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本文处理了锐边界椭圆截面等离子体柱的扭曲不稳定性,给出了用椭圆特征函数表示的色散关系的一般形式,对单模和两模扰动,给出了精确到椭圆率ε二级的结果。在任意椭圆率下进行了数值计算。结果表明,模数之间的耦合起解稳作用。当椭圆率增大时,稳定性所需的qΣ值迅速增加,在无导体壳和a/b>2时,近似地有qΣ-1∝(a/b)2。对于有限长度的系统,波长等于系统长度的扰动是最危险的。在小椭圆率情况下,对此种扰动而言,当系统的长度缩短(相应于环径比减小)时,对应的系统稳定性qΣ值仅稍为增大一点。导体壳有一定的稳定作用。但当变形足够大时,扰动的有限波长和导体壳的存在对系统稳定性qΣ值几乎没有多少影响。Kink instabilities of a sharp boundary plasma column with elliptical cross-section are studied. A general form of dispersion relation expressed in terms of elliptical eigenfunctions and analytical results for single-mode and double-mode perturbation (to second order in ellipticity ε) are given. For an arbitrary ellipticity, numerical calculations are carried out.Numerical results show that the coupling among modes has a destabilizing effect. qΣ required for stability increases rapidly with e. Accordingly, the number of coupled modes to be taken into account will also increase. When the coupled modes for a given e increases to a certain number, qΣ approaches a limit. With a/b > 2 and in the absence of a conductive shell, we obtain approximately: qΣ-l∝(a/b)2. For a system of finite length, perturbations having wavelength equal to the system length are the most dangerous ones. In the case of small ellipticity, as the system length shortens (i.e. the aspect ratio decreases) the value of qΣ required for those perturbations increases only slightly. A conductive shell close to the plasma has a stabilizing effect to some extent. However, if a/b is large enough, either perturbation with finite wavelength or any conductive shell has hardly any effect on the value of qΣ. In addition, in the presence of a conductive shell, qΣ changes abruptly at certain values of a/b. The stability condition is more stringent in the high-β system than in low-β system.
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