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Notes: Abstract On the basis of [1] this note examines nonlinear electromagnetic phenomena in a dense plasma brought about by the variation in its electrical conductivity as the electrical field changes. It is well known that the electrical conductivity depends on the electric field strength due to the following causes. The electrons in moving in the electric field receive energy from the field which may be considerable over the free path length. However it is difficult for this energy to be transferred to the heavy particles. In monatomic gases the energy exchange between electrons and heavy particles comes about basically as a result of elastic collisions. Thus a noticeable difference in electron and ion temperature, determined by the electron energy balance taking radiation losses into account, turns out to be possible even for relatively weak electric fields. In molecular gases, on the other hand, the fundamental energy exchange mechanism is the excitation of the rotational and oscillatory degrees of freedom of the molecules. Thus the electron energy in these gases is dissipated relatively easily, and the electron temperature is not observed to be noticeably higher than the atomic temperature. The concept of the characteristic “plasma field” Ep is introduced in [2], which is determined for an Isotropic plasma by the relation $$E_R = \sqrt {3kTme^{ - 2\delta } (\omega ^2 + v_0 ^2 )} .$$ Here k is the Boltzmann constant, T is the plasma temperature in the absence of a field, m and e are the electronic charge and mass, & is the mean fraction of energy transferred to a heavy particle by an electron on collision,ω is the frequency of field variation, ν0 is the electron-ion collision frequency in the absence of a field. In weak electromagnetic fields (E≪Ep) the plasma maintains thermodynamic equilibrium, and the electrical conductivity of the plasma is independent of the field. In strong electric fields (E≫Ep) there is a sharp difference of electron temperature and the voltage-current characteristics of the plasma become nonlinear. The question of nonequilibrium electrical conductivity has been fairly fully studied [3–5] as regards monatomic gas plasmas like argon and potassium mixtures. It was shown in [3] that for the plasmas which were considered the dependence of the electrical conductivity on the electric field with no magnetic field present could be satisfactorily described by a power function of the absolute current density, i.e., σ =c∣j∣ γ , where c is a function of the atomic temperature. This function has also been confirmed experimentally for an argon-potassium plasma for a temperature of the order of 0.2 eV and a pressure of the order of 1 atm. [3]. In the following we consider electromagnetic phenomena in a dense plasma with an electrical conductivity of the type σ =c∣j∣γ when it is in motion in a traveling magnetic field. It is assumed that the plasma parameters and limits of variation of the independent quantities (j, Te) are such that the function σ =c∣j∣γ is stable [4]. In addition the plasma is taken as having the properties of an ideal incompressible fluid. These last assumptions together with the assumption that the gradients of static pressure and pondermotive forces are only in the direction of plasma motion allow us to commence from the equations of electrodynamics.