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The Lorentz polarization term for magnetospheric whistler propagation


  • Hal J. Strangeways


If the particles of a dielectric are arranged in a cubic lattice, the effective field acting on a particle is E + lPo, where l = 1/3. The second term is the Lorentz polarization term. Appleton believed that this term should be omitted from magneto-ionic theory, whereas Hartree included it. Various arguments have been presented to prove Appleton's contention that this term is zero for a plasma. Some proofs have considered the perturbation of the individual orbits of the electrons, but careful consideration of these treatments shows that they would predict a nonzero Lorentz term for some velocity distributions. It has also been argued that l ≠ 0 would violate causality but it can be shown that this only applies in the zero frequency limit for positive l. Other proofs that have been presented also possess significant limitations, in particular being limited to rather simpler plasma configurations than exist in the magnetosphere and weak field strengths. The theoretical problem for more general conditions is very difficult and thus an appeal to experiment results is considered relevant. It is shown that a very small nonzero Lorentz term would be significant for whistler-mode propagation. The observed lower cutoff frequencies of whistlers put a very low limit (l ∼ 10−5) on the maximum value of positive l but put no limit on negative l. It is shown, however, that l < 0 would increase the cutoff frequency for ducted propagation. Thus the upper cutoff frequency is determined for values of l in the range −5×10−6 to −2×l0−3 by ray tracing in a model Gaussian cross-section duct in a realistic model of the magnetospheric plasma corresponding to winter night conditions. Cutoffs (normalized to the equatorial electron gyrofrequency determined by curve fitting to the ray-traced whistler spectra) are found to be in the range 0.49 to 0.55 for a 15% enhancement duct. The range of cutoffs for l ∼ −10−4 is in much better agreement with experimentally observed whistler cutoffs than the assumption that l = 0 (no Lorentz term). This provides experimental evidence for a nonzero (negative) Lorentz term for ducted whistler propagation.

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