Nonlinear island dynamics

Coherent non linear magnetic structures, such as magnetic islands, have been widely studied in the limit of zero frequency. In this case the plasma current density distribution is constant on magnetic surfaces. In high temperature plasmas however, small amplitude magnetic perturbations, such as resistive instabilities, are found to propagate with a finite frequency when diamagnetic and/or finite gyro-radius effects are accounted for. It is thus important to investigate the dynamics of propagating nonlinear magnetic structures. Such structures are characterized by a current density distribution that is no longer constant on magnetic surfaces and to develop large currents at magnetic separatrices. In the highly non-collisional regimes of interest, an important effect limiting these large currents comes from the inertia of the electrons. In these regimes the conservation of the magnetic flux is replaced by the conservation of the generalized electron fluid momentum. In this paper we derive a set of non-linear two-component equations which describe single helicity perturbations and investigate the effect of electron inertia. A preliminary discussion is presented of the solutions in regimes where the amplitude of the perturbations exhibit spatial variations on a scale which is small compared to the ion gyro-radii. In the opposite limit, where the scale is large compared to the ion-gyroradii, the electric potential maintains the same functional dependence on the helical flux function. (author) 3 refs