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Electromagnetic ion cyclotron (EMIC) waves lead to rapid scattering ofrelativistic electrons in Earth's radiation belts, due to their largeamplitudes relative to other waves that interact with electrons of this energyrange. A central feature of electron precipitation driven by EMIC waves isdeeply elusive: moderate precipitating fluxes at energies below the minimumresonance energy of EMIC waves occur concurrently with strong precipitatingfluxes at resonance energies in low-altitude spacecraft observations. Here weexpand on a previously reported solution to this problem: nonresonantscattering due to wave packets of finite size. We first generalize thequasi-linear diffusion model to incorporate nonresonant scattering by a genericwave shape. The diffusion rate decays exponentially away from the resonance,where shorter packets lower decay rates and thus widen the energy range ofsignificant scattering. Using realistic EMIC wave packets from $\delta f$particle-in-cell simulations, we then perform test particle simulations, anddemonstrate that intense, short packets extend the energy of significantscattering well below the minimum resonance energy, consistent with ourtheoretical prediction. Finally, we compare the calculatedprecipitating-to-trapped flux ratio of relativistic electrons to ELFINobservations, and infer the wave power spectra that are consistent with themeasured flux ratio. We demonstrate that even with a narrow wave spectrum,short EMIC wave packets can provide moderately intense precipitating fluxeswell below the minimum resonance energy.

Nonresonant scattering of energetic electrons by electromagnetic ion cyclotron waves: spacecraft observations and theoretical framework