Equilibrium of a toroidal pinch in a static magnetic field and in a high-frequency large-amplitude field

The authors consider the equilibrium confinement of a toroidal plasma pinch in a static magnetic field and in a high-frequency large-amplitude field in the general case where the gas-kinetic plasma pressure NT is comparable with the pressure of the high-frequency field . It is assumed that the high-frequency field in the range of frequencies 1-10 MHz has a helical or multipole configuration and is excited by given external high-frequency currents passing through the current sheath surrounding the pinch.At high amplitudes of the high-frequency field, it is necessary to allow for the effect of the toroidicity of the system on the equilibrium conditions. In a first approximation with respect to the small parameters Δ/rp and rp/R (Δ is the displacement, rp is the radius of the pinch, R is the major radius of the torus) expressions are found for the high-frequency fields in a system with a displaced pinch and the condition for equilibrium of the pinch as a whole along the major radius is obtained. The equilibrium displacement of the pinch is determined from this condition, making use of the field values of the first approximation at the plasma boundary.It is shown that the use of high-frequency large-amplitude fields offers additional possibilities of controlling the equilibrium displacement. In particular, the effect of the toroidicity of the high-frequency field leads to the occurrence of an additional foree, which in a number of cases causes the pinch to be displaced to the inner wall of the toroidal chamber. When , it is also possible to have a paramagnetic effect when the pinch is forced out by a non-uniform static field towards the side where the intensity of the field is higher, i.e. to the inner wall of the torus. Under certain conditions the phenomena making positive or negative contributions to the equilibrium displacement of the pinch may be mutually compensating, so that the displacement can be made fairly small or even eliminated by suitable choice of the system parameters.The minimum displacement of the pinch for a given amplitude of the high-frequency current in the circuit practically always occurs in the case of quadrupole systems.It is shown that equilibrium confinement of plasma by high-frequency fields is also possible in systems where the plasma pinch is surrounded by a continuous conducting shell (so-called "high-frequency tokamak").The theoretical results obtained are in agreement with the results of experimental investigations.