Quantum relativistic theory of the cyclotron radiation in strongly-magnetized plasmas: Fine structure of the spectra and maser effect

Full quantum relativistic treatment of the cyclotron/synchrotron emission and absorption in tenuous plasma with superstrong magnetic fields is developed for the case when the radiation modes are linearly polarized. Spectra of emission, absorption and polarization are investigated both analytically and numerically for the thermal distribution of the radiating particles and for distribution with anisotropic temperature. Quantum relativistic effects lead to a fine structure of the cyclotron harmonics with typical spacing (at B ≪B_c = 4.41 × 10¹³ G) ∼vΩ_B(B/B_c), where ν=1,2, ... is the harmonic number, and Ω_c is the cyclotron frequency. The fine structure is the most developed for subrelativistic temperatures and magnetic fields at not too small angles {Mathematical expression} between the field and the wave-vector. For essentially non-relativistic temperatures the fine structure can be observed in a wide angle range, {Mathematical expression}, if {Mathematical expression}, i.e., for distributions with strong transverse anisotropy T_⊥≫T_{{norm of matrix}} The transverse anisotropy may also lead to the maser amplification of the cyclotron radiation in the narrow frequency ranges corresponding to the fine structure peaks in the emissivity spectra. This occurs for sufficiently high fields B≥B_c(T_{{norm of matrix}}/T_⊥), and angles {Mathematical expression} not too close to 0 or π/2. These effects can be observed in X-ray and gamma-ray radiation of the objects associated with strongly magnetized neutron stars (particularly of the gamma-ray bursters).