Analytical bounds on the whistler mode refractive index

The refractive index mu for whistler mode plane waves in a magnetized electron-proton plasma is considered as a function of normalized wave frequency omega/Omega(e) at fixed density and angle of propagation. A factorization into an increasing function of frequency times a decreasing function of frequency is found, valid for any value of omega(pe)/Omega(e), for omega between (Omega(e)Omega(i))(1/2) and the smaller of Omega(e) and omega(pe). This leads to lower and upper bounds on mu(2) over any given frequency subinterval. The bounds can be directly applied to a quasilinear formulation of velocity-space diffusion of electrons in the Earth's radiation belts, in a generalization of previously developed techniques to low density conditions found outside the plasma pause. (C) 2004 American Institute of Physics.