Growth rate of the clump instability

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Abstract
The instability of phase space density granulations or clumps has recently been reported. A theory for the growth rate of the clump instability in a one‐dimensional, ion–electron plasma is presented. Growth is predicted to occur in regions of velocity space where the average particle distribution functions have opposing velocity gradients. The free energy required for instability is significantly below the threshold necessary for the linear instability of ion acoustic waves. The growth rate increases with fluctuation amplitude and is proportional to the inverse of the nonlinear trapping time. The effect of particle discreteness and clump self‐energy on the growth rate is discussed. The growth rate is in reasonable agreement with recent particle simulations.