On the possibility of the sheath-driven, finite-beta modes localized near the divertor plate

It is shown that, in a finite beta plasma, there may exist sheath-driven modes whose amplitude decreases exponentially with the distance from the divertor plate. The modes are sensitive to the radial tilt of the divertor plate. The short-wavelength branch of the instability, with the cross-field wavelength lambda of the order of a few ion gyro-radii, is present in the case of a 'positive' tilt of the divertor plate, whereas the long-wavelength branch, with lambda, of the order of the 10 or so gyro-radii is unstable for the opposite sign of the tilt. The parallel e-folding length becomes less than the distance from the plate to the X-point (thereby making the mode insensitive to the processes near the X-point and the upper scrape-off layer) at plasma betas exceeding (2-3) x 10(-4). A detailed analysis of the dispersion relations is provided. The features of the modes that can be used for their experimental identification are discussed. It is pointed out that the analogue of these modes may also exist in linear plasma devices with shaped end electrodes.