Fig. 4. Comparison of f_e(v) evolution.

a The energization $\mathcal{G}$ as a function of the amplitude of a fluctuation, δB/B₀, and the scattering frequency, ν, for the numerically-computed Lorentz (solid) and Krook (dashed) operators, as well as the analytical solution. b Combined estimate of the evolution of the distribution function from magnetic pumping and compressional heating for the points denoted in colored lines in Fig. 2a, obtained by integrating Eqs. (1) and (6) for T = 15 × 2π/ω, with δB/B₀ = 0.7, and ν/(ω/2π) = 0.75. c Reproduction of Fig. 2e. The green dashed line denotes what the final distribution would look like if it only underwent compressional heating. Using these conservative parameters, ${\left(T_{\mathrm{Obs}}/T_{\mathrm{Exp}}\right)}_{\mathrm{Theory}}=0.83{\left(T_{\mathrm{Obs}}/T_{\mathrm{Exp}}\right)}_{\mathrm{MMS}}$, where most of this difference stems from the discrepancy in low energy particles.