Subluminal electrostatic noise in isotropic space plasmas. General formulas and nonrelativistic thermal limit
The properties of the collective subluminal electrostatic fluctuations in isotropic plasmas are investigated using the covariant kinetic theory of linear fluctuations based on the correct momentum-velocity relation. The covariant theory correctly accounts for the differences in subluminal and superluminal fluctuations in contrast to the non-covariant theory. The general formalism developed here is valid in unmagnetized plasmas and in magnetized plasmas for wavevectors of electrostatic waves parallel to the direction of the uniform magnetic field. Of particular interest are potential differences between the covariant and the non-covariant approach and the consequences of these differences in modifying observational predictions. For thermal particle distributions of protons and electrons with nonrelativistic equal temperatures, the covariant and non-covariant theories yield exactly the same dispersion function and relation for weakly damped electrostatic waves. Also, the quasi-equilibrium wavenumber spectrum of collective thermal electrostatic noise agrees in both theories apart from the important wavenumber restriction | k | > k c = ω p , e / c . While the non-covariant analysis also yields eigenmode fluctuations at small wavenumbers with superluminal phase speeds, the correct covariant analysis indicates that subluminal electrostatic fluctuations are only generated at wavenumbers | k | > k c by spontaneous emission of the plasma particles. As a consequence, the nonrelativistic thermal electrostatic noise wavenumber spectrum is limited to the wavenumber range ω p , e ≤ | k | ≤ k max . Within a linear fluctuation theory, superluminal electrostatic noise cannot be generated.