Parallel Simulation of Electron Cooling Physics for Relativistic

Parallel Simulation of Electron Cooling Physics for Relativistic Ion Beams – Status & Plans D. L. Bruhwiler, 1 G. I. Bell, 1 A. V. Sobol, 1 V. Litvinenko, 2 E. Pozdeyev, 2 A. Fedotov, 2 I. Ben-Zvi, 2 Y. Zhang, 3 S. Derbenev 3 & B. Terzic 3 1. Tech-X Corporation 2. Brookhaven National Lab 3. Thomas Jefferson National Lab Com. PASS All-Hands Meeting Tech-X, October 6, 2009 Supported by DOE Office of Science, Office of Nuclear Physics

Outline • Motivation • Brief review of what has been done – “conventional” electron cooling for relativistic ion beams § simulating dynamical friction with VORPAL – coherent electron cooling (CEC) § simulating a CEC modulator with VORPAL • Overview of recent DOE/NP SBIR awards • Future Plans

Motivation

Long-term motivation for electron cooling of relativistic hadron beams: the Electron-Ion Collider (EIC) concept C. Aidala et al. (The EIC Working Group), “A High Luminosity, High Energy Electron-Ion-Collider; A New Experimental Quest to Study the Glue that Binds Us All, ” White Paper prepared for the NSAC LRP (2007). http: //www. phenix. bnl. gov/WWW/publish/abhay/Home_of_EIC/NSAC 2007/070424_EIC. pdf

High luminosity relativistic ion beams require electron cooling • EIC requires orders-of-magnitude higher ion luminosity – can only be achieved by reducing phase space volume of beams § ions have no natural mechanism for phase space damping – hence, external cooling techniques are required § in some cases, stochastic cooling can be used; however… § 8. 9 Ge. V antiprotons in Fermilab accumulator ring require e- cooling § 250 Ge. V polarized protons will require e- cooling • Two EIC concepts are being considered in the US – e. RHIC (add energy recovery linac to the RHIC complex) – ELIC (add e- and ion rings to Jefferson Lab complex) § electron cooling is included in all present designs

ERL-based Layout for e. RHIC Image taken from 2007 e. RHIC position paper

ELIC Schematic (Electron – Light Ion Collider) 30 -225 Ge. V protons 15 -100 Ge. V/n ions Green-field design of ion complex directly aimed at full exploitation of science program. Parallel simulation of electron cooling physics… 3 -9 Ge. V electrons 3 -9 Ge. V positrons p. 7

Previous Work – Simulating Dynamical Friction

Dynamical friction is the key physical process for e- cooling • Case of isotropic plasma, with no external fields, was first explained 65 years ago – S. Chandrasekhar, Principles of Stellar Dynamics (U. Chicago Press, 1942). – B. A. Trubnikov, Rev. Plasma Physics 1 (1965), p. 105. eeee- – Physics can be understood in two different ways § Binary collisions (integrate over ensemble of e-/ion collisions) § Dielectric plasma response (ion scatters off of plasma waves)

VORPAL simulations support decision to use conventional wiggler for e- cooling of 100 Ge. V/n Au+79 • Culmination of years of work, beginning in 2002 A. V. Fedotov, D. L. Bruhwiler, A. Sidorin, D. Abell, I. Ben-Zvi, R. Busby, J. R. Cary, and V. N. Litvinenko, "Numerical study of the magnetized friction force, " Phys. Rev. ST Accel. Beams 9, 074401 (2006). A. V. Fedotov, I. Ben-Zvi, D. L. Bruhwiler, V. N. Litvinenko and A. O. Sidorin, "High-energy electron cooling in a collider, " New J. Phys. 8 (2006), p. 283. G. I. Bell, D. L. Bruhwiler, A. Fedotov, A. V. Sobol, R. Busby, P. Stoltz, D. T. Abell, P. Messmer, I. Ben. Zvi and V. N. Litvinenko, “Simulating the dynamical friction force on ions due to a briefly co-propagating electron beam”, J. Comp. Phys. 227 (2008), p. 8714. • Conventional wiggler could replace expensive solenoid – friction force is reduced only logarithmically

Full e- cooling sim’s are distinct from simulating micro-physics of a single pass • BETACOOL code is used to model many turns § § – a variety of electron cooling algorithms are available § – A. O. Sidorin et al. , Nucl. Instrum. Methods A 558, 325 (2006). A. V. Fedotov, I Ben-Zvi, D. L. Bruhwiler, V. N. Litvinenko, A. O. Sidorin, New J. Physics 8, 283 (2006). i. e. simple models for dynamical friction and diffusion various models for “heating” are included § intra-beam scattering (IBS), beam-beam collisions, etc. Fedotov et al. (2006)

Dynamical Friction Simulations for e- Cooling shed light on fundamental Plasma Physics • Ad hoc limits on rimpact removed from Coulomb logarithm – logarithmic singularities result from approximations § Infinite time for collisions to occur; weak scattering approximation § A. V. Sobol, D. L. Bruhwiler, G. I. Bell, A. Fedotov and V. Litvinenko, "Numerical calculation of dynamical friction in future electron cooling systems, including magnetic field perturbations and finite time effects, " submitted to New J. Physics. New algorithm used to obtain field-free dynamical friction - fast, serial, C - finite-time, asymmetric - arbitrary velocities - assumes uniform density modified Pareto distribution

Previous Work – Coherent Electron Cooling

Coherent e- Cooling (Ce. C) offers dramatically shorter cooling times E < Eh Eh Dispersion section ( for hadrons) Hadrons E < Eh Eh Modulator E > Eh l 1 High gain FEL (for electrons) E > Eh Kicker l 2 Electrons Litvinenko & Derbenev, “Coherent Electron Cooling, ” Phys. Rev. Lett. 102, 114801 (2009). • Coherent Electron Cooling concept – uses FEL to combine electron & stochastic cooling concepts – a CEC system has three major subsystems § modulator: § amplifier: § kicker: the ions imprint a “density bump” on e- distribution FEL interaction amplifes density bump by orders of magnitude the amplified & phase-shifted e- charge distribution is used to correct the velocity offset of the ions

Comparison of simulations with theory is underway, with good results • Recent analytical results for e- density wake G. Wang and M. Blaskiewicz, Phys Rev E 78, 026413 (2008). − theory makes certain assumptions: § § single ion; arbitrary velocities uniform e- density; anisotropic temperature o Lorentzian velocity distribution o now implemented in VORPAL § linear plasma response; fully 3 D • Dynamic response extends over many D and 1/wpe − thermal ptcl boundary conditions are important

Electrostatic PIC can be used to simulate the electron response in an idealized modulator, but df PIC is faster, quieter & more accurate PIC df PIC • Movies above show 2 D slice through e- density of 3 D simulations • R=1 (isotropic e- temperatures); T=Z=0 (stationary ion)

df PIC shows ~10% deviations from theory • Movie shows 1 D integral of edensity perturbation • • R=1 (isotropic e- temperatures) T=Z=0 (stationary ion) • Total e- shielding is shown in figure below • peak response is seen after ½ of a plasma period • ~5 x faster than PIC, due to fewer particles per cell

New DOE/NP SBIR Funding for CEC Simulations

“High-Fidelity Modulator Simulations of CEC Systems” (NP Phase I: DE-SC 0000835; PI: D. Bruhwiler) • Supporting proposed CEC proof-of-principle experiment at BNL • Need a different algorithm to benchmark CEC modulator simulations – PIC is marginal; d-f PIC looks extremely promising – no theory available for inclusion of important complicating effects • Crossing ion trajectories, space charge effects, beam edge effects (surface waves) • Implementing 2 D Vlasov-Poisson algorithm in VORPAL – x, vx, y, vy, which requires a 4 D mesh • Simulate e- wake due to single ion; idealized case & finite beam size – must be done in 2 D – Vlasov and d-f results will be benchmarked • Consider possibility of fully 3 D Vlasov-Poisson (requires 6 D mesh) – evaluate high-order algorithms to enable low resolution • Collaborating with Electron Cooling group at BNL – V. Litvinenko, E. Pozdeyev, A. Fedotov, I. Ben-Zvi

“Designing a Coherent Electron Cooling System for High-Energy Hadron Colliders” (NP Phase II: DE-FG 02 -08 ER 85182; PI: D. Bruhwiler) • Supporting proposed CEC proof-of-principle experiment at BNL • Goal: Integrated Simulation of Coherent Electron Cooling – VORPAL simulation of the modulator – GENESIS modeling of the free-electron-laser (FEL) amplifier – Map-based propagation of electrons and ions between components • • electrons are bent in and out of the ion beam ions go through a chicane to create a variable longitudinal phase shift – VORPAL simulation of the kicker • Collaborating with Electron Cooling group at BNL – V. Litvinenko, E. Pozdeyev, A. Fedotov, I. Ben-Zvi

Future Plans

Binary Collision Algorithm for Simulating Dynamical Friction – Plans for Moving Beyond 96 processors • Eight ions, many electrons • • close collisions more expensive • 12 cores per ion 60% efficiency • limited to 96 cores Moving to 100’s and 1000’s of ions • future use of 1, 000 to 10, 000 cores • Full transverse slice of ion/e- bunches • • • Space charge effects Ions near beam edge Ion trajectory x’ing

Support of Massively Parallel Computing Efforts for SBIR-funded CEC Simulations • VORPAL simulations of the CEC modulator and kicker – d-f PIC simulations of full transverse beam slices • small domain: ~1, 000 cores for ~2 hours • 50 x larger domain for full beam slice • aiming for >10, 000 cores before end of project • Use of Vlasov/Poisson for modulator simulations – by end of Phase I SBIR project, the 4 D mesh will likely support only 2 D domain decomposition – future efforts will (resources permitting) enable 4 D domain decomposition

Acknowledgments G. I. Bell, R. Busby, J. R. Cary, P. Messmer, A. Sobol I. Ben-Zvi, V. Litvinenko, A. Fedotov, E. Pozdeyev We thank T. Austin, O. Boine-Frankenheim, A. Burov, A. Jain, W. Mori, S. Nagaitsev, A. Sidorin, P. Stoltz, N. Xiang, G. Zwicknagel and members of the Physics group of the RHIC Electron Cooling Project for many useful discussions. We acknowledge assistance from the VORPAL development team. Work at Tech-X Corp. was supported by the US DOE Office of Science, Office of Nuclear Physics under grants DE-FC 02 -07 ER 41499 and DE-FG 02 -08 ER 85182. We used computational resources of NERSC, BNL and Tech-X.