Critical Initial States in Collisionless Plasmas

Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction

“…However, this result is qualitative. Actually, in spite of major recent advances in the analytical and computational fields [19,20,21,22,23,24,25,26], mostly in the full Vlasov-Poisson framework, as well as in experiments [27], no definite answer presently exists to this intrinsically nonlinear and time-asymptotic issue, in the sense that no quantitative threshold separating nonzero time-asymptotic wave amplitude states from zero ones is known. This is basically due to the facts that analytical reductions of the problem should e.g.…”

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.…”

“…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.…”

“…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 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.…”