Velocity Shear and Low-Frequency Plasma Instabilities

The effects of transverse velocity shear on the low‐frequency stability of a plasma are examined theoretically for a low‐β resistive plasma in a uniform magnetic field. Cylindrical geometry is used and the velocity shear is introduced by a nonuniform $\mathrm{E\hspace{0.17em}\times \hspace{0.17em}B}$ rotation. Both numerical and analytic methods are used. The principal analytic result is a dispersion relation for instabilities caused by a thin velocity shear layer. This dispersion relation describes the $Q$ machine edge oscillation, which is identified either as a Kelvin‐Helmholtz instability or as a velocity‐shear analog of the resistive drift wave, depending on the parallel wavelength. The numerical results show that properties of instabilities observed in several experiments agree reasonably well with theory. The effect of velocity shear on the drift instability is to make it into either a local or nonlocal type of normal mode.