Self-similar solutions for the supersonic implosion of a screw-pinch plasma

Self-similar solutions are obtained for the supersonic compression of a plasma containing an axial current and an entrained axial magnetic field (screw pinch). These solutions represent a complete generalization of previous works done on the Z-pinch and Θ-pinch schemes. The solutions presented herein represent a screw-pinch plasma with a diffuse current profile. Three separate plasma implosion modes are identified. These modes differ qualitatively from the Z-pinch and Θ-pinch schemes. They are comprised of the plasma annulus implosion, a converging transverse magnetohydrodynamic shock, and the propagation of fast magnetosonic waves toward the axis (weak discontinuity). These modes are chosen on the basis of their ability to achieve magnetic field cumulation during the course of the implosion. Analytic expressions describing the asymptotic behavior of the hydromagnetic profiles are obtained for each of the three implosion modes. Numerical examples for selected boundary conditions, representing realistic plasma parameters for the purpose of ultrahigh magnetic field generation, are presented