Abstract
A theory is developed for electrostatic waves with frequency ω below the ion bounce frequency ωbi in a plasma confined by a magnetic quadrupole. The dispersion equation for flute modes is derived in the form of a fourth-degree polynomial equation in ω with the effects of temperature gradients, first-order effects of curvature and finite ion Larmor radius, and terms of order ω2/ω2bi included. Growth rate and dispersion curves are calculated for flute modes in the shared flux region of the quadrupole at the University of Manchester Institute of Science and Technology. The present theory predicts an unstable mode with frequencies of the order of 1 kHz propagating in the electron diamagnetic drift direction as observed experimentally.
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