Acceleration theory for 5–40 keV ions at interplanetary shocks

Power-law spectra f(E)∝E^?2.7 of < 40 keV suprathermal ions within ～10⁷ km of propagating interplanetary shocks are explained by diffusive scattering near a plane shock. The theory fits the 25 November 1977 event with a mean free path perpendicular to the shock with is 0.01 AU in front of the shock and less than .0003 AU behind it, for 1 keV ions. The theory predicts a steepening spectrum at higher energies, of the form $\text{f(v)∝v}{}^{\mathrm{?4}}\text{exp(??λdv/ur)}\text{where}\text{u = (ΔV)}{}^2\text{/2V}{}_{\mathrm{W}}$ depends on the plasma velocity jump ΔV and the plasma speed V_W and mean free path λ in front of the shock