the earlier results [2]. As a result of non-linear interaction between the laser beam and the REB, the energy of the laser beam is converted in two ways-(l) the acceleration of REB, and (2) a scattered wave with lesser frequency. The scattered wave is determined through the following dispersion relation; where w (w0) and k (&0) are a frequency and wave number of the scattered (incident) electromagnetic wave, wpe ( = (4^we2/»z)1/2) the plasma frequency of the REB, (y^CTtZoeVtnV)1/2) the cyclotron frequency defined by the magnetic field of the incident laser beam, ve the thermal velocity of the REB and y is defined by 1/(1- ©Vc2)1/2. Here n is the density of the REB, e the unit charge, m the mass of electron, Io the energy flux of the incident laser beam, v the velocity of the REB and c the speed of light. The dispersion relation (1) is derived under the following condition; where kD is defined by Wp/ve. This condition is satisfied for the REB having a satisfactorily small temperature (i.e. small velocity spread). When the scattered wave derived from Eq. (1) is unstable (i.e. an imaginary part of the complex frequency (a, (=Im(a>y) is positive), the growth of the unstable scattered wave and the acceleration of REB can take place. Fig. 2 shows the frequency of the scattered wave for typical parameters. The frequency of the scattered wave is lesser than that of the incident laser beam, and becomes smaller for greater y. The acceleration of the REB is caused by a plasma wave which is induced in the REB as a result of a nonlinear interaction between the laser and REB. The upper limit of the fraction of energy which is converted to the REB acceleration is
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