LHeC Recirculator with Energy Recovery Beam Optics Choices
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1 LHeC Recirculator with Energy Recovery Beam Optics Choices Alex Bogacz in collaboration with Frank Zimmermann and Daniel Schulte Alex Bogacz 1
2 Alex Bogacz 2
3 Alex Bogacz 3
4 Alex Bogacz 4
5 Alex Bogacz 5
6 Alex Bogacz 6
7 Energy Recovery Recirculating Linacs - Motivation Future high energy (multi-tens of GeV), high current (tens of milli-amperes) beams would require gigawatt-class RF systems in conventional linacs a prohibitively expensive proposition. However, invoking energy recovery alleviates extreme RF power demands; required RF power becomes nearly independent of beam current, which improves linac efficiency and increases cost effectiveness. Energy recovering linacs promise efficiencies of storage rings, while maintaining beam quality of linacs: superior emittance and energy spread and short bunches (sub-pico sec.). RLAs that use superconducting RF structures can provide exceptionally fast and economical acceleration to the extent that the focusing range of the RLA quadrupoles allows each particle to pass several times through each highgradient cavity. GeV scale energy recovery demonstration with high ratio of accelerated-torecovered energies (5:1) was carried out on the CEBAF RLA (23) Alex Bogacz 7
8 Examples of ER RLA s CEBAF ER Exp & Jlab s FEL Multi-pass linac Optics in ER mode Choice of linac Optics - 13 FODO vs No quad focusing Choice of quad gradient profile in the linacs Single pass wake-field effects Linear lattice: 3-pass up + 3-pass down Arc-to-Linac Synchronization - Momentum compaction Quasi-isochronous lattices Choice of Arc Optics -135 FODO vs FMC (Flexible Momentum Compaction ) Arc Optics Choice - Emittance preserving lattices Various flavors of FMC lattices in the second stability region (Im. t, DBA, TEM) Emittance dilution & momentum spread due to quantum excitations Magnet apertures Overview - Design Choices Alex Bogacz 8
9 LHeC Recirculator with ER Linac 1 1 GeV/pass.5 GeV Arc1, 3, 5 Arc 2, 4 Arc 6 Linac 2 1 GeV/pass IP 6.5 GeV LHC Alex Bogacz 9
10 CEBAF - ER Experiment (23) Modifications include the installation of: RF/2 path length delay chicane Dump and beamline with diagnostics Alex Bogacz 1
11 Transverse beam profiles Arbitrary Units Beam viewer near the exit of the South Linac ~ 1 GeV Accelerating beam ~ 55 MeV Decelerating beam Distance (mm) 3-wire scanner x 2 beams = 6 peaks 2 Alex Bogacz
12 Volts.2 RF Response to Energy Recovery Gradient modulator drive signals with and without energy recovery in response to 25 sec beam pulse entering an RF cavity s without ER with ER Time( s) Alex Bogacz 12
13 JLAMP RLA FEL with ER Alex Bogacz 13
14 Linacs LHeC Recirculator with ER Linac 1 1 GeV/pass.5 GeV Arc1, 3, 5 Arc 2, 4 Arc 6 Linac 2 1 GeV/pass IP 6.5 GeV LHC Alex Bogacz 14
15 PHASE_X&Y Linac Optics 13 FODO Cell E =.5 GeV phase adv/cell: x,y= Q_X Q_Y cavities 2 8 cavities 7 MHz RF: linac quadrupoles Lc =1 cm Lq=1 cm 5-cell cavity GF=.13 Tesla/m Grad = MeV/m GD= Tesla/m E= MV Alex Bogacz 15
16 2 5 Linac 1 Focusing profile E = GeV quad gradient FODO cells ( = 576 RF cavities) Alex Bogacz 16
17 PHASE_X&Y Linac 3 (Linac 1, pass 2) Optics E = GeV 1 E L E ds min 18 betatron phase advance Q_X Q_Y 18 Alex Bogacz 17
18 Linac 1 multi-pass + ER Optics.5 GeV 1.5 GeV 6.5 GeV 5.5 GeV E GeV 3.5 GeV 4.5 GeV 3.5 GeV GeV 5.5 GeV 2.5 GeV 1.5 GeV Alex Bogacz 18
19 8 5 Linac 1 Multi-pass ER Optics 1 M 1 1 M 1 M M M M GeV 1.5 GeV 2.5 GeV 3.5 GeV 4.5 GeV 5.5 GeV 6.5 GeV Alex Bogacz 19
20 2 5 Linac 2 Focusing profile E = GeV (ER) quad gradient FODO cells ( = 576 RF cavities) Linac 2 multi-pass optics with ER mirror symmetric to Linac 1 Alex Bogacz 2
21 Linac 1 and 2 Multi-pass ER Optics Linac 1 Linac GeV 1.5 GeV 2.5 GeV 3.5 GeV 4.5 GeV 5.5 GeV 6.5 GeV 6.5 GeV 5.5 GeV 4.5 GeV 3.5 GeV 2.5 GeV 1.5 GeV.5 GeV Alex Bogacz 21
22 15 5 Linac 1 NO quad focusing profile E = GeV Zero quad gradient FODO cells ( = 576 RF cavities) Alex Bogacz 22
23 15 5 Linac 1 NO quad Multi-pass ER Optics GeV 1.5 GeV 2.5 GeV 3.5 GeV 4.5 GeV 5.5 GeV 6.5 GeV Alex Bogacz 23
24 15 15 NO quad vs 13 FODO E = GeV E x/ y 12.9 /12.7 cm / MeV Zero quad gradient 18 E x/ y 1.8 /1.6 cm / MeV 13 FODO 18 Alex Bogacz 24
25 Arcs LHeC Recirculator with ER Linac 1 1 GeV/pass.5 GeV Arc1, 3, 5 Arc 2, 4 Arc 6 Linac 2 1 GeV/pass IP 6.5 GeV LHC Alex Bogacz 25
26 15 Arc Optics FODO Cell PHASE_X&Y 5.5 GeV phase adv/cell: x,y= Q_X Q_Y Arc dipoles: $Lb=4 cm $B=2.2 kgauss $ang=.3 deg. $rho = 764 meter Arc quadrupoles $Lq=1 cm $G= 1.2 kg/cm Alex Bogacz 26
27 FODO Cell Emittance dispersion H averaged over bends Momentum compaction 2 2 H D 2 DD ' D' D M 56 ds bend D H m 2 M m Alex Bogacz 27
28 Quasi-isochronous condition Arc into Linac Momentum compaction D M ds D 56 bend p C M56 p RF 36 C 36 RF RF N cell M cell 56 p p p p N RF cell m 6 FODO M deg RF 2 m Alex Bogacz 28
29 Emittance growth due to quantum excitations N 2 3 C r q 6 5 C r q m, L H ds c mc H D 2 DD ' D ' m, H, N 2 3 C r q H 6 2 total bend of the arc :, for 18 arc : N 55 r c 48 3 mc H at 5.5 GeV H N m 82 micron rad Alex Bogacz 29
30 Momentum spread due to quantum excitations E L E c mc ds L 1 ds 3 2, total bend of the arc :, E 2 2 E 55 c mc for 18 arc : Alex Bogacz 3
31 Quasi-isochronous FMC Cell Emittance dispersion H avereged over bends Momentum compaction H D 2 DD ' D' H factor of 2.5 smaller than FODO 3 m D M 56 ds bend D 3 M m factor of 27 smaller than FODO Alex Bogacz 31
32 15 Arc Optics 135 FODO vs FMC Cell FODO FMC Cell H m H m 2 M m 3 M m Alex Bogacz 32
33 Quasi-isochronous condition Arc into Linac Momentum compaction D M ds D 56 bend p C M56 p RF 36 C 36 RF RF N cell M cell 56 p p p p N RF cell m 6 FMC M deg RF 3 m factor of 27 smaller than FODO FODO M deg RF 2 m Alex Bogacz 33
34 -.3 PHASE_X&Y FMC Imaginary t Cell 5.5 GeV second stability region: x,y > Q_X Q_Y Arc dipoles: Arc quadrupoles H M m 3 m $Lb=4 cm $B=2.2 kgauss $ang=.3 deg. $rho = 764 meter $G= kg/cm $G1= 5.6 kg/cm $G2= kg/cm $G3= 5.7 kg/cm Alex Bogacz 34
35 5 FMC Double Bend Achromat Cell PHASE_X&Y 5.5 GeV second stability region: x > Q_X Q_Y H M m m Arc dipoles: $Lb=4 cm $B=2.2 kgauss $ang=.3 deg. $rho = 764 meter Arc quadrupoles $G= 2.5 kg/cm $G1= 2.9 kg/cm $G2= -4.7 kg/cm $G3= 2.97 kg/cm Alex Bogacz 35
36 -.5 PHASE_X&Y FMC Theoretical Emittance Minimum Cell 5.5 GeV second stability region: x > Q_X Q_Y H M m m Arc dipoles: $Lb=4 cm $B=2.2 kgauss $ang=.3 deg. $rho = 764 meter Arc quadrupoles $G= 2.92 kg/cm $G1= 2.89 kg/cm $G2= -4.8 kg/cm $G3= 2.97 kg/cm Alex Bogacz 36
37 Arc Optics Cumulative emittance growth N 2 Cq r H, H D 2 DD ' D ' Arc 1, Arc2 Arc 3 Arc 4, Arc5, Arc 6 Imaginary t Optics DBA-like Optics TEM-like Optics BETA_X BETA_Y DISP_X DISP_Y BETA_X BETA_Y DISP_X DISP_Y H m H m H m factor of 18 smaller than FODO total emittance increase (all 5 arcs): x N = m rad =5.6 m rad Alex Bogacz 37
38 Highest Arc Optics Emittance growth N 2 3 C r q H GeV, = 1 5 E 2 2 E 55 c mc TEM-like Optics 29 emittance increase (last arc): x N = 4.5 m rad RMS fluctuations of E/E = total emittance increase (all 6 arcs): x N = m rad =5.6 m rad Alex Bogacz 38
39 Size_X[cm] Size_Y[cm].5.5 Arc 5 Beam envelopes, Magnet apertures x N = 5 m rad Last pass before IR, 5.5 GeV p/p= RMS (beam stay clear) ~ 48 mm TEM-like Optics Ax_bet Ay_bet Ax_disp Ay_disp 29 Alex Bogacz 39
40 Size_X[cm] Size_Y[cm] Arc 1 Beam envelopes, Magnet apertures x N = 2 m rad p/p= ER lowest pass, 1.5 GeV 12 RMS (beam stay clear) ~ 96 mm Imaginary t FMC Optics 29 Ax_bet Ay_bet Ax_disp Ay_disp 29 Alex Bogacz 4
41 Conclusions Proof-of-existence ER RLAs: Jlab FEL, CEBAF-ER Solution for Multi-pass linac Optics in ER mode Choice of linac Optics - 13 FODO Linear lattice: 3-pass up + 3-pass down Optimized quad gradient profile in the linacs (single-pass wake-field effects) Arc-to-Linac Synchronization - Momentum compaction Quasi-isochronous lattices Choice of Arc Optics - Flexible Momentum Compaction Arc Optics Choice - Emittance preserving lattices Arcs based on variations of FMC optics (Im. t, DBA, TEM) Acceptable level of emittance dilution & momentum spread Magnet apertures Alex Bogacz 41
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