Determination of recombination and attachment rate constants from ballistic experiments

We present measurements of the electron concentration in wakes behind aluminum spherical models flying in air with velocity 3.4–5.7 km/sec at a pressure of 10–80 torr. We have calculated the heating and entrainment of aluminum from the surface of the models as they move within the flight range. We show that condensation of Al vapor may occur at distances of more than 100 diameters of the body and pressure $\gtrsim$ 80 torr. We pose and solve the inverse problem of determining (from experimental data) the effective attachment coefficient for attachment to air molecules and the attachment rate constants for Al + $e$ $\to$ AlO$^-$, AlO$_2$ + $e$ $\to$ AlO$_2^-$.