For each beam pulse:
[math] ADC_{ave}^{pulse}=\frac{\sum_{i=1}^{16}{ADC_{i}*i}}{\sum_{i=1}^{16}{ADC_{i}}};[/math]
For distribution over all beam pulses (assuming it's Gaussian):
[math] ADC_{ave}=\frac{\sum_{i=1}^{pulses}{ADC_{ave}^{pulse}}}{pulses};[/math]
[math] ADC_{sigma}={ \sqrt{\frac{1}{pulses}\sum_{i=1}^{pulses}{\left(ADC_{ave}^{pulse} - ADC_{ave}\right)^{2}}}};[/math]
Below is the plot of the charge in Faraday cup (pC) as a function of magnet current (vertical axis, A) (basically magnetic field) and ADC (horizontal axis).
