Beam Match and Emittance Saturation within Plasma Wakefield

Beam Match and Emittance Saturation within Plasma Wakefield Acceleration …and preview of ion motion simulations! By Joel Frederico 1

Plasma Wakefield Acceleration*† • • 2 Experimentally Confirmed (2014 -Present) • High energy • Meter scale • High gradient • Low energy spread • High efficiency Preserved emittance? • Priority- frequently “prime directive” • Integral to PWFA applications • Colliders • FEL • …etc. * Litos, M. et al. High-efficiency acceleration of an electron beam in a plasma wakefield accelerator. Nature 515, 92– 95 (2014). † Litos, M. et al. 9 Ge. V energy gain in a beam-driven plasma wakefield accelerator. Plasma Phys. Control. Fusion 58, 034017 (2016).

Beam Parameters • Beam Distribution • • Emittance • • • Area in transverse phase space plane • Conserved under linear uncoupled optics (Liouville’s Theorem) Beta • • • Minimum at waist Alpha • • 3 Zero at waist

Match Condition • Blowout leaves circular ion region • Linear focusing Plasma • • Electron motion and beam moments under focusing Match defined as constant spot size • • 4

Emittance Evolution (https: //youtu. be/3 e. HUb. Tabr. RE)

Emittance and Action-Angle Formalism* • Change of coordinates • �� i and �� i are initial ‘action’ and ‘angle’ • • Phase evolution depends on energy • • Emittance assumes randomized �� • • PWFA represents another change of coordinate • Energy spread randomizes new �� • Average (projected) emittance may increase * Raubenheimer, T. , Decker, F. -J. & Seeman, J. T. Beam distribution function after filamentation. in Particle Accelerator Conference 5, 3291– 3293 (IEEE, 1995). 6

Emittance Saturation Distribution is approx. Gaussian • Wraps on interval (0, 2 pi) • Becomes uniform when max and min is small: • • For a 5% energy spread: • • Simulation reveals emittance, match asymptotes • • • 7 Centroid-matched case:

Ion Motion • • Ion densities spoil emittance • Nonlinear focusing fields • Non-constant match condition Simple model for ion motion • • Assumes beam density greater than plasma density Simulate theory assumptions • HPC simulation

Ion Motion Model • Radially-symmetric Gaussian relativistic beam • 2 D Model Acts as transverse potential in central force problem • • Ion motion has two limits • Small-amplitude motion is SHM: • • • Large-amplitude motion • Exact motion: • f is periodic: • Approximate motion: Similar equations in one dimension 9

Ion Motion Simulation Approach: Particle to mesh fields to particle • • Master/slave architecture: trivial scaling • Particles are partitioned to slaves • Calculate fields (slaves) • Process fields and redistribute (master) • Push particles (slaves) • Linear in number of particles • Current approximations 10 • Static beam • All forces small wrt drive beam

Future Directions • • Emittance Mismatch • Integrate acceleration • Integrate density ramps Ion Simulations • Implement quasi-static approximation (validated in Quick. PIC) • Evaluate ��-slice emittance evolution • • Demonstrate limited projected emittance spoiling Benchmark with Quick. PIC/OSIRIS