Estimates of lifetimes against pitch angle diffusion

We consider timescales on which particle distributions respond to pitch angle diffusion. On the longest timescale, the distribution decays at a single rate independent of equatorial pitch angle α0α0, even though the diffusion coefficient, and the distribution itself, may vary greatly with α0α0. We derive a simple integral expression to approximate this decay rate and show that it gives good agreement with the full expression. The roles of both the minimum and loss cone values of the diffusion coefficient are demonstrated and clarified.