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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. 

Magnetic wave perturbations are observed in the solar wind and in the vicinity of Earth's bow shock. For such environments, recent work on magnetic pumping with electrons trapped in the magnetic perturbations has demonstrated the possibility of efficient energization of superthermal electrons. Here we also analyse the energization of such energetic electrons for which the transit time through the system is short compared with time scales associated with the magnetic field evolution. In particular, considering an idealized magnetic configuration we show how trapping/detrapping of energetic magnetized electrons can cause effective parallel velocity ( $v_{\parallel }$ -) diffusion. This parallel diffusion, combined with naturally occurring mechanisms known to cause pitch angle scattering, such as whistler waves, produces enhanced heating rates for magnetic pumping. We find that at low pitch angle scattering rates, the combined mechanism enhances the heating beyond the predictions of the recent theory for magnetic pumping with trapped electrons. 

We present a drift kinetic model for the free expansion of a thermal plasma out of a magnetic nozzle. This problem relates to plasma space propulsion systems, natural environments such as the solar wind, and end losses from the expander region of mirror magnetically confined fusion concepts such as the gas dynamic trap. The model incorporates trapped and passing orbit types encountered in the mirror expander geometry and maps to an upstream thermal distribution. This boundary condition and quasineutrality require the generation of an ambipolar potential drop of 5Te=e, forming a thermal barrier for the electrons. The model for the electron and ion velocity distributions and fluid moments is confirmed with data from a fully kinetic simulation. Finally, the model is extended to account for a population of fast sloshing ions arising from neutral beam heating within a magnetic mirror, again resulting in good agreement with a corresponding kinetic simulation.