HOM damping and Energy spread of SRF cavities

HOM damping and Energy spread of SRF cavities in e. RHIC ERL design Chen Xu#, 1, I. Ben-Zvi 1, 2, Michael M. Blaskiewicz 1, Yue Hao 1, Vadim Ptitsyn 1 1) Collider-Accelerator Department, Brookhaven National Lab, Upton, NY 11973, USA 2) Physics & Astronomy Department, Stony Brook University, Stony Brook, NY 11794, USA Electronic address: chenxu@BNL. gov

e. RHIC project Proposal in BNL 1. An electron accelerator will be built. Two possible solutions are given: ERL and accumulating ring designs. 2. To get >1033 cm-2 s-1 luminosity, the electron current would be ~0. 5 A. Large current requires e- source and HOM control development. 3. 3 mm bunch: HOM are very board bandwidth and high power. Surface Resistance depends on BCS. 4. Further study will integrate HOM Power up to 6 GHz. After that, we use the single bunch loss. (2 KW. ) 5. Conservatively speaking, the HOM/cavity would be <30 KW/cav. 6. Total HOM power is >2 MW. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

ERL Bunch time pattern and LINAC Setup Nominal design The electron beam parameter for different e. RHIC operation modes and stages. Ultimate design Max total Max energy current mode 10 24 14 24 8. 3 20 11. 7 20 26 6 50 6 charge, 2. 8 0. 6 5. 3 0. 6 current, 340 145 500 145 Total number of recirculations Collision energy, Ge. V Source current, m. A Bunch n. C Total MA 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

A cavity for example: Use this impedance to reconstruct wake HOM Damping cavity: P Single=KQI=3. 392 KW P Multiple=435. 388 W. 1. 28 V/p. C <3 GHz 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

HOM vs Current spectrum TH nd

Monopole modes for HOM power All Eigen solution results are obtained by ACE 3 P software. ACE 3 P is parallel FEM software in NERSC. OR + OR 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Integrated HOM power 3. 09 KW : : : Total ~25 KW. 0. 88 KW α=28. 6% 3 KW 1. 4 KW : : : 0. 87 KW 0. 4 KW 1. Below 2 Ghz, the HOM power is around 18 k. W from all longitude modes, and the power increases by 5 k. W after 2 GHz. Another 28% increase. 2. The ratio stays the same. The sum of geometric progression array is 1. 4. 3. 2. 6 GHz band adds ~3 k. W power. Because the Qe are low, aligned with 9 MHz would not change much in HOM power. 4. The major HOM power comes from 1. 2 -1. 25 GHz range. Tuning them away would be a good idea to minimize HOM power. 5. Conservatively speaking, the HOM/cavity would be <30 KW. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Impedance of monopole and dipole modes. Spurious!!! 3000 modes: Computational difficulty 1. Put dipole into GBBU code to get current 2. BBU is not only determined by high shunt impedance modes at low frequency. 3. The threshold current is also determined by 1/f. Very little R at High frequency modes can kill the current threshold. 4. Previously (<2 GHz) gives 18 m. A. Threshold current now is m. A without alignment. 5. When aligned with 78. 5 khz, Threshold current is … 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

High frequencies HOM: MC tracing vs FEM: Fresnel Integration vs Helmholtz equations. 1. FEM is limited on the High frequency wake simulation b/c meshing. 2. Modes number too many. Could we say the E(t). ^2=I*cos(ωt+phase) H(t). ^2=I*Sin(ωt+phase) 3. High frequency RF acts like photons with a phase. Tracking Photon can recover EM fields. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd. 46 cm Wavelength ~650 MHz

How Diffraction model works? • It is a Monte Carlo simulation. • The RF incident waves are treated as photon ray and rough surface will give them diffusive reflection. The absorption rate is given by the material Ɛ and μ. • The outcome waves have an angle distribution and diffract into The diffractive ray-lets. The phase delay on the surfaces are ignored. • Ray tracing in the cavity records the interaction with SRF surfaces. Thus obtain the RF loss directly.

Results for different numbers of cavities with ridge waveguide. Changing the cavities number and estimate the total cryo loss. 35 cm long ~7 cm radius Beam pipe absorber. Surface absorbing coefficient of 10 -5 for the MC due to computational time limitations. Note that if Rs=1000*10 -9Ω, then the absorbing coefficient is 10 -7. The absorber material’s absorbing coefficient in this simulation is 0. 6, and that is based on the experiment results. The absorbing coefficient on the end of waveguide is 1, This suggests that there wont be any reflection from waveguide. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Total HOM loss vs Cavity number # of Cavities 3 4 5 6 7 8 9 Length( m) 7. 85 9. 68 1. 150 1. 3323 1. 5144 1. 6962 e 2 e+03 1. 87 70 e+ 03 % of Si. C the tota Cu l abs. Nb 91. 49 82. 22 68. 34 65. 76 62. 68 60. 16 58. 1 4. 72 6. 0 14. 44 9. 12 9. 02 8. 32 3. 79 11. 66 17. 22 24. 8 28. 2 30. 82 33. 5 8 Total Surface HOM loss 6 kw 8 kw 10 kw 12 kw 14 kw 16 kw 18 kw 234 w 928 w 1722 w 2976 w 3948 w 4931 w 6044 w 1 e-7 (1μΩ) 2. 3 w 9 w 17 w 29 w 39 w 49. 3 w 60. 4 w # of Cavities Coaxi Ridge Taper al WG Ridge WG 4 bare cavitie s 1 e-5 WG 52. 41% 56. 34% 65. 15% 0 Absorb er 46. 40% 42. 80% 34. 14% 93. 19% Nb+tra nsition 1. 2% 0. 86% 0. 71% 6. 8% 52: 46 56: 43 65: 34 0: 93 Power ratio, coupler ports to beam pipe absorber Cryo loss on 2 K system: 34 W + <1 W + 5 W >40 W per a cavity @2. 7 e 10. In this computation: 1) This is the result without any insertion HOM coupler. 2) The total surface HOM loss in the last two rows is given per cryomodule, assuming 2 k. W per cavity integrated HF HOM. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Wake potential from Eigen solution (Multi-mode ~exclude fundamental mode) Single bunch without superposition. The reconstructed wake potential has no limitation of length. The figure shows a wake potential of 3. 8 km (RHIC length). Greatest Common Divisor? Or 0. 82 e-7 s -> 12 MHZ This zoom in figure shows a multiple modes beating effect but one bunch. The HOM eigen solution is upto 3 GHz. With a given R/Q, Qe and F, the wake potential show a beating effect even without superposition. Cancellation after multiple macro bunch can be periodic. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Consider abort gap: Superposition the wake (green) + bunch (blue) Steady state? The energy gain from 110 macrobunch (9 MHz) reach a saturation after 25 th macrobunch train. Steady state! 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd. We will study the energy spread after steady state is reached.

Study the th 40 marcobunch trains. • The bunch are already in steady state and energy spread are identical train by train. • The envelop width is 8 KW and max energy ranges 14 KW within trains. • Head and tail of the macro bunches has different energy gains. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Energy gain difference vs energy spread! • This study shows the energy gain from HOM (exclude fundamental modes). The energy gain difference shown is per a cavity. • After passing a cavity, the energy gain difference are less than 14 Ke. V level from HOM, compared with fundamental mode energy gain is 20. 7 Me. V @18 MV/m. • This growth rate will remain along the whole linac. • The energy gain spread would be 5. 3 n. C, and the energy spread is 3. 71 e-3. • Aligned with 9 MHz will introduce more energy gain difference. • The energy gain difference is not energy spread, but comparable. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Conclusions • The total HOM power generation is given <30 KW. HOM spectrum is also given for the HOM damping materials optimization. • RF loss on the cavities wall are given by FEM and photonic diffraction model. The loss total loss <60 W/cavity. Thus cryo plant capacity would be estimated. • Threshold current for BBU for dipole modes and energy spread from longitude wake fields are given, and they are within the acceptable ranges. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

Intra Bunch train energy gain difference Each Nth micro bunch has different base energy when enter a SRF cavity. Each Nth micro bunch across the macro bunches, see different energy gain. The max energy gain is shown and it is less than 8 k. V. The Voltage are chosen at the longitude centroid of the micro bunches. Max energy difference of microbunch with in the macro bunches. Because the wake is beating, thus the energy gain difference is beating too. 17 TH Advanced Accelerator Concept Workshop MD USA. Aug 2 nd.

1. 217673 E+09 5. 45 E+05 4. 16 E-01 0. 822 2. 27 E+05 1. 249860 E+09 1. 22 E+05 1. 27 E+01 1. 249902 E+09 1. 34 E+05 1. 28 E+01 1. 217619 E+09 2. 67 E+05 3. 74 E-01 90. 896 9. 97 E+04 High R/Q High Qe 9. 291340 E+08 2. 73 E+03 3. 01 E+01 0. 019 8. 22 E+04 1. 236181 E+09 2. 70 E+05 2. 05 E+00 9. 293467 E+08 3. 83 E+03 3. 04 E+01 90. 013 1. 16 E+05 1. 236198 E+09 3. 24 E+05 2. 07 E+00 120. 231 6. 72 E+05 1. 217619 E+09 2. 67 E+05 3. 74 E-01 1. 217673 E+09 5. 45 E+05 4. 16 E-01 High R/Q -1. 051 1. 55 E+06 88. 978 1. 72 E+06 31. 148 5. 55 E+05 90. 896 9. 97 E+04 0. 822 2. 27 E+05 High Qe 1. 265064 E+09 1. 03 E+04 1. 44 E+01 1. 265090 E+09 1. 04 E+04 1. 44 E+01 6. 647 1. 49 E+05 96. 626 1. 50 E+05 1. 526390 E+09 5. 53 E+05 2. 25 E-01 1. 526391 E+09 6. 00 E+05 2. 25 E-01 87. 564 1. 24 E+05 -2. 416 1. 35 E+05

8. 018492 E+08 5. 94 E+03 5. 10 E+00 8. 021034 E+08 6. 45 E+03 5. 37 E+00 High Qe -0. 124 3. 03 E+04 89. 891 3. 46 E+04 High R/Q 7. 696344 E+08 1. 23 E+05 2. 19 E-01 7. 697367 E+08 1. 38 E+05 2. 17 E-01 8. 280697 E+08 7. 54 E+02 4. 42 E+01 0. 013 3. 34 E+04 -0. 512 2. 69 E+04 89. 468 3. 00 E+04 1. 197901 E+09 5. 75 E+04 2. 98 E-01 1. 198041 E+09 5. 66 E+04 2. 80 E-01 High R/Q 90. 606 1. 71 E+04 0. 66 1. 59 E+04 High R/Q High Qe 9. 358241 E+08 4. 83 E+03 8. 70 E+00 9. 359479 E+08 6. 78 E+03 8. 33 E+00 0. 072 4. 21 E+04 90. 08 5. 65 E+04 1. 491705 E+09 8. 29 E+03 1. 38 E+00 1. 492072 E+09 7. 92 E+03 1. 46 E+00 -0. 389 1. 15 E+04 89. 657 1. 15 E+04