Theoretical Investigations of Drift Waves in a Magnetic Quadrupole.

The objective of this research is to develope theories and conduct numerical investigations of electrostatic drift waves in a plasma confined in a magnetic quadrupole. A linear theory is developed for drift waves with frequencies between the electron and ion bounce frequencies in a collisionless plasma confined to a magnetic quadrupole. An integro-differential eigenvalue equation which allows for large ion-Larmor-radius effect, temperature gradients, and radial variation of the eigenfunction is derived from the linearized Vlasov equation. The fundamental drift mode observed in the UMIST steady-state quadrupole has one full wavelength around a closed magnetic field line with the electrostatic wave potential antisymmetric about the maximum field points. By numerical solution of the eigenvalue equation, the theoretical dispersion curve for this mode is extended to short wavelengths and the variation of the corresponding potential along a field line is determined. The drift wave instability in a magnetic quadrupole is studied. Formulas are derived for the growth rate due to a dissipative trapped-electron mechanism and the damping rate due to ion viscosity. A numerical study is made of the drift waves which occur spontaneously in the shared flux region of the UMIST quadrupole. The effects of electron-neutral collisions on drift waves in a plasma confined by a magnetic quadrupole are investigated. A new formula for the growth rate is derived which includes nondetrapping as well as detrapping collisions and is not based on the small ion-Larmor-radius approximation. A numerical study has been made of the fundamental drift mode and the next harmonic which has two full wavelengths around a closed magnetic field line. The damping rates of electrostatic waves due to ion-ion and ion-neutral collisions in a plasma confined by a magnetic quadrupole are investigated. Calculations of the damping rates are made for the fundamental drift mode observed in the UMIST quadrupole. Finally a numerical method of solving the integro -differential eigen value equation is presented.