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Mutual Exclusion of Normal Particle Diffusion in Velocity and Configuration Space

There is growing evidence that fluctuating electric fields might be important not only in the context of particle diffusion in laboratory plasmas and stochastic particle acceleration in solar flares but also for particle transport in the interplanetary solar wind plasma expanding toward the outer heliosphere. Based on first principles involving the Newton-Lorentz equation, a general approach is outlined that combines a simultaneous particle random walk in position and velocity space. Two special limits are considered. For weak turbulent electric fields, it is shown that particle diffusion in velocity space, commonly known as stochastic acceleration, is subdiffusive and therefore suppressed if particle diffusion in configuration space is normal (Markovian). For strong turbulent electric fields, normal diffusion in velocity space is obtained, but particle transport in position space must then be superdiffusive. Simultaneous normal particle diffusion in configuration and velocity space is mutually exclusive, at least for the limit of weak and strong electric fields. For the latter limit, a relation between spatial and velocity diffusion coefficients is derived and compared with recent simulation results obtained in the context of particle acceleration in solar flares. A good agreement is found.