Abstract
A model for the excitation of a non-linear ion-wake mode by a train of plasma electron oscillations in the non-linear time-asymmetric regime is developed using analytical theory and particle-in-cell based computational solutions. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton. The near-void and radially-outwards propagating ion-wake channel of a few plasma skin-depth radius, is explored for application to "Crunch-in" regime of positron acceleration. The coupling from the electron wakefield mode to the ion-mode dictates the long-term evolution of the plasma and the time for its relaxation back to an equilibrium, limiting the repetition-rate of a plasma accelerator. Using an analytical model it is shown that it is the time asymmetric phases of the oscillating radial electric fields of the nearly-stationary electron bubble that excite time-averaged inertial ion motion radially. The electron compression in the back of the bubble sucks-in the ions whereas the space-charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure with on-axis and bubble-edge density-spikes. Once formed, the channel-edge density-spike is sustained over the length of the plasma and driven radially outwards by the thermal pressure of the wake energy in electrons. Its channel-like structure is independent of the energy-source, electromagnetic wave or particle beam, driving the bubble electron wake. Particle-In-Cell simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration in the "Crunch-in" regime.
Highlights
Plasma ions are generally assumed to be stationary in the theory of ultrarelativistic plasma electron waves [1]
Its radial motion is sustained by the thermalizing wake energy in electrons. (ii) We show that an ion-wake channel, which can be meter scale for the beam-driven plasma electron waves, can be used for a novel hollowchannel mode in the “crunch-in” regime [9,10]
Once the fields die out to nearly a hundredth of their initial value and the wake electrons thermalize into a non-isothermal spatial distribution sustaining radial electron temperature gradients supported by the electrostatic forces of electron-ion charge separation, we show that the driven nonlinear ion-acoustic waves is in the form of a cylindrical ion soliton
Summary
Plasma ions are generally assumed to be stationary in the theory of ultrarelativistic plasma electron waves [1]. The evacuation of electrons and ions behind the soliton results in a channel-like ion-wake structure which persists over many hundreds of plasma electron periods and is here shown to be suitable for exciting nonlinear hollow-channel electron modes driven by relativistic positron and electron beams, first investigated by the author. We use an analytical model based on the fields of a nonlinear bubble plasma wave and simulations to demonstrate the inertial phase of the ion wake in Sec. III, while the fields of the bubble persist. In the Appendix we present considerations and assumptions made to derive the ion-wake model
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