Two types of unstable eigenmodes of resistive tearing instabilities, namely, symmetric and anti-symmetric modes, in a double current sheet configuration are analyzed by means of both an eigenvalue solver and initial value simulation. It has been clearly identified that these two types of eigenmodes are different from the two independent single tearing modes even though the symmetric eigenmode in a double current sheet configuration shares the same properties of the single tearing mode near each current sheet. In the case with finite separation Δx between two current sheets, an arbitrary phase disturbance between two current sheets can lead to “phase instability,” i.e., the transition from the symmetric mode to the anti-symmetric mode. For a large Δx limit, both anti-symmetric and symmetric modes share the same properties of the single tearing mode. Thus, the superposition of two independent single tearing modes with arbitrary phases and arbitrary amplitudes at two current sheets can become the linear combination of symmetric and anti-symmetric eigenmodes. The same growth rate/eigenvalue of symmetric and anti-symmetric eigenmodes infers that an arbitrary superposition of two independent single tearing modes is still the eigenmode of the double current sheet configuration.

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对剪切板几何中双撕裂不稳定性的不稳定本征模的基本理解

通过本征值求解器和初始值仿真，分析了双电流板配置中两种类型的电阻撕裂不稳定性的不稳定本征模，即对称模和反对称模。已经清楚地识别出，即使在双电流板配置中的对称本征模式在每个电流板附近共享单撕裂模式的相同特性，这两种类型的本征模式也不同于两个独立的单撕裂模式。在具有有限的分离Δ的情况下X两个电流片之间，两个电流层之间的任意相位干扰可导致“相不稳定性”，即，从对称模式向反对称模式的转变。对于一个大的Δ X在极限情况下，反对称和对称模式都具有与单个撕裂模式相同的属性。因此，在两个电流面上具有任意相位和任意振幅的两个独立的单一撕裂模式的叠加可以成为对称和反对称本征模式的线性组合。对称和反对称本征模式的相同增长率/特征值可以推断出，两个独立的单撕裂模式的任意叠加仍然是双电流片结构的本征模式。