Mhd Stability of Toroidal Plasma with Modulated Curvature Planar Magnetic Axis

Mercier‘s localized perturbed criterion of stability near an arbitrary modulated curvature magnetic axis of a non-circular toroidal plasma cross section is investigated. In this magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. The influence of the non-circular cross section of the magnetic surface and that of the modulation of the magnetic axis on the domains of equilibrium and stability are studied. 1. I N T R O D U C T I O N MERCER’S general geometric criterion of stability for a magnetic toroidal configuration of a modulated curvature magnetic axis and circular plasma cross section is calculated by SHAFRANOV (1968). ADAMS and MERCER (1969) and MIKHAILOVSKII and ABURDZHANNA (1978, 1979), but with a different method from that used here. In the present work, we study the equilibrium and analyze Mercier‘s criterion of stability (MERCER, 1964) near an arbitrary modulated curvature planar magnetic axis (with zero torsion and variable curvature) of non-circular (elliptically and triangularly deformed) toroidal plasma cross section with high pressure. A longitudinal uniform current is allowed to flow through the plasma. Also, we study the influence of the modulation of the magnetic axis on the equilibrium and stability of this plasma configuration. By introducing the coordinates (p, 8, s) (see Fig. 11, where (p. 8 ) is the polar coordinate and s is the curvilinear coordinate. The curvature of modulated curvature planar magnetic axis (hereafter referred to as m.a.) is represented by (l/R(s)) = ak exp (27~kislL) where a-l, = ack and L = $ ds is the total length of the magnetic axis. If all the k’s are even, this curve will be closed with a0 = 2 d L . The simplest form for the closed modulated curvature planar magnetic axis is given by: where F k = ak/ao is the depth of modulation and a. = 27~/L. At this point, one would like to mention that the magnetic surfaces rotate -k (= the number of modulation periods or the resonance index related to the resonant Fourier coefficient aL) times around the magnetic axis (Lcc er al.. 1974). This rotation d’(s)/2 (= 27rkiL) which is associated with the non-vanishing longitudinal current Is, is necessary in order to apply the method of helical images. Also, one can see from the equilibrium solution considered here, that this rotation is important when the magnetic surface chosen has a non-circular or circular (at * Present address: 10 Josyln St.. Newport. Maine 04953. U.S.A. 385