> f**Fermilab** Doc Number: Beams-doc-2803

Version: 1.0

Type: Note

##################### Measurement of Booster Beam Halo using the C836A and C838A Collimators in the MI8 Beamline {#measurement-of-booster-beam-halo-using-the-c836a-and-c838a-collimators-in-the-mi8-beamline .Heading}

Bruce C. Brown

*Main Injector Department*

*Fermi National Accelerator Laboratory\**

*P.O. Box 500*

*Batavia, Illinois 60510*

11 June 2007

\*Operated by the Fermi Research Alliance under contract with the U.S.
Department of Energy

##################### Measurement of Booster Beam Halo using the C836A and C838A Collimators in the MI8 Beamline {#measurement-of-booster-beam-halo-using-the-c836a-and-c838a-collimators-in-the-mi8-beamline-1 .Heading}

#####################  {#section .Heading}

########### Abstract

########### 

########### During high intensity operation for NuMI, the MI8 Collimators have been used to measure the halo in the horizontal and vertical planes. The collimators are positioned to scrape the beam halo. Losses were recorded using LM8C1 through LM8C4 whose response is shown to be approximately linear with lost beam intensity. Measurements are reported using the MI836A collimator and 90^o^ phase advance downstream at C838A. The sensitivity was calibrated using the change in transmission from toroids I:TOR806 to I:TOR852. The integrated loss is found to be exponential from above 1% to nearly 0.01% or below. The sensitivity of the halo measurement is limited by a measured loss which is independent of collimator positioning. 

########### 

########### Introduction

########### 

Since commissioning the MI8 Collimators in January 2007 (see
Beams-doc-2618), the MI8 Beam has been collimated at 836 and 838. This
study has re-measured the sensitivity of the loss monitor system, shown
that it responds linearly to losses originating from a given collimator
jaw (top, bottom, left, right), but responds somewhat differently to the
same loss created on another jaw, and has documented the halo shapes
using each of the four jaws of the C836A and C838A collimators. Other
effects concerning losses both locally and downstream are noted.

########### Measurement Setup

#####################   {#section-4 .Text-1}

#####################  Attempts to make this measurement with \'knob-plots\' with the Fast Time Plot facility were found to be unsatisfactory. Using the I88 histogram facility, the values of 4 parameters {#attempts-to-make-this-measurement-with-knob-plots-with-the-fast-time-plot-facility-were-found-to-be-unsatisfactory.-using-the-i88-histogram-facility-the-values-of-4-parameters .Text-1}

##################### were recorded. In later measurements, two copies of I88 were employed. For example, C836AV measurements used the following histograms and the graphs were stored in the E-Log: {#were-recorded.-in-later-measurements-two-copies-of-i88-were-employed.-for-example-c836av-measurements-used-the-following-histograms-and-the-graphs-were-stored-in-the-e-log .Text-1}

#####################  C836AV, TOR852/TOR806, LM8C1, LM8C2 {#c836av-tor852tor806-lm8c1-lm8c2 .Text-1}

#####################  TOR806, VP836, VP837, VP838 {#tor806-vp836-vp837-vp838 .Text-1}

#####################  {#section-5 .Text-1}

##################### Data was recorded by I88 on T:UFEVT (User Friendly Event Timer) which was set to sample on \$23 events after data from one of the NuMI beam pulses was available. When the system was ready to record data, the collimator locations were documented in the E-Log from I63\<34\> and the collimators were moved to non-scraping locations (the faster-moving horizontal collimators were moved to position 0 while the slower-moving vertical collimators were moved to positions hundreds of mils from the scraping location.  {#data-was-recorded-by-i88-on-tufevt-user-friendly-event-timer-which-was-set-to-sample-on-23-events-after-data-from-one-of-the-numi-beam-pulses-was-available.-when-the-system-was-ready-to-record-data-the-collimator-locations-were-documented-in-the-e-log-from-i6334-and-the-collimators-were-moved-to-non-scraping-locations-the-faster-moving-horizontal-collimators-were-moved-to-position-0-while-the-slower-moving-vertical-collimators-were-moved-to-positions-hundreds-of-mils-from-the-scraping-location. .Text-1}

#####################   {#section-6 .Text-1}

##################### When preparations for the measurement were complete, a collimator for study was moved to a desired location and the histograms in the two I88 instances were started. Twenty or more pulses were recorded. Copies of the graphs were stored in the E-Log and the collimator position was changed. Typically the sequence was to move from the initial nominal location where a fraction of 1% was scraped, toward a high scrape (few percent), then stepping back through the 1% region and across to center the collimator. Periodically, histograms of the Texas Multiwires, especially the 836 Horizontal and 836 Vertical were also recorded in the E-Log. When data was complete for one jaw, the collimator move was continued beyond 0 to scrape with the other jaw.  {#when-preparations-for-the-measurement-were-complete-a-collimator-for-study-was-moved-to-a-desired-location-and-the-histograms-in-the-two-i88-instances-were-started.-twenty-or-more-pulses-were-recorded.-copies-of-the-graphs-were-stored-in-the-e-log-and-the-collimator-position-was-changed.-typically-the-sequence-was-to-move-from-the-initial-nominal-location-where-a-fraction-of-1-was-scraped-toward-a-high-scrape-few-percent-then-stepping-back-through-the-1-region-and-across-to-center-the-collimator.-periodically-histograms-of-the-texas-multiwires-especially-the-836-horizontal-and-836-vertical-were-also-recorded-in-the-e-log.-when-data-was-complete-for-one-jaw-the-collimator-move-was-continued-beyond-0-to-scrape-with-the-other-jaw. .Text-1}

#####################  {#section-7 .Text-1}

#####################  {#section-8 .Text-1}

![](media/image1.png){width="2.9972222222222222in"
height="2.4881944444444444in"}![](media/image2.png){width="2.9972222222222222in"
height="2.4881944444444444in"}

Figure 1. Typical I88 Histograms for MI8 Collimator Study

########### 

########### Loss Monitor Calibration Data

The toroids calibrations differ by up to several percent. Additionally,
the beam transmission varies with Booster beam quality and the beamline
tune-up. However, the efficiency remains quite steady for hours at a
time when external programmatic changes do not cause intensity or other
variations. This permits us to calibrate the ionization loss monitors
against transmission. Loss monitor LM8C1 is located adjacent to the 836
Marble Mask, LM8C2 is against the wall above and just downstream of the
Marble Mask, LM8C3 and LM8C4 mimic the LM8C1 and LM8C2 locations in the
838 half-cell.

![](media/image3.jpeg){width="3.290277777777778in"
height="2.495833333333333in"}

##################### Figure 2. Loss Monitor LM8C1 is shown adjacent to the Marble Mask. Loss Monitor LM8C2 is visible at the top of the picture, hanging on the wall. {#figure-2.-loss-monitor-lm8c1-is-shown-adjacent-to-the-marble-mask.-loss-monitor-lm8c2-is-visible-at-the-top-of-the-picture-hanging-on-the-wall. .Text-1}

#####################  {#section-10 .Text-1}

+------------------+------------+------------+------------+------------+
| ##########       | ####       | ####       | ####       | ####       |
| ########### Loss | ########## | ########## | ########## | ########## |
|  Monitor {#loss- | ####### LM | ####### LM | ####### LM | ####### LM |
| monitor .Text-1} | 8C1 {#lm8c | 8C2 {#lm8c | 8C3 {#lm8c | 8C4 {#lm8c |
|                  | 1 .Text-1} | 2 .Text-1} | 3 .Text-1} | 4 .Text-1} |
+------------------+------------+------------+------------+------------+
| ############     | ######     | ########   | ########   | ########   |
| ######### Units  | ########## | ########## | ########## | ########## |
| {#units .Text-1} | ##### Prot | ### Proton | ### Proton | ### Proton |
|                  | ons/(R/s)  | s/(R/s) {# | s/(R/s) {# | s/(R/s) {# |
|                  | {#protonsr | protonsrs- | protonsrs- | protonsrs- |
|                  | s .Text-1} | 1 .Text-1} | 2 .Text-1} | 3 .Text-1} |
+------------------+------------+------------+------------+------------+
| ####             | 1.18E+10   | ####       | 7.03E+09   | ####       |
| ################ |            | ########## |            | ########## |
| # From Hor Posit |            | #######  { |            | #######  { |
| ive {#from-hor-p |            | #section-1 |            | #section-1 |
| ositive .Text-1} |            | 1 .Text-1} |            | 2 .Text-1} |
+------------------+------------+------------+------------+------------+
| ####             | 1.30E+10   | ####       | 1.07E+10   | ####       |
| ################ |            | ########## |            | ########## |
| # From Hor Negat |            | #######  { |            | #######  { |
| ive {#from-hor-n |            | #section-1 |            | #section-1 |
| egative .Text-1} |            | 3 .Text-1} |            | 4 .Text-1} |
+------------------+------------+------------+------------+------------+
| ######           | 1.5178E+10 | 1.0685E+11 | 1.1035E+10 | 9.8180E+10 |
| ###############  |            |            |            |            |
| From Vert Positi |            |            |            |            |
| ve {#from-vert-p |            |            |            |            |
| ositive .Text-1} |            |            |            |            |
+------------------+------------+------------+------------+------------+
| ######           | 9.5584E+09 | 9.7697E+10 | 9.19E+09   | 7.94E+10   |
| ###############  |            |            |            |            |
| From Vert Negati |            |            |            |            |
| ve {#from-vert-n |            |            |            |            |
| egative .Text-1} |            |            |            |            |
+------------------+------------+------------+------------+------------+

##################### Table 1. Sensitivity of LM8C1 and LM8C2 to losses due to C836A. Sensitivity of LM8C3 and LM8C4 to losses due to C838A. See fits results in the following figures. {#table-1.-sensitivity-of-lm8c1-and-lm8c2-to-losses-due-to-c836a.-sensitivity-of-lm8c3-and-lm8c4-to-losses-due-to-c838a.-see-fits-results-in-the-following-figures. .Text-1}

#####################  {#section-15 .Text-1}

##################### ![](media/image4.wmf){width="5.993055555555555in" height="4.097222222222222in"} {#section-16 .Text-1}

![](media/image5.wmf){width="5.993055555555555in"
height="4.097222222222222in"}Figure 3. Calibration of LM8C1 vs.
Transmission using horizontal scans (top) and vertical scans (bottom).

![](media/image6.wmf){width="5.993055555555555in"
height="4.097222222222222in"}

![](media/image7.wmf){width="5.993055555555555in"
height="4.097222222222222in"}

Figure 4. Calibration of LM8C3 vs. Transmission using horizontal scans
(top) and vertical scans (bottom).

![](media/image8.wmf){width="5.993055555555555in"
height="4.097222222222222in"}

![](media/image9.wmf){width="5.993055555555555in"
height="4.097222222222222in"}

Figure 5. Calibration of LM8C2 vs. LM8C1 (top) and

LM8C4 vs. LM8C3 (bottom)

**[Beam Profile Data and Results]{.underline}**

In order to study the beam profile, we first convert the loss monitor
readings to the lost beam intensity. Using a linear fit to Transmission
(TOR852/TOR806) vs. Loss (LM8C1 or LM8C3) as shown in Figure 3 and
Figure 4, we find a slope and intercept. The slope (loss fraction/(R/s)
is converted to a sensitivity (Lost Protons/(R/s)) by multiplying by the
average Booster beam pulse intensity (\<TOR806\>). These calibration
values are shown in Table 1. Most of the data is taken with constant
Booster intensity (about 5E12 p/pulse) but we plot the beam fraction vs.
collimator position to further minimize the effects of intensity
variation. Figures 6 -- 9 show the beam loss profile for each axis of
motion of C836A and C838A. We plot to lost protons (integrated), not the
local intensity since that is what is directly measured. Note that the
motion is labeled by the collimator position so the beam edge which is
scraped is opposite.

We see in Figure 5 that the response of LM8C4 is mostly proportional to
the LM8C3 measurement of loss. There is a clear tendency for higher
losses to produce more than linearly higher response in LM8C4 but the
effect is modest (about 10%). Using the average ratio LM8C4/LM8C3, a
calibration for LM8C4 is shown in Table 1. The response of LM8C2 is much
more loosely correlated with the loss recorded by LM8C1. The average of
some points with moderate lost beam is used to provide a nominal
calibration for LM8C2. One should assume that this determination has
large errors.

Using this calibration (for each end of each axis) we convert our
measurement of loss monitor reading vs. collimator position to produce
plots of integrated loss vs. collimator position. Figures 6 -- 9 show
these results. The data is clearly quite exponential except for the
portion which is independent of collimator position. We find that almost
all the data is well represented by an exponential fall plus a constant
background. The background is due to the loss observed by the loss
monitor which is independent of the collimator position (probably due to
upstream sources). It is typically a signal corresponding to a local
loss of about 10-4 of the beam. The constant term is subtracted off and
the Excel fit function, LOGEST, is used to a capture the exponential
shape.

![](media/image10.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image11.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 6. Horizontal Lost Beam Profiles at C836A

![](media/image12.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image13.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}Figure 7. Horizontal Lost Beam Profiles at
C838A

![](media/image14.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image15.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 8. Vertical Lost Beam Profiles at C836A

![](media/image16.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image17.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 9. Vertical Lost Beam Profiles at C838A

We stopped the scraping without scraping the core of the beam. The
Gaussian profile measured (and fit) by the multi-wire systems appears to
provide a good representation of the beam core. We can use the measured
sigma at 836 to predict widths at C836A and C838A based on measured beta
values. The match was fairly satisfactory but it was decided that a
comparison of the shape would be more effective if the mean and sigma
was adjusted. In practice, the assumed beta and center were adjusted to
visually match the Gaussian to the measured halo distributions. The
above data along with the Gaussians were re-plotted in Figures 10 -- 13
to show integrated loss vs. beam edge

edge = ±1000 +collimator position.

![](media/image18.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image19.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 10. Integrated Beam Loss Profile at C836AH.

![](media/image20.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image21.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 11. Integrated Beam Loss Profile at C838AH.

![](media/image22.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image23.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 12. Integrated Beam Loss Profile at C836AV.

![](media/image24.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image25.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 13. Integrated Beam Loss at C838AV.

It is of direct interest for operations to determine whether the halo is
symmetric. Since one edge will be scraped by the A collimator and the
opposite edge by the B collimator, if an asymmetry is demonstrated, then
one may wish to optimize this choice. To examine the symmetry, the data
in Figures 6 -- 9 has been re-plotted with the collimator negative
reading reversed and an offset added. The offset was adjusted to
visually match the integrated loss at high loss levels. These results
are shown in Figures 14 and15.

![](media/image26.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image27.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

![](media/image28.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image29.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 14. Comparison of beam edges. Above for C836AH, Below for C838AH,
Left for measurements, right for exponential fits to measurements.

![](media/image30.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

![](media/image31.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}![](media/image32.wmf){width="2.9965277777777777in"
height="2.048611111111111in"}

Figure 15. Comparison of beam edges. Above measured and fit for C836AV.
Below left C838AV measured. Below right C838AV fit.

Using the LOGEST fits shown in the above figures, one can get a
representation of the halo which is more physically obvious by
converting from the power-law representation to an exponential
representation. We choose to show the results for a normalization at the
1% integrated loss point as follows:

LOGEST: y = b \* m\^x

Table II: y = 0.01 exp( ( x -- x_0) / a)

a = -1 / (ln m) ; x_0 = -ln(100 \*b) / (ln m)

The collimator position is reported in the same coordinate system
orientation as is the beam profiles so positive is above or to the
right. The above values of x_0 give the collimator position at which the
collimator scrapes 1% of the beam. We will use X_0 to define the beam
coordinate for which 1% of the beam lies at a larger distance from the
beam center. Thus for the positive edge of the beam, we use measurements
with the negative collimator setting and the 1% edge of the beam is
given by X_0 = 25.4 + x_0 (assuming x_0 has been converted to mm). For
the negative edge of the beam, the X_0 = -25.4 + x_0. Table II will show
the fit quantities converted to exponential format.

  ---------------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ----------
  Table II: Fitted                                                                              
  Results for                                                                                   
  Exponential                                                                                   
  (10-2                                                                                         
  exp(-(x-x0)/a)                                                                                

                                                                                                 

                   a                     x_0                   X-0                   Width      Center
                                                                                     (98%)      

                   mm         mm         mm         Mm         mm         mm         mm         Mm

                   Negative   Positive   Negative   Positive                                     

  836AH            1.527737   -1.41537   -21.9094   12.58068   3.490604   -12.8193   16.30993   -4.66436

  838AH            1.30119    -1.29762   -19.9798   14.5959    5.420246   -10.8041   16.22435   -2.69193

                                                                                                 

  836AV            0.93456    -1.30073   -16.7922   22.45753   8.607842   -2.94247   11.55031   2.832687

  838AV            1.041336   -1.21198   -20.1474   17.87796   5.252579   -7.52204   12.77462   -1.13473
  ---------------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ----------

  ------------ -------------------- ------------ ------------ ------------
  Table III:                                                  
  Lattice Beta                                                
  Values                                                      

               MJY Oct06                         Gaussian     

               Beta_x               Beta_y       Beta_x       Beta_y

  836          41.08                8.65                       

  C836A        28                   16.6         28           14

  C836B        25.5                 18.7                       

  838          48.7                 13.6                       

  C838A        34.1                 22.9         29           17

  C838B        31.1                 25.3                       
  ------------ -------------------- ------------ ------------ ------------

The MI8 lattice has been measured and adjusted several times by Ming-Jen
Yang. Table III Columns 2 and 3 show results the current lattice tune
which was measured in October 2006. Columns 4 and 5 show the beta values
which were employed to achieve the results shown in Figures 10 -- 13. We
note that the agreement is good for C836AH but the other three profiles
are fit with an apparently narrower Gaussian profile. The beam center is
found from these scans is a few mm different than that inferred from the
beam position monitors which are in the same region. We note that VP836
is immediately upstream of C836A so little interpolation is required.
These discrepancies may bear further examination.

**[Further Discussion]{.underline}**

A few items noted during these measurements are worth calling to our
attention. The naïve interpretation of the loss monitor readings in the
regions beyond the exponential fall would be that the radiation is from
upstream and not related to the losses on that collimator. We note,
however, that some of the scans show some distinctive features:

-   The loss pattern on the beam right (collimator negative) shows a
    flattening at about 1.3E-4 of the beam but later falls to 0.8E-4.

-   The differences in loss plotted on the left and right side of C838AH
    is due to the different calibration applied. The measured loss
    monitor readings were more similar.

-   The scan on C836AV negative collimator side was made more
    challenging by numerous changes in Booster operation, both timeline
    changes for NuMI only vs. Mixed Mode and many changes in the
    intensity (number of Booster turns. The two very different levels of
    loss on the positive edge of the beam between 10 mm and 15 mm were
    observed. Further study would be required to determine if the higher
    level is repeatable or if beam conditions which caused it can be
    controlled to avoid the higher loss.

-   On the negative side of the beam at C838AV (positive collimator
    position), the beam loss fell to a very low level of 4E-5 for C838AV
    = 380 mils but scanning further to the middle showed higher losses
    of around 1.4E-4. Whether the very low reading is due to some
    masking of LM8C3 or some other effect has not been determined. It
    was repeatable for one or two additional measurements.

> It was noted that the peak scraping resulted in higher losses both in
> the MI8 line to the Main Injector and in the MiniBooNE line. Further
> investigation of this may be warranted.

![](media/image33.png){width="2.9972222222222222in"
height="2.49375in"}![](media/image34.png){width="2.9972222222222222in"
height="2.49375in"}

Figure 16. Losses reported by D44 Datalogger during scan of C838AV. Left
is losses at LM870 and TLI864. Right is losses at LM848 and LM853.

> These results were obtained on April 9, May 9 and May 16, 2007. The
> measurements are in the Main Injector E-Log. The data analysis was
> carried out with EXCEL and the spreadsheet
> (MI8_Col_Scrape_Spring_2007.xls) is stored as a part of this document
> (Beams-doc-2803).

**[Conclusions]{.underline}**

The loss monitors have been calibrated by comparing the loss monitor
response to the number of protons lost on the 'A' collimators. The LM8C1
and LM8C3 show a linear response to the number of lost protons with
average response of 1.24E+10 protons / (R/s) for LM8C1 and 9.49E+09
protons / (R/s) for LM8C3.

We have demonstrated that beyond the Gaussian central portion of the MI8
Beam, we have measured halo (beam tails) which are substantially above
the Gaussian projection. These tails are well described by exponential
distributions. Note that we have fit an exponential to the integrated
loss vs. position, but this would also imply an exponential distribution
of the beam intensity profile. In Table II, we show that the beam tails
in the horizontal plane are fairly symmetric with the 'a' parameter
being 6% larger on the beam positive side (collimator negative side) at
C836AH and less than 0.3% larger for the C838AH measurement. However,
the situation in the vertical plane demonstrates asymmetric halos with
the 'a' parameter being 40% larger (halo falls off more quickly) on the
downward (beam negative or collimator positive) side at C836AV and 16%
larger at C838AV.

**[Acknowledgments]{.underline}**

The assistance of Denton Morris, Dave Capista, Phil Adamson, Dave
Johnson and especially Ming-Jen Yang are gratefully acknowledged.