Finite β and nonlocal calculation of collisionless and dissipative drift instabilities

Collisionless and dissipative drift waves, driven by gradients in the plasma density and/or temperatures, are believed to dominate or at least influence the transport properties of a variety of plasma confinement devices. In a study begun in reference to transport in the Field Reversed Configuration (FRC), we have developed a theory of these waves in a high β plasma, including the effect of perturbed flow in the direction of the plasma density. This study was a natural extension of previous calculations; the β = 1 nature of the FRC makes a proper treatment of high β effects vital to an understanding of that device. In the course of this study we have obtained a comprehensive dispersion relation which shows clearly how the numerical dissipative drift wave instabilities evolve in wavenumber as β increases. A major finding from this is that the effect of finite β begins to dominate long before β → 1; the expansion parameter is βf(k, ai, K, ω, Ln) where f can be substantially greater than 1, depending on the wavenumber of the wave parallel to the magnetic field (K), the wavenumber parallel to the particle drifts (k), the wave frequency (ω), the strength of the density gradient (Ln), and the ion gyroradius (ai). The fact that finite β effects can onset for quite small β make this study applicable to confinement schemes such as tokamak in which β ∼ 1--10% in addition to the natural application to the FRC. A second surprising fact from the study was that including finite β could result in a compressional flow in the direction of the density gradient, and also a perturbed electric field in that direction, which changes the perturbed orbits