# BCM calibration (d2n)

## Final Results for Beam Charge calibration

Hall A's standard beamline equipment includes two resonant RF cavities, stainless-steel cylinders with a high ($\sim 3000$) Q factor, which are tuned to the fundamental beam frequency of 1.497 GHz. These Beam Current Monitors (BCMs) are denoted upstream (u) and downstream (d), based on their relative positions on the beamline. Each produces a voltage signal proportional to the measured current; this signal is fanned out, amplified by a gain factor of 1, 3, or 10, and fed to a VtoF converter. The resulting signals -- three for each BCM, or six altogether -- may be read out by scalers in the HRS and BigBite arms for a continuous measurement of the beam current and hence the accumulated beam charge.

In order to calibrate these readouts, it is necessary to take dedicated calibration runs, systematically stepping through several beam current set points. There are two steps in this calibration process. First, at the injector, the OL02 resonant cavity is calibrated to the Faraday cup, a water-cooled copper beam dump that can be inserted into the center of the beam path so as to collect all of the current. No beam can be received downstream of the Faraday cup while it is in place, but the injector cavity does not disturb the beam, so it is the OL02 injector cavity's current reading that is compared directly to the Hall A BCM readouts in the second step.

Fig. 1: Calibration of OL02 signal to Faraday cup measurement

Figure 1 shows the OL02 current measurement as a function of the absolute measurement taken by the Faraday Cup. A linear fit reveals that the OL02 measurement is approximately 99.7% of the actual current value in $\mu$A. With this information, we can plot the rate measured in each of the six beam-current scalers as a function of the beam current, derived from the OL02 readings during our calibration run (Figure~\ref{fig:bcm_scalercal}). From a linear fit to the scaler readouts between 5 and 30 $\mu$A, we can determine the slope of the line relating our scaler rates to the beam current. The fit does not extend to zero because the BCM readouts are known to be nonlinear at low currents; instead, the offset (the scaler rate for zero current) is determined from a Gaussian fit to the scaler rates recorded over the course of five minutes with the beam off. The table shows the calibration constants resulting from these fits. Over a given time interval, these values allow us to extract both the beam current $I$ and the accumulated beam charge $Q$ from the scaler rate $\omega_n$ of the nth beam-current signal, according to the equations

Fig. 2: Calibrating the scaler rates to the beam current (from calibrated OL02 readings)

$\omega_n = \textrm{offset}_n + \textrm{slope}_n \cdot I$

$I = \frac{\omega_n - \textrm{offset}_n}{\textrm{slope}_n}$

$Q = I \cdot t = \frac{t \left( \omega_n - \textrm{offset}_n \right)}{\textrm{slope}_n}$

This calibration was performed with the scalers on the BigBite arm; the scalers on the Left HRS arm record the same signal, and yield consistent results.

Scaler Slope (Hz/uA) Offset (Hz)
u1 2101 $\pm$ 1 395.8 $\pm$ 0.05
u3 6480 $\pm$ 2 453.393 $\pm$ 0.05
u10 19731 $\pm$ 11 770.66 $\pm$ 0.05
d1 2152 $\pm$ 1 154.58 $\pm$ 0.05
d3 6658 $\pm$ 3 133.27 $\pm$ 0.05
d10 21008 $\pm$ 10 293.48 $\pm$ 0.05

## Strategy

• Use special run to calibrate OL02 cavity against Faraday cup
• Calibrate EPICS bcm variable by calibrating BCMs against OL02
• Calibrate BB/LHRS scalers against OL02

## Key for BcmLog files

Column headings for BCM log file (from Vince via Kalyan):

• Entry #
• BCM 1 voltage (upstream BCM)
• BCM 2 voltage (downstream BCM)
• Unser (not used)
• Faraday Cup (if extracted = 0)
• 0R07 (not used)

## Results for BCM calibration

Final results relating scaler rates (e.g. u1r) in Hz to Beam Current in uA:

The equations follow the form u1r = Slope*(Beam Current in uA) + Offset

Using scripts in Diana's ifarm account, /u/home/dseymour/d2n_analysis/bcm_calibration

From MakeBCMPlotHists, calibrating BCM1 & 2 to OLO2 for each current set point:

BCM1 = 0.020673 * OLO2 - 0.001692

• $\sigma_m = 0.000035$
• $\sigma_b = 0.000243$

BCM2 = 0.020990 * OLO2 - 0.001710

• $\sigma_m = 0.000037$
• $\sigma_b = 0.000276$

From MakeBCMPlotError, calibrating OLO2 to Faraday cup from linear fit to entire run (minus 12 outlier points). Data points given arbitrary error bars of 0.1 in x and y.

FARA = 0.9971 * OLO2 + 0.0171

• $\sigma_m = 0.0003$
• $\sigma_b = 0.0104$

Combining these equations gives the overall real current (in $\mu$A) from the BCM readings:

$\mu$ = 48.24 * BCM1 + 0.0987

• $\sigma_m = 0.0829$
• $\sigma_b = 0.0157$

$\mu$ = 47.51 * BCM2 + 0.0983

• $\sigma_m = 0.0849$
• $\sigma_b = 0.0167$

## Relevant HALOG entries

• Feb 17 BCM cal data: