ALetterofIntentto The J-PARC 50 GeV Proton Synchrotron Experiments. The PRISM Project. A Muon Source of the World-Highest Brightness by Phase Rotation

Transcription

1 ALetterofIntentto The J-PARC 50 GeV Proton Synchrotron Experiments The PRISM Project A Muon Source of the World-Highest Brightness by Phase Rotation PRISM Working Group January 1st, 2003

2 2 The PRISM Working Group Members Shinji Machida, Yoshiharu Mori,Chihiro Ohmori, and Takeichiro Yokoi Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tatsushi Nakamoto, Toru Ogitsu, and Akira Yamamoto Cryogenics Science Center, High Energy Accelerator Research Organization (KEK), Yoichi Igarashi, Shigeru Ishimoto and Koji Yoshimura Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Noboru Sasao Department of Physics, Kyoto University, Yoshihisa Iwashita Accelerator Laboratory, Institute for Chemical Research, Kyoto University, Hiroyuki Ohnishi Graduate School of Engineering, Kyushu University, Masaharu Aoki, Yoshitaka Kuno,FumitakaMaeda, Kengo Nakahara, Norihito Nosaka, Akira Sato, and Yosuke Takubo Department of Physics, Graduate School of Science, Osaka University. The mark indicates the contact persons.

3 Abstract We, the PRISM working group, would like to express our interest to construct a muon beam facility of the highest beam brightness in the world, based on a novel technique of phase rotation. The facility is called PRISM. PRISMstands for Phase Rotated Intense Slow Muon source. Itwouldprovide a muon beam having an intensity of about µ ± /sec, a narrow momentum width of a few %, and no pion contamination. The aimed beam intensity is about four orders of magnitude higher than the highest presently available. The energy of the PRISM beam is relatively low (20 MeV in kinetic energy), since it is aimed to be used for stopped muon experiments in general. For particle physics interest, in particular, an experimental search for lepton flavor violating µ e conversion with PRISM is being planned. The PRISM-II is another muon source with its momentum of around 500 MeV/c and high muon polarization. It would provide a beam for an experimental search for the muon electric dipole moment (EDM). And it could serve, in future, as the first ring for a neutrino factory. PRISM and PRISM-II will use a pulsed proton beam from the J-PARC 50 GeV proton synchrotron (50 GeV PS) by fast extraction. Experimental apparatus and PRISM/PRISM-II will be placed at a proposed pulsed proton beam facility, which is not included in the Phase I plan of J-PARC. Some special arrangement to prevent soil activation at the potential beam extraction port to the facility is requested.

4 Contents 1 Executive Summary 5 2 PRISM Overview Phase Rotated Intense Slow Muon Source PRISM Specification PRISM-IISpecification Proton Beam Overview Proton Beam Power and Time Structure Why is 50-GeV Proton Beam used? Bunch Operation Bunch Operation Pion Capture System Pion Production by 50-GeV Proton Incident Pion Production Target Pion Capture Optimization of the Pion Capture System Superconducting Solenoid Magnet Pion Decay And Muon Transport System Adiabatic Transition From a High to a Low Magnetic Field Curved Solenoid Section Decay Solenoid Design Dispersion Matching Phase Rotation System Principle of Phase Rotation Phase Rotation by FFAG Advantage of Circular Machines Advantage of FFAG PRISM-FFAG Design PRISM-FFAGSimulations

5 CONTENTS Spread ofmuon Arrival Time RF Shape Dependence PRISM-FFAG Acceptance Study Muon Survival Rate in the PRISM-FFAG Estimation of Muon Yield and Beam Emittance Muon Yield Pion Contamination in a Beam PRISM-II Overview PRISM-II Muon Beam Line Pion Capture at Forward Take-off Angle Pion Decay and Muon Transport Solenoid Selection of Pion Momentum to Improve Muon Polarization PRISM-II FFAG EstimationofMuonYield andmuonpolarization A Pulsed Proton Beam Facility for PRISM Overview Proton Beam Line Experimental Area Layout Request at Phase-I Conclusion 51 A 90-Bunche Operation of the 50-GeV PS 53 A.1 Procedure A.2 Issues A.3 Bunched Beam Extraction BSimulation on Pion Production and Capture by using MARS 56 B.1 Pion Production by 50-GeVProtonIncident B.2 Solenoid Pion Capture B.3 Radiation Heating to Superconducting Magnets C Extraction from the Pion Decay Section 64 DIntroduction to the FFAG 67 D.1 The Principle of a FFAG Accelerator D.2 Zero Chromaticity D.3 Large Acceptance D.4 Radial and Spiral Type D.5 Historical Background

6 4 CONTENTS E PRISM-FFAG Design 71 E.1 Triplet Radial Sector E.2 Lattice Design E.3 Magnet Design E.4 RFDesign F Hardware Design of PRISM-FFAG 77 F.1 RFSystem F.2 Magnet F.2.1 Yoke Free Design offfagmagnet F.2.2 Kicker Magnet Design GR&DofFFAGmachines in Japan 82 G.1 R&D of the POP FFAG Machine G.1.1 Results of the Accelerator Studies G Beam Acceleration G Tune Survey G Beam Position G.1.2 Aperture Survey G.1.3 Summary of POP FFAGR&D G.2 R&D of the 150-MeV Proton FFAG Machine G.2.1 Main Features of 150-MeV FFAG G.2.2 R&D Status andconstruction Schedule HAlternativePhaseRotator Scheme 92 H.1 Phase RotatorLinac H.2 System Overview H.3 Magnetic Field Distribution along the Axis H.4 Phase Rotatorwith Linac H.5 Muon Yield Simulation

7 Chapter 1 Executive Summary PRISM : PRISM is a project to construct a dedicated source of a high intensity muon beam with narrow energy spread and small beamcontamination. PRISM stands for Phase Rotated Intense Slow Muon source. The aimed muon beam intensity is about µ ± /sec, four orders of magnitude higher than that available at present. The narrow beam energy spread can be achieved by a novel technique of phase rotation, which accelerates slow muons and decelerates fast muons by a radio frequency (RF) field. In the present design scheme, by phase rotation, the original momentum spread (of about ±30 %) would be squeezed down to ±3 %. Because of this, the brightness within ±3 % momentum spread is increased by a factor of about ten. Regarding small beam contamination, in particular, pions of the level of in a beam can be achieved by a long flight path of the beam so that most of pions decay out. Physics Motivation : One of the important particle physics topics achievable with PRISM is a search for lepton-flavor violating muon rare processes. Lepton flavor violation attracts much attention, theoretically and experimentally, since it would have a large discovery potential to new physics beyond the Standard Model, for instance supersymmetric extension to the Standard Model. An example of proposed experiments of such at PRISM is a search for µ e conversion process in a muonic atom at a sensitivity of PRISM Specification: The energy of the PRISM muon beam is set to be relatively low, such as 20 MeV in muon kinetic energy (68 MeV/c in momentum). The PRISM beam specifications are listed in Table 1.1. PRISM-II for the Muon EDM Measurement: In addition to PRISM, there arises an additional significant demand to have a highly intense muon beam of around 0.5 GeV/c in momentum. It is a separate facility called PRISM-II, since a different beam line and a ring are needed. One of the main physics topics with PRISM-II is asearchforthe electric dipole moment (EDM) of the muon with a sensitivity of less than e cm. PRISM-II would provide muons with high intensity ( /sec) 5

8 6 CHAPTER 1. EXECUTIVE SUMMARY Parameters Design goal Comments Beam Intensity µ ± /sec protons/sec is assumed. Muon kinetic energy 20 MeV p µ =68MeV/c Kinetic energy spread ±( ) MeV Beam Repetition Hz Table 1.1: PRISM Beam specifications and high polarization (P µ =0.6) after phase rotation. Requested Arrangement at Phase I : From the budget profile presently planned at J-PARC, the construction of the pulsed proton beam facility could be after Phase I. Even under this condition, at Phase I, we would like to ask the management of J-PARC a special arrangement to avoid soil activation at the location of proton extraction port to a planned facility. Once soil is activated, future excavation would become almost impossible. To be more specific, we would like to request placing concrete shielding blocks at the location of future extraction. The details are given in this note, in Section 9.4. Finally, the physics programs with PRISM and PRISM-II have a large discovery potential of new physics beyond the Standard Model. We would like to request strong support to realize PRISM and PRISM-II at the earliest date as possible.

9 Chapter 2 PRISM Overview 2.1 Phase Rotated Intense Slow Muon Source PRISM is a project to provide a dedicated source of a high intensity muon beam with narrow energy-spread and small beam contamination. PRISM stands for Phase Rotated Intense Slow Muon source. The aimed beam intensity is µ ± /sec, four orders of magnitude higher than that available at present. It is achieved by a large solid-angle pion capture with a high solenoid magnetic field. Narrow energy spread can be achieved by phase rotation, which accelerates slow muons and decelerates fast muons by a radio frequency (RF) field. The pion contamination in a muon beam can be removed by a long flight path in PRISM so that most of pions decay out. PRISM consists of a pulsed proton beam (to produce a short pion pulsed beam), apioncapture system (with large-solid angle by a high solenoidal magnetic field), apiondecay and muon transport system (in a long solenoid magnet of about 10 m long), and a phase rotation system (which accelerates slow muons and decelerates fast muons by an RF field). Some of the key components are explained in detail in the following sections. The conceptual structure of PRISM is shown in Fig PRISM Specification The PRISM beam characteristics are summarized in Table 2.1. In the pion capture system, low-energy pions (and cloud muons) are trapped in a high solenoidal magnetic field to achieve high intensity. The magnetic field and the inner bore radius of the surrounding superconducting magnet would determine an 7

10 8 CHAPTER 2. PRISM OVERVIEW Superconducting Solenoid Magnet Proton Beam rf Cavities Pion Production Target Solenoid Pion Capture Section Pion Decay Section Phase Rotation Section not in scale Figure 2.1: Conceptual Components of PRISM. It has the pion capture system, the pion decay system, and the phase rotation system. Table 2.1: Anticipated PRISM beam design characteristics Parameters Design goal Comments Beam Intensity µ ± /sec protons/sec is assumed. Muon kinetic energy 20 MeV p µ =68MeV/c Kinetic energy spread ±( ) MeV Beam Repetition Hz effective transverse momentum (p t )cut.givenan effective p t cut, a number of pions captured can be estimated. If p t is about 0.1 GeV/c, about0.2pions per proton can be anticipated from Monte Carlo simulation. Since the proton beam intensity of the J-PARC 50-GeV synchrotron is about /sec, about pions /sec is expected. When a magnetic field is higher, the beam emittance of muons becomes better and smaller. Therefore, the higher magnetic field is preferable. In the phase rotation system, slow muons are accelerated, and fast muons are decelerated by a strong radio-frequency (RF) electric field to yield a narrow longitudinal momentum spread. Aschematicview of the basic concepts of solenoid capture and phase rotation is shown in Fig. 2.1, where the solenoid capture system followed by the phase rotation system is seen.

11 2.3. PRISM-II SPECIFICATION 9 Schematic layout of PRISM is shown in Fig.2.2. It combines high-field pion capture, the π-µ decay system of a 10-m long superconducting solenoid magnet, and phase rotation system. One of the features of PRISM is to do phase rotation at a Fixed-Field Alternating Gradient synchrotron (FFAG), which has several advantages, such as a large momentum acceptance. 2.3 PRISM-II Specification In addition to PRISM that is for experiments with stopped muons, there arises additional significant demand to have a highly intense muon beam of around 0.5 GeV/c in momentum. One of the main physics topics is a search for the electric dipole moment (EDM) of the muon with a sensitivity of less than e cm. The current limit of the muon EDM is (3.7 ± 3.4) e cm. The search needs muons of about 0.5 GeV/c and injects them into a dedicated ring (EDM ring). The PRISM-II would provide muons with high intensity and high polarization after phase rotation. The most important requirement is N µ P 2 µ > 10 16, where N µ is a number of the muons available and P µ is the muon polarization. The specifications of the PRISM-II muon beam are shown in Table 2.2 Table 2.2: Anticipated PRISM-II beam design characteristics Parameters Design goal Comments Beam Intensity µ ± /sec protons/sec is assumed. Muon kinetic energy 597 MeV p µ = 500 MeV/c Kinetic energy spread ±2 % Muon polarization P µ > 0.6 Beam Repetition Hz In order to fulfill these requirements, the design of PRISM-II is slightly different to that of the original PRISM in the following places; (1) longer pion decay system, (2) larger FFAG phase rotator. The pion capture system could be the same as PRISM. It should be noted that the design of the PRISM-II FFAG ring is the same as the first FFAG ring of the Japanese Neutrino Factory. The first ring would accelerate muons from 0.3 GeV/c to 1.0 GeV/c. In future, therefore, the PRISM-II FFAG ring would serve an important role toward the realization of a neutrino factory in Japan.

12 10 CHAPTER 2. PRISM OVERVIEW PRODUCTION TARGET PRIMARY PROTON PROTON BEAM DUMP MATCHING SECTION SOLENOID CAPTURE SOLENOID INJECTION SYSTEM 5 M FFAG RING RF CAVITY EJECTION SYSTEM Figure 2.2: Schematic layout of PRISM.

13 Chapter 3 Proton Beam 3.1 Overview Proton Beam Power and Time Structure Anumberofproduced pions (and therefore their daughter, muons) is proportional to beam power which is given by the product of beam energy and beam current. Roughly speaking, as long as the beam power is the same, the pion yield would be almost the same. It is based on the fact that the pion cross section increases linearly as proton beam energy. At the initial stage of PRISM, beam power of 0.75 MW (50 GeV and 1.5 µa) is assumed at the initial stage 1 The time structure of protons is critical for phase rotation. PRISM would require a pulsed proton beam produced by fast extraction, since phase rotation needs muons (and therefore their parents, pions) to be within a narrow time spread before phase rotation 2.Ifatimespread of the muon beam is larger, the energy spread after phase rotation becomes worse. A pulse width of much less than 10 nsec is needed. Although a pulsed proton beam from fast extraction should be used for PRISM, since there is no room in the neutrino beam line to build a dedicated experimental hall for PRISM, we would like to request the construction of a new experimental hall and a beam line for fast-extraction. This issue will be presented later in Chapter Why is 50-GeV Proton Beam used? If PRISM is constructed at J-PARC, a proton beam from the J-PARC 50-GeV proton synchrotron (PS) would be used. It should be noted that a proton beam from the 3-GeV PS can not be used. The reasons are thefollowing: (1) PRISM needs a narrow pulsed beam of protons, but in the present extraction scheme, a beam from the 3- GeV PS has a pulse width of more than 100 nsec, and (2) it is of technical difficulty 1 It will be adopted to accommodate future proton upgrade of 4.4 MW, where the target issue has to be such as a liquid mercury jet target being developed at a neutrino factory R&D. 2 The details of phase rotation will be described in Chapter 6. 11

14 12 CHAPTER 3. PROTON BEAM to make a narrow pulse of 3 GeV since a space-charge effect, which blows a beam away, is more severe at lower energy, and (3) in the present muon-science facility, afulltarget (of about 1-2 interaction lengths) can not be placed since it is located upstream from the neutron scattering facility in the same proton beam line Bunch Operation At the 50-GeV proton synchrotron, the beam intensity of proton per cycle and a cycle time of 0.3 Hz are expected. The 50-GeV protons are extracted to the nuclear-particle (NP) experimental hall by slow extraction, and to the neutrino beam line by fast extraction. When operated in a slow extraction mode, the average beam current and the duty factor are 15 µa and 0.20 respectively. To have the best performance of phase rotation, it is necessary to have a narrow pulse width of the proton beam. The present pulse width in the J-PARC 50-GeV proton synchrotron is 6 nsec in sigma 3. The typical cycle structure of the J-PARC 50-GeV PS is illustrated in Fig Four batches (each of which contains 2 bunches) from the 3-GeV PS are injected into the 50-GeV PS ring when it stays at a low field. When 8 buckets out of 10 are filled with beams, the 50-GeV ring starts acceleration. The time period of every bunch is about 535 nsec (1.67 MHz) and a gap separation is about 300 nsec (i.e. 50 % filling) Bunch Operation As mentioned before, PRISM would require asharppulse width to achieve a better performance of phase rotation. And the search for the µ e conversion process with PRISM would require many beam bunches with relatively low beam instantaneous intensity. To accomplish this, a new novel idea of 90-bunches operation has come out. By handling 90 bunches in the ring, the above two requirements would be met. The detail parameters are shown in Table 3.1. It is worth to mention that muon (g 2) experiment also needs 90 bunching as might be discussed in an independent Letter of Intent. To realize 90 re-bunching, the proposed scheme is the following. 1. After the proton acceleration, a beam will be de-bunched by shutting RF off. It is the same as in slow beam-extraction. 2. A beam will be re-bunched by an RF of 90 bunches. 3. A bunch will be kicked out one by one (single-kicking mode). Since a bunch separation is about less than 52 nsec, a fast kicker magnet is also needed. A repetition frequency of the single bunch depends on the experimental requirements 3 The accelerator people generally use a ±3 sigmawidthasafull pulse width. Therefore, this case implies a full width of 36 nsec.

15 BUNCH OPERATION nsec at 50 GeV 3 4 Main-Ring ( 3 to 50 GeV ) Neutrino (1) Injection at 3 GeV RF: 1.82 MHz( at 3GeV ) 2 1 K-arena Abort 549 nsec (at 3GeV ) Booster ( 400MeV to 3GeV ) Figure 3.1: Typical machine cycle structure Table 3.1: Main parameters of the 90-bunches operation. Parameters Revolution time Revolution frequency RF frequency of 90 bunches atime period between bunches (central position) values 5.23 µsec MHz 19.1 MHz 52 nsec and technical feasibility. In particular, for the search for µ e conversion process, either 100 Hz or 1000 Hz is being considered. An expected full pulse width (±3 sigma) in the 90 bunches scheme is 3.6 nsec (or 0.6 nsec sigma of the width) if a higher RF voltage is used to keep the bucket height the same as in the 10 harmonicsoperation.

16 Chapter 4 Pion Capture System The highest beam intensity in the world, which would be provided by PRISM, could be achieved by large-solid angle capture of pions at their production. 4.1 Pion Production by 50-GeV Proton Incident PRISM would provide a low energy muon beam for stopped muon experiments, in general. Therefore, to capture, pions of low energy, which are the parent particle of the muons are of interest. At the same time, high energy pions could become potential backgrounds to eliminate. To study pion capture, simulation was performed by using both MARS and GEANT3 with FLUKA. The MARS code is a hadron production code developed at Fermilab. Fig.4.1 shows the momentum spectra of π produced from a graphite target. It is seen that the maximum of transverse momentum (p T )isaround 100 MeV/c for 0 <p L < 200 MeV/c for both the forward and backward pions. The maximum of the total momentum for the backward pions is located at about 120 MeV/c, whereas that for the forward pions is about MeV/c. Isisalsoseen that pions at high energy are suppressed in the backward direction. From these reasons, we decided to use the backward pions for PRISM. 4.2 Pion Production Target Monte Carlo simulations have been also done to study a pion production target. Some of the results on the pion production targets are summarized as follows. The detailed studies can be presented in Appendix B. Aheavymaterial for the pion production target is better than a light material. For example, the pion yield by a tungsten target is about 3 times larger than that of a graphite target. The yield of pions at low energy is almost saturated at a target length of more than 2 interaction lengths. The increase of the yield from 2 to 3 interaction 14

17 4.2. PION PRODUCTION TARGET 15 p t (GeV/c) p l (GeV/c) p (GeV/c) p t (GeV/c) p t (GeV/c) Figure 4.1: Pion production in a graphite target. (top) correlation between p L and p T,(middle) Total momentum distributions for forward and backward π s, (bottom) p T distributions for 0 <p L < 0.2 GeV/c, 0.2 <p L < 0.4 GeV/c, and0.4 <p L < 0.6 GeV/c. lengths is very small, of about 10 %. Both a heavy and a light materials show the same tendency. The yield of pions at low energy decreases astheradius of the target increases. This would be explained by the absorption of pions at low energy. The optimum radius is about 0.5cm. One of the disadvantages of heavy metals is their low melting point. They might melt down when a proton beam of 1 MW beam power hits. On the other hand, it has been known that graphite could work with up to beam power of about 1 MW level, with either radiation-cooled or water-cooled configuration, but with the cost of arelatively low pion production yield (which issmaller by a factor of about 3 smaller than in heavier materials). It is however needed to replace frequently due to the radiation damage on the specific heat of graphite. R&D of the target system has just started. Several options, such as (1) a rotating metal band system, (2) a liquid mercury jet, (3) a tantalum fine particles packed in the titanium casing, and (4) a graphite with radiation or water cooling (as the basic option). All these are studied as the R&D works for the neutrino factory projects in the world-wide. We would like to keep exchange information among various foreign studies.

18 16 CHAPTER 4. PION CAPTURE SYSTEM 4.3 Pion Capture To collect as many pions (and cloud muons) of low energy as possible, they are captured under a high solenoidal magnetic field with a large solid angle. In this case, pions emitting in a half hemisphere can be captured within the transverse momentum threshold (p max t ). The p max t is given by a magnetic field strength (B) andtheradius of the inner bore of solenoid magnet (R) as p max T =0.3 B(kG) R(cm). (4.1) Optimization of the Pion Capture System The muon yield may depend on several parameters of the pion capture system, such as target material, target radius, target length, magnetic field strength and bore radius. In order to optimize those parameters, we performed several computer simulation studies. The study of the low energy pion yield, which was assumed to change proportionally to the low energy muon yield, by using MARS was already described. The muon yield including the effect of the pion decay in the decay solenoid were done by using GEANT3.21. The muon yields are estimated at 10 m from the entrance of the pion decay system, where most of pions decay into muons. Fig.4.2 shows the number of muons within the emittance of π mm mrad in horizontal and 2000 π mm mrad in vertical at the exit of the pion decay section 1 as a function of a pion capture magnetic field (4 T, 8 T, 12 T, and 16 T). It is seen clearly that the higher the pion capture magnetic field is, the better the muon yield at the exit of the pion decay system becomes 2. Therefore, a higher magnetic field is preferable. Once the magnetic field is chosen, the bore radius of the capture solenoid gives the maximum p T of the accepted pions by the Eq.4.1. According to Fig.4.1, placing p max T at around 200 MeV/c would be sufficient. As a matter of fact, the net muon yield does not seem to increase beyond p max T =90MeV/c since we are interested in the muon momentum being less than 84 MeV/c. That corresponds to R =10cmif B =6T. We should install radiation shield between the target and the superconducting solenoid magnet. This will further increase the total radius of the superconducting solenoid magnet. From the MARS simulation study on the radiation shielding shown in Appendix B, a thickness of the radiation shield would be about 30cm or more if it is made of tungsten. Detailed optimization of the bore radius strongly depends on the available technology of the superconducting solenoid magnet. For the moment, we employed the conservative basic design values, namely of B =6T,R =10cmandp max T =90 1 This is the basic acceptance of the phase rotation system at a later stage. 2 The other conditions assumed in this Monte Carlo simulation is 4 T for a pion decay system, a tungsten target.

19 4.3. PION CAPTURE 17 Figure 4.2: Muon yields at 10 m from the entrance of the pion decay system as a function of magnitudes of a pion capture field. MeV/c. The final design will be decided by considering the R&D studies on superconducting solenoid magnets (especially for the tolerance to the radiation heat load) as well as the available budget for the magnet procurement Superconducting Solenoid Magnet The radiation heat load to superconducting coils placed behind the radiation shield of tungsten of 30 cm in length is the level of W/g. The radiation heat come mostly from neutrons. If copper is used as the stabilizer of the superconducting coils, atotal thickness of the coil might be about 2 cm or more 3,andatotal impact on the 4.5 K refrigeration load is over 1 kw. In order to overcome this difficulty, we have started R&D works and come with the following new ideas. The aluminum stabilizer, instead of the copper stabilizer, is employed in order to reduce the total coil mass. Since the radiation heat load tothe coil increases proportionally to its total mass, the expected heat load to the aluminum-stabilized superconducting coil might be greatly reduced than that to the copper-stabilized coil. The coil is cooled down by using the combination of both conduction cooling and forced-flow cooling. With these ideas, we aim to develop the superconducting coil that can be operated under 500 W of the heat load. 3 Forexample, see MECO Superconducting Solenoid System Conceptual Design Report [3]

20 Chapter 5 Pion Decay And Muon Transport System 5.1 Adiabatic Transition From a High to a Low Magnetic Field Since the pions captured at the pion capture system have a broad directional distribution, it is intended to make them more parallel to the beam axis by changing a magnetic field adiabatically. From the Liouville theorem, a volume in the phase space that beam particles occupy do not change. Under a solenoidal magnetic field, the relation between the radius of curvature (R) andthetransverse momentum (p t ) leads to the relation given by p t R p2 t B =constant, (5.1) where B is a magnitude of the magnetic field. Suppose the magnetic field decreases gradually, p t also decrease, yielding a more parallel beam. This is the principle of the adiabatic transition. Namely, when a magnetic field is reduced by a factor of two, p t decreases to a half. On the other hand, since p t R B R 2 =constant 1, (5.2) the radius of curvature increase by a factor of 2. Therefore, the inner radius of a magnet in the pion decay section has to be 2timesthat of the pion capture. With the cost of a beam brow up, a pion beam becomes more parallel. Furthermore, it is not effective in reality to have a long magnet with a high magnetic field, and a magnetic field has to be lowered at some point. Fig.5.1 illustrates the principle of adiabatic transition. 1 It implies that the magnetic flux is conserved. 18

21 5.2. CURVED SOLENOID SECTION 19 p t p l z Figure 5.1: Adiabatic transition from a high magnetic field to a low magnetic field. This adiabatic transition reduces the magnitude of transverse magnetic field. 5.2 Curved Solenoid Section To bring pions and muons into the experimental area, a beam has to be bent. Also it is necessary to make a hole in the solenoid magnets for initial protons to enter. These could be achieved by introducing a curved solenoid magnets. It is known that a center of the helical trajectory of charged particles is drifted in acurvedsolenoid field. The drift (D[m]) is given by D = B s R p2 l p2 t p l (5.3) where B[T] is a magnetic field at the axis, s [m] and R[m] are a path length and the radius of curvature of a bent solenoid. Namely, s/r is a bending angle. p l and p t [GeV/c] areparallel and transverse momentum respectively. Charged particles with opposite sign move in the opposite direction. This can be used for charge and momentum selection if a suitable collimator is placed after the curved solenoid. This kind of curved solenoid magnets have been already adopted in the MECO (BNL-AGS E940) experiment. Unless two curved solenoid of opposite bent are installed, a dipole magnetic field to compensate a drift of the central momentum is needed. 5.3 Decay Solenoid Design To let pions decay into muons, we need a long flight path. Also to contain those pions and decay muons in a limited space, a long solenoid magnet is required. At the momentum of about 100 MeV/c, ameandecay length is about 10 m, and therefore

22 20 CHAPTER 5. PION DECAY AND MUON TRANSPORT SYSTEM positron electron µ + µ - π + π - neutron proton Fraction Figure 5.2: Fractions of pions, muons and electrons at the end of a 10-m long solenoid decay system. aflightlength of 10 m is needed. Fig.5.2 shows the relative fractions of the pion, the muon and the electron at the exit of a 10-m solenoid magnet. At the exit of the long solenoid magnet, a fringing field might blow up the muon distribution. This was studied by using GEANT3.21 with a fringing magnetic field calculated with POISSON/SUPERFISH. It was concluded that although most of the muons will spread out at the fringing field region, the core parts in the good emittance, which can be accepted by the PRISM-FFAG ring, would be contained within ±50 cm, where the next focusing elements should capture them. The detailed study is described at Appendix C. 5.4 Dispersion Matching When the muons are injected into the PRISM-FFAG ring, it is necessary to make a muon beam dispersive to match the acceptance of the PRISM-FFAG. This requirement is placed by the FFAG characteristics. In order to make the muon beam dispersive, a system consisting of double bending magnets is adopted (dispersion matching section), and it would be located between the pion decay and muon transport system and the phase rotation system. A schematic layout is shown in Fig.5.3. The preliminary lattice design of the dispersion matching has been done, and is shown in Fig.5.4.

23 5.4. DISPERSION MATCHING 21 particle orbit in FFAG (simulation) (MeV/c) radius(mm) high mom. low mom. Figure 5.3: Dispersion matching section consisting of double bending magnets. It does make a dispersive beam where muons of particular momentum come to a particular radial position. Figure 5.4: Designed lattice of the dispersion matching section.

24 Chapter 6 Phase Rotation System 6.1 Principle of Phase Rotation Phase rotation is a method to achieve a beam of narrow energy spread. The principle of phase rotation is to accelerate slow muons and decelerate fast muons by a strong radio-frequency (RF) electric field, in order to yield narrow longitudinal momentum spread. It corresponds to 90 rotation of the distribution of the muons in the beam in the energy-time phase space, as schematically shown in Fig.6.1. After phase rotation, the projection of the phase space onto the energy axis becomes narrower and sharper. To identify fast and slow muons, a time of flight (TOF) from the time of production of their parent pions is used. It implies that slowmuons come late and fast muons come early after a long drift of 10 m in the pion decay system. The muon distribution in p total vs. a time of flight (TOF) space, which is calculated by Monte Carlo simulations, is shown in Fig.6.2. By phase rotation, the initial time spread is converted into the final energy spread. The narrow width of a pulsed proton beam is very critical for a net performance of phase rotation. Since stopped-muon experiments are one of the main subjects for PRISM, the central muon momentum is set to be about 68 MeV/c (corresponding to a kinetic Energy Decelerate High Energy Advanced Phase Energy Narrow Energy Spread Low Energy Delayed Phase Accelerate Phase Phase Figure 6.1: Principle of phase rotation shown in the energy-time phase space. The initial narrow time spread is converted into the final narrow energy spread. 22

25 p total(gev/c) 6.2. PHASE ROTATION BY FFAG ToF(ns) Figure 6.2: Distribution of Ptotal versus TOF. energy of 20 MeV). From Monte Carlo simulation studies, the original momentum spread of about ±30 % is reduced down to ±3 %, after phase rotation. 6.2 Phase Rotation by FFAG One of the features of the phase rotation in PRISM is to adopt a circular (ring) machine based on a Fixed-Field Alternating Gradient synchrotron (FFAG) Advantage of Circular Machines A linear system (such as a linac) has been discussed for phase rotation1. Instead of a linear system which is generally considered, a circular system has been adopted for PRISM. The reasons are described as follows. Since the muons of interest for PRISM are relatively low in energy and are nonrelativistic, their velocities (β) within p = ±30% are quite different in magnitude. After a drift, thereby, they spread longitudinally in space. To capture them in an accelerating electric field used for phase rotation, it must have a long wavelength. A possible scheme is either an induction linac or a low-frequency RF with its frequency of 1 10 MHz. For the low frequency RF, the electric field gradient achievable is not high, at the best, less than MV/m. Thus, a total length of the phase rotation system becomes usually very long. For instance, the central momentum of 68 MeV/c with the initial momentum spread of ±30 %, a total length of about 150 meters is needed. In addition to RF, to contain the muons in space, transverse focusing such as a solenoid field is needed along the path. Therefore a long solenoid magnet of a total length of 150 meters has to be built. From these reasons, a linear system is very expensive. 1 See Appendix H for our study on the linear phase rotation system

26 24 CHAPTER 6. PHASE ROTATION SYSTEM Acircular machine, instead, could have smaller and compact in geometrical size. The number of RF cavities and the required electric power is greatly reduced by afactoroftheturns necessary for phase rotation. Therefore, a total cost can be significantly smaller Advantage of FFAG Among various circular machines (such as a synchrotron and a cyclotron), a FFAG has several advantages, which are listed below. Synchrotron oscillation for phase rotation : Since we need synchrotron oscillation to do phase rotation, we can notuse a cyclotron which is isochronous. Large momentum acceptance : It is necessary to accept large momentum distribution (for instance ± %) at the beginning to do phase rotation. Unfortunately, a synchrotron has a limited momentum acceptance (of 1 %), and therefore it can not be used. Large transverse acceptance :Sinceamuonbeam is broad in space, a circular ring has to have a large transverse acceptance. Only FFAG (and probably acyclotronwhichcannotbeusedforthe other reason above) have a large transverse acceptance (both horizontal and vertical). From these reasons, a FFAG is an only choice for a circular machine to do phase rotation. 6.3 PRISM-FFAG Design Apreliminary design of the PRISM FFAG ring and its lattice function are shown in Fig.6.3. The PRISM-FFAG accelerator consists of a normal conducting magnet. The diameter is about 10 meters. It has 8 straight sections. One straight section is for the muon injection, and another straight section is for the muon extraction. In the rest of 6 straight sections, a total of 12 RF cavities are installed. From acceleration point of view, the straight section should be as longaspossiblesoastoinstallasmany RF cavities as possible. Fig.6.4 shows an example layout of the PRISM-FFAG phaserotator ring. Table 6.1 summarizes the main specifications of the PRISM-FFAG ring. 6.4 PRISM-FFAG Simulations Since the beam optics in FFAG is non-linear, Monte Carlo tracking is needed instead of linear optics. Three-dimensional Monte Carlo simulations for the PRISM-FFAG have been done based on GEANT Multiple scattering of muons, interactions,

27 6.4. PRISM-FFAG SIMULATIONS 25 Figure 6.3: A lattice design of the PRISM-FFAG ring and the beam orbit parameters. and pion and muon decays are taken into account. The magnetic field of the PRISM- FFAG magnets were calculated by a 3-dimensional magnetic field calculation code, TOSCA. A typical muon track of its injected momentum of 54.5 MeV/c is shown in Fig.6.5. Since the PRISM-FFAG has momentum dispersion, the radius of the muon orbits becomes gradually larger.

28 26 CHAPTER 6. PHASE ROTATION SYSTEM Spread of muon Arrival Time The muons of interest for PRISM ( p = ±30%) come at a different timing to the PRISM-FFAG ring owing to their different velocities and path length. Fig.6.6 shows the result of Monte Carlo simulations, in which it is shown that a net difference of their arrival timing is within ±20 nsec. The RF frequency of the PRISM-FFAG should accept all the muons in this time range. The RF frequency considered is 5 MHz, and it would covers those. For the muons of the same momentum, owing to their different pitch angle, their arrival time is different. This spread affect the performance of phase rotation and therefore it should be minimized. The Monte Carlo simulation result in Fig.6.6 shows that the time spread for the same momentum is less than ±5 nsec. In the following phase rotation simulation, this effect has been taken into account RF Shape Dependence A shape of the RF field is critical to carry out phase rotation since the muon velocity is related in a non-linear way to the muon momentuminthemomentum range of our interest. The relation of velocity and momentum is shown in Fig.6.2. To optimize an RF shape, two different RF types were studied. One was a si- Vacuum Pump Figure 6.4: Layout of the PRISM-FFAG ring

29 6.4. PRISM-FFAG SIMULATIONS 27 Table 6.1: Main parameters of PRISM-FFAG. Parameters values Central Energy 20MeV number of sector 8 kvalue 5 transition gamma 2.45 average radius 5m B@F/D 0.435/ T F/2 angle rad Dangle rad F/2 bend angle 26 degree packing f 0.18 tune(h/v) 3.404/2.641 µ Figure 6.5: An example of the muon trajectory in the PRISM-FFAG ring. The muon has its initial momentum of 54.5 MeV/c and its curvature becomes larger as phase rotation is applied. This is calculated by the Monte Carlo tracking method.

30 28 CHAPTER 6. PHASE ROTATION SYSTEM MeV/c t=0,+-5ns 10ns 10ns Figure 6.6: Difference of the arrival timing of muons with different momentum. nusoidal shape and the other was a saw-tooth shape. They are shown in Fig.6.7. In the Monte Carlo study shown in Fig.6.7, the muons at the same phase (0 )with some assumed initial phase distribution (about ±5 nsec) are injected (as shown in red points). After each turn, the muon distributions are shown in points with different colors (green for the 1st turn, blue for the 2nd turn, yellow for the 3rd turn, pink for the 4th turn, and sky-blue for the 5th turn). The spread of the same color points reflects the initial phase spread of the injected muons. From Fig.6.7, it is found that in the case of simple sinusoidal RF shape (left), phase rotation is not perfect, yielding p/p = ±6%. However, in the case of the saw-tooth RF shape (right), it is more complete, yielding p/p = ±2%. To realize a saw-tooth RF shape, it is necessary to include higher-harmonics in an RF shape. Fig.6.8 shows the case when the fundamental frequency of 5 MHz is modulated with higher harmonics, such as of its double and triple frequencies so as to create a saw-tooth-like RF shape. The performance of phase rotation by this RD shape is shown in the upper plot in Fig.6.8. From Fig.6.8, it can be concluded that inclusion of the double and triple frequencies (with a ratio of fundamental : double : triple = 3 : 2 : 1) would be sufficient to simulate a saw-tooth RF wave form in terms of the performance of phase rotation. There will be two solutions to include higher harmonics. One is to operate one RF cavity with the fundamental frequency modulated with the double and triple frequencies. In this case, the RF cavity should have a broad band width (low Q). The other is to operate 12 RF cavities with different frequency, for example, 6 cavities for

31 6.4. PRISM-FFAG SIMULATIONS 29 Figure 6.7: (left) sinusoidal RF shape, and (right) saw-tooth RF shape. The upper figures show muon distribution in the p/p vs. their phases with respect to the RF phase (arbitrary), and the lower figures are an RF shape. the fundamental frequency, 4 for the double, 2 for the triple frequency. In this case, an RF cavity with high Q can be used for each, and therefore a higher RF field can be achieved. At this moment of writing, we are still under studies to determine which is better PRISM-FFAG Acceptance Study It is needed to demonstrate that FFAG has a large horizontal acceptance by Monte Carlo simulation. Five different momenta (54.4 MeV/c, 61.2 MeV/c, 68.0 MeV/c, 74.8 MeV/c, 81.6 MeV/c) were selected. And, muons of these five momenta with large emittance are generated in Monte Carlo simulations and are injected into the corresponding radius. The simulation result for the horizontal and vertical acceptances are shown in Fig.6.9 and Fig.6.10, respectively. In Fig.6.9, it is found that the PRISM-FFAG of the present design has more than about 10,000 πmm mrad in the horizontal acceptance for 5 turns. Also, it is seen in Fig.6.9 that the closed orbit of muons with five different momenta are located at five different radii, the smaller radius for the lower momentum under a fixed magnetic field. When phase rotation is done after 5 turns, the orbits with different radii come into the orbit of central momentum. The vertical acceptance is shown in Fig.6.10, where the vertical acceptance of more

32 30 CHAPTER 6. PHASE ROTATION SYSTEM Figure 6.8: Convolution of higher harmonics than 2000 πmm mrad is expected. It is known that this acceptance is limited by the vertical physical aperture of the FFAG magnet. It is therefore being considered to have a wider gap of the FFAG magnet to improve the vertical acceptance Muon Survival Rate in the PRISM-FFAG Phase rotation is completed after 5 turns which corresponds to about 1 µsec. After 5 turns, it is known that the survival rate of muons in the ring is about 60 % in average. The momentum dependence of survival rates is shown in Fig.6.11, where a difference with and without a muon-decay can be seen. From Fig.6.11, at lower momenta, a survival rate is smaller. It should be noted that smaller events at higher momenta is due to the iron yoke structure of the PRISM-FFAG. It has a smaller magnet gap at the larger radius (namely for muon tracks of higher momentum). To improve this, a new type of iron yoke, where the magnet gap is relatively flat at any radius is being considered.

33 6.4. PRISM-FFAG SIMULATIONS After 3turns Initial Phase MeV/c After 1 turn After 4 turns After 2turns After 5turns Figure 6.9: Horizontal acceptance of the PRISM-FFAG by Monte Carlo simulation MeV/c Initial Phase After 1 turn After 2 turns After 3 turns After 4 turns After 5 turns Figure 6.10: Vertical acceptance of the PRISM-FFAG by Monte Carlo simulation.

34 32 CHAPTER 6. PHASE ROTATION SYSTEM Figure 6.11: Surviving muon events (counts) in the PRISM-FFAG as a function of muon momentum. Two points at the same momentum value represent a number of surviving muons after 5 turns with and without muon decays. The muons in the ring decay in their flight. When an electron from muon decay survive in the ring, it will form a beam contamination. From Monte Carlo simulation, it is found that no electrons from muon decays survive in the ring out of 1600 muons. It implies that the survival rate of electrons is less than 1/1600, which is limited by statistics that was tried in the Monte Carlo simulation.

35 Chapter 7 Estimation of Muon Yield and Beam Emittance 7.1 Muon Yield The muon yield (Y µ )atprismcanbegivenby Y µ = N p N π ε π-decay ε mom ε time ε emittance ε dispersion ε FFAG ε µ-decay, (7.1) where N p is a number of protons per second, N π is a number of pions captured at the pion capture system, ε mom, ε time, ε emittance, ε dispersion, ε FFAG, ε π-decay,andε µ-decay are, respectively, the momentum acceptance (50 MeV/c <p µ < 90 MeV/c), the timing acceptance (of about ±5 nsec), the beam emittance acceptance of the PRISM-FFAG ring, the efficiency of the dispersion matching between the muon transport system and the PRISM-FFAG, the survival rate during 5 turns in the PRISM-FFAG, the pion decay rate, and the muon survival rate due to muon decay. They can be estimated by using Monte Carlo simulations with the assumption of particular design based on some technologies employed. The technology choice has a large impact on the muon yield. In particular, N π and ε emittance have strong dependence on the target material and length, the magnitudes of the pion capture field (capture field) and of the pion-decay and muon-transport system (transport field). Although we have not fully optimized, typical sampling cases are listed in Tables 7.1, where the numbers of muons per protons per second (J-PARC phase I) and protons per second (J-PARC phase II) are shown 1.Inthisestimation, the 3-interaction target length of 120 cm and of 28.8 cm for graphite and tungsten respectively are used. The factor ε π decay was included in Monte Carlo simulation of the pion capture system. The factor ε µ decay was estimated with another Monte Carlo simulation dedicated to the FFAG phase rotation, and it is about 60%. At the 1 At 4 MW beam power( protons per second), it is known that the solid targets, like graphite and tungsten, might not be able to be used. Several alternatives are discussed such as a mercury liquid jet, a rotating band target, a tantalum fine-particle target. 33

36 34 CHAPTER 7. ESTIMATION OF MUON YIELD AND BEAM EMITTANCE time of writing, detailed studies on ε dispersion and ε FFAG have not been completed yet, and therefore they are assumed to be 100 %. 7.2 Pion Contamination in a Beam At PRISM, a total flight length is about 150 meters. The survival rate Nsurvival π is given by Nsurvival π =exp( L ) (7.2) cβγτ µ where β, γ, andτ µ are the Lorentz factors and the mean lifetime of the pion, respectively. For the pions of about 68 MeV/c, itgives N π survival (7.3) Therefore, there is absolutely no pion contamination for the particles with 5 turns in the PRISM-FFAG ring. One of the issues is that when late pions, which come between the proton pulse, enter into the PRISM-FFAG ring, there would become pion contamination. To eliminate them, (1) theproton extinction between the pulses should be small(10 3 )and(2)thekickermagnet at the entrance of the PRISM-FFAG has to have additional extinction for late charged particles. Our naive estimation shows that the reduction of those late pions can be achievable at our desirable level of

37 7.2. PION CONTAMINATION IN A BEAM 35 Table 7.1: Negative Muon yields (Y µ )persecond for various target materials, pion capture magnetic fields, muon transport magnetic fields with protons/sec (J- PARC Phase-I) and protons/sec (J-PARC Phase-II). The top table is for ε emittance of 10,000 πmm mrad in horizontal and 2,000 πmm mrad in vertical, whereas the bottom table is for ε emittance of 20,000 πmm mrad in horizontal and 3,000 πmm mrad in vertical. Target material Capture Transport Muon yield per Muon yield per field field protons protons Graphite 16 T 4T T 2T T 4T T 2T T 4T T 2T T 4T T 2T Tungsten 16 T 4T T 2T T 4T T 2T T 4T T 2T T 4T T 2T Target material Capture Transport Muon yield per Muon yield per field field protons protons Graphite 16 T 4T T 2T T 4T T 2T T 4T T 2T T 4T T 2T Tungsten 16 T 4T T 2T T 4T T 2T T 4T T 2T T 4T T 2T

38 Chapter 8 PRISM-II 8.1 Overview In addition to PRISM that is for experiments with stopped muons, there arises additional significant demand to have a highly intense muon beam of around 0.5 GeV/c in momentum. One of the main physics topics is a search for the electric dipole moment (EDM) of the muon with a sensitivity of less than e cm. The current limit of the muon EDM is (3.7 ± 3.4) e cm. The search needs muons of about 0.5 GeV/c and injects them into a dedicated ring (EDM ring). The PRISM-II would provide muons with high intensity and high polarization after phase rotation. A separate Letter of Intent on the search for the electric dipole moment of the muon is submitted. Details are available there. The most important requirement is N µ Pµ 2 > 1016,whereN µ is a number of the muons available and P µ is the muon polarization. The other specification of the PRISM-II muon beam is as follows. Table 8.1: Anticipated PRISM-II beam design characteristics Parameters Design goal Comments Beam Intensity µ ± /sec protons/sec is assumed. Muon kinetic energy 597 MeV p µ = 500 MeV/c Kinetic energy spread ±2 % Muon polarization P µ > 0.6 Beam Repetition Hz 8.2 PRISM-II Muon Beam Line The search for the muon EDM at a sensitivity of e cm requires a polarized muon beam with high intensity, which has never existed so far. Such a highly intense muon 36

39 8.2. PRISM-II MUON BEAM LINE 37 beam can only be achieved by anovelschemeofprism. Since the momentum acceptance of the muon storage EDM ring would be only a level of p/p 2%, it is desirable to employ the phase rotation technique to improve the energy spread of the polarized muon beam. The momentum spread of the muon beam could be thus reduced by almost an order of magnitude by phase rotation, namely from p/p = ±30% to p/p ±2%. This would provide us a sufficient number of the polarized muons injecting into the muon storage EDM ring. To accomplish the phase rotatedmuon beam forthe EDM experiment, a new beam line has to be constructed. We call it PRISM-II. The major difference from PRISM (which is primarily for the µ e conversion experiment) exists in the momentum range of the muon beam; 68±20 MeV/c for PRISM and 500±150 MeV/c for PRISM- II. This difference results in the two major replacements; (1) construction of a new FFAG phase rotator for 500 MeV/c muons, (2) installation of torus solenoids to select the pion momentum to improve the muon polarization, (3) installation of a longer pion decay solenoid. Regarding the target and the pion capture solenoid, the same designs as those in PRISM can be used. PRISM-II consists of, as similar to PRISM-I, 1. pion capture system 2. semi-adiabatic transfer from a high to a low magnetic field, 3. selection of the pion momentum, 4. pion decay and muon transportation system 5. selection of the muon momentum, and 6. phase rotation system Pion Capture at Forward Take-off Angle Table 8.2 summarizes the current design parameters of the pion capture section and the pion decay and muon transport section of PRISM-II. As discussed before, the central momentum of the polarized muons should be about 500 MeV/c. Thus, the requirement to the muons injected into the PRISM-II FFAG is to provide polarized muons with momentum range of 350 MeV/c <p µ < 650 MeV/c with N µ P 2 µ as large as reasonably achievable, where N µ is a number of the muons available to the experiment and P µ is the muon polarization. Figure 8.1 shows the Monte-Carlo simulated result on the dependence of the (longitudinal) muon polarization as a function of initial pion momentum, where the pion in corresponding to the muons of momentum between 350 MeV/c <p µ < 650 MeV/c are shown. It is seen that the pions, which produce the muons in this momentum range, can distribute from 350 MeV/c to 1.1 GeV/c. In order to avoid pion contamination in the polarized muon beam, it is better to select the muons whose momenta do not overlap with the initial pion momentum. Thereby, backward decay muons

40 38 CHAPTER 8. PRISM-II Table 8.2: The design parameters of the pion capture and decay beam line component of the muon EDM experiment. Production Target Material Graphite Length 80 cm Diameter 2.0 cm Superconducting Pion Capture Solenoid Magnetic Field Strength 6T Length 120 cm Inner Bore Radius 10 cm (inside the radiation shield) Transverse Momentum Acceptance < 100 MeV/c Material of the radiation shield Tungsten Thickness of the radiation shield 30 cm Maximum heatload to the cold coil less than 500 W Superconducting Matching Solenoid Magnetic Field Strength 6T 1T Length 450 cm Inner Bore Radius 10 cm 45cm Transverse Momentum Reduction Factor 40% Superconducting Torus Solenoid Magnetic Field Strength 1T(atthecenter of bore) Compensation Field Strength 0.60 T Major Radius 5m Inner Bore Radius 45 cm Angle of Arc 50 Transmission Efficiency 90% for GeV/c Sharpness of the Cut-off 80 MeV/c (10 90%) Superconducting Decay Solenoid Magnetic Field Strength 1T Inner Bore Radius 45 cm Length 20 m Fraction of Pion Decays 25% are employed. In addition, Fig.8.1 shows thatthe backward decay muons provide a rather higher polarization than that from the forward decay muons. By selecting the pions with p π > 0.7 GeV/c, N µ Pµ 2 can be maximized. Afield strength of a superconducting solenoid magnets in the present technology would be as high as 12T or more. However, if a potential heat load to the magnet by high neutron flux coming from the production target is considered, it would be conservative reasonable to start considering a lower field strength such as of 6 T. Thus, a6t-superconducting solenoid magnet for the pion collection magnet is assumed in

41 8.2. PRISM-II MUON BEAM LINE 39 Muon Longitudinal Polarization Initial π momentum (GeV/c) Figure 8.1: Muon longitudinal polarization versus initial pion momentum. Muons are those selected with horizontal and vertical acceptances 800π mm mrad each and momentum acceptance 350 MeV/c <p µ < 650 MeV/c. the present design. Figure 8.2 shows p T distribution of the initial pions with the condition of beam emittance of their daughter muons being 800π mm mrad forboth horizontal and vertical axises and 350 MeV/c <p µ < 650 MeV/c in momentum. From Fig.8.2, the muon yield may not drop significantly with the cut of p T < 100 MeV/c to the initial pions. Therefore, the inner bore of the solenoid magnet could be 10cm at 6 T. It is the same design of the entry level of PRISM Pion Decay and Muon Transport Solenoid The pions collected by the capture solenoid are transferred to the pion-decay and muon-transport solenoid, in which the pions decay in flight into muons. Since the momentum range of the initial pions are around 1 GeV/c, and its τβγc is almost 80m length, the decay solenoid should be desirably over 80 m. However it would be difficult to accommodate a 80-m solenoid magnet in the experimental hall. Therefore, asolenoid magnet of 20 m long is considered in the present design. It ends up with about 25 % pions decaying into muons. If it is possible to make a longer transport solenoid is placed, the muon yield would be greater. If the high magnetic fields at the pion capture section and the low magnetic field of the pion decay section are connected without any magnetic field leakage and the field gradient being sufficiently small, the charged particles traversing through the channel will take place a so called adiabatic transfer. In adiabatic transfer, B/p 2 T and BR 2 are preserved, where B is the magnetic field strength, p T is the transverse

42 40 CHAPTER 8. PRISM-II Counts per 2 MeV/c Transverse Momentum of Pion (GeV/c) Figure 8.2: Transverse momentum of pions from a production target with a condition of those daughter muons being selected with horizontal and vertical acceptance of the muon storage ring (800π mm mrad) and momentum acceptance 350 MeV/c <p µ < 650 MeV/c at the exit of the decay solenoid. momentum and R is the radius of the helix of the charged particle. Thus, Rp T is independent of the field strength in the adiabatic transfer. On the other hand, the muon yield into a fixed acceptance at the exit of the decay solenoid takes linear scale to R 2 p 2 T of the beam. As a result, the muon yield is almost independent of the magnetic field strength of the decay solenoid as longastheadiabatic transfer being maintained. This increases the freedom of design and the field strength of the decay solenoid could be much less than that of the capture solenoid. We chose 1T as the field strength of the decay solenoid for the current design. However, the connection between the capture solenoid and the decay solenoid is actually not the perfect adiabatic transfer but rather imperfect way (semi-adiabatic) for 1 GeV/c pions since the pitch of helix of the pion trajectory becomes a level of several meters or more for this momentum region. If the length of the matching section was about 20 m or more, the adiabatic transfer would be restored for 1 GeV/c pions at a cost of expensive price of the solenoid magnet system. In the current design, we performed Monte Carlo simulations and estimated the phase space of pions after the matching section, and found that the length of 4.5m of the matching solenoid would result in similar pion distributions as the adiabatic transfer. Although it is not the adiabatic transfer, but only the choice of the length of the matching solenoid happens to match the pitch of helix for 1 GeV/c pions. The expected size of pion beam after 4.5 m of the matching section would be R D =10cm 6T/1 T 25 cm. Muons from the pion decay would have influenced

43 8.3. PRISM-II FFAG 41 by the transverse momentum kick (maximum 30 MeV/c), and which would result in the further blow-up of the beam size with 20 cm maximum. The radius of the decay solenoid is chosen to be about 45 cm so that the muons from pion decay would be safely contained without hitting the wall of inner bore of the decay solenoid Selection of Pion Momentum to Improve Muon Polarization The pions momentum selection could be achieved by using a curved solenoid. It was also adopted in the MECO (BNL-E940) experiment. In the curved solenoid, namely torus, a charged particle follows helical trajectories with a drift towards the direction perpendicular to the plane of the curved solenoid. The distance of the drift (D[m]) after traversing a length s[m] in the torus is expressed as D = 1 0.3B s R (p2 L p2 T )/p L, where R[m] is a curvature of the torus, and p T and p L [GeV/c] arethe perpendicular and parallel momentum components, respectively. The amount of drift can be further controlled by applying an additional magnetic field (called a compensation field) along perpendicular to the plane of the curve; the net drift of the particle with the particular p T and p L could be thus adjusted to zero. Figure 8.3 shows a momentum spectrum of the charged particles at the exit of 50 -curved solenoid, when particles are generated equally for GeV/c at the entrance of the solenoid. The torus field is 1T, and the compensation magnetic field is 0.60 T, the inner bore radius of the torus is 45 cm, and the radius of curvature is 5 m for the present calculation. It is clearly seen that the momentum selection of the pion being more than 0.7 GeV/c can be easily achieved with almost 90% of the transmission efficiency. The momentum width of the transmitted particles and the position of the transmission window can be easily adjusted by changing the length of the arc and the compensation field, respectively. It is worth to mention here that the current design is not a unique solution to the muon beam line for the muon EDM experiment. The pion capture, semi-adiabatic transition, and curved solenoid could be replaced with hone magnet system. Further optimization studies will be done. 8.3 PRISM-II FFAG A preliminary design of the PRISM-II FFAG ring has been made. The PRISM-II FFAG accelerator can be either a normal conducting magnet FFAG or a superconducting one. The main difference is a bending strength and an average radius; 1.8 T and 21 m, respectively, for the normal conducting, and 2.8 T and 10m for the superconducting, respectively. Fig.8.4 and 8.5 show a footprint of the normal conducting

44 42 CHAPTER 8. PRISM-II Transmission Efficieny Pion Momentum (GeV/c) Figure 8.3: The transmission probability of charged particles as a function of momentum for the curved solenoid, where the field strength at the center of solenoid being 1 T, major radius of the curved solenoid being 5 m, minor radius of the curved solenoid being 45 cm, and thedegree of curve being 50. version and its lattice functions in one sector and those for superconducting one, respectively. Table 8.3 summarizes main parameters of the PRISM-II FFAG ring. The normal conducting one has to have more cell, twice as much, although the length of each cell is about the same for two versions, that is 4m, resulting in the similar maximum value of beta functions. The dispersion function of the superconducting version is 50% more. The superconducting one can be accommodated in the initial proposed area of the experimental hall. It should be noted that the design of the PRISM-II FFAG ring is the same as the first FFAG ring of the Japanese Neutrino Factory. The first ring would accelerate muons from 0.3 GeV/c to 1.0 GeV/c. The PRISM-II FFAG ring would serve an important role towards the realization of a neutrino factory in Japan Estimation of Muon Yield and Muon Polarization Monte Carlo simulations by using GEANT 3.21+FLUKA were performed to estimate the muon yield and muon polarization. The Monte Carlo simulation was made from pion production down to the exit of the muon transport solenoid. The original GEANT3.21 code was modified so that it can handle transportation of the muon polarization in a magnetic field. RF acceleration of muons in the PRISM-II FFAG phase rotator would be a level of 1MeV/m. Thus,muons of 750 MeV/c should travel through the ring for almost 150

45 8.3. PRISM-II FFAG 43 Figure 8.4: Normal conducting version of the PRISM-II FFAG ring.

46 44 CHAPTER 8. PRISM-II Figure 8.5: Superconducting version of the PRISM-II FFAG ring.

47 8.3. PRISM-II FFAG 45 Table 8.3: Main parameters of PRISM-II FFAG. Parameters normal conducting super-conducting number of sector kvalue transition gamma orbit excursion 0.50 m 0.77 m average radius 21 m 10 m B@F/D 1.8 T 2.8 T F/2 angle rad rad Dangle rad rad F/2 bend angle 17 degree 26 degree packing f phase advance(h/v) 120/61 deg. 131/103 deg. drift length m m BF length m m BD length m m m to get decelerated down to 500 MeV/c. The length of 150 m corresponds to only 2.5 turns in the superconducting FFAG phase rotator (and even if a packing factor of RF cavities it is not long). Muon depolarization due to the g 2precession would be thus negligible. The decay loss of the muons in the FFAG phase rotator can be only several percents. A tracking study in the PRISM-II FFAG ring with computer aided simulation is being undertaken. Table 8.4 summarizes the expected muon yield and polarization. The estimated N µ P 2 µ is about ,and which is sufficient for our goal. Table 8.4: Theexpected muon yield and NP 2 for the PRISM-II Momentum Acceptance of the downstream FFAG MeV/c Horizontal and Vertical Acceptance of the PRISM-II FFAG 800π mm mrad Muon Yield per 50 GeV/c proton 0.04% Muon Polarization (Longitudinal) 60% Expected N µ Pµ 2 per 1-year runatj-parc

48 Chapter 9 APulsed Proton Beam Facility for PRISM 9.1 Overview As described in Chapters 3 and 6, an initial proton beam has to be pulsed with very narrow width to carry out phase rotation of muons. The present nuclear and particle experimental hall (NP hall) at the 50-GeV PS is planned to have only a continuous proton beam from slow extraction, and does not have any capability having a pulsed proton beam. The neutrino beam line which uses a fast-extracted proton beam can not accommodate a room for other experiments. Therefore, we would like to strongly request the construction of a dedicated pulsed proton beam facility. Apossible location will be north from the 50-GeV PS tunnel near the pacific ocean. A preliminary layout of the pulsed proton beam facility is presented in Fig.9.1. A letter of intent on the pulsed proton beam facility is separately submitted. Here, a brief overview is presented. 9.2 Proton Beam Line Proton bunches in the 50-GeV ring are kicked off outward with respect to the 50-GeV ring toward the pulsed proton beam facility, in a single-kicking mode. It is noted that protons to the neutrino beam line are kicked inward. The presently-designed kicker magnet does already have a both-side kick since there is an abort beam line outside the 50-GeV tunnel. Our proton beam line is split from the proton abort line, and is extended to the experimental hall. Fig.9.2 shows a possible layout of such a beam line. When 8 (or 18) bunch running mode is used for PRISM, the same kicker magnet can be used. When 90 bunches is available, a new fast kicker magnet, which will be installed near by, is used to kick 90 bunches into the proton beam line. 46

49 9.3. EXPERIMENTAL AREA LAYOUT Far facility 47 Near facility Pulsed proton beamline PRIME Detector 2nd pbar ring/ experimental hall Fast extraction Kicker PRISM FFAG EDM Ring PRISM-II FFAG Beam Dump Production Target g-2 ring Figure 9.1: A possible layout of the pulsed proton beam facility, which consists of the near facility and the far facility. 50 GeV abort dump Bunched proton beamline Neutrino beamline Fast extraction Kicker 50 GeV Ring Figure 9.2: A possible layout of the pulsed (bunched) proton beam line. 9.3 Experimental Area Layout Fig.9.1 shows a possible layout of the experimental facility, which consists of the near facility (closer to the 50-GeV PS) and the far facility (beyond the public road).

50 48 CHAPTER 9. A PULSED PROTON BEAM FACILITY FOR PRISM PRISM and PRISM-II will be installed in the near facility, whereas the muon g 2 ring and the anti-proton facility are located at the far facility. Alayout of the near facility is shown in Fig.9.3. The area is composed of two areas. One is for PRISM (of low momentum muons with backward extraction) and PRISM-II (of muons of 500 MeV/c with forward extraction). They may be place at different heights so that the injection and extraction beam lines do not interfere. The other is the experimental area, in which detectors are installed. The target stations may be different between PRISM and PRISM-II. Thus, experiments using a beam from either PRISM or PRISM-II will be carried out in a time-sharing way 1 Also, a full proton beam dump is needed. PRIME Detector EDM Ring PRISM FFAG PRISM-II FFAG Beam Dump Production Target Figure 9.3: A possible layout of the near facility where PRISM and PRISM-II are installed. 9.4 Request at Phase-I The construction of the pulsed proton beam facility is not included in the Phase-I plan of J-PARC according to the J-PARC schedule. However, it is important to keep 1 Primarily a search for µ e conversion process is planned at PRISM and a search for the muon electric dipole moment is planned at PRISM-II.

51 9.4. REQUEST AT PHASE-I 49 its possibility at the phase-i construction. One concern is activation of soils around the area of the fast extraction port from the50-gev protons in the ring. If soils at that area are activated, future excavation for the tunnel of the proton beam line would become severely difficult. To avoid activation, we like to place some concrete shielding blocks at the location of proton extraction. Possible arrangement which we are considering is shown in Fig.9.4. The thickness of the shielding blocks required was calculated based on the Moyer formula which assumes a linear radiation loss. From the calculation, with a concrete shielding of 2.2 meter thick in addition to the 0.8 meter thick of the 50-GeV tunnel wall, soil activation would be about 0.07 msv/h and 0.02 Bq/g. It is much less than the acceptable level of 0.3 msv/h and 0.1 Bq/g. From this, it is shown that the concrete shielding blocks of 2.2 meter thickness would be sufficient.

52 50 CHAPTER 9. A PULSED PROTON BEAM FACILITY FOR PRISM Shield Block To Facility Shield Block A-A Cross section Figure 9.4: Possible arrangement to avoid soil activation around the location of proton extraction.

53 Chapter 10 Conclusion We, the PRISM working group, would like to express our interest to construct the muon beam facility of the highest beam brightness in the world, based on a novel technique of phase rotation (PRISM). PRISM provides a muon beam of its high intensity of about µ ± /sec with narrow momentum width of a few % and almost no pion contamination. The aimed muon intensity is about four orders of magnitude better than the highest muon beam intensitypresently available. The PRISM beam is intended to be used in general stopped-muon experiments. As an example, for particle physics, we like to carry out an experimental search for the lepton flavor violating process of µ +(Z, A) e +(Z, A) (µ e conversion) by using a high intensity muon beam from PRISM. PRISM-II is another muon source with its momentum of around 500 MeV/c and higher muon polarization. It is mostly designed for the muon electric dipole moment (EDM) measurement. PRISM, PRISM-II and its experimental apparatus could be placed at the proposed pulsed proton beam facility (of fast proton beam extraction). We would like to request strongly the construction of the pulsed proton beam facility. Since it is not included in the J-PARC Phase I budget, its construction will be in a later time. To be competitive to the other programs in the world, the pulsed proton beam facility together with PRISM and PRISM-II should be constructed at the earliest possible time. At the Phase I construction, we would like to ask a special arrangement to avoid soil activation at the location of proton extraction port to the pulsed proton beam facility. Once soil is activated, future excavation would become almost impossible. To be more specific, we would like to request placing concrete shielding blocks at the location of future extraction. Finally, the physics programs considered with PRISM and PRISM-II would have alarge discovery potential of new physics and phenomena. They are the most competitive, and the opportunity should not be missed for future success. 51

54 Bibliography [1] Huhtinen M and Mokhov N V, FERMILAB-FN-697 FERMILAB preprint 2000 A Cross-Comparison of MARS and FLUKA simulation codes [2] Brun R, Caillat M et al., CERN-DD/85/1 CERN preprint 1985 The GEANT3 Electromagnetic Shower Program and a Comparison with the EGS3 code [3] the Massachusetts Institute of Technology Plasma Science and Fusion Center MECO Superconductiong Solenoid System Conceptual Design Report, 2002 [4] Fujieda M et al in Proceedings of the European Particle Accelerator Conference (EPAC 98), Stockholm, p

55 Appendix A 90-Bunche Operation of the 50-GeV PS As mentioned before, PRISM would require a sharp pulse width to achieve a better performance of phase rotation. And the search for the µ e conversion process with PRISM would require many beam bunches with relatively low beam instantaneous intensity. To accomplish this, a new novel idea of 90 bunches operation has come out. By handling 90 bunches in the ring, the above both requirements would be met. The detail parameters are shown in Table A.1. Table A.1: Main parameters of the 90 bunches operation. Parameters Revolution time Revolution frequency RF frequency of 90 bunches atime period between bunches (central position) values 5.23 µsec MHz 19.1 MHz 52 nsec It is worth to mention that muon g 2 experiment also needs 90 bunches operation as might be discussed in the independent letter-of-intent. A.1 Procedure To realize 90 re-bunching, the proposed scheme is the following. 1. After the proton acceleration, a beam will be de-bunched by shutting RF off. It is the same as in slow beam-extraction. 2. A beam will be re-bunched by an RF of 90 bunches. 53

56 54 APPENDIX A. 90-BUNCHE OPERATION OF THE 50-GEV PS 3. A bunch will be kicked out one by one (single-kicking mode). Since a bunch separation is about less than 52 nsec, a fast kicker magnet is also needed. A repetition frequency of the single bunch depends on the experimental requirements and technical feasibility. In paricular, for the search for µ e conversion process, 100 Hz or 1000 Hz are being considered. An expected full pulse width (±3 sigma) in the 90 bunches sheme is 3.6 nsec (or 0.6 nsec sigma of the width) if a higher RF voltage is used to keep the bucket height the same as in the 10 harmonics operation. The main parameters of the RF cavities is summarized in Table A.2. A total of 5 RF cavities will be used to produce a total of accelerating field of kv and a total power of 1.25 MW. Table A.2: The main parameters of the 90-bunches RF cavity (one unit). Parameters 90-bunches RF Nufact-J RF Frequency 26 MHz 19.1 MHz Average accelerating field 0.5 MV/m 1.0 MV/m Cavity Voltage 0.5 MV 1.5 MV Shunt Impedance about 1 M ohm about 1.5 M ohm Power 250 kw 500 kw A.2 Issues There are several issues to be considered. They are listed as follows. Estimation of a time required for de-bunching and re-bunching: Itisguessed to be from 0.1 second to 1.0 second, Estimation of a possible beam loss in the process of beam de-bunching and rebunching: There is a possibility to change a lattice in such a way that the momentum compaction factor from to so that longitudinal motion is accelerated. Estimation of a pulse width after re-bunching, Estimation of feasibility on an RF of 90 bunches, and Estimation of feasibility on a kicker magnet which has 40 nsec of both rise and fall time.

57 A.3. BUNCHED BEAM EXTRACTION 55 A.3 Bunched Beam Extraction In the 90 bunching scheme, the bunch spacing is only about 50 nsec thus a kicker magnet should have both rise and fall time much less than 50 nsec. In order to see the brief idea of the difficulty of the development of such a kicker magnet, we could refer to the kicker magnet design at TRIUMF KAON project. Table A.3 shows the major parameters of the C-ring injection kicker magnet at TRIUMF KAON project. Flat top and magnet length could be much small in PRISM kicker magnet, and which Table A.3: The major parameters of the C-ring injection kicker magnet of the TRI- UMF KAON project. Parameters C-ring inj. our gola xaperture 76 mm yaperture 68 mm 100 mm frequency 50 Hz Hz flat top 659 ns 25 ns rise and fall time 82 ns 40 ns V PFN per module 44 kv No. of module 3 V PFN 131 kv peak current 874 A impedance 25Ω length m 1m would conpensate the difficulty of improving the rise and fall time by factor two.

58 Appendix B Simulation on Pion Production and Capture by using MARS B.1 Pion Production by 50-GeV Proton Incident The pion production is evaluated by the MARS simulation code developed at Fermilab [1], and also by the FLUKA hadron code in GEANT Figs.B.1 and B.2 show the momentum spectrum of pions produced by 50-GeV protons, calculated by MARS for graphite and tungsten targets respectively. In this simulation, the graphite target was 40 mm in radius and 3 interaction lengths, whereasthe tungsten target was 5 mm in radius and 3 interaction lengths. A negative value of the longitudinal momentum p L implies the backward-direction. A number oftheproduced particles were recorded at the surface of the target. The momentum spectrum of negative particles is almost the same as that of positive one for a 50-GeV proton beam. Pions at low energy are of interest for PRISM, whereas those at high energy could become some backgrounds. From Fig.B.1 and B.2, it is clearly seen that less pions in high energy are emitted backward. Therefore, the backward extraction has been adopted for PRISM. Fig.B.3 shows the π yields (of their momenta less than 200 MeV/c) frombackward extraction as a function of target length and radius for tungsten and graphite targets. It should be noted that this simulation was done under no magnetic field. Figs.B.4 and B.5 show the spectra of π produced from a graphite and tungsten target respectively. From these, it is seen that the maximum of transverse momentum (p T )isaround 100 MeV/c for 0 <p L < 200 MeV/c for both forward and backward pions. The maximum of the total momentum distribution for the backward pions is about 120 MeV/c, whereasthat of forward pions is about MeV/c. B.2 Solenoid Pion Capture To collect as many pions (and cloud muons) of low energy as possible, they are captured under a high solenoidal magnetic field with a large solid angle. In this case, 56

59 B.2. SOLENOID PION CAPTURE 57 event/0.2gev/100k proton p l (GeV/c) event/25mev/100k proton p l (GeV/c) Figure B.1: Longitudinal momentum spectra of π ± and µ ± from 50-GeV protons from a graphite target. Top plot is all pions (and muons), and the bottom plot is an extended one for their longitudinal momentum of p L < 2GeV/c. event/0.2gev/100k proton p l (GeV/c) event/25mev/100k proton p l (GeV/c) Figure B.2: Longitudinal momentum spectra of π ± and µ ± from 50-GeV protons from a tungsten target. Top plot is all pions/muons, and the bottom plot is an extended one for their longitudinal momentum of p L < 2GeV/c.

60 58APPENDIX B. SIMULATION ON PION PRODUCTION AND CAPTURE BY USING MARS Figure B.3: Backward π yields as a function of target length and radius for tungsten and graphite targets in the case of no magnetic field. Here, the pions with their momentum less than 200 MeV/c (p < 0.2GeV/c) areplotted. pions emitting in a half hemisphere can be captured within the transverse momentum threshold (p max T ). The maximum transverse momentum of pions captured (p max T )isgivenby a magnetic field strength (B) andtheradiusofthe inner bore of solenoid magnet (R). It is given by p max T (GeV/c) =0.3 B(T) R(m). (B.1) 2 The simulation of pion capture under high solenoidal magnetic field has been done. The simulation program was based on MARS code. The kinetic energy of incident proton was 50 GeV with its point beam size. Various sizes of the targets have been

61 B.3. RADIATION HEATING TO SUPERCONDUCTING MAGNETS 59 studied for tungsten and graphite uder a magnetic field of 6 T, 12 T ant 16 T. The number of backward extracted π s, which have momentum oflessthan200 MeV/c, were counted. The results is shown in Fig.B.6. In comparison with the pion yield under no magnetic field shown in Fig.B.3, the π yield under a magnetic field is smaller for all the cases. This would be an effect of re-hitting to the target owing to their helical motion under a magnetic field. As the radius of the target is larger, this reduction is larger. It is studied that an optimized target radius of tungsten and graphite targets are 0.5 mm. Regarding a target length, for more than 2 interaction length the pion yield are almost saturated. And the pion yield for tungsten is larger by about three times than those of graphite. The dependence of the π emittance on a magnetic field has been studied. Figure B.7 shows the pion radial beam size under a different magnetic field. As the magnetic field is higher, the π beam size becomes better. The pion size would affect the final muon yiled at PRISM. B.3 Radiation Heating to Superconducting Magnets Aheat load to the superconducting solenoid magnet for pion capture must be reduced down to a level of 100 W in total from the practical point of view. However, a heat load to materials around the pion production target exceeds 100 kw for the full intensity (namely, protons/3-seconds spill) of the J-PARC 50-GeV proton synchrotron. Therefore, to reduce a heat load, a thick radiation shield must be employed between the pion production target and the superconducting solenoid magnet. We have done Monte Carlo simulation to study a shield material and thickness. In this Monte Carlo simulation, the MARS13 code was used to generate hadrons including neutrons. Fig.B.8 shows typical energy deposit distributions in the radiation shield made of tungsten, as a function of radial position for various region of z coordinates (along the beam axis). Fig.B.9 shows those for the shield made of the combination of tungsten and paraffin, where the first 14 cm is tungsten followed by 20 cm paraffin.

62 60APPENDIX B. SIMULATION ON PION PRODUCTION AND CAPTURE BY USING MARS p t (GeV/c) p l (GeV/c) p (GeV/c) p t (GeV/c) p t (GeV/c) Figure B.4: Pion production in a graphite target. (top) correlation between p L and p T,(middle) Total momentum distributions for forward and backward π s, (bottom) p T distributions for 0 <p L < 0.2 GeV/c, 0.2 <p L < 0.4 GeV/c, and0.4 <p L < 0.6 GeV/c. p t (GeV/c) p l (GeV/c) p (GeV/c) p t (GeV/c) p t (GeV/c) Figure B.5: Pion production in a tungsten target: (top) correlation between p L and p T,(middle) Total momentum distributions for forward and backward π s, (bottom) p T distributions for 0 <p L < 0.2 GeV/c, 0.2 <p L < 0.4 GeV/c, and0.4 <p L < 0.6 GeV/c.

63 B.3. RADIATION HEATING TO SUPERCONDUCTING MAGNETS 61 Figure B.6: Negative pion yields as a function of target length and radius for tungsten and graphite targets. Here, the pions with their momentum less than 200 MeV/c (p <0.2 GeV/c) areused.

64 62APPENDIX B. SIMULATION ON PION PRODUCTION AND CAPTURE BY USING MARS Figure B.7: Radial profile of negative pions with momentum less than 200 MeV/c, extracted from backward. Here, the target length is 3 interaction lengths and its radius is 0.5 cm.

65 B.3. RADIATION HEATING TO SUPERCONDUCTING MAGNETS 63 Energy deposit(w) z :-20cm ~ -10cm z :-10cm ~ 0cm z : 0cm ~ 10cm z : 10cm ~ 20cm z : 20cm ~ 30cm z : 30cm ~ 40cm Energy deposit(w) Shield depth(cm) Magnet depth(cm) Energy deposit (W) Shield Postion z (cm) Shield depth(cm) Energy deposit (W) Magnet Position z (cm) Magnet depth(cm) Figure B.8: Energy deposit distribution in the shield and magnet. The shield consists of a total of 34 cm tungsten. The superconducting coil is assumed to be made of copper as a stabilizer. Energy deposit(w) z :-20cm ~ -10cm z :-10cm ~ 0cm z : 0cm ~ 10cm z : 10cm ~ 20cm z : 20cm ~ 30cm z : 30cm ~ 40cm Energy deposit(w) Shield depth(cm) Magnet depth(cm) Energy deposit (W) Shield Postion z (cm) Shield depth(cm) Energy deposit (W) Magnet Position z (cm) Magnet depth(cm) Figure B.9: Energy deposit distribution in the shield and magnet. The shield consists of 14-cm tungsten in front and 20-cm paraffin in rear. The superconducting coil is assumed to be made of copper as a stabilizer.

66 Appendix C Extraction from the Pion Decay Section At the exit of the pion decay and muon transport section consisting of a long solenoid magnet, a fringing field might blow up the muon distribution. To study this effect, a fringing magnetic field was calculated by the POISSON/SUPERFISH program. The POISSON/SUPERFISH code was developed at the Los Alamos Laboratory in US. In this calculation, a long solenoid magnet with an inner bore of 15 cm and an outer bore of 20 cm in radius was used. The central magnetic field of the solenoid magnet is 4 T. The fringing field distribution thus calculated is shown in Fig.C.1. Using the distribution of fringing magnetic field thus calculated, the muon distributions at different locations at the exit of the transport solenoid magnet (such as (a) inside the transport solenoid, (b) at the edge (z =0)ofthesolenoid, (c) z =50 cm from the edge of the solenoid, and (d) z = 100 cm from the edge of the solenoid) are shown in Figs.C.2 and C.3. Dark points represent the muons in the emittance envelops of 10,000 πmm mrad in horizontal and 2,000 πmm mrad in vertical and 20,000 πmm mrad in horizontal and 3,000 πmm mrad in vertical, for Figs.C.2 and C.3, respectively. From this, it is concluded that although most of the muons will spread CYCLE = 850 Figure C.1: Fringing magnetic field flux lines at the exit of a solenoid magnet, calculated by the POISSON program. (left) a magnetic field B z on the axis as afunction of position along the axis, and (right) a flux distribution at the exit with an iron yoke. 64

67 65 out at the flinging field region, the core parts in the good emittance, which can be accepted by the PRISM-FFAG ring, would not be broadened in their distribution at within 100 cm, where next focusing elements should be located. Figure C.2: Phase space distributions (left:horizontal and right:vertical) of the muons at the exit of the transport solenoid at various locations, (a) in the transport solenoid, (b) at the edge of the solenoid (z = 0), (c) z = 50 cm from the edge of the solenoid, and (d) z = 100 cm from the edge of the solenoid. Dark points represent the muons in the emittance of 10,000 πmm mrad in horizontal and 2,000 πmm mrad in vertical, respectively.

68 66 APPENDIX C. EXTRACTION FROM THE PION DECAY SECTION Figure C.3: Phase space distributions (left:horizontal and right:vertical) of the muons at the exit of the transport solenoid at various locations, (a) in the transport solenoid, (b) at the edge of the solenoid (z = 0), (c) z = 50 cm from the edge of the solenoid, and (d) z = 100 cm from the edge of the solenoid. Dark points represent the muons in the emittance of 20,000 πmm mrad in horizontal and 3,000 πmm mrad in vertical, respectively.

69 Appendix D Introduction to the FFAG D.1 The Principle of a FFAG Accelerator AFixed-Field Alternating Gradient (FFAG) synchrotron, as its name suggests, consists of DC operation of magnets. It is quite different from an ordinary alternating gradient (AG) synchrotron (hereafter simply referred just as a synchrotron ), in which magnets are AC operated in accordance of a beam momentum in such a way that the average radius (and therefore the path length) is constant. As a consequence, when aparticle of light rest-mass such as an electron is accelerated in a synchrotron, the particle reaches the speed of light quickly so that the revolution frequency becomes constant. However, a speed of a heavy particle such as a muon and a proton is slowly increased. Therefore, the revolution frequency varies with its momentum, although the path length is constant. In a FFAG, on the contrary, the average radius increases (or decreases in some peculiar field configurations), when a particle is accelerated. It is just like a cyclotron. However, unlike a cyclotron, particles of different momentum have different revolution frequencies. In other words, isochronous condition is violated on purpose. That makes longitudinal focusing and synchrotron oscillations. Of course, the RF frequency of an accelerating cavity has to follow the speed of a particle. But unlike proton synchrotrons, in which the RF frequency is determined with the excitation of bending magnets, the RF frequency pattern and therefore the momentum pattern in time is made solely by itself free from other references. Table D.1 shows the function of magnets and RF in various accelerators. Table D.1: Operation of magnet and RF in different accelerators constant frequency variable frequency constant bending field cyclotron FFAG synchrotron variable bending field electron synchrotron proton synchrotron 67

70 68 APPENDIX D. INTRODUCTION TO THE FFAG D.2 Zero Chromaticity In transverse directions, it has alternating gradient (or strong) focusing. Free from the isochronous condition that is required in a cyclotron, a field index of each gradient magnet can be large. It is determined only by the transverse stability of betatron oscillations. Careful optimization of transverse tunes to avoid strong resonances are possible. The strong focusing is valid for a wide range, for example a factor of 3 as a ratio of the highest momentum to the lowest one. In principle, the transverse tune is constant for that whole range. That is called, in terms of accelerator terminology, zero chromaticity. A type of FFAG with zero chromaticity satisfied is called a scaled machine. Zero chromaticity is desirable to accelerate a beam from injection to extraction with constant field magnets. It is also ideal to accumulate a beam of wide momentum spread. The first principle of FFAG with zero chromaticity can be described with the following two conditions. p ( K ) ϑ=const. =0, (D.1) K 0 where K 0 is an average curvature and K is a local curvature. θ is generalized azimuth. That imposes geometrical similarity. In addition < n p ϑ=const. =0, (D.2) where n is a field index of magnet. The constancy of n at corresponding orbit points is assured. Those conditions are satisfied by the magnet which has the function given by, B = B 0 ( r r 0 ) k (D.3) In fact, there is a FFAG with non zero chromaticity or a non scaled one, in which transverse tunes varies as a particle gets accelerated. That occurs because the magnetic field distribution in a real magnet is not perfect as described. In order to simplify magnet design, sometimes non scaled machine is introduced purposely. Those non scaling machines may be adequate for muon applications since there is only a few turns in each acceleration process. D.3 Large Acceptance In a synchrotron, acceptable momentum spread is limited by two factors. One is a bucket height in longitudinal phase space determined by RF voltage. Above that, aparticle is not bounded and no synchrotron oscillations is expected. The other is momentum acceptance. A higher momentum particle has larger bending radius so that it circulates (usually) outer orbit. Dispersion function is the measure of

71 D.4. RADIAL AND SPIRAL TYPE 69 displacement due to momentum spread. Since the vacuum pine has a limited radius in transverse plane, a higher or lower particle hits the wall of pipe even though a betatron amplitude is zero. The momentum acceptance is a few percent in terms of dp/p in an ordinary synchrotron. FFAG, onthe other hand, has a potential of acceleration of a beam with much higher momentum spread. As we have mentioned already, the magnets are DC operated and it covers focusing from injection to extraction. The momentum ratio through acycle is 3 for our design. In other words, the momentum acceptance is +-50% if we take the central momentum of a beam matched to the mean value of injection and extraction momentum. As for the bucket height, higher voltage makes higher bucket height. The bucket height is proportional to the square root of the voltage. D.4 Radial and Spiral Type Depending on the magnet profile in θ direction, there are mainly two kinds of FFAG; one is radial sector type and the other is spiral sector one. A radial sector type has amagnet whose entrance and exit faces are on radial line drawn from the machine center. There are normal and reverse bending magnets with nonlinear gradient which provide focus and defocus property in each transverse plane. Focusing and defocusing actions come also from an angle between entrance and exit orbit and the magnet face. A spiral sector type has no reversed bending magnets. The alternating gradient focusing action comes mainly from the edge angle. That edge focusing acts in alternative way at the entrance and at the exit in addition to the main body field which has the same field variation in a radial direction as that of radial sector type. Higher momentum particle needs stronger focusing action so that the edge angle becomes larger at outer radius resulting in spiral shape of magnets. D.5 Historical Background The FFAG idea was first introduced by several people independently in early 1950 s right after the AG principle was found. Electron models, both radial and spiral sector types, to prove the principle were made. They are a few meter in size and the output energy is less than 1 MeV. Extensive study was carried out at Midwestern University Research Associate (MURA) and a proposal to construct a few 10 GeV machine was made. However, an ordinary synchrotron was chosen for pursuing the energy frontier and the development as well as MURA itself died out in early 1960 s. By the way, a lot of inventions which are nowadays common to the community were first emerged in the MURA era. Those are RF stacking, adiabatic capture, and concept of separatrix, among others. In 1980 s, demands of high intensity machine draw people s attention to a FFAG accelerator. It is true that FFAG was not the right choice to explore the energy frontier because of relatively large magnets due to orbit excursion between injection

72 70 APPENDIX D. INTRODUCTION TO THE FFAG and extraction momenta. However, large acceptance and possible high repetition cycle are best for high intensity with medium energy machine. There were several study mostly in Europe and Japan but no real machine was constructed. Some difficulties still exist to realize a real scale FFAG. One is the modeling of a magnet. The magnet for FFAG requires nonlinear gradient as described in Eq. D.3. Shaping of magnet pole to make a design field needed iterative efforts. The other difficulty, that is most essential, is the RF cavity which works in wide frequency range with large physical aperture, especially in horizontal direction. Both items are overcome, recently. As for the magnet shaping, design is now efficiently done with a help of 3D magnetic field computation code like TOSCA. More fundamental breakthrough comes with a new type of a RF cavity equipped with magnetic alloy (MA). Because of the very high permeability, a MA cavity has both high shunt impedance and wide band frequency range at the same time. From the fabrication point of view, MA is a tape in its original form so that any kind of core shape is possible. With those recent development, another proof of principle machine, this time the proof of proton acceleration with 1 khz repetition rate, was constructed at KEK. The first beam is commissioned in June 2000 and the design procedure is established. About the status of the PoP machine and the larger machine followed will be described in the next appendix.

73 Appendix E PRISM-FFAG Design E.1 Triplet Radial Sector We adopted a scaled radial sector type FFAG with a triplet focusing. Compared with a spiral sector type FFAG, the radial one tends to have larger circumference ratio, which is the ratio of bending radius and average machine radius. However, easiness of magnet fabrication and better quality of fringing field of the triplet magnet is attractive enough to discard the spiral option. The triplet configuration has several advantages to other radial and spiral types. One is the field crump effects that is expected between adjacent focusing and defocusing magnets. Secondly, the length of each straight section becomes almost doubled because one focusing and two half defocusing magnets are combined together to make one multi function magnet. A minimum magnet unit has both focusing and defocusing. Therefore, the number of magnets is reduced. Finally, the lattice functions has mirror symmetry at the center of a straight section even though that may not beessential. An injection optics design is eased and diagnostics at that position produce better signal to be interpreted. There is another argument whether we need to make the machine scaled, in other words, zero chromaticity. In PRISM ring, the phase rotation is completed within 5 turns and it seems to be not enough time to develop any resonance behavior. We try to design a scaled machine in any case and later ease that requirement according to the further beam dynamics study and tolerance of magnet fabrication. E.2 Lattice Design In order to simplify the FFAG model and quickly estimate optical property, the following steps are taken. First, we assume that the FFAG consists of N identical sector. Thus, the total bending angle in each sector is 2π/N. Each sector consists of a normal bending magnet at the center and reversed bends on both sides. Those have nonlinear gradient. We name the normal bend at the center F magnet and the reversed bends on both sides D magnet. There are straight sections between adjacent sectors, not between F and D magnets. 71

74 72 APPENDIX E. PRISM-FFAG DESIGN In each kind of bending magnet, we assume that the bending radius is constant, which is not the case in reality. If we take the bending angle in F magnet as θ F and that in D magnet as θ D,thefollowing relation is satisfied; θ F 2θ D =2π/N. Once a closed orbit at a certain energy is fixed in that way, the focusing property is determined according to the linear field gradient derived nearby the closed orbit. Fig. E.1 shows one half of a sector, and Table E.2 explains the definition of symbols. All the nonlinear components at the large amplitude area are ignored. Again, we assume that the linear field gradient is constant along the closed orbit as we assumed the constant bending radius. In order to estimate the linear field gradient, we take average radius and expand the field with respect to it. θ ρ ρ θ β β Figure E.1: One half of a triplet radial sector FFAG and its approximated orbit. Table E.1: Definition of symbols. symbol definition N number of cell k field index β F opening angle of F/2 with respect to machine center β D opening angle of D with respect to machine center θ F bending angle of F/2 θ D bending angle of D ρ F bending radius of F ρ D bending radius of D L F path length of F/2 L D path length of D r 0 orbit radius of F center orbit radius of F exit r 1

75 E.3. MAGNET DESIGN 73 Now we know the path length in each magnet, bending angle, and gradient near the closed orbit, we can calculate linear lattice functions. That is done with an ordinary synchrotron design code SAD. Apreliminary design of PRISM FFAG ring and its lattice function are shown in Fig.E.2. The PRISM-FFAG accelerator consists of a normal conducting magnet. The diameter is about 10 meters. It has 8 straight sections designed to be as long as possible so as to install RF cavities as much as possible. Table E.2 summarizes main parameters of the PRISM-FFAG ring. Table E.2: Main parameters of PRISM-FFAG. Parameters values Central Energy 20MeV number of sector 8 kvalue 5 transition gamma 2.45 average radius 5m B@F/D 0.435/ T F/2 angle rad Dangle rad F/2 bend angle 26 degree packing f 0.18 tune(h/v) 3.404/2.641 E.3 Magnet Design The FFAG magnet produces a magnetic field of B(r) =B 0 ( r r 0 ) k, (E.1) where r is a radial position, and B 0 is a magnitude of a magnetic field at the radius of r 0. k is a constant. In our present design, k =5. And, the magnetic field of B Z (T) at a radius of r (m) should be given for the D-coil and F-coil magnets in the PRISM-FFAG ring by B Z = ( r r 0 ) 5 [T ] for the D coil,and B Z = ( r r 0 ) 5 [T ] for the F coil, (E.2) where r 0 is 5 m (for 68 MeV/c). In the present PRISM-FFAG magnet design, a magnetic field gradient is created by changing a magnet gap size. The cross section

76 74 APPENDIX E. PRISM-FFAG DESIGN Figure E.2: A lattice design of PRISM-FFAG ring and beam orbit parameters. of the magnet gap is shown in Fig.E.4, where the half of the gap size changes by ahalfgap = 10 ( 500 r )5 (cm). (E.3) Therefore, the shape of the iron yoke and gap is something like in Fig.E.4.

77 E.4. RF DESIGN 75 Vacuum Pump E.4 RF Design Figure E.3: Layout of the PRISM-FFAG ring The RF frequency of the PRISM-FFAG ring is chosen to be about 5 MHz. The PRISM-FFAG ring can have a total of 12 RF cavities. In each of the RF cavity has 4 gaps. 2 of RF cavities can be placed in one straight section of the PRISM-FFAG ring. The distance of the RF gap is designed to be about 25 cm. Therefore, one straight section of the PRISM-FFAG ring has to be more 2 m in length, as shown in Fig.E.5

78 76 APPENDIX E. PRISM-FFAG DESIGN r in =460 r r out =550cm Figure E.4: Shape of the PRISM-FFAG magnet gap as a function of radius. The innermost radius is 460 cm and the outermost radius is 550 cm. 25cm m Figure E.5: Two RF cavities in one straight section of the PRISM-FFAG ring. One RF cavity has 4-gaps with 25 cm gap distance.

79 Appendix F Hardware Design of PRISM-FFAG F.1 RF System A high-gradient and low-frequency RF system is very important to realize phase rotation in the PRISM-FFAG. In the PRISM-FFAG, an electric field gradient of more than 1 MV/m at a relatively low frequency (such as 5 MHz) is requested. Since the PRISM-FFAG ring has a large momentum acceptance, the accelerating time and acceptable momentum spread are solely limited by RF voltage. As possible candidates for high gradient and low frequency RF cavities, the following three types are being developed. They are (1) the inductive material loaded RF cavity using a new type of ferrite, (2) the capacitive material loaded RF cavity using high grain ceramic, and (3) the air gap RF cavity. F.2 Magnet F.2.1 Yoke Free Design of FFAG Magnet One of the problems of the conventional radial sector type of FFAG is that the sector magnets occupy most of the ring circumference. It results in the lack of free space for beam injection and extraction. Up to now, the FFAG triplet magnet developed in KEK employs the conventional H-type magnet, such that the field flux returns through the side yoke attached to its pole. The triplet magnet used in KEK POP FFAG synchrotron is a complex of three independent H-type sector magnets(see Appendix G). However, considering the field direction of the F-magnet and D-magnet of the triplet magnet, it is reversed each other. Thus, if the return yokes of F and D- magnets are removed, the flux circulates through the F-pole and the D-pole. Such flux generates the reversed field in F-pole and D-pole(see Fig. F.1). This is a rough explanation of the idea of a new type FFAG magnet, so called yoke-free magnet. In fact, if the return yoke is completely removed, the net flux of F-pole and D-pole should be equal. It is unsuitable for FFAG ring, since the field of D-pole should be 77

80 78 APPENDIX F. HARDWARE DESIGN OF PRISM-FFAG D-pole F-pole D-pole Figure F.1: Schematic view of the field flux in the yoke-free magnet weaker than that of F-pole. In order to reduce the flux in the D-pole, shunt yokes are installed at the side of D-pole. In addition, so as to apply fine tuning of the field strength, tuning coils are installed around D-pole. Schematic view of the typical yoke free magnet is shown in Fig. F.2. The return yoke of F-pole is completely removed. This structure is favorable for the beam extraction, since the beam radius becomes the maximum at the center of the F-pole. The beam could be extracted at that point. Up to now, a prototype yoke free magnet was made (see. Fig. F.3) by modifying the prototype magnet of POP FFAG, and the field measurement was carried out. The result shown in Fig. F.4 indicates good agreement with the numerical calculation by TOSCA. It should be mentioned that a new project to demonstrate the yoke-free magnet is under development(see Appendix G). F.2.2 Kicker Magnet Design Apreliminar design of the kicker magnets for beam injection and extraction from the PRISM-FFAG is shown. Regarding the PRISM-FFAG, the beam injection and extraction are one of the critical issues. To investigate possible schemes, a simple tracking simulation was carried out. It was assumed that about 80 % of the single straight section can be used for instruments needed for beam injection and extraction, and a drift space of 3m long is available. Fig.F.5 shows a typical extraction orbit. From the simulation result, the required field strength of the kicker magnet was found to be more than 500 gauss. In addition,

81 F.2. MAGNET 79 X350.0 Y150.0 X400.0 Y100.0 Z250.0 Y50.0 X450.0 Z200.0 Z150.0 X500.0 Z100.0 Y-50.0 X550.0 Z50.0 Y X600.0 Z0.0 Y /Jan/01 21:27:48 Page 44 OPERA-3d Pre-processor Figure F.2: View of a half pole of a typical yoke-free magnet from the simulation of PRISM-FFAG phase rotator, the required rise time of the magnet was found to be 50ns. Hardware requirements to realize such a kicker magnet has been investigated. The parameters are summarized in Table F.1. If one kicking is shared by fifteen small magnets, the voltage needed to the kicker power supply is reduced to a feasible value, typically below 100kV. It should be noted that due to a large muon beam size from the PRISM-FFAG, once it is kicked out by the kicker magnet, the beam could be severely distorted as traversing the sector magnet. Therefore, the scheme which installs plural kicker magnets can not be adopted. Table F.1: One example of hardware parameters of the extraction kicker beam emittance magnet aperture field strength rise time N A Total length 10,000 2,000 πmm mrad (H V) 40 15cm (H V) 500 gauss 50 nano seconds 6000 A Turn 3meters

82 80 APPENDIX F. HARDWARE DESIGN OF PRISM-FFAG Figure F.3: Prototype yoke free magnet B z (gauss) r=100cm r=85cm r=70cm measure calculation θ(degree) Figure F.4: Result of field measurement of the prototype yoke-free magnet

83 F.2. MAGNET 81 Y(m) X(m) Figure F.5: Simulated trajectories of the muons extracted out of the FFAG ring.

84 Appendix G R&D of FFAG machines in Japan In this appendix, research and development on the two FFAG machines developed at KEK is reported. G.1 R&D of the POP FFAG Machine Since the proposal of the FFAG principle proposed by Dr. Chihiro Owkawa in 1950 s, only an electron FFAG machine (the MURA project) was built. However, no proton FFAG accelerator has not been constructed. There were two major problems to construct a proton FFAG at the time. They are Lack of reliable numerical magnetic-field calculation codes, Lack of a high gradient RF cavity to make fast beam acceleration possible For the former, the FFAG machine obtains its focusing force through the strong non-linear field. In order to design the magnets with such a non-linear field, numerical calculations are indispensable. However, in 1960 s, there were no reliable code to calculate a magnetic field. Now, those difficulties has overcome. The high-gradient cavity using a magnetic alloy (MA) core has been developed at KEK, and it has solved the difficulty associated with RF acceleration. Also, we have now a developed 3D field calculation code, such as TOSCA, which offers a tool of numerical field calculations. Thereby, a time to build a FFAG machine has come. We could re-establish the FFAG principle with advanced accelerator techniques. Under the above motivations, the proof-of-principle (POP) FFAG machine was developed at KEK, to establish the FFAG principle, to prove fast acceleration by a FFAG synchrotron, and to demonstrate the large acceptance of FFAG synchrotron. 82

85 G.1. R&D OF THE POP FFAGMACHINE 83 It should be noted that it is the first proton FFAG accelerator in the world. The schematic layout and the photo of the POP FFAG are shown in Figs. G.1 and G.2, respectively Scale : 1m : ion source 2: chopper electrode 3: triplet-quadrupole magnet 4: steering magnet 5: solenoid magnet 6: beam slit 7: Faraday cup 8: septum electrode 9: bump electrode 10: sector magnet 11: F-magnet pole 12: D-magnet pole 13: beam position monitior 14: RF cavity 15: RF amplifier 16: vacuum bellows 17: turbo molecular pump 18: cryopump Figure G.1: Layout of the POP FFAG machine Figure G.2: A top-view of the POP FFAG machine Table G.1 summarizes the main design parameters.

86 84 APPENDIX G. R&D OF FFAG MACHINES IN JAPAN Table G.1: FFAG POP model parameters Type of magnet Radial sector type(triplet) No. of sectors 8 Field index(k-value) 2.5 Energy 50keV(injection) - 500keV Repetition rate 1kHz Magnetic field Focus-mag. : Tesla Defocus-mag. : Tesla Radii of closed orbit Betatron tune Horizontal : Vertical : RF frequency MHz RF voltage kvp G.1.1 Results of the Accelerator Studies When the construction of POP FFAG was complete, intensive accelerator studies were carried out to understand the characteristics of FFAG accelerator. The major items of the accelerator study are as follows. Demonstration of fast acceleration, a study of betatron tune and synchrotron tune in various conditions, astudy of beam positions in various energies, and a study of beam acceptance. In the following, the results of accelerator studies are briefly reviewed. G Beam Acceleration Compared to an ordinary synchrotron, the acceleration time of the FFAG synchrotron is not restricted by a ramping time of a pulsed magnet. Thus, the higher the acceleration field is, the quicker the acceleration is completed. It is one of the prominent merits of the FFAG synchrotron. To demonstrate this feature of FFAG acceleration is one of the strong motivation to develop the POP FFAG machine. In the case that a synchronous phase is set to be 20 degree, the RF voltage should be at least 1.3 kv during acceleration. We have developed a RF cavity using two rectangular FINEMET 1 which has a core of 1.1 m (width) 0.7 m (height). The thickness of the core is 30mm. A 55kW RF amplifier which consists of two tetrodes (Eimac 4CW25,000) was used. 1 For the details of FINEMET, see [4]

87 G.1. R&D OF THE POP FFAGMACHINE 85 Fig.G shows a typical beam signal observed by the inner and outer electrodes of the beam position monitor during acceleration of a proton beam. As seen in Fig.G.1.1.1, it indicates that, as it is accelerated, the beam moves outward. In the case of Fig.G.1.1.1, a flat-top energy is about 350 kev. The acceleration time is about 600 µsec. At present, the acceleration up to 500 kev completes within 1 msec, and the beam characteristics in different energies were measured. Some of them are presented in the following sections. Figure G.3: Typical BPM signal during acceleration in POP FFAG, Upper signal: inside, Lower signal: outside G Tune Survey Firstly, a betatron tune was measured in injection orbit in various field condition. In the FFAG machine, the betatron tune can be changed by varying the relative field strength between the focusing magnet and the defocusing magnet, which is called F/D ratio. Fig.G shows the betatron tune in various different F/D ratio. The results were consistent with the expectation from the computer simulation. The synchrotron tune was measured in the energy range from 50 kev to 500 kev. The result in Fig.G shows good agreement with the expected tune. G Beam Position In FFAG, the orbit position changes as the beam energy increases. The consistency of the beam position with the calculation is one of the measure to verify the current design strategy.