Magnetic Pumping: Plasma Heating to Particle Acceleration

One of the earliest mechanisms proposed for plasma heating was magnetic pumping (MP). However, its significance for astrophysical phenomena, including particle acceleration, has yet to be appreciated. MP-energized particles tap energy from magnetic-field oscillations. A particle's momentum component perpendicular to the local B-field increases during field growth by virtue of the adiabatic invariant $p_{\perp}^{2}/B=const$. The gained $p_{\perp}$ is then partially scattered elastically into the parallel momentum, $p_{\parallel}$, with $p^{2}=p_{\parallel}^{2}+p_{\perp}^{2}=const$, thereby retaining some fraction of the gained energy before the field decreases to its minimum. This scattering breaks the reversibility of energy exchange between particles and oscillating magnetic fields, thereby increasing the particle energy after each MP cycle. Field oscillations are often assumed to be sinusoidal, and the resulting MP is treated perturbatively. These simplifications restrict astrophysical applications, leaving objects with strong magnetic perturbations outside the scope of adequate treatment. We develop a nonperturbative approach to MP that is suitable for a broad spectrum of magnetic turbulence. The treatment comprises two steps. The first step is common: converting a kinetic equation into an infinite hierarchy of moments of the particle distribution function. The second step is new in MP treatments: we find an exact closure at an arbitrary level of the moment system. The heating is treated exactly at the second-moment closure. Particle acceleration generally requires a higher-level closure to determine the power-law index and the maximum energy of accelerated particles. We propose a method for extracting these crucial acceleration data from the second moment for a broadband random field.