Axial magnetic field and toroidally streaming fast ions in the dense plasma focus are natural consequences of conservation laws in the curved axisymmetric geometry of the current sheath

摘要

Direct measurement of axial magnetic field in the PF-1000 dense plasma focus(DPF), and its reported correlation with neutron emission, call for a freshlook at previous reports of existence of axial magnetic field component in theDPF from other laboratories, and associated data suggesting toroidaldirectionality of fast ions participating in fusion reactions, with a view tounderstand the underlying physics. In this context, recent work dealing withapplication of the hyperbolic conservation law formalism to the DPF is extendedin this paper to a curvilinear coordinate system, which reflects the shape ofthe DPF current sheath. Locally-unidirectional shock propagation in thiscoordinate system enables construction of a system of 7 one-dimensionalhyperbolic conservation law equations with geometric source terms, taking intoaccount all the components of magnetic field and flow velocity.Rankine-Hugoniot jump conditions for this system lead to expressions for theaxial magnetic field and three components of fluid velocity having high ionkinetic energy.