Dynamic Instability Criterion for Circular String Loops
Dynamic Instability Criterion for Circular String Loops
复制标题
圆弦环的动态不稳定性准则
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
X. Martín
中科院分区：
文献类型：
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作者：
B. Carter;X. Martín
本文导出了一个弹性弦模型的一般定态的动力学微扰方程，该模型是一种适合于表示超导宇宙弦的模型。在闭合弦环的圆平衡态的情况下，证明了基本轴对称（n = 0）和最低阶（n = 1）非轴对称微扰模永远不会不稳定。然而，高阶（n ≥ 2）模的稳定性与纵向扰动的特征传播速度c和相应的外部扰动速度v密切相关。对于每一个模式数的不稳定性的标准是存在的非实根的某一立方本征值方程相应的模式频率。对于所有根的真实性和因此不存在不稳定性，一个非常简单的充分但非必要的条件是特征速度比c/v大于或等于1。对低速（实验上可达到的）非相对论区的进一步研究表明，在该极限下，不稳定性的判据是无量纲特征比c/v小于临界值χc，其数值约为1 2。在与超导宇宙弦相关的相对论体系中，情况相当微妙，需要更详细的研究，但推迟到未来的工作。
Abstract Dynamic perturbation equations are derived for a generic stationary state of an elastic string model-of the kind ppropriate for representing a superconducting cosmic string - in a flat background. In the case of a circular equilibrium state of closed string loop it is shown that the fundamental axisymmetric (n = 0) and lowest order (n = 1) nonaxisymmetric perturbation modes can never be unstable. However, stability for modes of higher order (n ≥ 2) is found to be nontrivially dependent on the values of the characteristic propagation velocity, c say, of longitudinal perturbations and of the corresponding extrinsic perturbation velocity, v say. For each mode number the criterion for instability is the existence of nonreal roots for a certain cubic eigenvalue equation for the corresponding mode frequency. A very simple sufficient but not necessary condition for reality of all the roots and therefore absence of instability is that the characteristic velocity ratio, c/v be greater than or equal to unity. Closer examination of the low velocity (experimentally accessible) nonrelativistic regime shows that in that limit the criterion for instability is just that the dimensionless characteristic ratio c/v be less than a critical value χc whose numerical value is approximately 1 2 . In the relativistic regime that is relevant to superconducting cosmic strings the situation is rather delicate, calling for more detailed investigation that is postponed for future work.