4,068 research outputs found
Electron Parallel Closures for Arbitrary Collisionality
Electron parallel closures for heat flow, viscosity, and friction force are expressed as kernel-weighted integrals of thermodynamic drives, the temperature gradient, relative electron-ion flow velocity, and flow-velocity gradient. Simple, fitted kernel functions are obtained for arbitrary collisionality from the 6400 moment solution and the asymptotic behavior in the collisionless limit. The fitted kernels circumvent having to solve higher order moment equations in order to close the electron fluid equations. For this reason, the electron parallel closures provide a useful and general tool for theoretical and computational models of astrophysical and laboratory plasmas
Ion Parallel Closures
Ion parallel closures are obtained for arbitrary atomic weights and charge numbers. For arbitrary collisionality, the heat flow and viscosity are expressed as kernel-weighted integrals of the temperature and flow-velocity gradients. Simple, fitted kernel functions are obtained from the 1600 parallel moment solution and the asymptotic behavior in the collisionless limit. The fitted kernel parameters are tabulated for various temperature ratios of ions to electrons. The closures can be used conveniently without solving the kinetic equation or higher order moment equations in closing ion fluid equations
Electron Heat Flow Due to Magnetic Field Fluctuations
Radial heat transport induced by magnetic field line fluctuations is obtained from the integral parallel heat flow closure for arbitrary collisionality. The parallel heat flow and its radial component are computed for a single harmonic sinusoidal field line perturbation. In the collisional and collisionless limits, averaging the heat flow over an unperturbed surface yields Rechester-Rosenbluth like formulae with quantitative factors. The single harmonic result is generalized to multiple harmonics given a spectrum of small magnetic perturbations. In the collisionless limit, the heat and particle transport relations are also derived. © 2016 IOP Publishing Ltd
Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma
A general method of solving the drift kinetic equation is developed for an
axisymmetric magnetic field. Expanding a distribution function in general
moments a set of ordinary differential equations are obtained. Successively
expanding the moments and magnetic-field involved quantities in Fourier series,
a set of linear algebraic equations is obtained. The set of full (Maxwellian
and non-Maxwellian) moment equations is solved to express the density,
temperature, and flow velocity perturbations in terms of radial gradients of
equilibrium pressure and temperature. Closure relations that connect parallel
heat flux density and viscosity to the radial gradients and parallel gradients
of temperature and flow velocity, are also obtained by solving the
non-Maxwellian moment equations. The closure relations combined with the
linearized fluid equations reproduce the same solution obtained directly from
the full moment equations. The method can be generalized to derive closures and
transport for an electron-ion plasma and a multi-ion plasma in a general
magnetic field.Comment: 25 pages, 9 figure
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