EIC Beam Dynamics Overview EIC User Community Workshop

EIC Beam Dynamics Overview EIC User Community Workshop Accelerator Mini Workshop Trieste July 18 -22 Ferdinand Willeke

Topics • LINAC beam break-up • Electron cloud effect • Coherent single bunch instabilities • Electron beam heating • Coupled bunch instabilities • Electron-Ion Beam-beam effects • Beam dynamics with Crab Cavities • Dynamic aperture • Polarized beam storage • Acceleration of polarized beams • Intrabeam Scattering and electron cooling

LINAC Beam Break-Up • Single bunch: Transverse fields of short range wakefields induced by the head of an off-center travelling beam will affect energy and transverse in the tail 2 particle model: For Ei = 400 Me. V, G=25 MV/m W= 6 V/p. C/m 2 Q = 50 n. C get factor 20 increase of head tail? amplitude • Energy spread induced by short range wakefield for strong single bunch Better to accelerate less charge and accumulate in S. R. • Continuous multi-pass (multi bunch) operations: Residual HOM may built-up over the passage (bunches) or time unstable well defined intensity threshold depend on residual HOM (with HOM damping), bunch intensity and bunch spacing in the LINAC Cure: Low impedance RF structures, sufficient HOM damping Acc BBU at JLAB FEL Tennant et al, PRSTAB 8, 074403 (2005)

Transverse BBU, one recirculation • only relevant for ERL type EIC which is presently not actively pursued, but it is an interesting beam dynamics and technical issue which differs from usual LINAC beam break up With the following assumptions: • One cavity and one pass ERL, • HOM frequency is not on or very close to the frequency of the beam • The HOM energy exchange of one pass is small compared with the stored energy The threshold is represented by Beyond or below the threshold, the voltage of the HOM. The behavior can be expressed in effective Q or effective decay time. They can be measured by experiments, ~ factor 2 of simulation

Transverse BBU, multiple recirculations @ G. Hoffstaetter and I. Bazarov Multi-pass case: The ith and jth pass may interact each other. Theoretical approach is possible when there is only one HOM and one cavity: In extreme case, the threshold is scaled with number of passes quadratically. However, in general cases the relation is much more complicated in long linac and different optics between linacs. • Multiple cavities / Long linac • Multiple HOMs (as in 5 cell cavity structure for example) • Multi-passes (for example 4 -pass ERL) Multi HOMs: The threshold of multiple HOMs is approximately the worst one of those of single HOM if the frequency of HOMs is separate enough compared with its own width. Therefore HOM frequency spread will help. In 2007, the multi-pass BBU was observed at 2. 149 /2. 156 GHz in CEBAF after new cavities are installed, in a 3 pass/4 pass experiment. The optics is adjusted to increase the BBU threshold. Currently, we use GBBU to simulate the BBU threshold and guide the HOM damper design of the 647 MHz cavity. The nonlinearity and chromatic effect will also affects the BBU threshold (in the desire direction). The effect requires modification of the current simulation tool. @ R. Kazimi et. al, EPAC 08

HOM damping Ridge WG HOM Damper e. RHIC 647 MHz LINAC Cavity Ø Two versions of ridge waveguide is ongoing optimization: rectangular ridge waveguide and round ridge waveguide (prefer for mulitpacting-free). Ø Optimization condition: Dipole mode for BBU, and monopole mode for HOM power. Ø The BBU threshold of rect. Ridge. WG is well above (>a factor of 10) the requirement. Round Ridge waveguide BBU simulation has not done. 6

Electron Cloud Effect SEY > 1 • As all high intensity proton (positron, ion) accelerators with multiple bunches EIC will potentially suffering from accumulation of electrons in the vacuum chamber due to the electron cloud effect. Electron Cloud Density can accumulate over many turns and up to a very high electron saturation density by interaction of beam, e-cloud, residual gas and losses. 5 e. V 40 e. V 2 ke. V • This has been observed for example in LHC, KEK-B, Super-KEKB, and RHIC • Strong dependence on bunch length, bunch population, vacuum chamber wall geometry, material and condition (SEY, h), no satisfactory theoretical description need code; ~100 mm aperture range and ~10 ns bunch structure favor e-cloud Cloud built-up vs time var bunch length (Furman) Consequences: • Vacuum Pressure rise • Bunch position dependent tune shifts • Beam instabilities (e-cloud - beam interaction) • Emittance growth • Cryogenic load Beam intensity limitation Typical “stripe” structure of ecloud density (Zhang, BNL) SEY vs electron energy (Wolski)

Electron Cloud Cures in High Intensity Proton (Ion) Accelerators • Scrubbing with beam (improve h, SEY) • Grated Liner (normal incident of photons or other primary particles • NEG- Coating (complex surface structure traps electrons) • Cu- Coating (lower SEY, mitigates local peaks of cryo load) • Amorphous Carbon Coating (lowers SEY) • Additional pumping (avoids increase in vacuum pressure) • Solenoid fields (in warm straights) Needs extensive simulations, accelerator studies and bench marking

For RHIC: In situ Beam pipe coating • Photo of the magnetron assembly: 50 -cm long cathode magnetron and spring loaded guide wheels. Leading edge guide wheels are inserted in a full-size RHIC tubing section. • We have coated straight pipes and measured them, the surface resistivity is marginal. • We are updating the technique to include ion assisted deposition which will compact the surface and reduce Zsurf 9

Impedance Driven Instabilities (Electrons) • Electron bunches in the Storage Ring of an EIC can have up to 3 1011 particles per bunch. • Model broad band Zlong as a Q=1, fres =10 GHz resonator with |Z/n| = 0. 2Ω. • Transverse impedance Zy = 2∙R ∙ |Z/n| / b 2 = 0. 27 MΩ/m with same resonant frequency and Q • With large fs spread, single mechanism theoretical description are not very precise Need to use numerical algorithms such as TRANFT (M. Blaskiewicz) The algorithms are described (partially) in the TRANFT manual. • Can now simulate multibunch transverse and longitudinal instabilities due to cavity resonances. The algorithm tracks a few consecutive bunches and assumes a symmetric fill. • A thin lens beam-beam kick is implemented and provides good damping. • Eventually need a full impedance budget. • With |Z/n| = 0. 2Ω there is significant momentum spread increase. 10

Coherent Instabilities in the Electron Storage Ring Single Bunch Considerations: • With bunch intensities up to 50 n. C, heating of vacuum components (bellows, BPM, …) is a major issue. • Since Hadron bunch is much longer than electrons bunch, can afford to lengthen the bunch by introducing a higher harmonic RF system Reduce beam heating by reduced peak current (P ~ Ipeak ∙ Iav) Increase Landau Damping to suppress single bunch coherent instabilities • Reduce turbulent bunch lengthening • Large synchrotron frequency spread coupled with chromaticity provides transverse Landau damping (Kernel et. al. EPAC 00) • Nonlinear beam-beam force provides additional Landau damping (plan to accumulate charge in collisions) • Need very careful design of vacuum system in particular tapers, BPM-buttons, bellows • Preliminary results including both single and coupled bunch effects are shown. TMCI-like means no long range wakes, damper or beam-beam.

Coherent Instabilities in the Electron Storage Ring Multi bunch effects: • Beam will be subject to coupled bunch instabilities in all three modes of oscillation, even with s. c. cavities with relatively modest parasitic modes, modes m=0, 1 expected to be strongly driven by resistive wall effect Need to be controlled by active broadband damper systems EIC Issue: • Active damper needs to provide large gain Strong amplification of detector noise Hadron emittance growth due to electron multi-bunch damper Careful design of RF cavities avoiding trapped modes between cells and between cavities

Beam Loading, 3 rd Harmonic RF for bunch lengthening Beam Loading Compensation Quite challenging for amp beam current needs special attention Relative detuning due to transient beam loading needs to be controlled by actively powering the 3 rd harmonic system or by gaps in the bunch train One Gap Illustrative bunch profiles Two Gaps Four Gaps Breaking up the gap lessens the transient due to both a shorter gap and shorter interval between the gaps. Additional cavities or wide band feedback may be implemented.

Coupled Bunch Instabilities for JLEIC Electron Storage Ring • At low energy: Impedance of all RF cavities needed for High Energy is too large to control with reasonable feedback effort reduce the impedance by using less RF at low energy • At high energy, there is substantial radiation damping can use full number of cavities + feedback

EIC Beam-Beam Effect • Beam-beam force is limited by tune footprint size and formation of tails in Hadron Machines • … and by strong emittance blow-up, poor electron life time and coherent beam-beam instabilities for Electron machines • The concept of the EIC is to run each beam with the beam-beam parameters (tune shift) typical for its species. • This worked at HERA, though the beam-beam parameters for protons were not at the limit. • In EIC colliders, the beam-beam limit occurs by the following effect: Once the electron beam-beam force reaches a level where …. . the beam exhibits coherent oscillation of its centroid. • In an electron machine this will still allow to keep the beam colliding and on can run close to this beam-beam limit Simulation: Coherent beam-beam Instability Threshold: electron. Centroid • Red: Np=1011 stable • Blue: Np=3∙ 1011 unstable Proton. Centroid • In EI collisions, however, this leads to a rapid deterioration of the hadron beam emittance. Hadrons have to be dumped and refilled. Thus one cannot operate close to this limit because of the risk of major disruption of continuous colliding beam operations • Challenge: Some of the effects can only simulated by strong-strong beam calculations. These depend on modeling the beam-beam force based on super-particle coordinates. In simulating slow effects (emittance growth) the distinction between artificial numerical effects and real effects is difficult. • Complementary studies in the weak-strong model are necessary Simulation of strong beam-beam effects for e. RHIC Using several strong-strong codes. Beam-beam limit is factor 2 above anticipated operating parameters

EIC Specific Beam-Beam Issue • Since electron life time and electron spin lifetime is shorter than Hadron lifetime and hadron emittance growth • Electrons need to be more frequently replaced as Hadron • e. RHIC: replace an electron bunch every 6 min (18 Ge. V) one injection every second (360 bunches) • Ejected bunch to be replaced in several steps to avoid difficulties with accelerating a 50 n. C bunch • Cannot interrupt collisions by separating beams non adiabatic change of the hadron beam force • Potential issue with Hadron Emittance growth enhance by beam-beam nonlinearity • In linear approximation of beam-beam force: no substantial issue, • Taking into account full nonlinearities requires simulations Linear Estimate: expect linear growth rate Growth rate: 10% / 10 hr With 1 replacement every 6 minutes Nonlinear simulation 25% / 10 hr With 1 replacement every 6 minutes

Beam Dynamics with Crab Cavities • Luminosities of 1033 -1034 cm-2 s-1 in an EIC together with the acceptance requirement of an EIC detector can only be achieved with a fairly large crossing angle (>15 mrad). The effect of the crossing angle on the luminosity must be compensated by transverse RF resonators (CRAB Cavities • A pair of such crab cavities spaced with 90 dgree in betatron phase advance from the IP is the standard configuration (a single crab cavity may be possible as well) RF curvature may be corrected by two x two crab cavities which differ in RF frequency. • Beam dynamic with crab cavities is complicated by the fact that: Dispersion D or D’ at the crab cavity may lead to emittance growth Beam will also gain energy in the crab cavity for more than one reason • Crab cavity will lead to transverse-longitudinal coupling which may conspire with the beam-beam effect Thin lens 4 x 4 matrix representing a pair of crab cavities in linear approximation and the linear part of the beam-beam lens

Nonlinear Beam-Beam Forces and Crab Cavity Tracking Results for EIC (e. RHIC parameters) Weak-Strong Simulations, preliminary result: • No hadron beam emittance growth or other detrimental effects in the presence of Crab Crossing • Dispersion at the crab cavity is a crucial parameter • Further efforts with strong-strong beam simulations underway

Chromatic Correction Schemes • Using additional sextupole families to create orthogonal chromatic knobs to compensate off-momentum beta beam originating from low beta quadrupoles (traditional method) • Unmatched (partial) beta squeeze creates a beta wave in the arc which modulates the chromaticity compensating terms. It is in phase with off momentum beta beat. Need only two family sextupole compensation and periodic dispersion (Fartouk) • Compensate IR off momentum beta-beat by another beat from a high beta block (KEK-B, JLEIC) • Cancel the beta beat from one IR by the one of the 2 nd IR (HERA)

Alternative Chromatic Compensation Chromaticity • FFQs generate strong linear dependence of betatron tunes on momentum (linear chromaticity) due to their high • FFQs also generate large non-linear chromaticity by inducing momentum dependence of functions, / ( ) Local compensation of FFQ chromaticity in JLEIC • CCB creates / ( ) wave opposite to that of FFB • Geometric non-linear effects of CCB sextupoles compensated using -I pairs Large dynamic aperture CCB / ( ) FFB CCB IP np

Momentum Acceptance & Dynamic Aperture Linear optics of JLEIC Chromaticity compensation CCB -I -I Momentum acceptance Dynamic aperture with errors and correction 10 seeds collaboration with SLAC ± 50

e. RHIC Dynamic Aperture e. Ring lattice parameters: 18 Ge. V: 90 degree FODO lattice 10 Ge. V: 90 degree FODO lattice Peak beta in the IR: 500 -1000 m Significant local chromaticity • Need to compensate 2 nd order chromatics terms as they cause strong high order synchro-betatron resonances around the desired working point (polarization) near the integer resonance • Need 4 (6) sextupole families in the 90 (60) degree lattice • Alternative: Unmatched beta-squeeze will create a beta wave in the sextupoles which will cancel higher order chromaticity Reduction of dynamic aperture, recovered by additional (“geometrical”) sextupoles in dispersion free regions

Optimization Constraints Frist order chromatic terms (5) Frist order geometric terms (5) Amplitude tune dependence Second order chromaticity After driving term minimization, DA is optimized with tracking.

Momentum Acceptance

X-Y Acceptance

Intra Beam Scattering and Cooling e. RHIC Hadron beams for collision operation with L = 1034 cm-2 s-1 need emittance in the order of a few nm and short bunches (7 cm) at 1011 particles per bunch. Because of the corresponding high beam density the beam is subject to strong Intrabeam Scattering which is the effect of strongly Lorentz boosted particles which suffered from Coulomb scattering in the bunch in the longitudinal direction. IBS growth times of less than an hour require to be counteracted by strong cooling of the high energy Hadron beam. Such performance is quite a stress for known cooling mechanisms such as stochastic cooling or electron cooling. The possibility of a new method known as coherent electron cooling is discussed and being tested at BNL

Polarization • Hadron operation with polarized beams is being done and is not considered a major new issue. • Electron Polarization has a particular challenge: The beam need to be stored with spin up and spin down equally represented Sokolov Ternov effect will destroy the polarization of fully polarized injected bunches. • A rough estimate yields the result that !8 Ge. V bunches need to be replace every 6 minutes • This assumption need to be verified by spin tracking calculations which a just starting up.

Ion Polarization Curtesy Yuhong Zhang © V. S. Mozorov Figure-8 concept: Spin precession in one arc is exactly cancelled in the other Spin stabilization by small fields: ~3 Tm vs. < 400 Tm for deuterons at 100 Ge. V • Criterion: induced spin rotation >> spin rotation due to orbit errors 3 D spin rotator: combination of small rotations about different axes provides any polarization orientation at any point in the collider ring No effect on the orbit Polarized deuterons Frequent adiabatic spin flips Simulations in progress Start-to-end Zgoubi simulation of proton acceleration n=0 Zgoubi simulation of proton spin flip

Conclusion • An EIC combines the challenges of high luminosity hadron-hadron colliders and e+ e- colliders. • In addition, there are some beam dynamic issues which are specific to EIC colliders. • These constitute a rich field of beam dynamics study • While good progress is being made in validating the assumptions the EIC design is based upon, there remains a lot of work to be done to ensure the full performance of such a facility.