Ion Acceleration in Multi-Fluid Plasma: Including Charge Separation Induced Electric Field Effects in Supersonic Wave Layers

Ross Burrows

doi:10.3390/plasma3030010

Abstract

The need to understand the process by which particles, including solar wind and coronal ions as well as pickup ions, are accelerated to high energies (ultimately to become anomalous cosmic rays) motivate a multi-fluid shock wave model which includes kinetic effects (e.g., ion acceleration) in an electromagnetically self-consistent framework. Particle reflection at the cross-shock potential leads to ion acceleration in the motional electric field and thus anisotropic heating and pressure in the shock layer, with important consequences for the multi-fluid dynamics. This motivates development of a multi-fluid model of solar wind electrons and ions treated as fluid, coupled self-consistently with a small population of ions (e.g., pickup ions) dynamically treated as individual particles. Consideration of both the time dependent and steady state regimes, indicate that such a multi-fluid approach is necessary for resolving the, Debye scale, particle reflecting cross-shock potential and subsequent dynamics. To study charge separation effects in narrow, supersonic wave layers we consider a reduction of the system to the steady state for cold ions and hot electrons and find two types of solitary waves inherent to the reduced two-fluid system in this limiting case.

Highlights

Investigations of multiply reflected ion (MRI) acceleration at perpendicular shocks, where ions are treated as test particles, with detailed trajectories calculated from the Lorentz force equation, have found MRI to be an efficient mechanism capable of energizing ions up to energies on the order of ∼100 keV, as needed for injection into diffusive shock acceleration mechanisms [1,2,3,4,5] which further accelerate them to become the so-called anomalous component of cosmic rays
We develop a quasi-self-consistent system composed of a core two-fluid plasma solar wind (SW) background, which is acted on by a small population of ions to be dynamically treated as super-particles ( to the way are ions are treated in particle-in-cell (PIC) codes where the term super-particle implies that each PIC particle represents, on average, an arbitrary number of real particles) that are self-consistently coupled to the core SW
Though this coupled ordinary differential equations (ODEs) method might not be exact as the integral form, it has the advantage of being extensible for use in more complex cases, such as the coupled set of ODEs presented in the previous section

Summary

Introduction

Investigations of multiply reflected ion (MRI) acceleration at perpendicular shocks, where ions are treated as test particles, with detailed trajectories calculated from the Lorentz force equation, have found MRI to be an efficient mechanism capable of energizing ions up to energies on the order of ∼100 keV, as needed for injection into diffusive shock acceleration mechanisms [1,2,3,4,5] which further accelerate them to become the so-called anomalous component of cosmic rays. Much of this work treats the electromagnetic fields as fixed and ions as test particles. We have presented a two-fluid solar wind (SW) simulation with pickup ions (PUIs) coupled quasi self-consistently via inclusion of the PUI anisotropic pressure—calculated directly from their precisely tracked trajectories [6]. Continuing this work, here we consider a self-consistent inclusion of the back-reaction, due to ion acceleration, including their action on the electromagnetic fields as well as their anisotropic pressure. The possibility of self-consistently including ions, treated as particles (in a manner similar to particle-in-cell or PIC codes), using a 1-fluid MHD (magnetohydrodyamics) model, with source terms included to account for shock accelerated ions, has been rejected because, as considered below, only a multi-fluid plasma treatment can resolve important charge separation effects in supersonic wave layers.

Methods

Results

Discussion

Conclusion