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 ofwpa, whereais 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<<vthdoes the continuous spectrum tend to a Gaussian of widthk vth, characteristic of independent particles. The effect of the “load impedance” on the measurements is also discussed. © 2003 American Institute of Physics