A bounded active magnetized plasma over a wide range of collisionality

At the last GEC Sternberg gave a treatment of this problem in the collisionless limit, and with the magnetic field at a variable angle to the wall. This is extended to include the effect of collisions on the ion motion in the constant collision frequency for momentum model $\nu _{i}$. The relevant parameters are $\omega _{ci}$, the ion cyclotron frequency, the plasma half size L, the central Debye length $\lambda _{D0}$, and the ionization frequency Z. For $\nu _{i}$ = 0 the results of Sternberg and Poggie are recovered and the dimensionless quantities used in the description of the results here are $\lambda _{D0}$/L, $\omega _{ci}$/Z, $\nu _{i}$/Z and the angle $\Psi $. The eigenvalue is ZL/c$_{s}$. As $\nu _{i}$/$\omega _{ci}$ becomes greater than 1 the effect of the magnetic field is nullified, as is to be expected on physical grounds. Sternberg N and Poggie J (2004) IEEE Trans. Plasma Science \textbf{32}, 2217.