学位論文
学位: 京都大学論文博士(エネルギー科学), 2002年1月．
タイトル: Ideal Magnetohydrodynamic Spectra
of Static and Flowing Plasmas
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Abstract
One dimensional linear spectral properties for incompressible ideal magnetohydrodynamic (MHD) plasmas are explored for various situations.
The non-triviality of the problem mainly consists of two aspects.
One is that the infinite dimensionality of the generator induces continuous spectra.
The other is that the generator in case of finite shear flow becomes non-Hermitian (non-selfadjoint), which is not yet solved even in modern mathematics.
In addition to the viewpoint of mathematical physics, it is also deeply related to a future energy development, magnetic fusion.
For long sustainment of a fusion plasma, at least the linear stability of the equilibrium configuration is necessary.
Such stability analyses are accomplished by studying spectra of linearized MHD equations.
The spectral analyses are given for point spectra and continuous spectra for Hermitian operators (static equilibria).
Also, non-Hermitian problems due to the shear flow in magnetized plasmas are analyzed.
Point spectra and continuous spectra related to MHD modes are discussed, respectively, then the resonance between point and continuous spectra is investigated.
The main results are as follows.
Firstly, for static magnetized cylindrical plasmas, it is shown that the marginal stability is not described by the local criterion when pressure gradient disappears at the mode resonant surface.
Then the beta (ratio of plasma pressure to magnetic pressure) limit may increase for a stair-like pressure profile for a stellarator even with a magnetic hill.
For static magnetized slab plasmas with sharp density gradients, the rate of the shear Alfven continuum damping has been analytically calculated.
The result was compared with magnetic fluctuations observed in the pellet injection experiment of Heliotron-E.
Next, for a magnetized cylindrical plasma with a rigid plasma flow, the destabilizing mechanism of external kink mode has been clarified when the plasma is surrounded by a resistive wall.
Here, the closest position of the resistive wall to the plasma edge for the stabilization of resistive wall mode is proposed.
For a magnetized slab plasma with a linear flow and an ambient homogeneous magnetic field, complex behavior originating from the non-Hermiticity introduced by the shear flow has been shown for an interchange instability.
All linear instabilities will be suppressed asymptotically by the combined effect of Alfven wave propagation and linear flow profile with constant velocity shear.
Finally, for a slab plasma with a sheared flow, an exact spectral theory for a particular non-Hermitian flow profile has been constructed.
The mechanism of Kelvin-Helmholtz instability is clarified, and the eigenvalue problem is shown to be an incomplete approach.
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