Abstract
Recently, the energization of superthermal electrons at the Earth's bow shock was found to be consistent with a new magnetic pumping model derived in the limit where the electron transit time is much shorter than any time scale governing the evolution of the magnetic fields. The new model breaks with the common approach of integrating the kinetic equations along unperturbed orbits. Rather, the fast transit-time limit allows the electron dynamics to be characterized by adiabatic invariants (action variables) accurately capturing the nonlinear effects of electrons becoming trapped in magnetic perturbations. Without trapping, fast parallel streaming along magnetic field lines causes the electron pressure to be isotropized and homogeneous along the magnetic field lines. In contrast, trapping permits spatially varying pressure anisotropy to form along the magnetic field lines, and through a Fermi process this pressure anisotropy in turn becomes the main ingredient that renders magnetic pumping efficient for energizing superthermal electrons. We here present a detailed mathematical derivation of the model.
Highlights
Throughout the universe, energetic electrons represent the main source of electromagnetic radiation providing an important window into space and astrophysical phenomena
In the present paper we provide a detailed mathematical derivation of the model obtained by exploring the fast transit-time limit of a drift-kinetic plasma description, including the effects of electrons becoming trapped in the magnetic perturbations
While the model is derived with an assumption of small magnetic perturbations, it accurately accounts for the heating rates at large magnetic perturbation amplitudes
Summary
Throughout the universe, energetic electrons represent the main source of electromagnetic radiation providing an important window into space and astrophysical phenomena. Given the low collisionality common to astrophysical settings, the distributions of the constituent particles are typically far from thermodynamic equilibrium, and can deviate from Maxwellians often with the formation of energetic power-law tails where f ∝ v−γ. Determining the physical mechanism(s) which heats electrons and produces the common power-law signature is still an unresolved problem that is at the heart of the present analysis. Following the results reported in Lichko & Egedal (2020), we here present a detailed derivation of a model for superthermal electron energization via magnetic pumping. Magnetic pumping is known as a heating mechanism that transfers energy from magnetic fluctuations to a plasma and is most effective at the largest scale of the magnetic perturbations. In the present work we show that electron trapping renders
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