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 s β 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 g0 2 = 2 π n 0 Σ ( q s 2 β s 2 /θ s 2 ) 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.