Magneto-acoustic oscillations in a toroidal plasma

Theory of plasma heating by low frequency waves: Magnetic pumping and Alfvén resonance heating

“…It should be borne in mind that this method is rather generic, since it can be used in conjunction with any dissipative mechanism. The magnetoacoustic resonance involving collisional dissipation was studied in a number of papers by the Fribourg group [10,14,[16][17][18]23] in the late 1960s and early 1970s, and by the Australian group [41][42][43][44] in the late 1970s (see also Ref. [45]).…”

Parametric decay of magneto-acoustic oscillations in a cylindrical plasma

“…The possibility of parametric decay of magneto-acoustic oscillations into Alfve'n waves predicted theoretically by Montgomery & Harding (1966) and Vahala & Montgomery (1971), and certain aspects of the theory were verified experimentally by Lehane & Paoloni (1972), who observed the amplification of a launched torsional Alfve'n wave propagating in a region of magnetic field modulation. The general theory of parametric interactions is well known (see, for example, the review by Nishikawa & Liu (1976)) and interactions involving magnetohydrodynamic waves, in particular, have been studied in considerable detail (Cramer , 1976(Cramer , 1978Cramer & Hewitt 1975).…”

“…In the absence of modulation e = 0, and (8)-(10) are the linearized equations for MHD waves in a fully ionized, resistive plasma column. It is known (Sy 1977) that introduction of new variables…”

“…The excitation of two fast waves is strongly dependent upon the boundary conditions applied to the fields, because this wave does not propagate at a frequency less than the cut-off frequency w c = v A k c0 , where k cQ is the lowest value of k c given by (23). We may note that Vahala & Montgomery (1971) introduced uniformity of the pump by assuming that the relation w 0 a/v A = ye% held true, where a is the plasma radius and y is a number of O( 1), which results in the following simplification of the radial dependence of the pump fields:…”

“…(54) Since nonlinear dissipation is important when y > y u equations (53) and (54) yield a threshold condition given by For typical TO-1 tokamak parameters (Ivanov & Kovan 1975)^" ~ 0-02, whilst for typical TMI-VCh parameters (Vdovin et al 1973) !F ~ 0.1. However, it should be stated that in actual tokamak experiments toroidal effects tend to reduce field amplitudes at resonance (Sy 19786). Hence (52) represents an overestimate of e and the threshold amplitude given by (55) should be regarded as a lower bound for these applications.…”