We perform a numerical investigation of the supersonic expansion of a laboratory jet produced in Pilot-PSI. Pilot is a linear device consisting of a cascaded arc plasma source, a vacuum vessel for plasma expansion and magnetic coils for jet collimation. We concentrate here on (1) the neutral gas dynamics and the detailed steady jet morphologies resulting from experimentally realized nozzle configurations; and (2) the plasma collimation due to the applied magnetic fields. The former approach analyses numerical simulations modelled by means of the compressible hydrodynamic equations, comparing 1D spherical and 2D axially symmetric results with related experimental efforts. An in-depth analysis of the characteristics of the stationary flow pattern allows a study of the properties of the supersonic expansion: a well defined free-jet flow shock structure is formed in the first region of the expansion and fully described. Also, a predicted correlation between the variation of the pressure in the vessel and the position of the Mach disc is confirmed. We investigate changes in the supersonic jet structures due to a geometrical variation of the nozzle source diameter, revealing a more complicated shock structure which we analyse using the characteristic lines. A comparison with the free-jet flow is made and the influence of the nozzle geometry on the flow is discussed. The magnetic collimation of the plasma beam is demonstrated by means of single fluid magnetohydrodynamic simulations, which clearly show the transition from compressible gas to fully ionized plasma regimes. A qualitative agreement with measured Pilot-PSI density profiles indicates to which extent such single fluid descriptions aid in the interpretation of observed plasma jet dynamics.
SUMMARYThis paper is focused on analysis of the properties of material operators for geometrical methods on tetrahedral grids. The stiffness matrix in electrodynamics, as well as the one in electrostatics, are mathematically proven to be the same for every material operator satisfying a condition which is sufficient for the consistency of the numerical scheme. This gives a new and better insight into the strong similarities existing between the finite element method (FEM) and the finite integration technique (FIT).A symmetrization of the microcell method, which also ensures the positive definiteness of the material operators, based on geometrical properties of tetrahedra, is proposed. Numerical results in time and frequency domain for resonant cavities are presented and compared to the FEM.
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