Theory of drift-universal and drift cone modes of collisionless plasma in cylindrical geometry
Thesis. The problem of the collisionless electrostatic drift universal and flute-like drift-cone instabilities of a hot, fully ionized plasma in a magnetic field in cylindrical geometry is considered. A discussion is given of the validity of the electrostatic approximation, and the restrictions of the electrostatic assumption on the value of BETA (ratio of plasma pressure to magnetic pressure). The work introduces a rigorous kinetic formulation of the radial eigenmode problem of a collisionless plasma in cylindrical geometry. The cylindrical model includes, in principle, those sources of free energy available to drive microinstabilities inherent in many plasmaconfinement devices, viz., radially varying density gradients, temperature gradients and temperature anisotropies in the directions perpendicular and parallel to the magnetic lines of force,- and velocity space loss-cone''-like distribution functions common to mirror devices. Our zeroth order density distribution is a Gaussian in the radial direction. The general problems of cylindrical equilibrium in the presence of gradients in the temperature and density, and velocity-space anisotropies are considered. A singular integral equation is derived for the Hankel transform for each azimuthal component of the perturbed electrostatic potential in the plasma. The treatment includes the finite Larmor radius corrections to all orders of a/sub i//R (a/sub i/ is the ion Larmor radius, R the plasma radius) for those cases for which the ratio is less than unity. The nature of the radial eigenmodes of the plasma are determined for the drift- universal and drift-cone modes of an inhomogeneous plasma without resorting to the local'' approximation often employed in the literature in solving the integrodifferential dispersion equation for the perturbed potential. The results give the cylindrical marginal stability boundaries for the drift and drift-cone modes for various values of the azimuthal mode number. The cylindrical results indicate that the critical values of R/a/sub i/ necessary to stabilize the drift- cone modes are substantially lower than those previously estimated by others. In particular, the cylindrical results are applied in the parameter regime suitable to the Livermore 2X machine, and it is found that stability is predicted for values of the azimuthal mode number, l, less than 5. The results for the drift- cone modes show that the threshold frequency is relatively insensitive to a/sub i/ /R, but is quite sensitive to the ratio of the ion to electron temperature. (auth)
- Research Organization:
- Massachusetts Inst. of Tech., Cambridge (USA)
- DOE Contract Number:
- AT(11-1)-2168
- NSA Number:
- NSA-29-009193
- OSTI ID:
- 4421166
- Report Number(s):
- TID-26472
- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 30-JUN-74
- Country of Publication:
- United States
- Language:
- English
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