Several publications cited in Lab Publications cover the work
discussed much more thoroughly than can be done here.Ion transport in velocity-space, as opposed to real space, can be studied experimentally using the laser induced fluorescence (LIF) diagnostics at UC Irvine. We have done experiments to see how diffusion, Dvv , and convection, Cv , in velocity-space depend upon the initial ion velocities and the plasma parameters. A theoretical framework for predicting the ion transport is obtained with the Fokker-Planck formalism applied to plasma test-ions. To the right are the predictions for a classical, quiet plasma. LIF can create a small tagged population of ions at any specified velocity in the ion distribution function. A second LIF interrogation of the plasma at a later time reveals the velocity-space diffusion and convection of the test-ions. By creating test-ion populations throughout the ion distribution the dependence of velocity-space diffusion and convection on ion velocity can be determined. Our first experiments were to determine the diffusion and convection in the velocity component parallel to the confining magnetic field in a quiet plasma.
The diffusion parallel to the magnetic field exhibited the magnitude and velocity
dependence predicted by the Fokker-Planck equation. In the data at left, the open dots are
the diffusion for ions in a quiet plasma. The curved line is the prediction of the above
equations, plugging in the measured density and temperatures. In other words, the theory
is not normalized to the data. Next, when a plasma was created that had some turbulence
not thought to be negligible in the diffusive contribution, the velocity space diffusion
exhibited a change from the quiet plasma case. There was a sizable peak induced on one
side of the diffusion curve which may be due to the turbulent drift waves in the plasma.
This turbulence was induced by having a density gradient in the plasma.
Next, we held the laser-tagged
ion velocity constant and varied the plasma density in the quiet plasma. The Fokker-Planck
equation predicts a linear dependence of diffusion with background plasma density, as was
observed. Again, no adjustment of the theoretical prediction to fit the data was done. The
solid line is the prediction from the above equations.