Fig. 3: Field-particle correlations \({C}_{{E}_{z}}({v}_{z})\) and \({C}_{{E}_{z}}({v}_{z},{v}_{\perp })\).
From: Laboratory measurements of the physics of auroral electron acceleration by Alfvén waves
Results from a LAPD experiment, b, c AstroGK simulation, d, e an analytical Laplace-Fourier Transform solution of the z/λ evolution of \({C}_{{E}_{z}}({v}_{z})\), and g, f, h Liouville mapping. h is a re-plotting of (g) with axes for direct comparison with (a). Gyrotropic correlations \({C}_{{E}_{z}}({v}_{z},{v}_{\perp })\) in (b, f) are reduced to the parallel correlations \({C}_{{E}_{z}}({v}_{z})\) in (c, g) by integration over v⊥. The parallel phase velocity vph is noted by a black vertical line on all plots. WWAD measurements are unavailable in the region bounded by vertical dashed lines. The dashed horizontal line in (d) identifies the slice re-plotted in (e, a) and corresponds to the z/λz location of WWAD measurements in the experiment. The AstroGK \({C}_{{E}_{z}}({v}_{z})\) (c), with a bipolar signature centered on vph, is comparable to the largest values of z/λz in (d). The analytical (e) and Liouville mapping (g) \({C}_{{E}_{z}}({v}_{z})\) include finite z/λ of the experiment and produce a bipolar signature below vph similar to (a) the experimental \({C}_{{E}_{z}}({v}_{z})\). Error bars in (a) represent the standard deviation. The black arrows represent the path of analytical and numerical analysis leading to closure in the interpretation of our experimental measurements.
