On the Evolution Equations of Nonlinearly Permissible, Coherent Hole Structures Propagating Persistently in Collisionless Plasmas

Abstract

A fundamental study describing nonlinear plasma wave propagation is presented. Elementary linear wave theory describes small‐amplitude random waves, but lacks information about coherent structures. This improved wave model arises from the fact that structure formation is inevitably associated with particle trapping, which can only be properly addressed by the pseudo‐potential method instead of Bernstein, Greene, and Kruskal (BGK) ‐ likemethods. Only by using this method can legitimate nonlinear dispersion relations be obtained and reconciled with trapping scenarios. This privilege is used to derive evolution equations for five structures, the derivation being simplified by the acoustic nature of the permitted modes. The focus is on a special structure, the solitary electron hole of negative polarity, with which it can explain a spacecraft observation for the first time. Furthermore, it is shown that an intrinsically nonlinear structure can become macroscopically linear and thus harmonic by suitably adjusting the trapping scenario. An example is the monochromatic ion acoustic wave that propagates at ion sound velocity without dispersion. In this literature research, it also takes a critical look at a recently awarded work.

Comment on “Evolution Equations of Nonlinearly Permissible, Coherent Hole Structures Propagating Persistently in Collisionless Plasmas”

“…In a recent publication, [1] Schamel and Chakrabarti, make a point of contradicting some features of my papers concerning electron and ion holes. While I have in many places acknowledged the important pioneering work of Dr. Schamel concerning electron holes, there remain various important aspects of his claims on which we disagree.…”

“…In ref. [1] Schamel and Chakrabarti say concerning my comparison of the two methods that "Hutchinson… does not adequately acknowledge their differences. In particular, he sees no need for an independent derivation of a NDR".…”

“…They further say "he keeps making mistakes in his calculations" with the only justification being a reference to a longer version [4] of ref. [1]. (The authors call ref.…”