Abstract. We study numerically the collapse behavior of self-generated magnetic fields described by the nonlinear coupling equations in laser-produced plasmas. The results show that magnetic fields self-generated by transverse pumping plasmons near critical points may collapse, leading to the enhancement of magnetic fields about up to 0.18 MG and 1.8 MG at laser irradiances of 1012 W cm−2 and 1016 W cm−2 respectively, which are similar to the experimental results.

Abstract. The general theory of self-similar magnetohydrodynamic (MHD) expansion waves is presented. Building on the familiar hydrodynamic results, a complete range of possible field–flow and wave-mode orientations are explored. When the magnetic field and flow are parallel, only the fast-mode wave can undergo an expansion to vacuum conditions: the self-similar slow-mode wave has a density that increases monotonically. For fast-mode waves with the field at an arbitrary angle with respect to the flow, the MHD equations have a critical point. There is a unique solution that passes through the critical point that has ½γβ = 1 and Br = 0 there, where γ is the polytropic index, β the local plasma beta and Br the radial component of the magnetic field. The critical point is an umbilical point, where sound and Alfvén speeds are equal, and the transcritical solution undergoes a change from a fast-mode to a slow-mode expansion at the critical point. Slow-mode expansions exist for field-flow orientations where the angle between field and flow lies either between 90° and 180° or between 270° and 360°. There is also an umbilic point in these solutions when the initial plasma beta β0 exceeds a critical value βcrit. When β0 [ges ] βcrit, the solutions require a transition through a critical point. When β0 < βcrit, there is a smooth solution involving an inflection in the density and angular velocity. For other angles between field and flow, all the slow-mode waves are compressive. An analytic solution for the case of a magnetic field everywhere perpendicular to the flow with γ = 2 is presented.

Abstract. We present an analysis of the compression ratio in MHD shocks. Although the equation describing the compression ratio has been in the literature for decades, we believe that our results are interesting and complementary to the earlier research. We concentrate on the behavior of the compression ratio in a bow shock as a function of the angle between the shock normal and the plasma velocity. For this problem, we find non-unique solutions in certain regimes, which we investigate in detail. We also find regimes where the compression ratio in fast bow shocks achieves a local maximum in more than one location. In the last section, we consider the compression ratio in slow shocks and make some conclusions about the shape of the shock in this flow regime.

Abstract. A code has been developed to study self-organization in spheromaks using the Galerkin method in which the magnetic and velocity fields appearing in the incompressible dissipative MHD equations are expanded in a spectrum of Chandrasekhar–Kendall eigenstates of the curl. The ultimate goal is to apply the Galerkin method in actual spheromak geometry to calculate turbulence levels and associated transport. The present work employs the straight-cylinder approximation, known to give a good representation of internal ideal MHD modes in spheromaks and applied here to resistive tearing modes. Our main result to date is a demonstration that the Galerkin method can exhibit tearing island formation with only a few states in the spectrum. Example quasilinear calculations are presented for a decaying spheromak and for a spheromak created by gun injection.

The Zakharov–Kuznetsov equation describes the propagation of weak ion acoustic waves in a strongly magnetized plasma. Their dynamics have been studied in a series of papers, one of which gives growth rates of instabilities found numerically, as well as pictures of soliton collisions [J. Plasma Phys.64, 397 (2000) – Part I]. In the present paper, we find good approximate formulas for growth rates of the dominant instability, vastly improving those of Part I. This is done by proceeding to higher order in the expansion, combined with an incorporation of exact values for the boundaries of the unstable region in the formulas. The result is better than we had any right to expect. We next depart from linear stability analysis and look at nonlinear dynamics to obtain a pulse in time. The maximum amplitude of this pulse is seen to be proportional to the linear growth rate, a result that was so far suspected from numerics but not derived theoretically. (This paper can be read independently of Part I.)