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Subsections

Analysis of the beam scans

The main goal to the procedure is to obtain a reliable single number to quantify the quality of a beam scan. This number should certainly be closely related to the beam shape quality. But some peculiar beam shapes are not easily quantified.

A first look at the scans zoology

Lets have a look on typical scans that were taken during the runs.

A typical scan (Figure 5.3) when the MCC¹⁴ is tuning the beam, before reaching an optimal value, the beam is wide and non-homogeneous. (the saturation of the counting can be avoided by lowering the PMTs voltage).

**Figure 5.3:** Scan of a wide beam
$\begin{figure} \epsfxsize=10cm \centerline{\rotatebox{-90}{ \epsfbox {scan_3_09_02.eps} }}\end{figure}$

After the tuning, the beam may look like it is shown in Figure 5.4.

**Figure 5.4:** Scan of a well tuned beam
$\begin{figure} \epsfxsize=10cm \centerline{\rotatebox{-90}{ \epsfbox {scan_4_09_05.eps} }}\end{figure}$

The scan is very useful to point out problems and quality of the beam. During the September run, scans revealed that a big halo was surrounding the beam (figure 5.5). Usually it is because the beam is hitting something on the way. Users of the beam have to be warned about such a beam, because if the halo is too wide it will create unwanted events in the target support.

**Figure 5.5:** A halo is clearly visible on this scan
$\begin{figure} \epsfxsize=10cm \centerline{\rotatebox{-90}{ \epsfbox {scan_2_09_19.eps} }}\end{figure}$

To give a complete view of every channel that are scanned, a very good scan taken in June 97 is summarized in Figure 5.6. Every channel is represented.

Channels, from top left to bottom right :

Upstream counters (before the CLAS detector) : Top, Left, Bottom and Right (around the beam pipe).
Downstream counters (at the end of the Hall after the detector) : Top, Left, Bottom and Right (around the beam pipe).
Coincidences upstream : main coincidences Top-Bottom Left-Right
Tagger dump counters (In the dump after the tagger magnet) : Top, Left and Right.

**Figure 5.6:** A quite good scan
$\begin{figure} \epsfxsize=15cm \centerline{ \epsfbox {good_scan.eps} }\end{figure}$

Methodology for scans analysis

There were 144 scans available from the different runs we had. Perl scripts were written to automatically process each one and write a data file summarizing the quantity associated with fits and some other variables. A process was also printing the scan and fits on a single page (Figure 5.6).

Then, each scan received a subjective grade by hand, ranging from 0 (no beam) to 10 (what a lovely scan !¹⁵). As a very subjective measure, this could not be the only guide to check the quality. But at a first step, lets say that everything that was equal or below 3 was obviously unacceptable, and that's everything equal or superior to 6 was good. Values 4 and 5 are less well defined, but usually 5 is OK, and 4 is a bad beam. The initial repartition is showed in Figure 5.7. We did have 37 very good scans, 55, really bad, and respectively 28 evaluated at 4 and 24 evaluated at 5.

**Figure 5.7:** Repartition of the 144 scans over our subjective evaluation
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {score_0.eps} }\end{figure}$

Only the four upstream beam counters could be of any use, so cuts apply to this scan data only. Quite often, especially when the beam is not very good, there is some difference between 2 PMT outputs of the same scan. Instead of taking an average of some kind, cuts were made on the maximum and minimum of the four equivalent quantities measured on each PMT.

Non fitted scans

The most basic cut that can be applied is to remove scans that were not fitted at all. So every scan, where every four scans could not been read was declared as bad. This cut removed the most obviously bad scans we had as shown in Figure 5.8

**Figure 5.8:** Cut on the non fitted scans. Removed scans appear in darker pattern
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {zero_score.eps} }\end{figure}$

Cuts on the reduced $\chi^2$

The $\chi^2$ will tell if the fit was close to the data and report incoherent fitting. The value of the reduced $\chi^2$ should be around 1, too high, the data were not fitted correctly, too low there is something unexpected.

The distribution of reduced $\chi^2$ among data looks at first glance very random (Figure 5.9 and 5.10), but once plotted against our subjective evaluation, (Figure 5.11) a correlation clearly appears.

**Figure 5.9:** Distribution of the reduced $\chi^2$ on the u axis sigma (large values)
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {chi2n_dis1.eps} }\end{figure}$

**Figure 5.10:** Distribution of the reduced $\chi^2$ on the u axis sigma (around 1)
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {chi2n_dis2.eps} }\end{figure}$

**Figure 5.11:** $\chi^2$ against the subjective evaluation
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {chi2n_score_dis.eps} }\end{figure}$

Cuts were taken at $0.1 < \chi^2_r < 100$ and eliminated a lot of bad scans as we can see in Figure 5.12.

**Figure 5.12:** Result of the cut on $\chi^2$ over the scans
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {chi2n_score.eps} }\end{figure}$

Cuts on the errors of the fit

The second cut is based on the following approach : it is easy to tell if a beam is good by determining the sigma of the Gaussian and putting some threshold, unless the fit was either unsuccessful, or far from the beam shape. We can also add that if the fit is far from the real data, or if it was completely unsuccessful, it tells us that the beam was bad, because it has not the expected shape.

**Figure 5.13:** Distribution of the error on the u axis sigma (normalized on fitted sigma)
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {serror_dis.eps} }\end{figure}$

After plotting the values (Figure 5.13), a cut was placed at 0.035 for the normalized error over sigma on the x axis, and at 0.05 for the y axis.

The removed scans (summed with those already removed from the first cut) are shown in Figure 5.14.

**Figure 5.14:** Cut on the error over sigma. Removed scans appear in darker pattern
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {serror_score.eps} }\end{figure}$

These two basic checks combinated remove 31 from the 55 really bad scans from the 144 we had, and the apparently good scans removed were, after a second look, not that good.

Acceptable sigma

Now we should have a good fit at a well defined beam, so the remaining cuts should be reported on the sigma. A first look over the sigma show that our subjective guess was not that bad according to sigma measure (5.15), and predicts a good value for the fit that we found in Figure 5.16.

**Figure 5.15:** Sigma versus our subjective evaluation, not that bad
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {mean_1.eps} }\end{figure}$

**Figure 5.16:** Sigma repartition (u axis)
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {mean_2.eps} }\end{figure}$

From the plot we had, we chose to cut at 0.25 on the x axis and 0.2 on the y axis. After this fit we have a population quite well split between good and bad beam (See Figure 5.17). All these cuts have been implemented into a Perl script that begins to be able to answer to the question ``what is the beam quality ?''. But we still don't have a good quality factor that would summarize all that with a single number. This still has to be done. Several tries have not yet lead to convincing results.

**Figure 5.17:** Final cuts result
$\begin{figure} \epsfxsize=10cm \centerline{ \epsfbox {final_score.eps} }\end{figure}$

The Quality Factor

A selection function can easily be made using the various cuts we applied previously, as shown in previous section. But once this selection have been made, the distribution over the selected population of our diverse criteria is almost flat, and cannot be use further.

So we can certainly quantify how bad a (really) bad beam is, but we can't give a far more important number to answer the question ``How good is this good beam?''. Such a value could be everyday use in the counting house when people could say ``we took data with a beam of quality 8.5''.So we tried to found some function that would answer this question.

The most important factor for the beam quality on the transvbesral dimensions is to be small enough so that there are no risk it hit the support of the target.

Quantifying that roughly, we simply want that the beam stay inside some well delimited area. It will be 1 mm around the target.

$\begin{displaymath} Q = \frac{\sum_{scan away from beam} (data(x)-fit\_value(x)) dx} {\sum{fit} data(x) dx}\end{displaymath}$

The interest of such a function is that is gives a quantitative ratio between the quantity of electrons on the target versus the quantity of electrons outside the target. Although it's values is closely related to the quality of the beam, it is unable by itself alone to gives an accurate value of the beam quality, but it was neither able to discriminate better beam from less good beam in the selected scans of Figure 5.17.

A good function has not yes being found, the wrong ideas of this first attempt are that the cut is not smoothed and that very high counts at the center of the peak would mask even a significant halo.

Another, and certainly better solution would be to ponder the values with the distance from the peak (certainly exponentially, as we are supposed to obtain a Gaussian curve) and to use a logarithm scale to weight the importance of each bin, so that low but significant halo would be detected.

Footnotes

...MCC¹⁴: Machine Control Center, where the beam is controlled from
...!¹⁵: There was no 10, 8 was good enough for a good scan

Next: Conclusion Up: Scans Previous: The actual implementation

Garp patois@cebaf.gov