Theory of negative energy holes in current carrying plasmas

The theory of hole structures or phase-space vortices in a one-dimensional current-carrying plasma is extended, focusing on the energy of trapped-particle modes in comparison to a homogeneous plasma. It is shown how the energy expression presented in [J.-M. Griessmeier and H. Schamel, Phys. Plasmas 9, 2462 (2002)] is obtained for small amplitude structures. Parameter regimes admitting negative energy solutions are given. It is demonstrated how negative energy structures can be found analytically for the case of a generalized solitary electron hole (where ion trapping is shown to further lower the critical drift velocity), for a generalized solitary ion hole (where the influence of electron trapping increases the critical drift velocity) and for a harmonic (monochromatic) structure. Consequently, a plasma may become nonlinearly unstable well below linear threshold already for infinitesimal wave amplitudes