Tagger field mapping analysis
D. Sober 

Postings in reverse chronological order.

Results of Fall 2016 survey of beam elements - 30-Jan-2017

• Presentation to beam meeting 30-Jan-2017 (TAGH_new_survey.pdf),
• New data file of counter positions and angles (Counter_table2017.txt)
• New data file of TAGH energy bounds for 0-angle rays (counterbounds2017.out)

Calculations relating to possibility of scattering to counters in same plane - 02-November-2016

• (Scatter_to_same_plane.pdf)

First results from tagger Monte Carlo simulation -- 13-Jul-2016

• Powerpoint presentation to Beam meeting of 18-Jul-2016 (First_tagger_Monte_Carlo_results.pdf)

Derivatives files for high-energy rays (no quadrupole) -- added 03-Jun-2016

• ascii file of 8 derivatives d{x,x'}/d{x,x'} and d{z,z'}/d{z,z'}
• ascii file of the 4 non-zero "crossed" derivatives d{x,x'}/d{z,z'}

Tagger beam pipe collimation of low-energy electrons -- rev. 18-May-2016

Beam optics derivatives with quadrupole -- 11-May-2016

Plots of dervatives vs E_e for coarse steps in quadrupole gradient
• dz/dz0 (vertical magnification) (dzdz_vs_E-coarse++.pdf)
• dz/dz'0 (dzdaz_vs_E-coarse++.pdf)
• dx/dx'0 (horizontal focus) (dxdax_vs_E-coarse++.pdf)

Table of derivatives with quad gradient = -62.5 G/mm (derivs_q-125.out)

Plots of derivatives with quad gradient = 0 and -62.5 G/mm (From Quad_and_radiator_position.pdf, 26-Feb-2016)
• Derivatives w.r. to x0 and x'0 (derivs1-4qyn.pdf)
• Derivatives w.r. to z0 and z'0 (derivs5-8qyn.pdf)

Comparison of raytracing results at 12 GeV using measured map and Tosca field --07-March-2016

Quadrupole: Comparison of using Tosca field map and simple analytic form -- 03 March 2016

Raytracing with the quadrupole, and effects of radiator position -- 26 February 2016

Efficiency of the tagger fixed array -- 02 February 2016

Some input files for SNAKE at JLab -- 27 July 2015

• Directive files
  These files contain the names of the map files, which can be found on the GlueX docdb, and also on ~sober/HallD/maps at JLab.
  (The parameters in lines 2 and 3 are relevant only for spin rotation of protons, and are ignored here.)
  • Low-energy directive file (for E <= 6.99 GeV at E0 = 12 GeV)
  • High-energy directive file (for E >= 6.69 GeV at E0 = 12 GeV)
• Trajectory files for E0 = 12 GeV
  These files are requested during execution.
  • Low-E: In z=0 plane, 30 MeV steps from E = .18 to 6.99 GeV
  • Low-E: z = +1 mm, 30 MeV steps from E = .18 to 6.99 GeV
  • Low-E: theta_z = +1 theta_ce, 30 MeV steps from E = .18 to 6.99 GeV
  • High-E: In z=0 plane, 30 MeV steps from E = 6.69 to 9.00 GeV
  • High-E: z = +1 mm, 30 MeV steps from E = 6.69 to 9.00 GeV
  • High-E: theta_z = +1 theta_ce, 30 MeV steps from E = 6.69 to 9.00 GeV

Some new analysis notes -- July 2015

• Using the Field Maps (revised 23 July 2015)

Coordinate systems, endplanes and file formats needed to use the maps for raytracing

• Some Small Effects in Tagger Raytracing (17 July 2015)

Details on the effect of probe recalibration and omitting the FOCAL field box

• Interpolation between the field maps (2 July 2015)

  How to interpolate between the field map raytracing results for E0 = 6, 12 and 13.4 GeV (probably useless)

• Analysis of the Field Maps (2 July 2015)

Summary of the analysis procedure, including probe recalibration, revised contour plots, and E0-independence of the raytracing results.
Additional copies of figures in this note:
• Figure 1 - Mapping configuration boundaries
• Figure 2 - Probe calibration factors
• Figure 3 - Field boxes and endplanes
• Figure 4 - B vs x and y before recalibration
• Figure 5 - B vs x and y after recalibration
• Figure 6 - Contour plots before recalibration
• Figure 7 - Contour plots after recalibration
• Figure 8 - Error in energy due to using 1.5T map at 6 and 13 GeV

Revised derivatives from raytracing after probe recalibration -- 26 June 2015

• ascii file of 8 derivatives d{x,x'}/d{x,x'} and d{z,z'}/d{z,z'}
• ascii file of the 4 non-zero "crossed" derivatives d{x,x'}/d{z,z'}
  
• plots of derivatives d{x,x'}/d{x,x'}
• plots of derivatives d{z,z'}/d{z,z'}
• plots of derivatives d{x,x'}/d{z,z'}

Tagger dipole contour plots -- 19 November 2014
[Note: See later posting "Analysis of the Field Maps (2 July 2015)" for revised contour plots]

I have made contour plots of the uniform-field region for the three measured field maps, using contour levels spaced by 20 gauss at 1.5T and equivalent fractions of full field at 0.75T and 1.7T.
Specifically,
0.75T: B_max = 0.7506 T, contours = .751,.749,.748,.747,.746,.745,.74,.73,.70,.60,.50,.40.,.30
1.5 T: B_max = 1.5017 T, contours = 1.502,1.500,1.498,1.496,1.494,1.492,1.490, 1.48,1.46,1.4,1.2,1.0,.8,.6
1.7 T: B_max = 1.7021 T, contours = 1.7023,1.7000,1.6977,1.6955,1.6932,1.6909,1.6887,1.6773,1.6547,1.5867,1.3600,1.1333,.9067,.6800
The structure with a period of 4 cm in X is a consequence of imperfect probe calibration at the level of a few gauss. It should not have any detectable effect on the raytracing calculations.
• 0.75 T contour plot (pdf file)
• 1.5 T contour plot (pdf file)
• 1.7 T contour plot (pdf file)
• 3 plots on one page for easy comparison (pdf file)

New field analysis results -- 23 October 2014

• B(at NMR probe)/E₀ and B(at NMR probe)/Current using scaled field (Table and plots)

By ray-tracing through the measured and Tosca fields, I have calculated the scale factor needed to multiply the field to give a full-energy deflection of 13.400 degrees.

By interpolation in the field maps to the nominal position of the NMR probe (x=-12.8 cm, y=-283.0 cm) I have calculated the NMR value required to steer the full energy beam to the dump at E₀ = 12, 13.6 and 6 GeV, corresponding to the nominal map fields of 1.5, 1.7 and 0.75T.  Note that the interpolated field at the probe position at 1.7T differs by about 9 gauss from the actual NMR reading recorded in the mapping data files -- not a big effect (0.05%), but bothersome.


The Tosca field results vary significantly (by more than 0.1%) from the measured field. This is presumably related to the fact (noted earlier) that the measured fields increase slightly with x, while the Tosca fields do not -- probably because the poles deflect slightly when the field is on.

• Comparison of B vs y at different x with average B and B at NMR probe position (plots)

The large difference in B(at NMR)/E₀ at 6 and 12 GeV seen in the previous plot is due to a substantial difference in the field shape. The square data point on each plot shows the interpolated field at the NMR probe position. At 0.75T this is very close to the maximum field in the gap, while at 1.5T and 1.7T it is close to a minimum versus x. The horizontal line shows the average field along the line x=0.

The breaks in B seen at the transition between Configurations 1 and 3 (near y=0) are not as big as they look at first glance -- typically 2 or 3 gauss on each curve. I have not made any attempt to smooth things at that level.

The increased non-uniformity of B at 0.75T is surprising, but I saw similar effects with the Hall B tagger magnet. My interpretation is that it is due to the fact the permeability begins to decrease at low excitation, so that the lowest-energy field configuration is not necessarily the most uniform.

• Shifts of E/E₀ at the focal plane for 13.6 GeV and 6 GeV relative to 12 GeV (plot)

This plot shows that the energy calibration of the tagger focal plane as a function of E/E₀ is essentially independent of E₀. Using the 1.5T-derived map for all E₀ will give an error of less than 3 MeV, which is less than the resolution of any microscope or fixed-array channel.

Summary and directory of field maps for raytracing -- 21 July 2014

• Field_maps.html

Derivatives of beam optical quantities -- 21 July 2014

At the request of Richard Jones, I have calculated first derivatives of the focal plane quantities x_FP, x-angle, z_FP and z-angle, with respect to x, x', z and z' at the radiator, as a function of electron energy (assuming E0 = 12 GeV). These derivatives were calculated by taking positive offsets of 1 mm in x and z and 1 electron characteristic angle in x' and z', and comparing with the central ray.
I have checked that the dependence is essentially linear except for one case: dx_FP/dx'₀ vanishes at the point-to-point focal plane, which intersects the nominal focal plane at E_e ~ 3.3 GeV. In this region, the calculated first derivative is small and not very meaningful.
The table contains only 8 of the possible 16 derivatives. The derivatives of z and z' with respect to x and x' are exactly zero. The derivatives of x and x' with respect to z and z' are small and randomly distributed due to precision uncertainties of order 0.5 ppm, and have also been omitted.

• snakederivs.out (text file)

Using the new fixed-array counter positions from the mounting plates -- 02-July-2014

• Table of new counter positions (text file) (Excel file)
• Table of fixed-array counters with nominal and new energy boundaries and angles (text file) 
• Plot of difference between actual (mounting-plate) and nominal (Wiki table) fixed-array counter positions (pdf file)
The X and Y values are in Focal Plane coordinates. The blue + symbols show the nominal positions, and the red circles show the actual positions. The diagonal dashed lines show the normal Microscope region, in which the fixed-array counters are not installed.
The principal differences are
• Counters 1-131, which originally alternated between y=-8 and -13 cm, now alternate between -8 and -18 cm (counters 1-80) and then cycle between the 3 planes -8/-13/-18 cm for counters 81-131.
• Counters 194-274, in the "sampling" region below the Microscope, now (mostly) alternate between -8 and -18 cm instead of all being at -8 cm.
• Plot of revised energy boundaries of counters (pdf file)
This is a revised version of the plot of 26-June-2014 posted below. It shows the upper and lower energies relative to the nominal central energy, for both nominal and the revised calculations. The new calculations include both the new raytracing results and the corrected counter positions.
The largest change is seen in part of the sampling region (E_gamma between 5.6 and 7.3 GeV), where the alternation of the counters between the -8 and -18 cm planes now gives a substantial alternation in the energy limits. This is seen more clearly in the following plot.
• Plot of energy width and energy spacing of counters (pdf file)
The energy width (E_high - E_low) is plotted with blue squares, and the energy spacing (E_high_[n] - E_high_[n+1]) with red triangles. We see that the large variation in energy limits between 5.6 and 7.3 GeV is due to a variation in the energy spacing, which alternates between 57 and 63 MeV, rather than the nominal 60 MeV. Note that the alternation between the y=-8 and y=-18 cm planes has little effect on the energy width.
A more disturbing effect is seen between 8 and 10 GeV, where for some counters the energy spacing is smaller than the energy width, i.e. there is a partial overlap between adjacent counters even for central rays. For the full-coverage region above the Microscope (9-10 GeV) this overlap never exceeds 0.3 MeV out of a total width of 15 to 21 MeV, i.e. less than 2%. In the 8-9 GeV region, which will be installed only if the microscope is moved to lower energy, the overlap rises to 5%, plus one channel at 10%. We may wish to consider re-making the mounting plate for that region.

Some useful files -- 23-June-2014

• Position and angle of rays at tagger focal plane, 10 MeV steps (Excel file)
• Position and angle of rays at tagger focal plane, 30 MeV steps (Excel file)
• Table of fixed-array counters with nominal and new energy boundaries and angles (text file)   [Note: This file should be replaced with one with new counter positions -- see 2-July-2014 postings]
  The limits in the counter table are for central (zero-angle) rays only, and the counter thickness has been ignored. This table includes fixed-array counters in the normal Microscope position (Options 2 and 3). The counter widths for E_gamma between ~7.9 and ~8.2 GeV are not entirely consistent. I will update the table when I figure it out.

First raytracing results  --  23-June-2014

The processed field maps (described at the last meeting on 5-June-2014) have now been tested with SNAKE for the full range of electron energies, and agree quite well with previous calculations, as described below.

• Location and description of map files

For drawings and descriptions of the field boxes, endplanes and trajectories, see the files I posted for the previous beamline meeting (5-June-2014).

In case anyone is interested in using the map files, I have copied them to the JLab CUE in my directory /u/home/sober/HallD/maps .
A detailed description of the file formats and their intended use is given by the file Field_boxes_and_headers.pdf , which I have also copied to the /maps directory.


• Normalization of field maps
To make direct comparisons possible, each field map must be scaled so that the full-energy electron is deflected by 13.400 degrees. The necessary factors are as follows:
Nominal field    E0[GeV]    Measured map factor    Tosca map factor
    1.7 T        13.6        1.00114               : 0.998556   
    1.5 T        12.0        1.00029                0.996795
    0.75T         6.0        1.00097                0.999000


• Agreement of new raytracing with reference rays

Figure 1 shows some differences between the new rays using the 1.5T map and the "reference rays" (used in calculating the fixed-array counter placement) at the same electron energy. Except for the lowest energies (E_e < 1 GeV), the angles agree to better than 0.1 degree, and the perpendicular position x_perp=x_FPsin(theta) agrees to better than 2.4 mm. In the Microscope region (3 < E_e < 4 GeV), the x_perp differences are between 1.6 and 1.9 mm, or slightly less than one Microscope energy channel.

• Consistency of the three maps (1.7T, 1.5T, 0.75T) as a function of E/E₀

The curves labeled "1.7T - 1.5T" and "0.75T - 1.5T" in Figure 2 show the differences in x_FP and angle at the same value of E_e/E₀ between the corresponding pairs of maps. The angle differences are negligible (<0.04 degree), and the largest x_FP difference is about 2.5mm, which corresponds to a small fraction of a Microscope energy channel. The conclusion is that the raytracing results using the 1.5T map may be scaled to any incident energy without significant loss of accuracy.

• Consistency of field maps with Tosca fields

Figure 2 also shows the differences in x_FP and angle calculated using the measured field maps and using the Tosca field at the same excitation. These differences are again small (less than one Microscope channel). The results for the three fields are quite consistent with one another, and can be explained in sign and order of magnitude by the following argument:

• The full-energy electrons travel mainly through the region x < 0. (see figure from June 5 update)
• The low-energy electrons travel mainly through the region x > 0.
• As previously noted, the measured field between the poles increases slightly with x (Figure 3) , probably because of a very slight non-parallelism of the poles.
• The Tosca field shows no x-dependence.
• The field maps are normalized by the requirement that full-E electrons deflect by 13.4 degrees.
• Therefore the low-E electrons deflect more in the measured field than in the Tosca field
A difference of ~10 gauss (consistent with Figure 3) between the average field seen by the full-E and low-E electrons is sufficient to explain the observed differences.

The map-vs-Tosca differences shown here are about a factor of two smaller than the differences from the "reference rays" shown above. The reference rays were in principle calculated (not by me) from a different version of the 1.5 T Tosca map (with the grid in room coordinates.) I don't know the details. In any case, the differences are not large, and I don't think that this mystery is worth pursuing.

• Energy boundaries of fixed-array counters (plot revised 26-Jun-2014)
  Note: This plot was calculated using the old (2013) counter position table, not the actual mounting-plate positions.  See revised plot of 01-Jul-2014.

Figure 4 shows the upper and lower energies relative to the nominal central energy for each counter, plotted vs electron energy. The dashed curves show the nominal boundaries (symmetric about 0 by definition), and the solid curves show the results of the new raytracing analysis. Note that only on-axis rays have been traced for this analysis -- the actual boundaries will be diffuse and somewhat larger.
The energy regions have been labeled with the counter widths. The region populated by the 4 mm counters is normally occupied by the Microscope, whose fibers are 2 mm wide. Relative to the nominal boundaries, it is seen that the new analysis shifts the channel energy by no more than half a fixed-array counter (or one Microscope channel.)

• Eliminating angle error

The angles of the fixed-array counters are determined by the holes drilled in the mounting plates. Although the changes in angle relative to the reference rays are small (< 0.1 degree for E_e > 1.3 GeV, <0.05 degree in the Microscope region and beyond), it is worth seeing whether the angle error can be eliminated by shifting the x position of all or some of the mounting plates. Figure 5 shows the distance in cm by which each part of the focal plane must be translated in order that the local counters are aligned with the electron trajectory angles. (The enhanced region on the plot shows the position of the Microscope.) There is no single shift that would improve things everywhere, but, since the required shifts are increasing in the downstream direction, we may wish to consider inserting gaps between the mounting plates to improve the average angular alignment for each plate. However, given that our precision in angular alignment of the counters is in most cases worse than the error, this is probably a waste of effort.

Update on analysis of field maps  --  05-June-2014

I have completed the analysis and manipulation of the field maps, and am ready to begin raytracing calculations.
The following tables and figures illustrate the results. 
At each excitation I have produced 4 "field boxes" in the format used by the SNAKE code.  The boxes are named

• "Entry" - where all trajectories enter the field; based on config. 6
• "Main" - where most of the deflection occurs - based on config. 1-4
• "Exit" - where the highest energy electrons leave the field; based on config. 5
• "Focal" - between the main field map and the focal plane; calculated by Tosca

• Table of field map analysis results
• Table of the 4 field boxes for raytracing
• Drawing of field boxes and endplanes with reference rays and magnetic field values at exit.
• Drawing of field boxes and endplanes to actual scale

Progress summary (all regions completed 12-Feb-2014)

• Dot plot of all points measured  (Configurations 1 through 6) 

Entry beam pipe region (Configuration 6) (added 06-Feb-2014)

• Measured points compared to beam line

• Log plot vs Y_map
• Linear plot vs Y_map

Configuration 3 (mapped Feb 3-4, 2014) (added 07-Feb-2014)

• 1.5 T - uncalibrated
  • Plot of B vs y - central region (pdf file)
  • Plot of B vs y - fringe region (pdf file)
  • Plot of B vs x (-16.35 < Y < 56.15 cm)(pdf file)
  • Plot of B vs x (58.65 < Y < 131.15 cm)(pdf file)
• 1.5 T - calibrated
  • Plot of B vs y - central region (pdf file)
  • Plot of B vs y - fringe region (pdf file)
  • Plot of B vs x (-16.35 < Y < 56.15 cm)(pdf file)
  • Plot of B vs x (58.65 < Y < 131.15 cm)(pdf file)
  • Plot of B vs x (133.65 < Y < 206.15 cm)(pdf file)
  • Plot of B vs x (208.65 < Y < 256.15 cm)(pdf file)
  • Plot of B vs x (258.65 < Y < 308.65 cm)(pdf file)

Comparison with Tosca, and alignment tests (added 24-Jan-2014)

• General agreement with Tosca calculations
The field shape vs x near the long exit edge is in good agreement with the Tosca calculations, from full field down to about 300 gauss
• Log plot of 1.5T field (measured and Tosca) vs x for y=0,100,200 cm

I do not have actual power supply currents to compare with Tosca, but the ratios of field to power supply "PPM" values (using the prob calibration data at the center of the pole) are closely proportional to the Tosca B/NI ratios at 0.75, 1.5 and 1.7 T, which tells us that the saturation effects at high field are predicted correctly by Tosca. For B < 0.75 T, there is negligible saturation, and the ratio should be constant. The ratios at 0.05 and 0.1 T do not lie on the expected line, implying that there is a small (~2700 unit) offset in the "PPM" value, probably due to hysteresis effects.
• Field/current ratio compared with Tosca
(Note that on this scale, the probes are indistiguishable.)



• Alignment of Configuration 2
Matching the decrease of the field from maximum to ~1/2 max. with the Tosca calculation, the required offset in x is
22.44 cm at y=0,
22.48 cm at y=100cm,
22.49 cm at y=200cm
as compared with the nominal offset of 22.40 cm. These offsets are the same for all 3 fields.

• 1.5T field (at y=0) vs x:   measured and Tosca with offsets 22.40 and 22.44 cm


• Alignment of Configuration 1
The x alignment is hard to test, since the field falls by only a fraction of a percent at the minimum and maximum x values of Configuration 1, but this small drop is not in good agreement with Configuration 2 (at high x) or Tosca (at high or low x).
A shift of the Configuration 1 x-coordinate by 0.7 cm gives much better agreement at both ends (see figure.)  This effect is consistent at y=0, 100 and 200 cm, and at all 3 field values.
This shift is not important, because the field is essentially independent of x within Configuration 1 except for these end points.  We can ignore the highest 3 x-values from Configuration 1, since we have the Configuration 2 measurements for those points. (There are no electron trajectories in the region of the lowest x values.)

• 1.5T field (at y=0) vs x:   measured and Tosca with and without 0.7 cm shift of Config. 1
(probe calibrations not applied)

The Y alignment of Configuration 1 is easy to compare with Tosca, as there is a significant falloff at the last two values, 306.4 and 308.9 cm. (The 308.9 cm setting is missing from the 1.5T map.) Agreement with Tosca requires shifting the Y value of the measured points by about +0.85 cm.    Configuration 2 has no points near a Y field boundary.

• 1.7T field (Config. 1) vs y:   measured (with +0.85 cm shift) and Tosca
(probe calibrations not applied)

Configuration 2 (mapped Jan. 14-15, 2014)

• Configuration 2 at 1.5 T
  • Corrected raw data file 1.5T_conf2_001.txt (1110 records)
  • Corrected raw data file 1.5T_conf2_002.txt (39 records)
  • ASCII dot plot of measured points
  • Plot of B vs y,  11.5<x<30.5 cm
  • Plot of B vs y,  31.5<x<51.5 cm
  • Plot of B vs x,  -13.7<y<58.9 cm
  • Plot of B vs x,  61.4<y<133.9 cm
  • Plot of B vs x,  136.4<y<208.9 cm
  • Plot of B vs x,  211.4<y<276.4 cm

Configuration 1 at 1.5 Tesla (mapped Jan 8, 2014)

• Corrected raw data text file, 13.85 cm < Y < 306.35 cm, -14.5 cm < X < 9.5 cm
• ASCII "dot plot" showing number of measured values at each point of the full grid
• The "2"'s appear because Probe 1 reads the same point measured by Probe 5 on the previous pass.


• Plot of B vs y (pdf file)
• Plot of B vs y - central region (pdf file)
• Plot of B vs y - fringe region (pdf file)
• Plot of B vs x (-13.65 < Y < 58.85 cm)(pdf file)
• Plot of B vs x (61.35 < Y < 133.85 cm)(pdf file)
• Plot of B vs x (136.35 < Y < 208.85 cm)(pdf file)
• Plot of B vs x (211.35 < Y < 283.85 cm)(pdf file)
• Plot of B vs x (286.35 < Y < 306.35 cm)(pdf file)
• Plot of B vs x (286.35 < Y < 306.35 cm) - fine scale (pdf file)
• The first and fifth probes are averaged (but there is no visible difference if we use only one.)
• The periodic structure is due to Probe 4 (alias P2) reading high.


• Table of B vs y for -14.5 < X < -5.5 cm
• Table of B vs y for -4.5 < X < 4.5 cm
• Table of B vs y for 5.5 < X < 13.5 cm
• Table of B vs x for -13.65 < Y < 8.85 cm
• Table of B vs x for 11.35 < Y < 33.85 cm
• Table of B vs x for 36.35 < Y < 58.85 cm
• Table of B vs x for 61.35 < Y < 83.85 cm
• Table of B vs x for 86.35 < Y < 108.85 cm
• Table of B vs x for 111.35 < Y< 133.85 cm
• Table of B vs x for 136.35 < Y< 158.85 cm
• Table of B vs x for 161.35 < Y< 183.85 cm
• Table of B vs x for 186.35 < Y< 208.85 cm
• Table of B vs x for 211.35 < Y< 233.85 cm
• Table of B vs x for 236.35 < Y< 258.85 cm
• Table of B vs x for 261.35 < Y< 283.85 cm
• Table of B vs x for 286.35 < Y< 306.85 cm

Old information - 12 December 2013

Here are some files which may be helpful in analyzing the mapping data.
Updated versions of these files are available at JLab on ~sober/HallD/tagger_mapping, in case you are able to read them there.