1. 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 Parallel Simulation of Electron Cooling Physics for Relativistic Ion Beams – Status & Plans 1. Tech-X Corporation 2. Brookhaven National Lab 3. Thomas Jefferson National Lab ComPASS All-Hands Meeting Tech-X, October 6, 2009 Supported by DOE Office of Science, Office of Nuclear Physics

2. 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

3. Motivation

4. 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/NSAC2007/070424_EIC.pdf

5. 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 GeV antiprotons in Fermilab accumulator ring require e- cooling  250 GeV polarized protons will require e- cooling Two EIC concepts are being considered in the US –eRHIC (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

6. ERL-based Layout for eRHIC Image taken from 2007 eRHIC position paper

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

8. Previous Work – Simulating Dynamical Friction

9. 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. –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) e-e- e-e- e-e- e-e-

10. Culmination of years of work, beginning in 2002 VORPAL simulations support decision to use conventional wiggler for e- cooling of 100 GeV/n Au +79 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

11. Full e- cooling sim’s are distinct from simulating micro-physics of a single pass BETACOOL code is used to model many turns  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). –a variety of electron cooling algorithms are available  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)

12. Dynamical Friction Simulations for e- Cooling shed light on fundamental Plasma Physics Ad hoc limits on  impact 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

13. Previous Work – Coherent Electron Cooling

14. Coherent e- Cooling (CeC) offers dramatically shorter cooling times Modulator Kicker Dispersion section ( for hadrons) Electrons Hadrons l2l2 l1l1 High gain FEL (for electrons) EhEh E < E h E > E h EhEh E < E h E > E h Coherent Electron Cooling concept –uses FEL to combine electron & stochastic cooling concepts –a CEC system has three major subsystems  modulator:the ions imprint a “density bump” on e- distribution  amplifier:FEL interaction amplifes density bump by orders of magnitude  kicker:the amplified & phase-shifted e- charge distribution is used to correct the velocity offset of the ions Litvinenko & Derbenev, “Coherent Electron Cooling,” Phys. Rev. Lett. 102, 114801 (2009).

15. Comparison of simulations with theory is underway, with good results Recent analytical results for e- density wake −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 3D Dynamic response extends over many D and 1/  pe −thermal ptcl boundary conditions are important G. Wang and M. Blaskiewicz, Phys Rev E 78, 026413 (2008).

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

17.  f PIC shows ~10% deviations from theory Movie shows 1D integral of e- density 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 ~5x faster than PIC, due to fewer particles per cell

18. New DOE/NP SBIR Funding for CEC Simulations

19. “High-Fidelity Modulator Simulations of CEC Systems” (NP Phase I: DE-SC0000835; PI: D. Bruhwiler) Supporting proposed CEC proof-of-principle experiment at BNL Need a different algorithm to benchmark CEC modulator simulations –PIC is marginal;  -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 2D Vlasov-Poisson algorithm in VORPAL –x, v x, y, v y, which requires a 4D mesh Simulate e- wake due to single ion; idealized case & finite beam size –must be done in 2D –Vlasov and  -f results will be benchmarked Consider possibility of fully 3D Vlasov-Poisson (requires 6D 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

20. “Designing a Coherent Electron Cooling System for High-Energy Hadron Colliders” (NP Phase II: DE-FG02-08ER85182; 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

21. Future Plans

22. 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

23. Support of Massively Parallel Computing Efforts for SBIR-funded CEC Simulations VORPAL simulations of the CEC modulator and kicker –  -f PIC simulations of full transverse beam slices small domain: ~1,000 cores for ~2 hours 50x 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 4D mesh will likely support only 2D domain decomposition –future efforts will (resources permitting) enable 4D domain decomposition

24. G. I. Bell, R. Busby, J.R. Cary, P. Messmer, A. Sobol I. Ben-Zvi, V. Litvinenko, A. Fedotov, E. PozdeyevAcknowledgments 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-FC02-07ER41499 and DE-FG02-08ER85182. We used computational resources of NERSC, BNL and Tech-X.