Plasma Rotation and Instability in the Θ-Pinch Due to Transverse Magnetic Fields

Plasma rotation in a θ-pinch is analyzed theoretically on the basis of the mechanism proposed by Haines. The torque on the plasma is assumed to be due to the interaction of an axial Hall current with a weak transverse magnetic field component normal to the plasma axis. Such a transverse magnetic field is present when multipole fields of Ioffe type are used to prevent radial plasma drift. The Hall currents arise from the interaction of the main θ current with the transverse magnetic field. The problem is simplified by ignoring radial and axial plasma motion and assuming the plasma to be incompressible. The resistive decay of the plasma currents and the distortion of the initial transverse magnetic fields by the Hall currents are shown to be of primary importance in determining the characteristic growth time of rotation and the maximum rotational velocity. The condition for the appearance of flute instabilities as a result of plasma rotation is briefly discussed.