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Plasma and Radiation Hydrodynamics

We analyze only the radial motion of the plasma and thus assume a one dimensional model symmetry in all other dimensions. The equations are presented for curvilinear as well as cartesian coordinates. The radiation hydrodynamics equations are written in the laboratory frame and then transferred to the adaptive grid frame. They are solved along with a set of grid equations, based on Eq.(3), that describes how the grid system evolves in time. The explicit grid generation procedure prevents implicit coupling between the physical equations and the grid system. A conservative differencing scheme based on the control volume approach is chosen to retain the conservative nature of the governing equations. The numerical method to discretize the equations is a first-order upwind differencing scheme (donor cell). The dissipative characteristics of the upwind differencing are minimized with grid adaptation.

The governing equations for a nonrelativistic fluid in the frame of radiation magnetohydrodynamics (RMHD) are described as [3,4]

where and are energy density for plasma and radiation, and are radiation flux and pressure tensor. Also is the Joule heating term and is equal to , the rate of Joulean dissipation in fluid frame, plus , the rate at which the force does work. A relation is needed between the pressure, density and temperature to close the system. This relation can be found using the equation of state where is the average charge state, n is number density and T is temperature.

The state of the radiation field and the magnetic field are found through the radiative transfer equation, the Maxwell's equations and Ohm's law respectively. The radiative transfer equation is a mathematical statement of the conservation of photons and is given in the following form [5]

where I is specific intensity, and are called emissivity and extinction coefficients, and is the directional unit vector. The space-time evolution of the magnetic field in the MHD approximation is given as

where is the electrical conductivity of the plasma. The equation describes how the magnetic field lines are convected and diffused in the non-relativistic and low-frequency plasma fluid.



next up previous
Next: Implementation Up: Adaptive-Grid Methods for Plasma Previous: Adaptive-Grid Methodology



Osman Yasar
Thu Mar 21 14:48:13 EST 1996