不同类型偏振辐射的统一描述
Universal description for different types of polarization radiation
摘要：
当带电粒子在空间不均匀的凝聚介质附近或内部运动时，可能会产生不同类型的辐射：衍射辐射（DR），Smith-Purcell辐射（SPR），过渡辐射（TR），Cherenkov辐射（CR）等。我们指出，所有这些现象都可以用一种非常简单而普遍的方法来描述，其中场源是粒子外场在介质内部感应的极化电流密度，这是所有这些辐射过程物理等价性的直接证明。用这种方法找到了一个基本辐射问题的精确解：粒子通过任意宽度和介电常数$ε(ω) = ε^{\prime} + i ε^{\prime \prime}$的屏幕中的圆柱形通道的发射。根据几何形状，获得的辐射能量的公式描述了不同类型的偏振辐射：DR，TR和CR。还考虑了粒子轴向穿过真空和有限半径等离子体柱之间的尖锐边界时产生的辐射的特殊情况。对于任意值的光栅介电常数，解决了粒子在一组薄矩形条（光栅）附近运动时产生的表面等离子体共振问题。本文给出了适用于任意距离（包括所谓的波前区）极化电流密度场的麦克斯韦方程组的精确解。该解描述了极化辐射的横向场和与介电常数零点相连的纵向场。
英文摘要：
When a charged particle moves nearby a spatially inhomogeneous condensed medium or inside it, different types of radiation may arise: Diffraction radiation (DR), Smith-Purcell radiation (SPR), Transition radiation (TR), Cherenkov radiation (CR) etc. Along with transverse waves of radiation, the charged particle may also generate longitudinal oscillations. We show that all these phenomena may be described via quite simple and universal approach, where the source of the field is the polarization current density induced inside the medium by external field of the particle, that is direct proof of the physical equivalence of all these radiation processes. Exact solution for one of the basic radiation problems is found with this method: emission of a particle passing through a cylindrical channel in a screen of arbitrary width and permittivity $ε(ω) = ε^{\prime} + i ε^{\prime \prime}$. Depending on geometry, the formula for radiated energy obtained describes different types of polarization radiation: DR, TR and CR. The particular case of radiation produced by the particle crossing axially the sharp boundary between vacuum and a plasma cylinder of finite radius is also considered. The problem of SPR generated when the particle moves nearby a set of thin rectangular strips (grating) is solved for the arbitrary value of the grating's permittivity. An exact solution of Maxwell's equations for the fields of polarization current density suitable at the arbitrary distances (including the so-called pre-wave zone) is presented. This solution is shown to describe transverse fields of polarization radiation and the longitudinal fields connected with the zeros of permittivity.
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