Low-frequency electrostatic turbulence generated by the ion–ion beam instability was investigated experimentally in a double-plasma device. Real time signals were recorded and examined by a conditional statistical analysis. Conditionally averaged potential distributions reveal the formation and propagation of structures with a relatively long lifetime. Various methods for making a conditional analysis are discussed and compared. The results are discussed with reference to ion phase space vortices and clump formation in collisionless plasmas.

Conditional structures. or eddies. in turbulent flows are discussed with special attention to electrostatic turbulence in plasmas. The potential variation of these eddies is obtained by sampling the fluctuations only when a certain condition is satisfied in a reference point. The resulting structure has a simple physical interpretation. It' is here demonstrated that correlation functions of the type (4"(.Yi.r,)d(.Y2.r2)) for n = 1.2.. .. which are relatiiely easy to obtain. contain sufficient information to construct the conditional eddies. Experimentally obtained correlation functions illustrate the analysis. THE 5iOST commonly applied technique for analysing turbulent fluctuations. is probably the measurement of two point correlation functions. Indeed. for strictly Gaussian fluctuations these functions contain all the statistical information available. In many physical shsrems the signals follom Gaussian statistics to a very good accuracy. However. for turbulence in fluids and plasmas this statistical model will fail in general. by predicting that the relative phases of the Fourier components are completel! random. In fluid and plasma turbulence u e expect for instance three w a l e processes with a corresponding phase relation to play an important role. Consequently a Gaussian model is inherently inconsistent in these cases.This conclusion unfortunately implies that nom iti/itiile/j, many correlation functions of the tbpe (d~; 0: ---Q:.) may contain relevant physical information. (The brackets ( ') denote ensemble aierages.1Here 0" denotes the fluctuating quantity. sa! the potential for electrostatic plasma turbulence. raised to some power ti. and the numerical index 1. 2. . . . . .Y denotes a combination of positions and times as e.g. (r. r ) = ( T I . rl). The problem is then to determine U hich of all these functions contain some information having a meaningful physical interpretation. O n e very well documented option is to consider the quantit!

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Ion acoustic turbulence generated by an ion beam in an unmagnetized plasma is investigated by using electrostatic probes. Digital computed space-time corelation functions, power density spectra and phase spectra are presented. A linear relationship between frequency ω and wave-number k is obtained from the digital computed cross-power density spectra. The spatial evolution of the turbulence and the beam along the direction of the beam is also discussed.

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