Faraday Cup Analysis

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FC analysis using ADC channel current distribution

For each ADC channel:

[math] ADCSum^{channel}=\sum_{i=1}^{pulses}{ADC_{pulse}^{channel}}[/math]

[math] ADCErr^{channel}=\sqrt{\frac{\sum_{i=1}^{pulses}{ADC_{pulse}^{channel}}}{pulses}}[/math]

For distribution over all ADC channel:

[math] ADC^{avg}=\frac{\sum_{i=1}^{16}{ADCSum^{channel}*i}}{\sum_{i=1}^{16}{ADC_{i}}}[/math]

[math] ADC^{err}=\frac{\sum_{i=1}^{16}{ADCErr^{channel}*i}}{\sum_{i=1}^{16}{ADC_{i}}}[/math]

FC analysis using pulse by pulse ADC channel mean value distribution

For each beam pulse:

[math] ADC^{avg}_{pulse}=\frac{\sum_{i=1}^{16}{ADC_{i}*i}}{\sum_{i=1}^{16}{ADC_{i}}}[/math]

For distribution over all beam pulses:

[math] ADC^{avg}=\frac{\sum_{i=1}^{pulses}{ADC^{avg}_{pulse}}}{pulses}[/math]

[math] ADC^{err}={ \sqrt{\frac{1}{pulses}\sum_{i=1}^{pulses}{\left(ADC^{avg}_{pulse} - ADC^{avg}\right)^{2}}}}[/math]

Here is:
1. ADC# = bridge#
2. Pulse# = ReadOut# = Entry# = Event#

Some examples of ADC mean value distribution. Here are:
1. x axis: ADC mean value for one pulse
2. y axis: number of pulse w/ that ADC mean value

3D Faraday cup plot

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).

Faraday cup "Rain"

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