Beam Scattering Effects - Simulation Tools Developed at The APS A. Xiao and M. Borland Mini-workshop on Dynamic Aperture Issues of USR Nov. 12, 2010
Motivation A future light source requires: Ultra low emittance beam High particle density High quality beam is strongly affected by scattering processes: Small angle scattering: IBS effect emittance dilution in all dimensions. IBS growth rate Bjorken-Mtingwa's (BM) formula with Large angle scattering: Touschek effect particle loss. Piwinski's formula Arbitrary beam shape and energies with (for ) Beam scattering effects seriously limit achievable machine performance! 2
Example: PEP-X PEP-X: A Design Report of the baseline for PEP-X: an Ultra-Low Emittance Storage Ring, SLAC-PUB-13999 3
Concerns for a Linac-Based 4 th Generation Light Source The beam scattering effects in ERL are comparable to or more severe than in the APS. The formula need to be updated to handle energy variation (e.g., acceleration). The Linac beam has non-gaussian profile. Provided by X. Dong R ERL R APS 1. F / 2 ERL F / 2 APS 1/t d ERL 1/t d APS 185 G/ ERL G/ APS Particle distribution from optimized high-brightness injector simulation
Simulation Tools Developed at the APS Able to simulate: Beam scattering effects with energy variation A non-gaussian distributed bunch Simulation tools added to elegant For both Gaussian and non-gaussian distributed bunch Applicable to ring and linac tracking IBSCATTER: Intra-beam scattering TSCATTER: Touschek-scattering External simulation tools Simplified versions of above tools Use data typically provided by elegant Only for Gaussian distributed bunch ibsemittance applicable to ring+linac touscheklifetime applicable to ring only 5
Beam Scattering with Energy Variation ISCATTER or TSCATTER &insert_elements name = *, type = *[QSB]*, skip = 1, element_def = "TS0: TSCATTER", &end The beamline is divided into small sections by inserting special elements IBSCATTER (IBS) or TSCATTER (Touschek) in the beamline. The scattering rates are calculated locally using normalized beam parameters and integrated over each section. At each IBSCATTER: The beam size is enlarged according to the calculated scattering rate by modifying tracking particles coordinates. New beam parameters are used for the following section's simulation. At each TSCATTER: A bunch of scattered particles are generated using Monte-Carlo simulation, each representing part of the integrated scattering rate. Scattered particles are tracked, loss rate and loss position are recorded.
Simulation of Touschek Effect Well known effect in storage ring Single Coulomb scattering process. Small transverse momentum large longitudinal momentum. Main cause of short lifetime for low-emittance, high-charge bunches Approaches to lifetime computation Bruck's formula Flat beam, non-relativistic transverse momentum Piwinski's formula Arbitrary beam shape and energy Local scattering rate using local optical functions and momentum aperture Preferred over Bruck's formula, used in elegant and touscheklifetime Monte-Carlo simulation Gives loss distribution Not necessary for lifetime computation
Lifetime computation with touscheklifetime Only applicable to Gaussian-distributed stored beam. Required input Twiss parameter file from elegant Momentum aperture file from elegant Bunch parameter charge, coupling, bunch length required Emittance, dp/p optional Output Lifetime Local scattering rate R Example touscheklifetime -twiss=aps.twi -aperture=aps.mmap aps.life \ -charge=15 -coupling=0.01 -length=12
Touschek Scattering Simulation overview &touschek_scatter double charge = 0; double frequency = 1; double emit_nx = 0; double emit_ny = 0; double sigma_dp = 0; double sigma_s = 0; STRING Momentum_Aperture = NULL; STRING FullDist = NULL; STRING TranDist = NULL; long n_simulated = 5E6; double ignored_portion = 0.01; long i_start = 0; long i_end = 1; long do_track = 0; STRING output = NULL;... &end
Calculate Local Bunch Distribution Function By default assumes a Gaussian bunch For non-gaussian bunch, use SDDS-based histogram table Given by user from measurement or tracking For tracking, an MHISTOGRAM element is required to be inserted in front of every TSCATTER element. Input can be either 3 x 2D: need Xdist + Ydist + Zdist; 2D+4D: need TranDist + Zdist; (Used in our example) 6D: need FullDist; ideal but need large population of simulated input bunch for getting meaningful distribution function. Index: n sub-index counter: Long. - [N s N p ] Tran. - [N x N xp N y N yp ]
Monte Carlo Simulation 1 - Theory Scattering probability MØller cross section: Scattering rate: Gaussian or interpolate from realistic beam distribution histogram Monte Carlo integration: Particles with dp>delta_mev Total simulation sample events 1 Work started from S. Khan's work: Simulation of the Touschek Effect for Bessy II: A Monte Carlo Approach, Proc. Of EPAC 1994, 1192. 11
By default, elegant stop the simulation for M>1E6. This can be modified by user. 12
13
Monte Carlo Simulation non-gaussian beam At η=0, Piwinski's rate does not depend on input energy spread At η 0, Piwinski's rate depends on input energy spread, so results are un-reliable for linac bunch. Need real bunch distribution for calculation. 14
Simulation of Beam Loss Rate and Position Scattered particles from Monte Carlo simulation are collected and tracked from the scattering location to the end of beamline (linac) or multiple tunes (storage ring). Each scattered particle represents scattering rate of: R i = r i r l R P ds R MC i R P Particle loss position and associated scattering rate are saved. Total number of simulated scattered particles are M x N TS 15
Speed up Simulation Simulated scattering particles don't present same probability. Most of them are rare events. For efficient tracking, we only track those with high probability. What we care is the loss rate and loss position. The ignored part are particle's with large momentum deviation, and very likely, they are lost immediately after scattering. The relative simulation error will be ignored portion divided by the loss portion of tracked particles. For example if 50% (rate) tracked particles lost and the ignored portion is 1%, the relative simulation error is 2%. Try to use delta_mev close to the simulated momentum aperture as input (for example: 80%). Tracked 18% for 99.9% scattering! 16
Application to the APS Normal APS operation 24 bunches Bunch charge [nc] 15.6 x-emittance [nm] 2.53 Coupling 0.01 Bunch length [mm] 9 dp/p 9.5e-4 Momentum aperture 0.02 17
Application to APS ERL 0.5 pa APS Without optimized sextupoles With optimized sextupoles APS Simulation results confirms that the optimized APS ERL design could run without causing radiation hazards. 18
IBS Simulation The nature of IBS and Touschek effect are different We care more beam size evolution than the real particle distribution. The beam size dilution need time to develop Requires fewer ISCATTER element only needed when beam size has a noticeable change. For Gaussian bunch, use ibsemittance or IBSCATTER Bjorken-Mtingwa's (BM) formula: Vertical dispersion effect is included. IbsEmittance Input Twiss file from elegant Beam parameters charge, coupling, bunch length Output Emittance evaluation Local growth rate at given beam parameters Example: ibsemittance aps.twi aps.out -charge=15 -coupling=0.01 -length=10 \ -integrate=turns=50000,step=300 ibsemittance aps.twi aps.out -charge=15 -coupling=0.01 -length=10 -growth 19
20
IBS Simulation for Non-Gaussian Bunches For non-gaussian beams, use tracking with IBSCATTER elements Slice technique important for photo-injector beams Procedures: Bunch is sliced at the beginning of each section of the beamline. The IBS growth rates are calculated using BM formula for each slice, assuming particles in slice are Gaussian-distributed in (x,x',y,y',δ) and uniformly distributed in longitudinal. Particle coordinates are modified based on the calculated growth rate (smoothly or randomly). Particles from each slice are mixed and reform a new bunch. This bunch is ready for the simulation of next section. 21
IBS Growth Rate for Sliced and Unsliced Beam LCLS: 63.5 MeV to 4.4 GeV APS-ERL: 10 MeV to 7 GeV 1 nc, 1 µm normalized emittance. 22
IBS Simulated Beam Property 23
IBS Bunch Energy Spread Evolution 24
Example of using command line tools with elegant Task: evaluate APS stored beam performance as a function of energy Tools: elegant: compute nominal equilibrium properties vs energy haissinski: compute bunch length for specific bunch charge vs energy, using data from elegant ibsemittance: compute energy spread and emittance using results from elegant and haissinski touschecklifetime: compute Touschek lifetime using results from ibsemittance, haissinski, and elegant sddsbrightness: compute brightness tuning curves using data from ibsemittance and elegant sddsfluxcurve: compute flux tuning curves using data from ibsemittance and elegant Command line tools are readily scripted for fast turn-around 25
Results of energy scan 26
Results of energy scan using optimized superconducting undulators Gap The GoodEnough parameter shows how many photon energies within the 25-100 kev band can be provided with brightness that is within a factor 2 of the best achievable. For conservative magnetic gap, > 7 GeV is preferred. 27
Conclusion Tools to simulate beam scattering effects for both stored and linac beam with energy variation are developed Command line tools for quick, accurate ring evaluation Features in elegant for more fundamental simulation Beam loss rate and position information can be obtained precisely from Monte Carlo simulation using a realistic beam distribution. Beam size evaluation is obtained by applying the Bjorken-Mtingwa formula to a sliced bunch. Application results to an example APS ERL lattice show: The Touschek scattering effects is significant. The momentum aperture needs to be optimized carefully. A beam collimation system can be designed based on the result. The IBS growth rate is much higher compared to a normal stored beam Traveling time is very short IBS effect has no enough time to develop. No obvious effect on the machine's performance. Command line tools are very useful for ring design studies 28
Acknowledgment We would like to express our special thank to S. Khan for his original work on Monte Carlo simulation of Touschek effect. We also followed F. Zimmerman's work to include vertical dispersion to the IBS calculation. During the development, we had many useful discussions with L. Emery. 29