Electrostatic electron–cyclotron harmonic instability in outer planetary magnetospheres

Electrostatic electron–cyclotron harmonic (ECH) instability in the magnetospheres of the outer planets: Jupiter, Saturn, Uranus and Neptune is investigated using a kappa distribution with loss-cone for energetic electrons in the tail of the distribution function. We use a particle distribution function, which is a superposition of cold (Maxwellian) and hot suprathermal (kappa) electrons in conformity with the observations. A linear instability analysis is used without making any further approximation. Normalized temporal growth rates have been obtained at two radial distances for each planet. Peak growth rates have also been studied as a function of the cold electron density (nc), hot electron density (nh), cold electron temperature (Tc), hot electron temperature (Th) and radial distance to the planet (R). Calculated normalized temporal growth rates for ECH bands are found highest at Uranus. The relative amplitudes of the ECH bands and the number of bands strongly depend on the angle (ψ) between the wave normal and the ambient magnetic field. Frequency within the band shifts in general to a higher value as the angle ψ is reduced. Results of our calculations are discussed in the light of observations of ECH bands at outer planets.