Beam-return current systems in nonthermal solar flare models

Abstract

Previous investigations of return currents driven by suprathermal electron beams in solar flares have been based both conceptually and mathematically on analyses of electron beams in the laboratory environment. However, the physics of laboratory electron beams is fundamentally different from the physics of solar flare electron beams. Consider first the laboratory beam, which is injected into the plasma from an external source and is, therefore, modeled as a semi-infinite charged rigid rod. The longitudinal electrostatic field of such a charged rod has no preferred direction and therefore cannot drive a return current. Consequently, in the laboratory the return current is established inductively through the appearance of the changing magnetic field associated with the rising beam current, there being no offsetting displacement current term in such a geometry. It subsequently decays on the resistive time-scale; because of this decay, the net current of the system increases, and the lifetime of the electron beam becomes limited by self-pinching effects. Therefore, in the laboratory, the beam/return current system cannot reach a steady state.

By contrast, the electron beam in the solar flare forms in situ and the longitudinal electrostatic field is produced by charge separation. Such an electrostatic field does have a preferred direction and so can drive a cospatial return current. Further, the magnetic field generated by the beam current is always close to being offset by either the magnetic field associated with the displacement current (∂E/∂t) or the electrostatically-driven return current; hence, inductive fields are never important. Thus, in the solar flare the return current is principally established by electrostatic fields; the return current is continuously driven and does not decay resistively. Thus, if the acceleration mechanism drives a steady beam current, then the beam/return current system rapidly achieves a steady state. We present in this paper analytic expressions for the approach to this state.