[1] The whistler anisotropy instability is driven by an electron temperature anisotropy T ? /T k > 1 where ? and k denote directions perpendicular and parallel, respectively, to the background magnetic field B o . Here kinetic linear theory in a magnetized, homogeneous, collisionless plasma model is used to study this instability when the electron velocity distribution may be represented as the sum of a hot, anisotropic bi-Maxwellian and a cold, isotropic component. The critical b ke , the value at which the maximum growth rate of the instability changes from propagation parallel to B o to oblique propagation, decreases with increasing n c /n e , where n c is the cold electron density and n e is the total electron density. At parallel propagation the maximum growth rate increases with n c /n e up to n c /n e ≃ 0.8, but then diminishes with further increases of the relative cold electron density. Introduction of a cold electron component can reduce the hot electron anisotropy necessary to excite this instability by up to a factor of 2.
1] We confirm results from a previous derivation of the linear growth rate of the parallel propagating whistler wave instability when both cold and hot populations are present, and extend previous equations to describe the spatial growth rate. For moderate plasma beta, there is always a peak in the linear growth rate of the dominant mode with respect to the ratio of total plasma density to the hot plasma density. There is a similar peak in the linear convective growth rate for high anisotropy A hot = T ⊥ hot /T k hot À 1 but not for low anisotropy. We present these results for a large range of physical parameters. Our results can be used to quickly determine whether the growth rate will increase or decrease with respect to cold plasma density, and we demonstrate this for an event observed recently. We explain the observation that greater cold plasma density leads to a drop in the central frequency of the waves. Model equations can be used to predict the optimal cold plasma density for maximum temporal and spatial growth rate. A relativistic electromagnetic plasma dispersion code is used to show that the analytical formulas are roughly correct in the vicinity of the optimal cold density unless the thermal velocity is highly relativistic $0.5 c, where c is the speed of light. Comparison with the electromagnetic dispersion code WHAMP shows that our formulas are adequate for b k hot < 1 for realistic anisotropy.
(2015), One-and two-dimensional hybrid simulations of whistler mode waves in a dipole field, J. Geophys. Res. Space Physics, 120, 1908-1923, doi:10.1002 Abstract We simulate whistler mode waves using a hybrid code. There are four species in the simulations, hot electrons initialized with a bi-Maxwellian distribution with temperature in the direction perpendicular to background magnetic field greater than that in the parallel direction, warm isotropic electrons, cold inertialess fluid electrons, and protons as an immobile background. The density of the hot population is a small fraction of the total plasma density. Comparison between the dispersion relation of our model and other dispersion relations shows that our model is more accurate for lower frequency whistlers than for higher frequency whistlers. Simulations in 2-D Cartesian coordinates agree very well with those using a full dynamics code. In the 1-D simulations along the dipole magnetic field, the predicted frequency and wave number are observed. Rising tones are observed in the one-fourteenth scale simulations that have larger than realistic magnetic field spatial inhomogeneity. However, in the full-scale 1-D simulation in a dipole field, the waves are more broadband and do not exhibit rising tones. In the 2-D simulations in a meridional plane, the waves are generated with propagation approximately parallel to the background magnetic field. However, the wavefronts become oblique as they propagate to higher latitudes. Simulations with different plasma density profiles across L shell are performed to study the effect of the background density on whistler propagation.
Anti-eavesdropping channel estimation (ANECE) is a method that uses specially designed pilot signals to allow two or more full-duplex radio devices each with one or more antennas to estimate their channel state information (CSI) consistently and at the same time prevent eavesdropper (Eve) with any number of antennas from obtaining its CSI consistently. This paper presents optimal designs of the pilots for ANECE based on two criteria. The first is the mean squared error (MSE) of channel estimation for the users, and the second is the mutual information (MI) between the pilot-driven signals observed by the users. Closed-form optimal pilots are shown under the sum-MSE and sum-MI criteria subject to a symmetric and isotropic condition. Algorithms for computing the optimal pilots are shown for general cases. Fairness issues for three or more users are discussed. The performances of different designs are compared.
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