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A numerical modelling of the dynamics of an edge-localized mode (ELM) crash in the spherical tokamak is proposed by means of a three-dimensional nonlinear magnetohydrodynamic simulation. The simulation result shows a crash of the edge pressure profile due to the spontaneous growth of the ballooning mode instability. The simulation result shows good agreement in several characteristic features of the experimental observation of large scale ELMs in an appropriate time scale: (1) relation to the ballooning instability, (2) intermediate-n precursors, (3) low-n structure on the crash, (4) formation and separation of the filament and (5) considerable amount of convective loss of plasma, where n is the toroidal mode number. Furthermore, the model is verified by examining the effect of diamagnetic stabilization and by comparing the nonlinear behaviour with that of the peeling modes. The ion diamagnetic drift terms are found to stabilize some specific components linearly; nevertheless they are not so effective in the nonlinear dynamics such as the filament formation and the amount of loss. For the peeling mode case, no prominent filament structure is found to appear in contrast to the ballooning mode case.

Three dimensional MHD simulations are executed in a full toroidal geometry to clarify the physical mechanisms of the internal reconnection event (IRE) which is observed in spherical tokamak experiments. The simulation results reproduce several main properties of IREs. A notable property in the linear growth of modes is the simultaneous excitation of multiple low n modes, which grow together with similar growth rates. A spontaneous phase alignment mechanism among these excited modes is found in the non-linear stage of the development, which causes a bulge-like deformation of the torus and subsequent expulsion of heat energy to the external region through the occurrence of external reconnection.

We have executed nonlinear magnetohydrodynamic simulations in a heliotron-type configuration with a large pressure gradient to reveal the nonlinear dynamics of a collapse phenomenon. The simulation results reproduce the qualitative characteristics of the experimental observation on the so-called core density collapse events in the Large Helical Device plasma with the super-dense core profile. A long-term nonlinear behaviour on the event, including the flushing mechanism of the core pressure, is clarified. The simulation result shows the linear growth of the ballooning-like resistive instability modes with the intermediate poloidal wavenumbers. The growth of the modes are eventually saturated, and the system experiences the energy relaxation in about 1 ms. It should be noted that the linear mode structures are localized in the edge region, whereas the core pressure rapidly falls as the system reaches the relaxed state. Such coexistence of the edge perturbation and the core collapse is consistent with the experimental observations. The lost pressure forms a wide base in the peripheral region. The core pressure is, on the other hand, remarkably reduced at a certain period, although it had well withstood the disturbance before it. The most salient feature on this period is the disordering of the magnetic field structure. The system keeps the nested-flux-surface structure well at the beginning, whereas part of them are abruptly lost in this period. Such a situation can induce a flattening of the pressure profile along the reconnected field lines. By checking the place where the plasma loss due to this mechanism occurs, such plasma outlets are found to be located mainly on the disordered region. Thus, one can conclude that the core collapse can be caused by the disturbance of the magnetic field.