[en] Self-similar solutions are obtained for supersonic compression of a plasma containing an axial current and an entrained axial magnetic field (screw-pinch). The solutions presented here represent a screw-pinch plasma with diffuse current profile. Four separate plasma implosion modes are identified. The solutions representing the implosion modes differ qualitatively from Z-pinch and Θ-pinch schemes. They comprise of plasma annulus implosion, converging transverse MHD shock, propagation of fast magnetosonic waves towards the axis (weak discontinuities) and collapse of a hollow plasma liner. These modes are chosen on the basis of their ability to achieve magnetic field cumulation during the course of implosion. Analytic expressions describing asymptotic behavior of the hydromagnetic profiles are obtained for each of the four implosion modes. Numerical examples for selected boundary conditions, representing realistic plasma parameters for the purpose of ultra-high magnetic field generation, are presented for each of the four implosion modes. A special case representing the exponential implosion of a screw-pinch plasma has also been analyzed. It has been found that specifying an exponential dependence to the temporal contribution of the hydromagnetic variables, results in a more constrained solution space. This comparison is made with the case described above which has a power law type temporal contribution. Owing to the immense possible applications associated with plasma pinches, the time independent profiles of the hydromagnetic variables have been utilized in order to arrive at an estimate for the practical utility of the theoretical model. More specifically, the time dependent profiles of the hydromagnetic variables, and a piston condition for an external laser driven have been obtained. Numerical examples have also been provided for two cases representing screw-pinch plasma implosions occurring for realistic experimental parameters