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.