An extended analytical model of electron pitch angle diffusion coefficients for electron cyclotron harmonic waves

Electron pitch angle diffusion coefficients for resonant interaction with electrostatic electron cyclotron harmonic (ECH) waves have been calculated. Calculations have been performed at five values of the ratio of electron plasma frequency to gyro-frequency (2.0, 4.77, 8.0, 12.0, and 18.0), thirteen values of electron energy between 1 eV and 10 keV, and four magnetic latitudes (0 ∘ , 1 ∘ , 2 ∘ and 2.5 ∘ ). A dipolar magnetic field model is considered. Numerical coefficients have been fitted with a simple analytical expression. Differences between analytical and numerical coefficients are generally within a factor of 2 or 3 in magnitude. However, larger differences are noticed above 50 ∘ pitch angle, higher than 1000 eV energies and also for 2 ∘ and 2.5 ∘ latitudes. Diffusion coefficients at 2 ∘ and 2.5 ∘ latitudes are found one to two orders of magnitude smaller in comparison with coefficients at the magnetic equator. Analytical expressions may be used to calculate local or bounce-averaged diffusion coefficients for arbitrary pitch angle, electron energy, ratio of electron plasma to gyro-frequency and amplitude of ECH wave’s electric field. Bounce averaged diffusion coefficients have been calculated using the analytical expressions. The results are compared with other earlier works. Further, analytical expressions are quite general and can also be used for planets other than Earth, e.g., Jupiter and its satellite–Ganymede, and Saturn where ECH waves have been observed.