The linear Fokker-Planck equation characterizing charged-particle transport in a fully ionized plasma has been solved in one-dimensional spherical geometry by the techniques of Fourier transformation and Legendre expansion. The vacuum boundary condition at the plasma surface has been treated by appending to the plasma a fictitious medium in which angular dispersion is absent. The solution technique has been applied to the problem of alpha-particle slowing down in a fully ionized inertial confinement fusion plasma.