Abstract
An analytical model of the interaction between a localized wave packet and energetic electrons is presented. Electrostatic packets of tens to a hundred wavelengths are considered in order to emulate the Langmuir waves observed in the auroral zone and in the solar wind. The phase information is retained, so the results can be applied to wave–particle correlator measurements. The perturbed distribution function is explicitly calculated and is shown to be bounded over all phase space due to a broadening of resonance ascribable to the finite extent of the packet. Its resistive part (in phase or 180° out of phase with the electric field) maximizes for v=ω/k, so that the associated bunching of electrons enables assessment of the characteristic wavelength. The changes in the wave profile due to the interaction with the energetic electrons are calculated. Broad wave packets grow or decay ‘‘self-similarly’’ with a rate given by the standard expression for a plane wave. Narrow, growing packets, on the other hand, quickly widen to sizes determined by the local distribution function. This sets a lower bound to the sizes of observed packets. Present results are supported by test-particle simulations and are in accord with recent correlator data of intense, localized Langmuir waves in the auroral zone.
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