[Paper Review] Non-linear Ion-Wake Excitation by the Time-Asymmetric Electron Wakefields of Intense Energy Sources with applications to the Crunch-in regime

Aakash A. Sahai|arXiv (Cornell University)|Dec 12, 2016

Laser-Plasma Interactions and Diagnostics29 references3 citations

TL;DR

This paper proposes that time-asymmetric electron wakefields from intense laser or particle beams excite a long-lived, non-linear cylindrical ion-soliton wake in plasma, driven by radial electric field asymmetries in the electron bubble. The ion-wake forms a radially expanding, density-compressed channel sustained by electron thermal pressure, limiting plasma accelerator repetition rates and enabling the 'crunch-in' regime for positron acceleration via strong, linearly radial focusing fields.

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.

Motivation & Objective

• To understand long-term ion dynamics in plasma wakefield accelerators after intense driver pulses.
• To identify the mechanism by which time-asymmetric electron wakefields excite non-linear ion-wake modes.
• To model the formation and evolution of a cylindrical ion-soliton as a key driver of plasma relaxation and repetition-rate limits.
• To explore the application of this ion-wake structure to the 'crunch-in' regime for positron acceleration.
• To quantify the coupling from electron wakefield energy to non-linear ion-acoustic modes.

Proposed method

• Analytical modeling of ion dynamics under time-asymmetric radial electric fields from a nearly stationary electron bubble.
• Use of particle-in-cell (PIC) simulations to resolve non-linear ion-soliton structure and its driven propagation over hundreds of plasma skin depths.
• Modeling of ion motion using a single-bubble approximation to extrapolate to long train dynamics.
• Energy partitioning analysis between electron wakefield, quiver kinetic energy, and ion-mode excitation.
• Assessment of ion-wake sustainability via electron thermal pressure and radial expansion dynamics.
• Comparison of ion-wake evolution under non-linear electron oscillations with and without beam-loading effects.

Experimental results

Research questions

• RQ1 How does time-asymmetric electron wakefield structure lead to non-linear ion-wake excitation in plasma?
• RQ2 What physical mechanism enables the formation of a sustained cylindrical ion-soliton behind an electron bubble?
• RQ3 How does the ion-wake structure influence the relaxation time and repetition rate of plasma-based accelerators?
• RQ4 What is the role of electron thermal pressure in sustaining the radial expansion of the ion-wake channel?
• RQ5 How does the ion-wake enable the 'crunch-in' regime for positron acceleration with strong, linearly radial focusing fields?

Key findings

• A non-linear cylindrical ion-soliton forms behind the electron bubble due to time-asymmetric radial electric fields, with a radius of approximately 4c/ωpe.
• The ion-wake channel exhibits on-axis and bubble-edge density spikes, with δni/n0 > 1, indicating strong ion compression.
• The ion-soliton is sustained radially outward by electron thermal pressure, forming a long-lived structure over several hundred plasma skin depths.
• The ion-wake evolution is independent of the driver type—laser or particle beam—due to universal wakefield structure.
• The ion-wake limits the repetition rate of plasma accelerators by dictating the plasma relaxation time after each pulse.
• The 'crunch-in' regime is enabled by the ion-wake, which supports strong, linearly radial focusing fields of the order of wakefield-breaking fields, crucial for positron beam transport.