  We consider the weak turbulence of whistler waves in the in low-\beta\ inner
magnetosphere of the Earth. Whistler waves with frequencies, originating in the
ionosphere, propagate radially outward and can trigger nonlinear induced
scattering by thermal electrons provided the wave energy density is large
enough. Nonlinear scattering can substantially change the direction of the wave
vector of whistler waves and hence the direction of energy flux with only a
small change in the frequency. A portion of whistler waves return to the
ionosphere with a smaller perpendicular wave vector resulting in diminished
linear damping and enhanced ability to pitch-angle scatter trapped electrons.
In addition, a portion of the scattered wave packets can be reflected near the
ionosphere back into the magnetosphere. Through multiple nonlinear scatterings
and ionospheric reflections a long-lived wave cavity containing turbulent
whistler waves can be formed with the appropriate properties to efficiently
pitch-angle scatter trapped electrons. The primary consequence on the Earth's
radiation belts is to reduce the lifetime of the trapped electron population.
