Kappa distributions possess an enhanced high-energy tail characterized by a spectral index kappa. Here we consider how kappa distributions influence the whistler mode instability. In a relativistic regime, we analyze the effects of the bi-kappa and kappa loss-cone distributions on the linear and nonlinear growth of whistler mode waves. We find that for kappa = 2, the linear growth rate corresponding to the bi-kappa distribution exceeds that for a bi-Maxwellian distribution (kappa = infinity) for electron anisotropies less than a critical value. The threshold wave amplitude for nonlinear growth corresponding to a hot injected bi-kappa distribution can be sensitively dependent on the value of kappa, but also depends crucially on the electron anisotropy, parallel hot electron temperature, and wave frequency. We plot time profiles of the wave magnetic field, frequency, total nonlinear growth rate and local nonlinear growth rate, and examine how these depend on kappa. The sweep (chirp) rates of the whistler mode chorus waves are found to be in the range of observed values, for the adopted plasma parameters. For a given value of the loss-cone parameter sigma, realistic whistler mode wave profiles may only exist for a restricted range of kappa. For example, for sigma >= 4, realistic wave profiles require kappa >= 4 as well as a sufficiently large anisotropy. In summary, this new study finds that the influence of kappa distributions on the whistler mode instability is complex, not least because the instability depends on several system parameters as well as kappa.
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