Abstract
The initial value problem of the toroidal ion temperature gradient mode is studied based on the Laplace transform of the ion gyrokinetic equation and the electron Boltzmann relation with the charge neutrality condition. Due to the toroidal magnetic drift, the Laplace-transformed density and potential perturbations have a branch cut as well as poles on the complex-frequency plane. The inverse Laplace transform shows that the temporal evolution of the density and potential perturbations consists of the normal modes and the continuum mode, which correspond to contributions from the poles and the branch cut, respectively. The normal modes have exponential time dependence with the eigenfrequencies determined by the dispersion relation while the continuum mode shows power-law decay oscillation. For the stable case, the long-time asymptotic behavior of the potential and density perturbations is dominated by the continuum mode which decays slower than the normal modes.
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