The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet–Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

Abstract. An analytic expression is obtained for the free energy of fermions bound in an anisotropic harmonic potential in the presence of an arbitrary magnetic field, at a finite temperature. The specific heat and the magnetic moment are readily calculated. Our results consist of two parts, a steady part and an oscillatory one. The latter is similar to the well known de Haas-van Alphen oscillation, but persists in the absence of a magnetic field. Applications of our results to the nuclear shell model and surface effects of solids are briefly discussed.