DISPERSION RELATIONS IN A STATIONARY PLASMA. Interim Report No. 3

Technical Report · Sun Jan 01 04:00:00 EST 1961

OSTI ID:4833370

Tanenbaum, B S

Linearized hydromagnetic plasma equations are derived and used to investigate the oscillations which are possible within a stationary, homogeneous, fully ionized, macroscopically neutral plasma of infinite extent. Three cases are treated: no magnetic field, a longitudinal magnetic field, and a transverse magnetic field. In the field-free case, the well-known dispersion relations for the three simplest types of plasma oscillations (longitudinal electron waves, longitudinal ion waves, and transverse electromagnetic waves) were verified, and the properties of each of these waves are reviewed. Four dispersion relations were derived for the case of a longitudinal magnetic field, two being the same as longitudinal electron and ion waves in the field-free case and the other two being ordinary and extraordinary transverse waves which at high and low frequencies agree with the magneto-ionic theory of Appleton and the magnetohydrodynamic theory of Alfven, respectively. Four solutions to the dispersion relation are again derived for the transverse magnetic field case; one of the solutions is the ordinary transverse wave of magneto-ionic theory, while the remaining three each represent complex coupled oscillations in the plane perpendicular to the field. The solutions can be arranged in a form such that one type of oscillation is identical to the extraordinary waves in magneto-ionic theory, another is quite similar to the longitudinal electron waves in the field- free case, and the third coupled oscillation reduces to a longitudinal magnetohydrodynamic wave at low frequencies, an ordinary ionic wave at high frequencies, and a new type of wave at midfrequencies. (D.L.C.)

• Research Organization: Raytheon co., Waltham, Mass.
• NSA Number: NSA-16-002583
• OSTI ID: 4833370
• Report Number(s): AFCRL-43; AD-256060
• Country of Publication: United States
• Language: English

Related Subjects

CONFIGURATION
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELECTROMAGNETIC WAVES
ELECTRONS
FREQUENCY
IONIZATION
IONS
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
OSCILLATIONS
PHYSICS
PLASMA
PLASMA WAVES