Plasma surface waves are excited by a high frequency field in a semi-infinite plasma with a plane boundary when omega0- omegapapproximately=+or-( omegap/ square root 2) and omega0- omegapapproximately=+or-( omegapsquare root 2)- omega0( omega0being the frequency of the high frequency field and omegapthe plasma frequency). The instabilities, in effect, take place at (nc/n0)=3, 8.5*10-2, 0.72 and 2*10-2, where ncand n0are the critical and the particle densities respectively. Threshold conditions are derived for plasmas with and without a low density electron beam. In the absence of the beam the thresholds are more than the relativistic limit while its presence reduces the thresholds considerably under certain conditions.
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