The linear and nonlinear properties of a dust ion acoustic wave (DIAW) propagating in an electron-dust-ion plasma are investigated from both analytical and numerical perspectives by employing the two-fluid quantum hydrodynamic model. Ions and dust are assumed to be mobile while electrons are considered to be inertialess. Furthermore, quantum effects (diffraction as well as statistic) due to ions and electrons are incorporated. It is emphasized that the linear dispersion characteristics of the DIAW depend on the quantum diffraction effects of both ions and electrons as well as on the dust concentration. The one-dimensional Korteweg–deVries equation is derived for the quantum DIAW using the reductive perturbative technique. It is observed that the quantum electron diffraction term shrinks the width while the dust concentration enhances both the amplitude and width of the soliton.
A numerical modeling for the dynamics of an edge-localized mode(ELM) crash in the spherical tokamak is proposed with a consecutive scenario which is initiated by the spontaneous growth of the ballooning mode instability by means of a three-dimensional nonlinear magnetohydrodynamic simulation. The simulation result shows a two-step relaxation process which is induced by the intermediate-n ballooning instability followed by the m/n=1/1 internal kink mode, where m and n represent the poloidal and toroidal mode numbers, respectively. By comparing with the experimental observations, we have found that the simulation result can reproduce several characteristic features of the so-called type-I ELM 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 loss of plasma. Furthermore, the model is verified by examining the effect of diamagnetic stabilization and comparing the nonlinear behavior 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 formed in contrast to the ballooning case.
Nonlinear simulations based on the magnetohydrodynamic model have been executed to reveal the dynamics of the ballooning mode in the spherical tokamak plasma. The simulation results have reproduced the characteristic features of the edge-localized mode crash phase, where the filamentary structures are formed along the magnetic field in the edge region, and separated from the core plasma. Moreover, the finite Larmor radius effect is addressed.
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