Fluid Equations for a Collisionless Plasma including Finite Ion Larmor Radius and Finite β Effects

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Abstract
The distribution function is systematically expanded in the finite Larmor radius ordering scheme for a collisionless plasma in an axial magnetic field B z (x, y, t) , where the magnetic field variation is a direct result of finite plasma pressure (β ∼ 1) . Fluid equations are evaluated in both the guiding‐center frame and the center‐of‐mass frame. These equations are complicated by the velocity dependent ∇B drift which prevents strict closure of the moment equations. The effect of finite β is to include further terms in the stress tensor and in the energy equation in the form of a heat flux. An alternative derivation by a direct moment expansion is included. From these fluid equations the mechanism for producing radial differential rotation is rigorously shown. Secondly the stability of a rotating theta pinch is studied showing two finite β effects which can contribute to stability. The first is due to the increase in diamagnetic angular velocity (a result of creating a magnetic well) and the second due to the azimuthal equilibrium heat flow if the ion temperature decreases with radius.

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