a 90% water/10% glycerol solution, with glycerol used to increase the urea solubility and doping with a Gd-based contrast agent to shorten T1 which increases the potential SNR per unit time. For example, when Dotarem is added at a 3:1000 volume ratio the 13C-urea T1 is around 500 ms and T2 is around 100 ms. However, when testing pulse sequences influenced by T1 and T2, doping should be used carefully. This phantom is suitable for frequency calibration, transmit gain calibration, sequence testing, and as a fiducial marker when placed next to a patient. However, enriched 13C-urea has a relatively high cost compared to natural abundance compounds.

For larger volumes (>100 ml), the phantoms most often used contain undiluted ethylene glycol, glycerol, or dimethyl silicone. These compounds have sufficiently high carbon concentrations to provide sufficient 13C signal even with the 1.1% natural abundance of 13C. These larger phantoms matching the inner volume of an RF coil are useful for coil testing, including transmit

+) And Receive (B1

-) coil profile mapping, as well as to mimic acquisitions using in vivo FOV requirements. In this case, size and conductivity should match the expected subject size in order to mimic coil loading and get a realistic estimation of B1+. Large-volume natural abundance urea phantoms have also been used by some sites, but suffer from higher conductivity compared to biological tissues. Typically, it is easier to increase the conductivity and hence coil loading of the non-conductive phantom by adding NaCl to match physiological loading (16,78).

Dynamic phantoms that aim to mimic metabolite kinetics have also been developed (79–81), and have the potential to more closely mimic the HP experiment, but so far these are not widely used.

Prescan Calibration

Prior to performing an MRI acquisition, the so-called prescan procedure is used to set the shim parameters to maximize B0 homogeneity over the field of view (FOV) or a specific region of interest (ROI), the scanner center frequency (CF), the RF transmit gain, and the receiver gain.

While this calibration procedure is usually automated for 1H, the lack of sufficient natural abundance 13C signal prevents use of automated methods. (Although natural abundance 13C lipid signal has been detected, there are so far no reports on using this signal for prescan.) Table 3 shows current practices across sites.

Maximizing B0 homogeneity is independent of the nucleus and is therefore performed prior to 13C imaging using the 1H water signal and existing shimming tools, such as by a standard automated process (“Auto Shimming”) or using high order shimming routines. Similarly, the 13C CF can be calculated from the 1H CF using a predetermined scaling factor that depends on the target chemical shift (82). Another common approach used is to have a small, high-concentration 13C phantom, e.g. 8M 13C-urea, integrated in the RF coil or placed next to the scan subject (1). The reference frequency can also be based on real-time measurements after the HP injection but prior to imaging (83). Both the CF and B0 shimming are critical when using spectrally-selective RF pulses, as inmetabolite-specific imaging methods, where the desired excitation bandwidths are typically very narrow and frequency offsets can lead to a failure mode that is only apparent after injection.

The calibration of the RF transmit power is typically performed on a small, high-concentration 13C phantom placed near the region of interest during the scan or on a large 13C phantom of similar size and coil loading as the subject, prior to the subject scan. Reference power is often done by sweeping the power in a pulse-acquire sequence (53,62), or the Bloch-Siegert method (52,84). When using a small phantom, the location of the phantom, B1

+ Inhomogeneity As Well

as any shielding effects, e.g., when the phantom is integrated into a coil (1), may degrade the accuracy. Other methods include real-time Bloch-Siegert method measurements after the HP injection (83), and using the stronger natural abundance 23Na signal that is close enough to the 13C resonance frequency to be detected by 13C coils (82).

The receiver gain is predetermined, either systematically based on independent phantom measurements and assuming the dose and polarization of the HP compound is known prior to injection, or based on past HP imaging studies.

Power [Kw]

Phantom(s) - during study Phantom(s) - before study 13C Frequency

8

13C-bicarbonate doped with dimethyl silicone, various

Maximum Values

Table 3: Summary of the imaging systems, phantoms, and prescan procedures used at sites currently performing HP 13C-pyruvate human studies. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. *Previously performed studies with a Siemens 3T Tim Trio. The imaging systems, phantoms, and prescan procedures reported in the reviewed papers are shown in Supporting Table S1.

Summary

Commercially available 3T MRI systems are by far the most commonly used for human HP 13C-pyruvate studies, although a systematic investigation of the impact of B0 has only recently been investigated (73). The multi-nuclear RF transmit and receive chain has proven sufficient for current acquisition strategies, although many sites have observed artifacts due to RF interference, gradient interference, and residual eddy currents when operating at the 13C frequency. A variety of 13C RF coils, tailored for numerous anatomical targets, have been successfully demonstrated, with the main limitation that most transmit coils take up a lot of additional space inside the bore and provide relatively inhomogeneous B1

+ Profiles. The

phantoms used have converged into generally 2 categories - small phantoms containing 13C-enriched compounds that can be used during the study and human-sized phantoms containing compounds with high carbon concentrations but without 13C enrichment that are used to test and calibrate the coils. There are no standardized compositions or geometry, and dynamic phantoms that recapitulate in vivo kinetics would be desirable but are still an emerging area. Prescan calibration procedures were not well defined in most publications, so we surveyed individual sites to determine current practices. Calibration procedures for the B0 field (13C CF and shimming) for most sites take advantage of 1H signal and methods, while methods

For Calibration Of B1

+ is more variable across sites, likely a reflection of remaining challenges in how to perform this calibration. Standardization of both phantoms and calibration procedures would synergistically improve the robustness and reproducibility of HP 13C studies.

Acquisition And Reconstruction

Data acquisition strategies in human HP [1-13C]pyruvate MRI studies must account for multiple chemical shifts, efficiently utilize the non-renewable HP magnetization, and acquire data quickly relative to metabolism and relaxation decay processes. These studies require spectral encoding to separate metabolites, necessitating pulse sequences that efficiently encode up to 5D data (3 spatial + 1 spectral + 1 temporal dimension). RF pulses must efficiently sample without immediately saturating the non-renewable HP magnetization, and sequences must acquire data quickly and be robust to both experimental and physiologic variation (e.g. B1

+ Inhomogeneity,

variation in perfusion) to ensure reproducibility and minimize scan-to-scan variability. This section covers current successful practices for data acquisition in human [1-13C]pyruvate studies, and accompanying 1H imaging, from different anatomic regions, including scan parameters and image reconstruction.

Acquisition And Reconstruction Methods

The acquisition methods used in human [1-13C]pyruvate studies can be classified into 3 categories: 1) MR spectroscopy or MR spectroscopic imaging (“MRS/I”), 2) chemical shift encoding methods, and 3) metabolite-specific imaging (Fig. 5).

Mrs/I Methods Specifically

resolve a spectrum that can be analyzed to extract expected as well as unexpected resonances, making this approach very robust. It was used in many initial studies (1).

Chemical Shift

encoding methods, most commonly the Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) method, use imaging sequences acquired with multiple TEs and rely on a model-based separation of expected chemical shifts (85).

Metabolite-specific imaging methods use specialized RF pulses that are spatially and spectrally selective to excite individual metabolites which are then typically imaged with fast k-space trajectories such as echo planar imaging (EPI) or spirals (86).

Their Application To Different

organ systems is described below. The image reconstruction methods used in human [1-13C]pyruvate studies have typically been conventional methods (e.g. FFT, non-uniform FFT, or equivalent). The incorporation of accelerated imaging and advanced reconstruction methods including parallel imaging (4,57,87) and compressed sensing (7) has also been applied in human studies for improved spatial resolution, temporal resolution and coverage, but have the potential for additional artifacts as well as SNR losses due to ill-conditioning of the reconstruction (e.g. g-factor).

The Majority Of

published studies do not use accelerated imaging indicating the resolution and coverage achievable without acceleration is currently adequate for successful data collection. Performing coil combination, even with fully sampled data has also been shown to have specific challenges for HP human images: using naive sum-of-squares methods suffer from high noise amplification in the relatively low SNR regime of HP [1-13C]pyruvate (compared to 1H), motivating several HP 13C-specific methods that include data-driven coil sensitivity estimation which have shown obvious improvements over sum-of-squares (11).

More recently denoising techniques have been applied as post-processing of human HP data(41,42,44). The techniques applied are based on spatial-temporal singular value decomposition for unsupervised estimation of signal and noise components. They have shown improvements in apparent SNR in the brain and liver, while care must be taken to choose parameters such as the rank threshold to avoid oversmoothing and overfitting to the estimated signal components.

Prostate Studies

Prostate cancer was the first human application of HP [1-13C]pyruvate (1), and data was acquired with MRS/I methods: 1D dynamic MRS, single-slice 2D dynamic echo-planar spectroscopic imaging (EPSI), and single time point 3D EPSI. Advances in imaging strategies led to the development and application of new acquisition schemes, including undersampled 3D EPSI with compressed-sensing (7), model-based chemical shift encoding methods that use a priori information (47,59), and metabolite-specific EPI (10), all of which can provide volumetric whole-organ coverage and dynamic acquisitions.

The pyruvate bolus arrival in the prostate can vary by ± 10 s between patients, necessitating dynamic imaging to reliably and consistently capture the pyruvate bolus (18). For this reason, all currently ongoing studies acquire dynamic data. While MRS/I, chemical shift encoding, and metabolite-specific imaging can all achieve dynamic imaging, chemical shift encoding and metabolite-specific imaging provide greater dynamic and volumetric coverage (85). For scan prescriptions, the FOV is designed to provide full prostate coverage and typically to match the orientation of the anatomic imaging used for registration. Flip angles used in current studies are constant through time, as quantification with a variable-through-time flip scheme is highly sensitive to bolus timing (8) and errors in the RF transmit (B1 +) field (76).

Heart Studies

Data acquisition methods for 13C imaging in the heart must be designed to meet the demands of significant cardiac motion and blood flow. To cope with the periodic cardiac motion, most human heart studies to date used gating to the diastolic window, the longest cardiac cycle interval, which has reduced motion (2,22,28,30,35,36,38,45,52). The duration of the diastolic window limits the available data sampling time, making cardiac acquisitions the most time-constrained of the HP 13C MRI applications. The most common acquisition approach is metabolite-specific imaging with spiral k-space trajectories (2). Their single-shot imaging capability makes these methods particularly robust to motion effects. Furthermore, spiral k-space trajectories provide rapid k-space coverage and relatively benign flow and motion artifacts. The majority of studies have used 2D multi-slice acquisitions, but 3D encoding has also been used successfully (35).

Brain Studies

For HP 13C MRI of the human brain, the majority of studies have also used 2D (slice selective) acquisitions (10–12,14,16,28,33,40,41,44,51,53,60), with a trend toward volumetric coverage using 2D multi-slice metabolite-specific imaging. 3D metabolite-specific imaging of the whole brain, with phase encoding of the slice direction (34,57), has been shown to provide similar SNR efficiency (88) compared with multislice imaging. A number of studies have employed MRS/I (5,6,29,31–33,50,55) resulting in a spectrum from each voxel, which has the advantage of not requiring a priori information about which peaks to encode. This was important in early brain studies when it was not known which peaks would be detectable. Chemical shift encoding, using a set of images with different echo times and an iterative reconstruction of the individual resonances (i.e. the IDEAL approach (85)), has also been used (12,49,54), with the drawback that coverage in the slice direction was limited due to the time required to acquire multiple echo time images.

Abdomen And Breast Studies

The fundamental approaches to data acquisition and reconstruction in the abdomen and breast are largely similar to the aforementioned applications, but demand attention to particular challenges associated with these anatomic regions, especially relating to respiratory motion.

Although it has been shown that a basic 2D MRSI approach based on phase encoding and FID readout can be successfully applied for HP 13C imaging in breast (15) and kidney (13), major advantages in terms of spatiotemporal resolution and coverage have been realized using tailored approaches based on metabolite-specific imaging (43,62) and chemical shift encoding (43), which have facilitated multi-slice or 3D dynamic acquisitions over large FOVs in the abdomen (4,37,46).

The significant respiratory motion encountered in these regions can directly blur 13C images, and has further favored these rapid acquisition strategies. Motion also degrades B0 homogeneity, which can shift frequency-selective excitation profiles and introduce artifacts into rapid imaging readouts. This makes accurate determination of the acquisition center frequency and shimming essential in these regions which often cover large FOVs. (See “Prescan Calibration” section for more information). In some studies, breath-holding was used to minimize motion effects and enforce frame-to-frame data consistency (42). A pragmatic and reasonably effective approach for dealing with respiratory motion during 13C data acquisition is an initial breath-hold (as long as can be tolerated), followed by free-breathing (46,62).

1H Imaging

Collection of 1H imaging data is essential both for prescribing the 13C acquisition and for interpretation of the resulting 13C data. Multi-planar 1H scouts are acquired prior to 13C acquisition to enable graphical prescription of the 13C imaging region. All human HP 13C-pyruvate imaging studies acquire conventional MRI scans (e.g. T1- and T2-weighted volumes) for anatomic reference, aiming to cover at least the full 13C FOV. Acquiring these anatomic scans as close as possible to the time of 13C imaging (immediately before or after) minimizes potential misregistration between the data sets. Depending on the application, other advanced 1H sequences are also acquired (e.g. diffusion-weighted imaging for cancer imaging).

When contrast-enhanced data is acquired, it is done after 13C imaging, as paramagnetic contrast agents will accelerate 13C relaxation.

Reported Study Parameters

Figures 5 and 6, and Supporting Table S2 shows the reported acquisition study parameters for human HP [1-13C]pyruvate studies published as of September 2022. Figure 5 shows a mixture of MRS/I, metabolite-specific imaging, and chemical shift encoding methods have been successfully used, where spectroscopy-based methods have become less prevalent in recent studies. Figure 6 shows the acquisition timing, including the important start time and interval/temporal resolution, is quite variable across studies.

Figure 5: Acquisition methods used in published HP [1-13C]pyruvate human studies published up to September 2022, classified into: MR spectroscopy and spectroscopy imaging (MRS/I); chemical shift encoding methods, such as IDEAL, that use multiple TEs and model-based reconstructions; and metabolite-specific imaging methods that use spectrally-selective excitation to image a single resonance at a time.

Figure 6: Temporal acquisition characteristics reported in HP [1-13C]pyruvate human studies published up to September 2022. (a) Reported referencing of acquisition start times.

(B)

Acquisition start times reported when using dynamic imaging and when timing was reported relative to the end of the injection. (c) Temporal resolutions. “Not Applicable” indicates dynamic imaging was not used.

Summary

Three general categories of acquisition strategies have been used successfully for human HP 13C-pyruvate studies: MRS/I, model-based chemical shift encoding (e.g. IDEAL) methods, and metabolite-specific imaging methods. These have enabled successful studies in the prostate, heart, brain, abdomen, and breast. Recent studies increasingly have used the imaging-based strategies of metabolite-specific imaging and chemical shift encoding which are the fastest methods, although a heads-to–head comparison between techniques has not been performed.

Metabolite-specific imaging is quite popular because of its speed and compatibility with single-shot imaging, but is sensitive to B0 field variations and thus requires careful calibrations. Nearly all studies surveyed acquired data dynamically, allowing measurement of the bolus and metabolite kinetics. The exact timings and associated flip angles vary quite widely across reported studies, with no consensus yet as to how to choose these parameters. Image reconstruction is typically done directly using Fourier Transform methods, and accelerated imaging strategies are uncommon.

Data Analysis And Quantification

This section covers the analysis of data from human HP [1-13C]pyruvate studies, including modeling and metrics, visualization, as well as considerations for how to store data and metadata. Depending on study design, the analysis may need to give quantitative or semi-quantitative output reflecting a biological process or may just reflect a contrast between different regions of interest for quantitative evaluation.

Metrics

Figure 7: HP [1-13C]pyruvate raw data (A) have typically been quantified using four categories of metrics depending on the acquisition. Data acquired as a single time point are often quantified using normalized metabolite images or metabolite ratios (B). Dynamic data can be quantified using normalized metabolite images or metabolite ratios (B), or with metabolite timings such as time-to-peak (TTP) or pharmacokinetic (PK) models (C). The latter two require the data to be time-resolved. [1-13C]alanine and 13C-bicarbonate are analyzed similarly to [1-13C]lactate but omitted here for display.

Metabolite images are commonly used as summary metrics for HP MRI data, often including some form of normalization as well as summed over time as an area under the time curve (AUC) (17). These are analogous to the visual evaluation that is most used for routine clinical work (89,90). In these metabolite images, we expect that the [1-13C]pyruvate AUC signal is predominantly weighted towards perfusion and uptake, while [1-13C]lactate, [1-13C]alanine and 13C-bicarbonate AUCs represent metabolic conversion. The strength of this approach lies in its simplicity and relatively few underlying assumptions. Limitations to the use of single-metabolite images or AUCs include sensitivity to inhomogeneous coil profiles (57,87,91), the acquisition strategy and acquisition parameters, pyruvate polarization and concentration level, and signal relaxation rates (92). Further, the reader must be careful to interpret all the images in conjunction to better understand the underlying biology; for example, increased [1-13C]lactate in the presence of decreased [1-13C]pyruvate delivery can have a very different meaning compared to increased [1-13C]lactate with increased [1-13C]pyruvate delivery.

In an attempt to address variations in coil sensitivity, polarization level, and pyruvate delivery, AUC images are often computed by normalizing to a specified parameter, such as the maximum pyruvate or average lactate signals, or presented as a ratio such as lactate/pyruvate or divided by “total Carbon” - the sum total of HP 13C signal observed across all metabolites. The AUC ratios between metabolites and pyruvate are proportional to the corresponding forward kinetic rates (81,93), but are not directly comparable to rate constants when magnetization loss rates (e.g. relaxation and losses due to signal excitation) differ between studies. Similarly, the ratios between the produced metabolites (e.g. bicarbonate/lactate) can reflect the balance between downstream metabolic pathways (12,55). Care must be taken to consider how AUC images are calculated and normalized before comparing values between studies.

To further quantify the interpretation, pharmacokinetic (PK) modeling approaches were developed to compute the apparent kinetics of pyruvate-to-metabolite exchange (92,94–99). These yield semi-quantitative to quantitative apparent rate constants, given in s-1. Some models require a vascular input function, while others avoid this requirement (95). PK models can explicitly account for acquisition-specific details such as excitation angle and repetition time, and thus may reduce the effects of these details on quantification. An input-less model, provided in the Hyperpolarized-MRI-Toolbox (https://github.com/LarsonLab/hyperpolarized-mri-toolbox) (100) and thus frequently employed for human data, has been shown to fit well and robustly to prostate and brain data (8,20). PK models are quantitative in nature, arguably provide more relevant biological information (8,20), and appear to be reproducible across sites (51). However, rate constants derived from PK models are still apparent rates, and likely do not reflect a single biological characteristic.

Some additional considerations include whether complex or magnitude data is used, as the noise behaviors will impact the analysis differently. Additionally, cut-off thresholds or other criteria may be used to identify and avoid voxels with insufficient SNR before analysis to improve robustness (20,41).

Regardless of the analysis approach, the underlying biology is not always clearly represented by the data; instead, the metrics may be influenced by perfusion, barrier permeability, intercellular shuttles, enzyme activities, co-substrate concentrations, or combinations thereof, depending on the organ and disease of interest (19,43,94,101–103). This may be addressed by incorporating complementary information. As an example, HP 13C pyruvate data is influenced by perfusion, and thus addition of perfusion MRI could be important for interpretation (98,104,105).

All the methods outlined above have been explored in clinical studies, described in Supporting Table 3 and summarized in Figure 8. As of September 2022, approximately 52% of studies involving human subjects report rate constants derived from a PK model with a few different models reported. A nearly equal fraction (51%) of the studies report AUC ratio values.

Approximately 66% of these studies report metabolite-specific images or AUC values. About 40% report SNR values; this metric is particularly frequent in manuscripts that describe technical developments for clinical HP MRI. Approximately 16% of these studies summarize model-free metrics, and 10% report measurements from a single timepoint. Most studies report a combination of quantities.

Figure 8: Reported metrics used for analysis in HP [1-13C]pyruvate human studies published up to September 2022.

Visualization

A wide variety of approaches have been used for visualizing data from human HP 13C-MRI studies. The challenges and practical considerations are: 1) choosing the appropriate metrics to display, 2) how to encode the parameters (e.g. the colormap), and 3) choosing how to provide anatomical context and other multi-parametric data. The choice of visualization also depends on the goal which could be for diagnostic interpretation, but also quality control, reproducibility among readers and publication.

Metrics

The choice of HP 13C metrics is described in detail above. At this stage in HP 13C development where there is no standardized metric, often a combination of metabolite images and ratios or PK model parameters are shown.

Parameter Encoding

The mapping function chosen should provide an adequate, often quantitative, impression of the parameter mapped. There is a consensus in the visualization field that perceptually uniform maps are best suited to visualize continuous parameters, like the greyscale typically used by radiologists as well as other monochrome (black to blue) and color ranges (fire-type, rainbow-type) (106,107). Multi-color heatmaps have been the most frequently employed method for HP 13C data, while greyscale has infrequently been used but it ensures there is no coloring-based bias as well as facilitating later reuse (Fig. 9a). Among the color schemes employed in the clinical HP 13C literature, fire-type scheme seems to be the most common [similar to “Plasma” or “Inferno” in matplotlib.org]. Next most commonly employed is the rainbow-type scheme [similar to “Rainbow” in matplotlib.org].

Anatomical Context

HP MRI faces the challenge that it does not necessarily depict the anatomical features, similar to PET, and thus requires an anatomical reference. Most often, a grayscale anatomical image is overlaid with a HP colormap (Fig. 9c,d). This approach is very intuitive, but can skew perception as the grey-scale anatomical reference may affect the brightness of the HP data (e.g. signal in the skull). This bias does not occur when showing adjacent maps (Fig. 9a, b). Here, anatomical outlines may help to provide reference (Fig. 9b).

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