Abstract
In this paper, the Maxwell equations for the electric field in a cold magnetized plasma in the half-space of x≥0 cm are solved. The boundary conditions for the electric field include a pointwise source at the plane x=0 cm, the derivatives of the electric field that are zero statV/cm2 at x=0 cm, and the field with all its derivatives that are zero at infinity. The solution is explored in terms of the Laplace transform in x and the Fourier transform in y-z directions. The expressions of the field components are obtained by the inverse Laplace transform and the inverse Fourier transform. The saddle-point technique and power expansion have been used for evaluating the inverse Fourier transform. The model represents the propagation of a lower hybrid wave generated by a pointwise antenna located at the boundary of the plasma. Here, the antenna is the boundary condition. The validation of the model is performed assuming that the electric field component Ey=0 statV/cm and by comparing it with the model of electromagnetic waves generated by a local small antenna located near the boundary of a tokamak, and an experiment is suggested.
Highlights
In order to study the propagation of an electromagnetic (EM) wave inside the boundary of a tokamak, where the cold plasma approximation can be performed, we solve the Maxwell equations for a wave generated by a small antenna outside the plasma
The present study is a first attempt towards the development of diagnostics based on the onset of parametric instabilities driven by lower hybrid (LH) waves (LHWs)
We formulated a system of Maxwell equations for a magnetized cold plasma, which simulate the physical process of a point-like source localized in the origin (0, 0, 0) cm and a plasma located in the x ≥ 0 cm half-space
Summary
In order to study the propagation of an electromagnetic (EM) wave inside the boundary of a tokamak, where the cold plasma approximation can be performed, we solve the Maxwell equations for a wave generated by a small antenna outside the plasma. A proper solution of this equation system with suitable boundary values appears to be extremely complicated in a very simple geometry including a reduced model for the plasma density and magnetic field, which can be taken as constant all over the plasma space in the first attempt This last assumption can be naively justified considering that the wavelength involved in the process satisfies the inequality λ L, where L is the variation scale length of the macroscopic plasma parameters of density and confining magnetic field. We solve this model using the same analytical method, compare it with existing theoretical and experimental results, and propose an experiment.
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