A Simplified Model of Microwave Coupling in ECR Plasmas

A magnetized plasma strongly interacts with microwaves, when their angular frequency $\omega$ is around the electron cyclotron resonance (ECR) one, that is $\Omega=e\vert \mathrm{B}^{s}\vert /m_{e}$ , with $\mathrm{B}^{s}$ the static flux density. The case of small ion sources with $\mathrm{B}^{s}\cong 0.5$ to 1 T, where wavelength and plasma chamber radius are comparable, is studied with full wave equations, assuming a collision rate $v$ and a plasma of given density. Wave initially launched in the TE mode from a waveguide (TE 11 for a circular waveguide), aligned with the axis $z$ of a cylindrical plasma chamber and of $\mathrm{B}^{s}$ , are partially converted to $E_{z}$ waves; use of azimuthal symmetry to consider only the $m=1$ component is discussed. Large reflections are sometimes observed as a function of ratio of plasma angular frequency $\omega_{p}(z)$ and $\omega$ , possibly due to model simplification (density constant in $x$ and $y$ ). Extension to off-axis waveguides (perhaps rectangular or coaxial) is mentioned.