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The experiments during the next three weeks will deal with plasma waves. For simplicity, we start out with an unmagnetized discharge plasma and investigate ion acoustic waves. These waves have similarity with ordinary acoustic waves in the sense of being compressional waves. The waves are longitudinal, i.e., their electric field points in the direction of wave propagation. They are space charge waves which produce no currents or magnetic fields. The wave velocity (ion acoustic speed) is determined by the electron pressure and the ion inertia, cs = sqrt (kTe/mi). Low frequency sound waves are essentially dispersionless, w = kcs. This is an approximation to the full dispersion relation derived from fluid theory, w = kcs/sqrt (1+k2 lD2). The dispersion exhibits a cutoff at the ion plasma frequency, w pi = cs/l D = sqrt (ne2 /mieps0). The phase velocity exceeds the group velocity but at low frequencies (w << wpi) both are given by the sound speed.
Ion acoustic waves have many interesting properties: At large amplitudes they can form shock waves and solitons. In collisionless plasmas they can be Landau damped by particles moving close to the phase velocity of the wave. In plasmas with drifts (e.g. electron currents, ion beams) the waves can be unstable and grow spontaneously. In plasmas with temperature gradients the waves refract toward low temperature regions. Waves can couple and produce broadband turbulence. Plasma turbulence can scatter particles and produce "anomalous" resistivity. Acoustic waves can interact with other waves in "parametric" instabilities. Ion acoustic waves are important in many laboratory and space plasmas.
In the present laboratory experiment we will excite the waves with oscillating voltages on grids. The density fluctuations are observable in the ac component of the electron saturation current to a Langmuir probe. The spatial properties will be measured with an interferometer circuit. Specifically, the following initial experiments are suggested.
1. Dispersion Relation Measurement
Measure the wavelength of ion acoustic waves with an interferometer and plot the dispersion relation w vs.k =2(pi)/(lambda). Compare the electron temperature obtained from the sound speed with that obtained from a Langmuir probe. Observe and explain the wave damping.
2. 2D Phase Fronts of Ion Acoustic Waves
Using interferometry, measure the phase fronts and amplitude contours of ion acoustic waves in an r-z plane across and along the exciter grid surface normal. Are the waves plane waves?
3. Ion Ballistic Modes
Make interferometer measurements at different voltages applied to the grid. Observe the change in wavelength with voltage. Plot the energy 1/2m iv2 vs V grid and interpret the observed effect.
More measurements are suggested later.
Read your lab manual and the appropriate chapters in Chen'stextbook. A list of questions will follow in "Notes".
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