Collin variational study of charged conductors' energy in plasma environment

Abstract

Plasma, as a special state of matter, has an effect on its inner conductors. Practically in the plasma environment, the effect may induce surface to charge and discharge, and may degrade the performance of spacecraft. Therefore, this effect needs to be further studied in the electromagnetic compatibility. The energy in a conductors' system is a key factor of the effect, which can also be used to depict the system consisting of relevant conductors and plasma environment. In order to investigate the essence of the system, the variational method is adopted. So with considering the electromagnetic compatibility and protection of this system, the energy of related conductors should be estimated by the theoretical method in the plasma environment. In the stochastic movement, electrons are faster than the irons. Therefore, the negative energy is cumulated. Considering the definition of capacitance, the system energy can be represented by the conductor capacitance and charging potential. Meanwhile, from the plasma kinetic theory, the potential can be obtained in the steady state. Thus, the relations among electromagnetic parameters of conductors, environmental features of plasma, and systematic energy are established, from which the corresponding Collin principle is also investigated. The principle indicates the system essence in the complex electromagnetic environment. In order to illustrate the utility of the variational principle, a simple cubic model is theoretically analyzed directly. From the typical instance, the relation between the geometric dimension and electric energy is illustrated, which is in consistence with the results in the early literature. The relation between secondary electrons and systematic energy is also analyzed. Starting from these theoretical investigations, in order to estimate the complicated structures, the analysis needs to be generalized further. With the assistance of discrete technology, the numerical method is established for analyzing the system energy of the complex conductive system in plasma environment. The generalized method is based on the equation with integral operator, in the calculation of which the method of moment is practically employed. As an application, the estimated energy of cube in plasma environment is compared with the theoretical estimation and the numerical estimation, which are in good agreement with each other. And then a composited structure is numerically analyzed. Obviously, the vairational analysis is beneficial to investigating the physical and principal regulation for conductors in the plasma environment, and the generalized method has wide potential applications in controlling the energy of complex charged conductors, electromagnetic protection, compatibility engineering in plasma environment, etc.