Gyroresonance radiation produced by proton and electron beams in different regions of the magnetosphere

The gyroresonant interaction of an electron or proton beam with electromagnetic waves is studied at frequencies below the electron gyrofrequency ωB. Attention is drawn to the two cases of double roots that occur in the equation giving the emitted frequencies for a proton beam interacting with a whistler wave (p, R interaction). The emitted frequencies are very near to half the electron gyrofrequency (ωB/2) and twice the proton gyrofrequency (2ΩB). Three preferred regions of interaction exist in the magnetosphere, one in the equatorial plane and two at low altitudes <1200 km). It is suggested that the ‘high’ frequency radiation (ω ≃ ωB/2) is part of the explanation of the enhanced radio noise recently observed near 0.7 Mc/s by spaceborne equipment. Assuming mean values for the ionospheric parameters, calculations are made of the emitted frequency, altitude of emission, and energy of the interacting particles, for two different latitudes. The possibility of reflection of both waves and particles near the ends of the magnetic lines of force is taken into account, and the results are shown to be quite different from those for the homogeneous case. Amplification coefficients for the two double roots (ω ≃ ωB/2, ω ≃ 2ΩB) and for asymptotic cases (ω ∼ ωB, ω ∼ 0) are calculated, and comparisons are made with the (e, L) interaction (electrons and left-hand wave). It is shown that, for interactions over some finite length lc, protons are more efficient than electrons, and that the maximum amplification does not depend on the plasma parameters but only on the beam density n. Its value, 1.8×10−9 n1/2 le, in MKSA, is of the order of 5 db for realistic assumptions concerning n and le.