The Frequency shift of an extraordinary (X) wave propagating through plasma

The frequency shift is obtained for an extraordinary electromagnetic wave propagating through plasma as function of an external magnetic field. A linear theory is used here to calculate the frequency shift, and the numerical results are given for typical laboratory fusion plasma. A limit case where the wave is propagating through rarefied plasma in the presence of some weak magnetic field is also studied. Estimation is given on the basis of some simplifying approximation for the frequency upshift of a type III radio bursts interacting with the Earth's magnetosphere.