A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions
A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions
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无贝塞尔函数乘积的无限和的热磁化等离子体的等离子体磁化率张量的新推导
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
R. Davidson
中科院分区：
文献类型：
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作者：
H. Qin;C. Phillips;R. Davidson
热磁化等离子体的磁化率张量通常用贝塞尔函数乘积的无穷和来表示。对于粒子回转半径大于波长的应用，例如与低混合波相互作用的 α 粒子动力学，以及使用螺线管场聚焦带电粒子束，无限和会缓慢收敛。在本文中，提出了等离子体磁化率张量的新推导，它利用粒子轨道的对称性来简化沿未扰动轨迹的积分。结果，传统表达式中出现的无限和被一个回旋周期内的定二重积分所取代，并且所有阶的回旋共振都被单个项捕获。此外，二重积分可以用复阶贝塞尔函数来执行和表达，与先前使用纽伯格和规则推导的表达式一致。从这个新配方...
The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle’s gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle’s orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulatio...