The effect of electron-electron collisions on the potential of a slowly moving test charge in a plasma is considered. A new dipole-like term is found.
IntroductionThe electric field of a moving test charge in a uniform plasma has recently received increased attention. Thus, Montgomery and others [1,2] considered the far-field potential of a test charge in a collisionless plasma and found that it can decrease as the inverse cube of the distance. The effect of collisions has been considered recently [3,4] using simple models. It was found that an inverse-square distance dependence can appear. This conclusion is clearly of sufficient interest to justify further investigations of collisional effects. In this paper we reconsider the problem by means of a full BGK model collision operator [5]. In addition we show explicitly that some of the results [c.f. (18)] can be demonstrated to be valid for arbitrary collision processes.The full BGK collision term [5] conserves number density, momentum and energy. Thus it describes electron-electron scattering which cannot be accounted for by the simple BGK model [3] in which momentum is not conserved. For the same reason the present model does not correspond to any collisional contributions within a conventional macroscopic analysis [4]. The results in this paper are thus complementary to those of Refs.[3] and [4] in which electron-ion and electron-molecule collisions are treated. Finally we demonstrate that ion motion can be significant if the test charge velocity is very small.
Basic FormulationWe consider a homogeneous, isotropic electron plasma in the absence of external fields. The test particle is not affected by collisions in our model and it travels at a constant velocity Vo. where -qNo and qt6 (X-Vot) are the charge densities of the positive background and the test charge, respectively, and r is the potential due to the presence of the latter. The distribution function for the electrons is denoted by f, and C is the collision term [5]. The constant parameter v represents the electron-electron collision frequency. The density, mean velocity and normalized temperature are given by the following moments of the distribution function,
This paper considers the anomalous growth of the radiation intensity, which is caused by an EM wave incident on an inhomogeneous nonstationary plasma. The amplitude of the reflected signal can thus during relatively short time intervals be larger than that of the incident wave. The reason is that the plasma parameters can pass through values, for which linear resonance of leaking surface waves exist. An analytical expression is obtained for the maximum value of the intensity of the reflected wave for two different plasma density profiles, interacting with waves of different polarization. It is shown that the effect can occur repeatedly in a nonstationary plasma with a nonmonotonous density profile, if the region, where the inhomogeneity gradient changes sign, increases.* Below we consider only the case where the planes defined by the vectors k , , E and k, , 6 , ( 6 , is the unit vector along the z-axis) are identical.
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