Stability of Non-Uniform Plasma in a Magnetic Field Gradient

pressure plasma having a density gradient Vn confined by a strong magnetic field. These waves can become unstable (either hydrodynamically, or because of resonance with electrons moving along field lines) when finite ion orbit size is taken into account. This paper considers additionally the effect of a gradient in the magnetic field B, which may form a magnetic well, for example with ∇n * ∇B < 0. Particular attention is paid to the situation where the ion temperature Ti much exceeds the electron temperature Te as with an injected plasma. In this case the magnetic well is shown to have a pronounced stabilizing effect on the above waves. The stability condition can be written 1+(Ti/Te)(n/∇n)(∇B/B)<0. In the unstable case ∇n * ∇B > 0 one recovers the well known flute instabilities (kII = 0) which may be stabilized by finite ion Larmor radius ai if k⊥ is quantized and thereby greater than a certain critical value. However, there arise additionally less rapidly growing instabilities whose growth rate γ tends to (∇n/n) (T/(miTi)½)){(k2⊥a2i)/2 + (Ti/Te) n/(∇n)(∇B)/B}½ for 1 > k2⊥a2i > βmi/me with finite, though small, kII. These predictions are compared with experiment. The stability conditions required in closed, toroidal systems in which the magnetic field gradient alternates in sign along a field line are considered in some detail. It is shown that the half length L of a region of unfavourable gradient should not exceed ∼(Ti/Te)(n/k2⊥a2⊥n). (author)