| Abstract
| - Abstract. The steady state self-focusing of a Gaussian electromagnetic beam in a magneto-plasma has been studied. On a short time scale, a non-linearity in the dielectric constant of a plasma appears due to the ponderomotive force. This force in the case of the extraordinary mode has opposite signs forω>ωc andω<ωc, whereωc is the electron cyclotron frequency. The self-focusing due to this effect is predicted at frequencies except forωc/2<ω<ωc. The focusing of the ordinary mode is adversely affected by the magnetic field. On a larger time scale, the non-uniform heating of electrons by the beam and the resulting redistribution of the electron density is a source of non-linearity. This non-local non-linearity is several orders of magnitude higher than the ponderomotive non-linearity. We predict self-focusing of the extraordinary mode only above the gyroresonance (ω>ωc), while the ordinary mode can be focused at all frequencies.
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