Experimental Measurements of Phase Space

Direct measurements of integrated phase-space densities, e.g., $f(x,v_y,t)$, have been made in an experiment. Using spectroscopically active ions, measurements in a plasma show the ion response, $f_i(\mathrm{x},\mathrm{v},t)$, to linear and nonlinear waves and phase-space particle bunching. Time-resolved measurements show coherent and incoherent phase-space density changes in the presence of waves, indicating that transitions to turbulence and chaos may be studied. The time, space, and velocity-space resolution may allow experimental tests of predictions from the Boltzmann equation.