Thermal excitation of modes in a non-neutral plasma

We examine theoretically the thermal fluctuations in a non-neutral plasma, as observed on a segmented electrode surrounding the plasma, using the Nyquist theorem. The fluctuation spectrum is peaked at frequencies which correspond to modes of the plasma. Measurement of these fluctuations and of the input admittance of the plasma in the vicinity of one of the mode resonances can be used to give a completely experimental, and non-destructive, measurement of the plasma temperature. Since some of the modes are negative energy modes and exhibit negative absorption due to the plasma rotation, a direct application of the Nyquist theorems will not give correct results for the non-axisymmetric modes. This problem is circumvented by first calculating the fluctuations in a frame rotating with the plasma and transforming to the laboratory frame. This results in a modification of Nyquist's theorem. Measurement issues are discussed