Resonant Interactions between Particles and Normal Modes in a Cylindrical Plasma
Resonant Interactions between Particles and Normal Modes in a Cylindrical Plasma
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圆柱形等离子体中粒子与简正模之间的共振相互作用
DOI：
10.1063/1.1693439
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发表时间：
1971
影响因子：
4.6
通讯作者：
A. Kaufman
中科院分区：
文献类型：
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作者：
A. Kaufman
本文研究了一种圆柱对称的等离子体位形，其中包含轴向和方位向磁场以及径向电场，且电场沿径向任意变化。粒子运动由三个精确的作用量不变量参数化：径向作用量、正则角动量和正则轴向动量;在小回转半径的极限下，它们等价于磁矩、径向导向中心位置和平行速度。微扰的弗拉索夫-麦克斯韦方程组导致一组简正模，它们可以与粒子共振相互作用。这种相互作用的量子速率方程，连同能量守恒定律、角动量和轴向动量，导致（在经典极限下）粒子作用空间中的福克-普朗克方程，以及模能量的演化方程。这些耦合的动力学方程满足H定理，这意味着正则分布的单调逼近：粒子的刚性转子分布和模式的广义瑞利-金斯分布。然而，这种渐近状态可能是无限制的。量子跃迁几率是从发射率的经典计算中推导出来的。得到了模式增长率和粒子扩散张量的显式表达式。最后，通过使用Kramers-Kronig关系，从生长速率推导出Vlasov电导率核。
A plasma configuration with cylindrical symmetry is studied, containing axial and azimuthal magnetic fields and radial electric field, with arbitrary radial variation. The particle motion is parameterized by three exact action invariants: radial action, canonical angular momentum, and canonical axial momentum; in the limit of small gyroradius they are equivalent to magnetic moment, radial guiding‐center position, and parallel velocity. The perturbed Vlasov‐Maxwell equations lead to a set of normal modes, which can interact resonantly with the particles. The quantum rate equations for this interaction, together with the laws for conservation of energy, angular momentum, and axial momentum, lead (in the classical limit) to a Fokker‐Planck equation in action space for the particles, and to an equation of evolution for mode energy. These coupled kinetic equations satisfy an H theorem, which implies a monotonic approach to a canonical distribution: a rigid‐rotor distribution for particles, and a generalized Rayleigh‐Jeans distribution for the modes. This asymptotic state may, however, be unconfined. The quantum transition probability is deduced from a classical calculation of emissivity. Explicit expressions are obtained for the mode growth rate and for the particle diffusion tensor. Finally, the Vlasov conductivity kernel is deduced from the growth rates, by the use of the Kramers‐Kronig relations.