Nonlinear treatment for solar radio spikes - I. Basic equations

We emphasize that a nonlinear treatment is required to realize the diagnostic potentiality of solar spiky emission. The observational constraints including the latest data on the harmonic structure, degree, and sense of polarization are discussed. A set of coupled equations for energy density of high-frequency normal modes of a magneto-active plasma involving the most important nonlinear effects within the three-wave approximation is deduced. The equations include both previously known and new effects. The qualitative evaluations of the equations obtained have provided a few new findings: (i) quasi-linear relaxation of fast electrons on quasi-potential waves (ω_) occurs in a characteristic time scale of the order of 10 ms if the frequency, f, is about 1 GHz; (ii) the stimulated scattering of the transverse waves on the background plasma particles is shown to be important if the brightness temperature of the spiky emission exceeds 10¹⁵-10¹⁶ K; (iii) the Raman scattering of the transverse waves on background plasma density inhomogeneities may suppress the electron cyclotron maser instability if 〈Δn_e²〉/n_e² ≳ 3 × (10^-4-10^-5).