Superposition of nonlinear plasma waves

Persistent subplasma-frequency kinetic electrostatic electron nonlinear waves

“…Some mathematical refinements have also been added by Dorning and co-workers. [13][14][15][16] Lastly there are miscellaneous explorations of the behavior of 1D phase-space vortices ͑"holes"͒ and the like. [17][18][19][20][21][22][23] For historical completeness one should also note a particular laboratory experiment done in a Q-machine resulting in the creation of a single KEEN-like cell rather than in a long wave train.…”

“…11 This common method was simply to begin by setting up by some BGK analytic prescription for the velocity distribution in phase space, as an approximation to the desired final state and see if this state survived. 3,7,[12][13][14][15][16][17][18] In order to be able to respond to comments related to the constructive or initial-value method, it was examined in some detail, of which only the most essential points are given in this paper. One should recall that the BGK concept, when reduced to its essentials, is the assertion that, for steady state behavior in the wave frame, the distribution function in that frame should be a function of space only implicitly, i.e., through the behavior of any space-varying potential in relevant canonical particle conserved quantities.…”

“…The theory just cited [4][5][6][7] and work by many others [9][10][11][12][13][14][15][16] ͑previous to the work by Strozzi et al 8 ͒ addressed the problem of the possible persistence of such EAW-style modes but only when imposed as initial states ͑with necessarily complicated structure in the electron velocity distribution function near the phase velocity͒. No obvious means exist to impose such complicated initial states other than by a simple act of will by theorists in a computer model.…”

“…The acronym EAW has been previously used to denote waves in the linear wave frequency gap between the electron and ion plasma frequencies, with phase velocities not far from the electron thermal velocity, in contexts ranging from ionosphere observations, possibly in plasmas with appropriate amounts of clearly defined populations of cold and hot electrons, 4,5 or in plasmas with Landau damping set equal to zero ͑perhaps because of some special adjustment to the electron distribution function at some designated phase velocity͒, 3,6,7 or as a postulated initial plasma distribution function. 6,7,[9][10][11][12][13][14][15][16] Rather than postulating such distributions, when we drove up the distribution function from the initial Maxwellian by using a limited-time PF driver with a chosen pair of frequency and wavenumbers, we found ͑as described below͒ that the trapped electrons obtained kinetically were not simply a means of negating Landau damping but an essential oscillation component quite distinct from and equal in effect to the rest of the ͑untrapped͒ electrons. It also appeared that it would be quite difficult to produce such waves at very low amplitudes, so they should not be confused with the result of any linear perturbation.…”

Evolution of nonlinear waves in compressing plasma

“…It also provides a practical example of the limits of the nonlinear superposition principle derived in Ref. 17, which states that only at small enough amplitude can two BGK modes traveling at sufficiently different phase velocities form a plasma equilibrium state. A similar effect was observed in colliding driven BGK modes, 18 where the fast interaction of two counterpropagating electron holes resulted in some degradation of their structure.…”