Energetic particles that undergo strong pitch-angle scattering and diffuse through a plasma containing strong compressible MHD turbulence undergo diffusion in momentum space with diffusion coefficient D _ { p } .
If the rms turbulent velocity is of order the Alfvén speed v _ { A } , the contribution to D _ { p } from slow-mode eddies is \simeq ( 2 p ^ { 2 } v _ { A } / 9 l ) [ \ln ( lv _ { A } / D _ { \parallel } ) +2 \gamma - 3 ] , where l is the outer scale of the turbulence , \gamma \simeq 0.577 is Euler ’ s constant , and D _ { \parallel } is the spatial diffusion coefficient of energetic particles , which is assumed to satisfy D _ { \parallel } \ll lv _ { A } .
The energy spectrum of accelerated particles is derived for this value of D _ { p } , taking into account Coulomb losses and particle escape from the acceleration region with an energy-independent escape time .

Slow modes in the D _ { \parallel } \ll lv _ { A } -limit are an unlikely explanation for electron acceleration in solar flares to energies of 10-100 keV , because for solar-flare conditions the predicted acceleration times are too long and the predicted energy spectra are too hard .
The acceleration mechanism discussed in this paper could in principle explain the relatively hard spectra of gyrosynchrotron-emitting electrons in the 100-5000 keV range , but only if D _ { \parallel } \ll lv _ { A } for such particles .