Thermal Fluctuations: Modes versus the Continuum

Abstract

The thermal fluctuation spectrum of the signal received on a patch electrode is examined and it is shown that the spectrum shows both the modes of the plasma and a continuous spectrum related to the independent-particle motions of plasma electrons. Modes whose axial phase velocity are more than 3–4 times the electron thermal speed are lightly Landau-damped and are clearly separated from the continuum. Long wavelength modes are "acoustic" in nature. If the axial phase velocity of a mode becomes less than 1–2 times the electron thermal speed, then the mode becomes strongly Landau-damped and it merges into the continuum. The mode velocities are of the order of wpa , where a is the plasma radius, so that the plasma radius must be at least several deBye lengths in order to have lightly damped modes. In general, the spectrum is a mixture of a continuous spectrum together with a finite number of modes which are Landau-damped by varying amounts, depending on their phase velocity relative to the electron thermal speed. Only in the extreme limit, wpa << vth does the continuous spectrum tend to a Gaussian of width k vth, characteristic of independent particles. The effect of the "load impedance" on the measurements is also discussed.

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