Abstract
A self-consistent electrostatic odd-symmetric eigenmode (OEM) is analytically found in a solitary type Bernstein-Greene-Kruskal (BGK) equilibrium. The frequency of the OEM is order of the electron bounce frequency and it is spatially odd-symmetric with the scale comparable to that of the solitary BGK equilibrium structure. Such an OEM is consistent with the recent observation from particle-in-cell simulation of the solitary wave [Dokgo et al., Phys. Plasmas 23, 092107 (2016)]. The mode can be driven unstable by trapped electrons within the hole structure of the solitary wave. Such a low frequency, pure electron mode, which may possibly interact resonantly with the ion acoustic mode, provides a possible damping mechanism of the BGK equilibrium.
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