Beam loading and rf power evaluation for highcurrent

Beam loading and rf power evaluation for high-current colliders Ivan Karpov Acknowledgments: Philippe Baudrenghien, Elena Shaposhnikova, Rama Calaga, Andrew Butterworth, Dmitry Teytelman, Alessandro Gallo, Heiko Damerau, Helga Timko BE seminar, 06. 12. 2019

Beam interaction with surroundings Bunch in perfectly conducting beam pipe Wake fields are excited in presence of discontinuities Radio frequency (rf) cavity is special type of discontinuities Beam induced effects in rf cavities are referred as beam loading Simulations using ABCI (Azimuthal Beam Cavity Interaction) code, http: //abci. kek. jp/abci. htm 2

Beam interaction with surroundings Bunch in perfectly conducting beam pipe Wake fields are excited in presence of discontinuities Radio frequency (rf) cavity is special type of discontinuities Beam induced effects in rf cavities are referred as beam loading Simulations using ABCI (Azimuthal Beam Cavity Interaction) code, http: //abci. kek. jp/abci. htm 3

High-current colliders at CERN 4

Outline • Future Circular Colliders (FCC) Large Hadron Collider (LHC) 5

Beam loading for uniformly filled ring 6

Heiko Damerau Beam loading CERN accelerator school, Advanced Accelerator Physics, 9 -21 June 2019, Slangerup, Denmark 7

FCC & LHC rf system building blocks Circulator Coupler Generator rf cavity Beam Load Low level rf – + How to model interaction of beam with rf system? 8

Beam loading model: rf cavity Stored energy Quality factor Power loss 9

Beam loading model: rf cavity Stored energy Quality factor Power loss 10

Beam loading model: rf cavity Stored energy Quality factor Power loss 11

Beam loading model: rf cavity Stored energy Quality factor Power loss Cavity detuning rf frequency 12

Beam loading model: beam Beam – current source. All rf buckets are filled with identical bunches 13

Beam loading model: beam Beam – current source. All rf buckets are filled with identical bunches dc beam current rf component of beam current Complex form factor Stable phase (electron machine convention) 14

Beam loading model: coupler Relation between voltage and currents: 15

Beam loading model: main equation Current in LRC circuit 16

Beam loading model: main equation Current in LRC circuit 17

Beam loading model: main equation Current in LRC circuit 18

Beam loading model: main equation Current in LRC circuit 19

Beam loading model: main equation Generator current Generator power 20

Minimization of generator power Optimal detuning Optimal quality factor Minimum power 21

FCC-ee Z parameter choice 22

Power requirements for FCC-hh Phase of synchronous particle 23

Power requirements for FCC-hh 24

Beam loading for realistic beams with gaps 25

Transient beam loading Gaps in machine filling will result in modulation beam parameters (bunch length and phase) Usual approaches: • Small signal Pedersen model in frequency domain, which assumes small modulations (but we have 100% modulation of beam current!) • Particle tracking simulations (difficult for 16640 bunches in FCC-ee Z and 10600 in FCC-hh) 26

Model for transient beam loading Energy loss per turn Energy gain for acceleration 27

rf beam current Peak rf current 28

Results for FCC-ee Z 29

Results FCC-hh at flattop 30

Compensation of transients Passive: Abort gap matching (for example in LHC). Requires two rings with identical fill patterns, rf, and total currents. For HL-LHC still remaining impact due to Crab Cavities Active: beam loading compensation schemes acting via rf feedback system 31

Beam loading during injection 32

Half-detuning compensation scheme 0 Power needs to be optimized in presence beam and no beam segment Minimum power consumption 33

FCC & LHC rf system building blocks Circulator Coupler Generator rf cavity Beam Load Low level rf – + How to model interaction of beam with rf system? 34

LHC low-level rf system delay + + – Digital rf feedback Analog rf feedback + + + One turn delay feedback BLon. D and stand-alone implementations of detailed model were developed 35

Comparison with measurements in steady-state Comparison with MD data is ongoing (dedicated working group) *T. Mastoridis, P. Baudrenghien and J. Molendijk, PRAB 20, 101003 (2017) 36

Comparison with measurements in steady-state Comparison with MD data is ongoing (dedicated working group) *T. Mastoridis, P. Baudrenghien and J. Molendijk, PRAB 20, 101003 (2017) 37

Summary Beam loading affects the design of high-current colliders. Impact of transients need to be carefully evaluated to avoid luminosity reduction. Transient beam loading can be compensated by means of rf feedback around cavity. Power requirements, however depend on detailed implementation of llrf system. 38

Thank you for your attention! 39

Spare slides 40

Beam interaction with surroundings Bunch in perfectly conducting beam pipe Wake fields are excited in presence of discontinuities Radio frequency (rf) cavity is special type of discontinuities Beam induced effects in rf cavities are referred as beam loading Simulations using ABCI (Azimuthal Beam Cavity Interaction) code, http: //abci. kek. jp/abci. htm 41

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Beam loading model: rf cavity Stored energy Quality factor Power loss 43

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Optimal detuning 45

Optimal quality factor 46