Theoretical cross-spectrum of the microfield measured by two small dipoles in a warm isotropic plasma

We suggest that the electron density and temperature of a plasma could be determined by immersing two small dipole antennae in it, and by measuring, as a function of frequency, the cross-spectrum of the random signals that they receive. When the plasma is in thermal equilibrium, this spectrum is related simply, by Nyquist's theorem, to the real part of the mutual impedance of the two antennae. We have studied the case where, in addition, the plasma is collisionless and no magnetic field is present. The spectrum has a main resonance peak slightly above the plasma frequency, while for still higher frequencies it exhibits oscillations, the amplitudes of which decrease as one moves away from the plasma frequency. The main resonance peak becomes sharper, but smaller, as the distance between the antennae becomes large compared with the Debye length.