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We consider the weak turbulence of whistler waves in the in low-\beta\ innermagnetosphere of the Earth. Whistler waves with frequencies, originating in theionosphere, propagate radially outward and can trigger nonlinear inducedscattering by thermal electrons provided the wave energy density is largeenough. Nonlinear scattering can substantially change the direction of the wavevector of whistler waves and hence the direction of energy flux with only asmall change in the frequency. A portion of whistler waves return to theionosphere with a smaller perpendicular wave vector resulting in diminishedlinear damping and enhanced ability to pitch-angle scatter trapped electrons.In addition, a portion of the scattered wave packets can be reflected near theionosphere back into the magnetosphere. Through multiple nonlinear scatteringsand ionospheric reflections a long-lived wave cavity containing turbulentwhistler waves can be formed with the appropriate properties to efficientlypitch-angle scatter trapped electrons. The primary consequence on the Earth'sradiation belts is to reduce the lifetime of the trapped electron population.

Weak Turbulence in the Magnetosphere: Formation of Whistler Wave Cavity by Nonlinear Scattering