Longitudinal instabilities affecting the moving critical layer laser-plasma ion accelerators

In this work we analyze the longitudinal instabilities of propagating acceleration structures that are driven by a relativistically intense laser at the moving plasma critical layer [1]. These instabilities affect the energy-spectra of the accelerated ion-beams in propagating critical layer acceleration schemes [2][3]. Specifically, using analytical theory and PIC simulations we look into three fundamental physical processes and their interplay that are crucial to the understanding of energy spectral control by making the laser-plasma ion accelerators stable. The interacting processes are (i) Doppler-shifted ponderomotive bunching [1][4] (ii) potential quenching by beam-loading [2] and (iii) two-stream instabilities. These phenomenon have been observed in simulations analyzing these acceleration processes [5][6][7]. From the preliminary models and results we present in this work, we can infer measures by which these instabilities can be controlled [8] for improving the energy-spread of the beams.