When a plasma is of finite transverse cross section, space-charge waves may propagate even in the absence of a drift motion or thermal velocities of the plasma. Some of the properties of these space charge waves have been investigated by regarding the plasma as a dielectric and solving the resulting field equations. The effect of a steady axial magnetic field is considered, but motion of heavy ions and electron temperature effects are neglected. Waves are found to exist at frequencies low compared with the plasma frequency as well as waves with oppositely directed phase and group velocities (backward waves). Many of the features of these waves have been verified experimentally by measuring phase velocity and attenuation of waves along the positive column of a low pressure mercury arc in an axial magnetic field. Measurements of electron density have been made using these waves and the results are compared with those obtained by other methods. An interesting feature of these measurements, of value in plasma diagnostics, is that they can be made with frequencies which are small compared with the plasma frequency.

Measurements of the spatial structure of tokamak edge density fluctuations n have been made using compact probe arrays in the Caltech tokamak. The results indicate that the structure of n in the tokamak edge is characterized by very short auto-correlation times and short cross-correlation lengths, i.e. that the edge density fluctuations consist of small-scale 'turbulence'. The space-time structure of this ff turbulence is consistent with several recent non-linear edge instability models. The structure of the local electrostatic potential 0 is measured to be qualitatively similar to that of n, and local cross-correlation between n and 0 indicates large outward radial particle transport similar to predictions of the edge instability models.

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It is shown that if a longitudinal wave is excited in a collision-free plasma and Landaudamps away, and a second wave is excited and also damps away, then a third wave (i.e., the echo) will spontaneously appear in the plasma.

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