Structural Requirements for Ion-Acoustic Double Layers: A Parametric Perturbation Analysis of the Maxwellian Limit
arXiv:2607.13306
The paper shows that ion‑acoustic double layers can form in plasmas when the electron distribution deviates from a strict Maxwellian, using two perturbation parameters to derive analytic thresholds for their existence.
Abstract
Standard Maxwellian plasmas exhibit a mathematical \textit{rigidity}, possessing insufficient degrees of freedom to support electrostatic double layers (DLs) and yielding only soliton solutions. This study investigates the hypothesis that the formation of DLs is a generic consequence of breaking this structural rigidity through parametric perturbation. By introducing two independent continuous control parameters, and , into the electron distribution, we demonstrate that DLs are a structural property of any plasma model that relaxes the strict Maxwellian constraint. Through a Gardner small-amplitude expansion, we analytically prove that a perturbation must modify both the quadratic and cubic density coefficients to decouple the nonlinear structure and generate physical, supersonic double layers, deriving small-amplitude acoustic-limit threshold conditions of and . We show that these theoretical boundaries broaden for large-amplitude, nonlinear structures. By mapping the exact existence regions of DLs in phase space, we demonstrate how higher-order terms relax the weak-amplitude limits, confirming that the Maxwellian state represents a singular point where the DL solution collapses.
18 pages, 2 figures