Stochastic acceleration of suprathermal particles under pressure balance conditions
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The acceleration of suprathermal charged particles in the heliosphere under pressure balance conditions including for the first time the radial spatial particle diffusion and convection in the solar wind is investigated. The physical conditions are derived for which the stationary phase space distribution of suprathermal particles approaches the power-law distribution f ∝ p −5,which is often seen in spacecraft observations. For separable source distributions in momentum and position we analytically solve the stationary particle transport equation for a radially constant solar wind speed V0 and a momentum-independent radial spatial diffusion coefficient. The resulting stationary solution at any position within the finite heliosphere is the superposition of an infinite sum of power laws in momentum below and above the (assumed mono-momentum) injection momentum pI . The smallest spatial eigenvalue determines the flattest power law, to which the full stationary solution approaches at large and small enough momenta. Only for the case of a reflecting inner and a free-escape outer spatial boundary, does one small eigenvalue exist, yielding the power-law distribution f ∝ p −5 at sufficiently largemomentum values. The other three spatial boundary conditions imply steeper momentum spectra. Momentum spectra and radial profiles of suprathermal particles are calculated by adopting a uniform outer ring spatial source distribution.