LONG WAVELENGTH OSCILLATIONS OF A QUANTUM PLASMA IN A UNIFORM MAGNETIC FIELD II

The self-sustained oscillations of a quantum mechanical electron gas in a uniform magnetic field are discussed in the time-dependent Hartree approximation, or random phase approximation. The full electromagnetic interaction between electrons is taken into account, and spin effects are included. The...

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Bibliographic Details
Main Authors: Celli,Vittorio, Mermin,N David
Format: Report
Language:English
Subjects:
CYCLOTRON RESONANCE
ELECTRONS
ELECTROSTATICS
EQUATIONS
FREQUENCY
GASES
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
MATRICES(MATHEMATICS)
OSCILLATION
PROPAGATION
QUANTUM THEORY
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Summary:The self-sustained oscillations of a quantum mechanical electron gas in a uniform magnetic field are discussed in the time-dependent Hartree approximation, or random phase approximation. The full electromagnetic interaction between electrons is taken into account, and spin effects are included. The resulting dispersion relation reduces to the AppletonHartree equation of classical magnetohydrodynamics in the limit of long wavelengths. It is found that this classical equation holds even for a highly degenerate electron gas or for magnetic fields so strong that only a few Landau oscillator levels are appreciably occupied. The validity of long wavelength expansions is discussed for the various normal modes, particular attention being given to the low frequency transverse mode, a particular case of which is the helicon or whistler. It is also shown that the normal modes with appreciable longitudinal currents are correctly described over a wide range of wavelengths by the electrostatic approximation, in which only Coulomb forces between electrons are retained. (Author)