Nonlinear Coupling of Plasma Waves Modified by Separatrix Dissipation

Quantitative measurements of the nonlinear coupling of diocotron modes characterize both the expected conservative coupling term and a new term arising from separatrix dissipation. Here, the pure electron plasma columns have a controllable axial trapping separatrix created by an applied $\theta$-symmetric wall ``squeeze'' voltage. Prior experiments\footnote{A.A. Kabantsev and C.F. Driscoll, {\it Phys. Rev. Lett.} {\bf 97}, 095001 (2006).} established that this separatrix 1) enables and damps the ``Trapped Particle'' diocotron mode, and 2) damps $m_\theta \!\! \ne \!\! 0$ $k_z \!\! \ne \!\! 0$ plasma modes; and, in combination with external $\theta$-asymmetries, 3) damps $m \! \ne\!\! 0$ $k \!\! = \! 0$ diocotron modes, and 4) causes enhanced bulk plasma expansion and loss. The present experiments observe the resonant interaction between the traditional $m \!\! = \! \!2$ $k \!\! = \!\! 0$ diocotron mode and the $m \!\! = \!\! 1$ TP diocotron mode. The initial parametric decay of $m\!\! = \!\! 2$ into $m \!\! = \!\! 1$ is adequately predicted by the conservative nonlinearity arising from the continuity equation. However, the late-time evolution clearly requires (and quantifies) a dissipative nonlinear term which is not yet understood theoretically. This same dissipative coupling is also observed for {\it non-resonant} interactions, as in bulk plasma transport from field errors.