Two-dimensional equilibrium of a low temperature magnetized plasma

A two-dimensional steady-state model is developed, in which, even though ion inertia is retained, a variable separation allows us to analyse separately the axial and the radial transports. For the axial transport (along magnetic field lines) an integral dispersion relation is derived that includes a nonlinear form that is obtained from the ion–neutral collision operator. The dispersion relation is solved for various values of the Paschen parameter, and the electron temperature and the axial profiles of the plasma density and plasma potential are calculated. The solutions of the dispersion relation are shown to have three asymptotic limits: collisionless, linear diffusion and nonlinear diffusion. For the radial transport, the rate of which is determined by electron cross-field diffusion, the full equations are numerically solved. The calculations are compared to probe measurements performed at various locations inside our helicon source for various magnetic field intensities and wave powers. The proposition that the measured increase in the plasma density with the increase of the magnetic field intensity is a result of an improved confinement, is examined. For the parameters of the experiment described here, this proposition implies that the electron collisionality is much larger than expected from electron–ion and electron–neutral collisions. A different explanation for the dependence of the density on the magnetic field intensity is suggested, that the density increase that follows an increase of the magnetic field intensity results from an improved wave–plasma coupling via the helicon interaction, causing a larger fraction of the total wave power to be deposited inside the helicon source.

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