Self-focusing of local plasma currents

For a Boltzmann distribution function, neglecting collisions and in the presence of a longitudinal external magnetic field, the self-consistent equilibrium configuration is found for a plasma with components s; this configuration represents an infinitely extended plane layer consisting of periodically recurring quasi-filaments of current for each of which the Bennett self-focusing condition I = 2 θ_s/q_sβ_s is fulfilled. The filaments may be considered the result of the continuous topological transformation of a homogeneous plane layer having the characteristic dimension k_g0² = 2 π n₀ Σ (q_s² β_s²/θ_s²) since the condition indicated is fulfilled for an element of the homogeneous layer in the range —∞≤ x ≤∞, —π/k_g0 ≤ y ≤ π/k_g0. During this transformation the characteristic dimensions, the total current and the energy of the y component of the magnetic field of the filaments remain constant. With increasing depth of the modulation, characterized by the parameter only the energy of the x component of the magnetic field grows (proportionally to y in the linear case).

The authors examined the stability of a homogeneous plane layer with respect to perturbations of the type j_z=j_z(x) exp (ωt+i ky), as well as the factors giving rise to filaments and their in high current discharge processes.