# Non-linear r.f. heating of ionospheric plasma

TL;DR: In this paper, the nonlinear heating of electrons in the ionospheric plasma due to high-power radio wave propagation was investigated through an integro-differential equation derived from Boltzmann velocity-moment equations.

Abstract: The non-linear heating of electrons in the ionospheric plasma due to high-power radio wave propagation has been investigated through an integro-differential equation derived from Boltzmann velocity-moment equations. Various processes appropriate to the situation under study are taken into account. The numerical solution of the derived equation is presented graphically.

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01 Jan 1964

TL;DR: In this paper, an open-diagram technique is introduced which simplifies the calculation of absorptive parts of the conductivity tensor for long-wavelength electromagnetic waves in uniform, weakly interacting plasmas near equilibrium in the absence of external magnetic fields.

Abstract: Green's function techniques are used to treat the propagation of electromagnetic waves in uniform, weakly interacting plasmas near equilibrium in the absence of external magnetic fields. The frequency and the damping of electromagnetic waves in a medium are related to the local complex conductivity tensor, which is calculated by the diagrammatic techniques of modern field theory. Physical quantities are calculated in terms of a consistent many-particle perturbation expansion in powers of a (weak) coupling parameter. An open-diagram technique is introduced which simplifies the calculation of absorptive parts. For longwavelength longitudinal waves (i.e., electron plasma oscillations) it is found that the main absorption mechanism in the electron-ion plasma is the two-particle collision process appropriately corrected for collective effects and not the one-particle (or Landau) damping process. Electron-ion collisions produce a damping effect which remains finite for long wavelengths. The effect of electron-electron collisions vanishes in this limit. The absorption of transverse radiation is also considered; calculations for the electron-ion plasma are in essential agreement with the recent work of Dawson and Oberman. The results for the absorptive part of the conductivity tensor for long-wavelength electromagnetic waves in a plasma where the phase velocity au/k is much greater than the rms particle velocity is for the electron-ion plasma: O„O,~kgb C, ( )

1,404 citations

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TL;DR: In this paper, the authors investigated the role of self-action in the propagation of a radio wave in the ionosphere of a homogeneous electric field and showed that the effect of cross-modulation in Isotropic Plasmas can be seen as a function of the number of collisions with neutral particles.

Abstract: Introduction 139 1. Plasma in a Homogeneous Electric Field (Elementary Theory) 141 1.1. Electron Current. Dielectric Permittivity and Conductance of Plasma 141 1.2. Electron Temperature 143 2. Plasma in Homogeneous Electric Fields (Kinetic Theory) 147 2.1. Kinetic Equation 147 2.2. Transformation of the Collision Integral 150 a) Elastic Collisions with Neutral Particles (Molecules) 150 b) Inelastic Collisions with Neutral Particles 152 c) Collisions with Ions 153 d) Collisions between Electrons 154 2.3. Solution of Kinetic Equation. Stronglyionized Plasma 155 a) Distribution Function (Maxwellian Distribution) 156 b) Effective Number of Collisions 158 c) Relative Fraction of Energy Transfer 158 d) Electron Current. Dielectric Permittivity and Conductance of Plasma 159 e) Electron Temperature 162 2.4. Weakly-ionized Plasma 163 a) Case of Elastic Collisions 163 b) Molecular Plasma 164 c) Inert Gases 165 d) Electron Current and Average Electron Energy 166 2.5. Arbitrary Degree of Ionization. Elementary Theory 166 a) Transition for Strongly-ionized to Weakly-ionized Plasma 166 b) Conditions of Validity of Elementary Theory 168 3. Nonlinear Effect in the Propagation of Radio Waves in a Plasma (Ionosphere) 3.1. Propagation of a Radio Wave in a Plasma with Allowance for Nonlinearity (Self Action of the Plasma) 3.2. Role of Self Action of a Plasma in the Propagation of Waves in the Ionosphere a) Short Waves (λ≤ 200 m; ω ≥ 107). b) Average Waves (200 2000 m; ω < 106). d) Resonant Self-remodulation near the Gyro Frequency 3.3. Nonlinear Interaction of Modulated Radio Waves (Cross Modulation), a) Cross Modulation in Isotropic Plasma, b) Calculation of the Effect of a Permanent Magnetic Field. Resonant Effects near the Gyro Frequency 3.4. Results of Experimental Investigations of Cross Modulation in the Ionosphere. a) Absolute Value of Depth of Cross Modulation, b) Dependence of μΩ and ΦΩ on μ0 and Ω, n) Dependence of μΩ on the Power of the Interfering Station, d) Dependence of μΩ on the Frequencies ω1 and ω2. e) Resonance of Cross Modulation at ω1 ~ ωH. 3.5. Nonlinear Interaction of Unmodulated Radio Waves, a) Variation of Conditions of Wave Propagation, b) Sideband Waves (Waves with Combination Frequencies). c) Nonlinear Effects Connected with Variation of the Electron Concentration Concluding Remarks Literature Cited

198 citations

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TL;DR: In this article, the authors used data from the Chatanika, Alaska incoherent scatter radar to deduce atmospheric heating rates associated with particle precipitation and joule dissipation.

Abstract: Observational data from the Chatanika, Alaska incoherent scatter radar have been used to deduce atmospheric heating rates associated with particle precipitation and joule dissipation. During periods when Chatanika is in the vicinity of the auroral oval the height-integrated heat input to the lower thermosphere can be as large as 100 ergs per sq cm per sec with joule and particle heating rates of comparable magnitude. Altitude profiles of these heat inputs are also obtained, showing that the energy liberated by joule dissipation tends to peak at a substantially higher altitude (about 130 km) than that due to particles (100-120 km). As a consequence, it follows that joule heating can be expected to provide a rapid means for creating thermospheric disturbances. It is also pointed out that joule and particle heating are permanent features of the auroral oval and polar cap. As such, expansion of the auroral oval leads to an increase in the total global heating and, hence, to the close relationship between magnetic disturbances and thermospheric perturbation.

139 citations

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TL;DR: In this article, an ionospheric volume in the F layer subjected to high power high frequency illumination is observed to be an effective scattering medium for radio signals and a field-aligned scattering geometry is considered.

Abstract: An ionospheric volume in the F layer subjected to high power high frequency illumination is observed to be an effective scattering medium for radio signals. Experimental results are representative of a field-aligned scattering geometry. Scatter of the incident wave into electrostatic waves by these strongly field-aligned density irregularities is considered. This model explains the large decreases in radio wave reflectivity seen during the ionospheric modification.

80 citations

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