# Analytical Solution of the O-X Mode Conversion Problem

## TL;DR

This paper provides an analytical solution to the O-X mode conversion problem in overdense plasma, deriving a formula for the angular dependence of the transmission coefficient.

## Contribution

It introduces an analytical approach using parabolic cylinder equations to solve the mode conversion problem in plasma physics.

## Key findings

- Derived an explicit formula for the transmission coefficient's angular dependence.
- Solved the mode conversion problem analytically in the context of overdense plasma.
- Provided insights into wave behavior at the critical layer in plasma.

## Abstract

The excitation of a slow extraordinary wave in a overdense plasma from an ordinary wave impinging on the critical layer in the plane spanned by the density gradient and magnetic field is solved analytically by formulating the problem in terms of a parabolic cylinder equation. A formula for the angular dependence of the transmission coefficient is derived.