Efficient numerical modelling of the emittance evolution of beams with finite energy spread in plasma wakefield accelerators

Abstract

a b s t r a c tThis paper introduces a semi-analytic numerical approach (SANA) for the rapid computation of the transverse emittance of beams with finite energy spread in plasma wakefield accelerators in the blowout regime. The SANA method is used to model the beam emittance evolution when injected into and extracted from realistic plasma profiles. Results are compared to particle-in-cell simulations, establishing the accuracy and efficiency of the procedure. In addition, it is demonstrated that the tapering of vacuumto-plasma and plasma-to-vacuum transitions is a viable method for the mitigation of emittance growth of beams during their injection and extraction from and into plasma cells.

Erratum: Great moments in kinetic theory: 150 years of Maxwell's (other) equations (2017 Eur. J. Phys. 38 065103)

“…The solid curves are computed using the moment approach and the dashed and dashed-dotted curves show results from PIC simulations. Figure 6 demonstrates that the results obtained with the moment approach are in excellent agreement with the PIC results (see [48] for further details).…”

“…After employing (10) and truncating the chain of moment equations with an Ansatz, this method entails a finite number of coupled ordinary differential equations for each subset. The moments of the subsets can be found by numerically (or in specific cases analytically) solving the differential equations for each subset and subsequently combining the results in a prescribed manner to yield the overall beam averages [48].…”

Analytical model for the uncorrelated emittance evolution of externally injected beams in plasma-based accelerators

“…This formalism is then applied to two scenarios with increasing complexity -a single beam slice without energy gain and a single beam slice with energy gain, both propagating at a fixed co-moving position behind the driver. The obtained results are then compared to particle-in-cell (PIC) simulations as well as results obtained using an semi-analytic numerical approach (SANA) [1]. We find excellent agreement between results from the analytical model and from SANA and PIC.…”

“…with the phase space beam moments x 2 , p 2 x , xp x 2 . We chose an ansatz to evaluate Equation (2) which relies on a separable beam distribution function (as outlined in [1]). We assume that the beam particle slice possesses an initial phase space distribution f 0 (x 0 , p 0 , γ 0 ) (with the normalization f 0 dx x,0 dp x,0 dγ 0 = 1), where the initial transverse position x 0 and the initial transverse momentum p x,0 are not correlated with the energy.…”

“…Over these lengths, no significant drive beam head erosion can be observed in the simulations, allowing us to assume E z to be constant for the simulation time and distance. Since we are concerned with a single slice of electrons without acceleration, we can ignore correlated emittance growth due to an energy chirp for a witness beam of finite length (see [1,10]) and focus on the uncorrelated emittance growth. However, while the macroparticle slice in the PIC simulations was chosen to be as thin as possible in the longitudinal direction (σ ζ k −1 p,0 ), it nevertheless samples the electric field variation over its length and around the zero-crossing of E z , thus deviating from the assumption of no energy variation for the witness beam, potentially contributing to a slightly higher emittance value than the one we calculated using the analytic model.…”