Cold Plasma Waves

1. Elementary properties of a plasma.- Plasma.- Equations of drift motion.- Isothermal atmosphere in equilibrium.- Types of wave.- Effect of collisions.- The continuity equations.- 2. Maxwell’s equations.- Equations in terms of current and charge densities.- Equations in terms of electric moment per unit volume.- The exponential wave function.- The concept of a dispersion relation.- Calculation of the dispersion relation (electric current method).- Calculation of the dispersion relation (electric moment method).- 3. Isotropic plasma.- Mobility and conductivity of an isotropic plasma.- Susceptibility and dielectric constant of a collisionless isotropic plasma.- The plasma frequency.- Refractive index of a collisionless isotropic plasma.- Wave dispersion in a collisionless isotropic plasma.- Effect of collisions in an isotropic plasma.- Importance of ordered kinetic energy in a plasma.- Poynting’s theorem in a plasma.- The energy significance of the complex dielectric constant of an isotropic plasma.- 4. Alternating current in a magnetoplasma.- Mobility tensor for a magnetoplasma.- Conductivity tensor for a magnetoplasma.- Low-frequency conduction properties of an infinite homogenous magnetoplasma.- Low-frequency conduction properties of a slab of magnetoplasma.- Effect of plasma scale on wave propagation.- 5. General properties of phase propagation in a magnetoplasma.- Susceptibility tensor for a magnetoplasma.- Alternative expressions for the susceptibility tensor components in the absence of multiple ion species.- Dispersion relation for a magnetoplasma.- Elliptic polarization.- Alternative derivation of the dispersion relation for a magnetoplasma.- The radio and hydromagnetic approximations.- Effect of collisions in a magnetoplasma.- 6. General properties of group propagation in a magnetoplasma.- Frequency and angular spectra.- Velocity of a wave packet.- Relation between phase and group propagation.- Method for calculating group velocity in a magnetoplasma.- Formulae for group velocity in a magnetoplasma.- Beam radiation in a magnetoplasma.- 7. Propagation of phase along the imposed magnetic field.- Circular polarization.- The dispersion relation for longitudinal propagation.- Longitudinal Alfvén waves.- The violin-string approach to longitudinal Alfven waves.- The hydromagnetic approximation for longitudinal propagation.- The radio approximation for longitudinal propagation.- The Eckersley approximation for longitudinal propagation.- Comparison of approximations.- Pass and stop bands of frequency for longitudinal propagation.- Particle vibration for longitudinal propagation.- Plasma motion in a longitudinal Alfvén wave.- Longitudinal propagation in low-density and high-density magnetoplasmas.- Effect of collisions on longitudinal propagation.- Effect of an additional ion species on longitudinal propagation.- Pass and stop bands of ionization density for longitudinal propagation.- 8. Energy flow and group velocity for longitudinal propagation.- Electromagnetic energy density for longitudinal propagation.- Kinetic energy density for longitudinal propagation.- Energy flow and group velocity for longitudinal propagation.- Energy in a longitudinal Alfvén wave.- Faraday rotation for longitudinal Alfvén waves.- A resonator for longitudinal Alfvén waves.- The mode of operation of a hydromagnetic violin-string.- Freezing of the magnetic field in the plasma (longitudinal Alfven waves).- Energy in a longitudinal whistler wave in the band ?Mi ? ? ? ?Me.- A resonator for longitudinal whistler waves in the band ?Mi ? ? ? ?Me.- Freezing of the magnetic field in the electron gas (longitudinal whistler wave).- Solid-state plasmas.- 9. Propagation of phase transverse to the imposed magnetic field.- The O wave.- The X wave.- Superposition of the O and X waves.- Pass and stop bands of frequency for transverse propagation.- The hybrid resonant frequencies.- Transverse propagation in a low-density magnetoplasma.- Pass and stop bands of ionization density for transverse propagation.- Effect of collisions on transverse propagation.- 10. Elliptic polarization of the X wave for transverse propagation.- The electric ellipse for transverse propagation of the X wave.- Frequency dependence of the electric ellipse.- Particle vibration for transverse propagation of the X wave.- Plasma compressions and dilations for transverse propagation of the X wave.- Non-reciprocity.- 11. Energy behaviour of the X wave for transverse propagation.- Electromagnetic energy density for transverse propagation of the X wave.- Kinetic energy density for transverse propagation of the X wave.- Energy flow and group velocity for transverse propagation of the X wave.- A resonator for transverse Alfvén waves.- The mode of operation of a hydromagnetic organ-pipe.- Freezing of the magnetic field in the plasma (transverse Alfvén waves).- 12. Propagation at any angle to the imposed magnetic field..- The zeros in the frequency dispersion curves.- Nomenclature for the characteristic waves.- The cross-connection phenomenon for frequency dispersion curves.- Frequency dispersion curves for nearly transverse propagation.- Frequency dispersion curves for nearly longitudinal propagation.- The elliptic polarizations of the O and X waves at the plasma frequency.- Effect of an additional ion species on cross-connection phenomena.- The infinities in the frequency dispersion curves.- Permitted regions for the frequency dispersion curves.- The cross-connection phenomenon for ionization dispersion curves.- Permitted regions for the ionization dispersion curves.- Propagation into a magnetoplasma from free space.- 13. The radio approximation.- The radio approximation to the dispersion relation.- Frequency dispersion curves in the radio band.- Frequency dependence of elliptic polarization in the radio band.- Frequency dependence of the direction of group propagation in the radio band.- Variation in the angle of squint of a rotating broadside antenna in the radio band.- Dependence of refractive index on ionization density in the radio band.- Dependence of elliptic polarization on ionization density in the radio band.- Dependence of the direction of group propagation on ionization density in the radio band.- 14. The hydromagnetic approximation.- The hydromagnetic approximation to the dispersion relation.- Frequency dispersion curves in the hydromagnetic band.- Effect of ionic collisions in the hydromagnetic band.- The fit between the hydromagnetic and radio approximations.- Frequency dependence of elliptic polarization in the hydromagnetic band.- Frequency dependence of the tilts of the electronic and current ellipses in the hydromagnetic band.- Frequency dependence of the direction of group propagation in the hydromagnetic band.- Polar diagrams for group velocity in the hydromagnetic band.- Dependence of refractive index on ionization density in the hydromagnetic band.- Dependence of elliptic polarization on ionization density in the hydromagnetic band.- Dependence of the direction of group propagation on ionization density in the hydromagnetic band.- 15. The quasi-longitudinal and quasi-transverse approximations.- The transition angle between the quasi-longitudinal and quasi-transverse approximations.- The regions of validity for the first- order angular approximations.- Importance of avoiding angular approximations that upset an infinity of a refractive index.- The regions of validity for angular approximations of practical value.- Accuracy of ?2n/??p2 using angular approximations.- The quasi-transverse approximation when ? ? ?Mi.- The quasi-longitudinal approximation when ? ? Max(?N,?Me).- The quasi-longitudinal approximation when ?Mi ? ? < ?Me ? ?N.- Group propagation for the whistler wave when ??1 ? ? < ?Me ? ?N.- Comparison of the zero-order quasi-longitudinal approximation in the whistler band with the unapproximated formulae.- 16. Directional behaviour of group velocity in a magnetoplasma.- Group propagation of the X wave in the pass band ? > ?C2.- Group propagation of the O wave in the pass band ? > ?N.- Group propagation in the upper part of the whistler band [??1 < ? < Min(?N,?Me)].- Group propagation in the lower part of the whistler band (? ? ??1).- Group propagation of the O wave in the pass band ? < ?Mi.- Group propagation of the X wave in the pass band ?C1 ?Me.- Group propagation of the X wave in the pass band ?C1 < ? < ??2 when ?N < ?Me.- 17. The field of an antenna in a magnetoplasma.- Axes of coordinates.- Angular spectra of O and X waves.- The predominant directions of group and phase propagation in the far field.- The method of steepest descent.- Simplification of the notation.- The power density in the far field.- Use of the angle of phase propagation as an independent variable.- Radiation from a gaussian dipole in a homogeneous magnetoplasma.- A reference isotropic medium.- Radiation ?C2.- Radiation in the frequency band ?C2 > ? > ??2.- Radiation in the frequency band ?? > ? > ?N.- Radiation in the frequency band ?N > ? > ?C1.- Radiation in the frequency band ?Me > ? > ??1.- Radiation in the frequency band ??1 > ? > ?Mi.- Radiation in the frequency band ? < ?Mi.- Frequency dependence of radiation resistance.- The relation between beaming and guidance in a homogeneous magnetoplasma.- The relation between beaming and guidance for the whistler wave when ??1 < ? ? Min (?N, ?Me).- The relation between beaming and guidance for the O wave when ? ? ?Mi.- The relation between beaming and guidance for the combined O and X waves when ? ? ?Mi.- Effect of energy absorption on Alfvén guidance.- Symbols.- Index of subjects.