Error Assessment of the Ion Acoustic Wave Velocity Measurement of the Concentration of Two Ion Species Plasma

The ion-acoustic-wave method of Hala and Hershkowitz (2001) infers the concentrations of two ion species from the measured wave speed and electron temperature through a cold-ion dispersion relation. Eight later works have drawn concentrations or the system sound speed from it, yet no error budget has been published. We construct one from the original figures, digitized, together with kinetic theory, disc-launcher diffraction and ion-burst kinematics. Eleven terms enter the measured quantity v2/Te; the literature quotes only the time-of-flight slope precision and, once, the probe Te error. The original pure-xenon signal behaves as a collisionally damped wave: its lobe width holds at 9.4 μs over 3– 8 cm, and its attenuation implies a charge exchange cross-section near 1.1 × 10−14 cm2. Its speed, 917 ± 5 m/s, sits 2% above cs and inside the launching grid’s near field, which biases the timing by +1.6%. Neglecting ion temperature overstates light-ion fractions by 0.03–0.11 under the original conditions and by up to 0.30 under those of Yip et al. (2010). A kinetic correction and an independent calibration on each series’ pure-gas endpoints both lower the original xenon-rich Ar/Xe fractions by 0.07–0.09. The pure-xenon endpoints read 0.086 and 0.021, 3.5–11 times the plotted error bars. The qualitative result, ion fractions differing from neutral fractions with the heavy ion enhanced, survives every correction; concentrations quoted to ±0.01–0.05 do not. Eight tests are specified that close the error budget.