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Laser-beam propagation in a long solenoid

An analysis of the propagation of a laser beam in a cylindrical magnetically confined plasma with parabolic density profile is presented. The normal modes which are self-trapped are given. It is found that the largest mode that can be trapped by the plasma is given by (1/2) where R0 is the radius of the plasma column and w is the fundamental mode width. It is found that all the trapped modes in a finite plasma can easily propagate distances of the order of one kilometer. An exact solution for the amplitude of the electric field for an incident Gaussian beam has been obtained. The solution exhibits alternate focusing and de-focusing of the beam. The effect of this on the plasma heating is discussed.