Electron-cyclotron maser observable modes

We investigate wave amplification through the electron-cyclotron maser mechanism. We calculate absorption and emission coefficients without any approximations, also taking into account absorption by the ambient thermal plasma. A power-law energy distribution for the fast electrons is used, as indicated by X-ray and microwave observations. We develop a model for the saturation length and amplification ratio of the maser, scan a large parameter space and calculate the absorption and emission coefficients for every frequency and angle. Previous studies concluded that the unobservable Z mode dominates in the nu(p) approximate to nu(B) region, and that millisecond spikes are produced in the region nu(p)nu(B) < 0.25. We find that the observable O and X modes can produce emission in the 0.8 < nu(p)nu(B) < 2 region, which is expected at the footpoints of a flaring magnetic loop. The important criterion for observability is the saturation length and not the growth rate, as was assumed previously, and, even when the Z mode is the most strongly amplified, less strongly amplified O or X modes are still intense enough to be observed. The brightness temperature computed with our model for the saturation length is found to be of order 10(16) K and higher. The emission is usually at a frequency of 2.06 nu(B), and at angles of 30 degrees-60 degrees to the magnetic field. The rise time of the amplified emission to maximum is a few tenths of a millisecond to a few milliseconds, and the emission persists for as long as new fast electrons arrive in the maser region.