Hollow beam distribution of energetic electrons and higher harmonics of electron cyclotron maser

The variations of the growth rates of ECM at first four harmonics in X-, Z-, and O-modes excited by a hollow beam distribution of weakly relativistic electrons with a parameter _p/_e are presented in this paper. The results show that the second harmonic of ECM in X-mode dominates the instability if < 1, and if 1.2 , 2 or 2.2 3 the third or fourth harmonic will dominate. The second and third harmonics of Z-mode waves grow faster only if 2 2.2 and 3 3.2, respectively, so it would not be a competition in most cases. It is suggested that the ECM emission at these harmonics in X-mode is a possible mechanism to produce solar spike emissions with high brightness temperature at shorter and longer decimetric wavelengths.Proceedings of the Workshop on Radio Continua during Solar Flares, held at Duino (Trieste), Italy, 27–31 May, 1985.On leave from the Department of Astronomy, Nanjing University, Nanjing, The People's Republic of China.