Scaling FFAG lattices for muon acceleration T. Planche, Y. Mori, - PowerPoint PPT Presentation

Scaling FFAG lattices for muon acceleration T. Planche, Y. Mori, Kyoto University.

Muon acceleration for a neutrino factory Constraints on the accelerating apparatus: (i) Fast acceleration requires static magnetic guide field and fixed rf frequency acceleration. (ii) Muon beams have a huge transverse emittance, even after cooling (~ 30000 π mm.mrad in both horizontal and vertical planes). Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 2

Muon acceleration for a neutrino factory Current status of the Cost/Performance balance: Linac : expensive but cost-effective at low energy NS-FFAG : the most cost effective, but the longitudinal amplitude RLAs : less expensive growth with large transverse amplitude than linac but limited limits its use the the number of passes, and higher energy stage. need one arc per pass. Figure 1 - Schematic diagram of the ISS baseline accelerator complex. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 3

Motivations Find a better balance using scaling FFAG instead of RLA The amplitude dependance of the time of flight which limits the NS-FFAG acceptance is not an issue for scaling FFAG. We would like to show that is it possible to use scaling FFAG with constant rf frequency acceleration at lower energy than NS-FFAG. Two possible schemes Stationary bucket Using harmonic number or acceleration! jump acceleration Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 4

Contents Part I - Scaling FFAGs for Stationary Bucket acceleration 1 - Principle 2 - Example of lattice parameters 3 - Acceptance study at fixed energy 4 - Full 6D simulation results 5 - Summary on SB acceleration Part II - Scaling FFAGs for Harmonic Number Jump acceleration 1 - Principle and constraints of the HNJ acceleration 2 - FFAG ring with insertion based of FD doublet cells 3 - Use of dFDf quadruplet cells 4 - Summary on HNJ acceleration Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 5

Part I Scaling FFAG lattices for Stationary bucket acceleration Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 6

Principle With constant rf frequency scheme, accelerate particles following a pass from the bottom to the top of a stationary bucket. 120 100 Figure 2 - Longitudinal phase space showing a 6-turn acceleration cycle 80 of a muon beam (red), as well as Hamiltonian contour (black lines) ! 60 40 20 0 0.2 0.4 0.6 0.8 1 rf phase/2 " Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 7

Example of lattice parameters Stationary bucket acceleration for 3.6 to 12.6 GeV muon RF frequency = 200 MHz Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 8

Example of lattice parameters 164 163 Lattice example for 3.6 to 12.6 GeV 162 y [m] muon acceleration: 161 160 159 Lattice type scaling FFAG FDF 158 -6 -4 -2 0 2 4 6 Injection energy 3.6 GeV x [m] Extraction energy 12.6 GeV 150 RF frequency 200 MHz 100 Mean radius ∼ 161 m Synchronous energy (kinetic) 8.04 GeV 50 Hormonic number h 675 y [m] Number of cells 225 0 Field index k 1390 RF peak voltage (per turn) 1.8 GV -50 Number of turns 6 B max (at 12.6 GeV) 3.9 T -100 Drift length ∼ 1.5 m Horizontal phase advance per cell 86.13 deg. -150 Vertical phase advance per cell 37.90 deg. -150-100 -50 0 50 100 150 Excursion 14.3 cm x [m] Figure 3 - Scaling FFAG lattice for 3.6 to Table 1 - lattice parameters. 12.6 GeV muon acceleration. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 9

Example of lattice parameters µ + Simultaneous acceleration of and beams: µ − 164 163 3 β s λ rf 162 y [m] 161 160 159 158 -6 -4 -2 0 2 4 6 x [m] µ + In order to allow the simultaneous acceleration of and beams, µ − the synchronous particle orbit length is adjusted to be equal to . The size of the long drift is design for two rf cavities with 3 β s λ rf gaps distant of to be installed in it. 1 2 β s λ rf Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 10

Example of lattice parameters We use step-wise particle tracking in geometrical field model to determine the lattice linear parameters and study the beam dynamics. 4 16 14 3 12 2 10 1 B z [T] ! [m] 8 0 6 -1 -2 4 -3 2 0 -4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 s [m] s [m] Figure 4 - Mid-plane field distribution along the Figure 5 - Horizontal (red) and vertical (purple) beta closed orbits at 3.6, 8 and 12.6 GeV function at 3.6 Ge. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 11

Transverse acceptance at fixed energy Transverse normalized acceptance is greater than 40000 π mm.mrad in both horizontal and vertical planes. 15 25 20 10 15 10 5 R' [mrad] Z' [mrad] 5 0 0 -5 -5 -10 -15 -10 -20 -25 -15 160.76 160.8 160.84 160.88 160.92 160.96 -120 -80 -40 0 40 80 120 R [m] Z [mm] Figure 6 - (R, R') plane (@ middle of the long drift) Figure 7 - (Z, Z') plane (@ middle of the long drift) showing a multi-turn tracking of 2 particles with showing a multi-turn tracking of 2 particles with different initial horizontal amplitudes, with an initial different initial horizontal amplitudes, with an initial vertical displacement = 1 mm. vertical displacement = 1 mm. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 12

Full acceleration cycle - 6D tracking 13 15 12 10 11 5 R' [mrad] 10 0 E kin [GeV] 9 -5 8 -10 7 -15 160.8 160.9 161 161.1 6 R [m] 15 5 10 4 5 Z' [mrad] 3 0 0.2 0.4 0.6 0.8 1 0 rf phase/2 ! -5 Figure 8, 9 and 10 - 6D tracking simulation results. Initial -10 particle distribution is a homogeneous (Waterbag) distribution in the transverse 4D ellipsoidal phase space -15 -80 -40 0 40 80 + homogeneous distribution in the 2D longitudinal phase Z [mm] space. Initial transverse beam emittance is Initial (green) and final (red) particle distribution 30.000 π mm.mrad in both horizontal and vertical of the particles in the horizontal (top figure), planes, and 0.17 eV.sec in longitudinal. and vertical (bottom figure) phase space. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 13

Summary on harmonic number jump Works well! * Very large transverse acceptance. * Large longitudinal acceptance @ 200 MHz. * No emittance degradation during acceleration! * Simultaneous acceleration of μ + and μ - possible. It is a good and robust alternative to RLAs for a Neutrino Factory! Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 14

Summary on stationary bucket acceleration It is a good and robust alternative to RLAs for a Neutrino Factory! 3.6-12.6 GeV scaling FFAG! 150 100 50 y [m] 0 -50 -100 -150 -150-100 -50 0 50 100 150 x [m] Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 15

Part II Another way for constant frequency acceleration in scaling FFAG: The Harmonic Number Jump acceleration Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 16

Principle and constraints of the HNJ acceleration 1 To jump one harmonic every turn: T i +1 − T i = f rf Figure 11 - Revolution time as a function of particle energy in the case of a 3 to 10 GeV scaling FFAG ring, with k = 145 and average radius = 120 m. 1 Energy gain per turn must follow: ∆ E i = f rf · [ ∆ T ∆ E ] Ei Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 17

Principle and constraints of the HNJ acceleration Need for dispersion suppressor insertions: 1 Harmonic jump condition: T i +1 − T i = f RF ∆ C i In the same time: = T i +1 − T i β c c = λ RF In case of highly relativistic particles: ∆ R i ≈ 2 π f RF 2 π average excursion = λ RF · N turns Need for excursion 2 π reduced areas! Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 18

Dispersion suppressor with FFAG magnets k 1 k 2 k 3 k 2 k 1 2 1 1 with k 2 + 1 = k 1 + 1 + k 3 + 1 Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 19

Principle and constraints of the HNJ acceleration Need for a double beam lattice: Assuming that the initial number of harmonic h 0 is large we get (*) : f k ≈ f 0 (1 − 1 · k N ) h 0 Every cavity working at a constant frequency f k but Figure 13 - N cavities the frequency has to be tuned to a slightly different homogeneously distributed around the ring. value! μ + and μ - beams cannot be accelerated simultaneously if they circulated in opposite (*) look at the proceedings of directions... PAC’09 for all details. Scaling FFAG Lattices For Muon Acceleration ミューオン科学と加速器研究 - Feb. 2010 - T. Planche 20