Modeling narrow trailing beams and ion motion in PWFA Chengkun Huang (UCLA/LANL) and members of FACET collaboration SciDAC COMPASS all hands meeting 2009 LA-UR

a multi-stage PWFA-LC with 25GeV energy gain per stage in meter-long plasma A few 10s nm beam size and emittance PWFA Linear Collider concept

Radiation reaction effect can be observed in current generation experiments and it is in modeled in QuickPIC : Abraham-Lorentz-Dirac force: run-away solution and pre-acceleration numerous other models exist O’connell-Ford equation (Phys. Lett. A, 2003; Jackson 3 rd ed.) Synchrotron radiation Relativistic Larmor's formula Relative energy loss rate for a matched beam in PWFA: Particle tracking in QuickPIC enable radiation diagnostics. Radiation loss could be enhanced by ion motion.

nonlinearity and local enhancement of the focusing force arise  emittance growth change longitudinal wakefield increase radiation loss effect of ion motion on main beam is of major concern. Ion collapse when n b /n p > m i /m e >>1 (Rosenweig PRL 2005), PWFA Linear Collider concept Matched beam spot size shrinks at large γ, low  n For future collider - e ny down by 10 2 (e.g., 10nm-rad) - γ up by n b up by Ion motion must be included in design/models ion motion for a future collider Drive beam H+ ion

Reducing ion motion Analytical solutions are difficult, predictive quantitative study of the effects of ion motion on acceleration and beam quality requires accurate modeling. Possible solutions: Other possibilities: emittance matching section? weaker wake?

estimate the computation requirements for the main beam. collider beams are asymmetric, smallest emittance of the main beam in a TeV collider is 0.04 mm·mrad. the matched spot size of the main beam at 500 GeV in a plasma of 1×10 17 cm -3 will be 30 nm, which is three orders of magnitudes smaller than the longitudinal spot size or the plasma wavelength. transverse dimension of the beam is 6 nm at the final focus if a plasma lens is used. the transverse box size needs to be around 20 c/ ω p, which is ~300 microns. This is 10 5 times larger than the required resolution. in the longitudinal direction, the plasma wavelength needs to be well resolved using O(1000) grids. a realistic 3D simulation of the accelerated beam would need 10 5 ×10 5 ×1000 = 1×10 13 grids and 4×10 13 particles (assuming 4 particles/cell). time step and the number of time steps for meter-long propagation distance are ~0.002 fs and 1×10 9 for a full PIC simulation, or ~ 16 ps and 208 for a quasi-static simulation. Computation requirements for modeling ion motion

High resolution PWFA simulation Milestone: Realistic 3D simulation of PWFA Drive beam: 2.9  electrons, Main beam: 1  1010 electrons, Both are 25 GeV, modeled with ~4,200,000 macro- particles. Nominal PWFA-LC stage Main beam emittance: mm·mrad Matched spot sizes 100 nm for n e =1  cm -3. Drive beam emittance: 10 mm·mrad, typical for current state-of-the-art linac. Drive beam matched spot size 1 µm High resoluton: required for TeV collider beam Simultion resolution: 49nm  49nm  304nm 8192  8192  1024 grid points 8192 processors on Franklin. 4 particles per cell for plasma electron and ion respectively. Resolve real atom separation of ~20 nm at 1  cm -3. High resolution: required for ion dynamics First PWFA PIC simulation to simulate nearly all the particles in a real plasma.