Steady state densities in a plasma confined by a dipole magnet: Diffusion induced transport explored through direct measurements and modeling

Steady state densities in a plasma confined by a permanent dipole magnet are determined through detailed experiments and modeling. Two diffusion models are developed, and the resulting equations are solved numerically to yield the radial and angular plasma density profiles, which are compared with those obtained experimentally. The models consider the fluid and continuity equations along with Fick's law and take into account the experimentally determined electron temperature (T-e) and the static dipole magnetic fields (B) in space, as a common input. In model I, the equation of motion for both charges (ions and electrons) is used to self-consistently generate the ambipolar electric field (E), while model II considers the electron equation of motion and takes into account the experimentally determined plasma potential (Vs) as another input, whose gradient provides the ambipolar electric field. Results indicate that the plasma density peaks around r similar to (2-12) cm depending on the polar angle and the discharge pressure and decreases for large r, while its angular variation shows a maximum in the equatorial plane (theta = 90 degrees) and decreases toward the polar regions. T-e and V-s are higher in the polar cusp regions and decrease toward the equatorial plane, with the profiles becoming more spherically symmetric away from the magnet. The numerically obtained density profiles from the models agree well with those obtained experimentally. The phenomenon of inward diffusion resulting in peaked density profiles as reported by earlier authors is found to be a natural outcome of the solution of the diffusion equation.