A model for ideal m=1 internal kink stabilization by minority ion cyclotron resonant heating

A generalized energy principle is used to determine the effect of ion cyclotron resonant heating (ICRH) on the stability of m=1 internal kink displacements in the low-frequency limit: such displacements are associated with sawtooth oscillations. An integral expression is obtained for the contribution to the plasma energy of an ICRH-heated minority ion population with strong temperature anisotropy, which relates the former to the ICRH power input and its deposition profile. The link is provided by a realistic, but analytically tractable, new model for the distribution function of the heated ions, which is based on the approach of Stix [Nucl. Fusion 15, 737 (1975)]. Numerical evaluation of the integral expression is carried out using parameters inferred from ICRH experiments in the Joint European Torus (JET) [Campbell et al., Phys. Rev. Lett. 60, 2148 (1988)]. It is shown that the ideal m=1 internal kink is stable at values of the poloidal plasma beta βp which typically lie in the range 0.4–1, depending on the radio-frequency power input and the radius r1 of the q=1 surface. Stability is thus possible at values of βp lying significantly above the magnetohydrodynamic instability threshold (≂0.3). If the perpendicular temperature T⊥ of the hot ions exceeds the parallel temperature by a factor of 10 or more, and r1 is greater than about one-third of the plasma minor radius, trapped ions have a greater stabilizing effect than passing ions. Stabilization is most easily achieved, however, if r1 is small. The hot-ion plasma energy depends strongly on the value of T⊥, but for fixed T⊥ is insensitive to the degree of anisotropy.