D. Sober 12-May-2013
The dependence of the tagger magnet on excitation current must be understood before field mapping begins, so we can determine at how many excitations to obtain maps.
I have been studying the Tosca field maps calculated by Yang for
various magnet excitations, corresponding to central fields of 6,
9, 12, 14, 15, 16 amd 17 kG. These files (B_y at y=0 versus x and
z in 1-cm steps) were posted by Richard Jones at https://halldweb1.jlab.org/wiki/index.php/Tagger_Magnetic_Field_Maps
See the section titled “Dipole centre plane at different fields”.
This file also lists the number of Ampere-turns used for each
field setting.
[Note: These files are self-extracting perl scripts, BUT perl seems to skip (without comment) occasional records in which 0 is replaced by a very small real number, leading to a lot of frustration. I ended up extracting data from the original large files. ]
The origin of the coordinate system is at the center of the inner edge (toward the return yoke) of the pole. The x coordinate (normal to the long pole edges) extends from -25 cm (inside the return yoke) to 100 cm (far into the fringe field). Because of symmetry, only positive z values (0 to 400 cm) are calculated. It appears that the nominal exit edge, called x=0 in Sascha’s and my previous calculations, is at approximately x=43 cm in the new files.
To compare the fields at various excitations, it is useful to compare the normalized quantity
B[Gauss]/NI[Ampere-turns], which in the case of infinite-permeability iron would be independent of excitation and depend only on the gap width as (in SI units)
Bgap = μ0 N I / d.
For a 0.030 m gap, this gives B/NI = 4.189×10-5 T /Amp-turn = 0.4188 Gauss/Amp-turn.
The values of B/NI obtained for the Tosca calculation vary from
0.828 Gauss/Amp-turn at low excitation (6 and 9 kG) to 0.74
Gauss/Amp-turn at 17 kG. The first value is very close to double
the infinite-permeability result, which means that Yang has listed
the ampere-turns per coil,
and not the total for both coils, so the actual number of
ampere-turns is twice his value. I have continued to use Yang’s
number in the denominator.
The following table gives the maximum and central (z=0, x=20 cm)
values of the field and of B/NI for each of the seven calculated
maps.
| Nominal B [kG] |
NI [Ampere-turns] |
Max. B [Gauss] |
Max. B/NI [Gauss/Amp-turn] |
Center B [Gauss] |
Center B/I [Gauss/Amp-turn] |
| 6 |
7241.67 |
6003.59 |
0.829033 |
6001.06 |
0.828685 |
| 9 |
10880.06 |
9003.54 |
0.827527 |
8999.51 |
0.827156 |
| 12 |
14573.25 |
12006.71 |
0.823887 |
12000.29 |
0.823446 |
| 14 |
17152.56 |
14010.17 |
0.816797 |
14000.32 |
0.816223 |
| 15 |
18643.50 |
15046.22 |
0.807049 |
15032.72 |
0.806325 |
| 16 |
20393.10 |
16019.43 |
0.785532 |
16000.31 |
0.784594 |
| 17 |
23051.25 |
17047.89 |
0.739565 |
17004.86 |
0.737698 |
The most informative single plot is probably the one labeled "Plot vs B" under "B vs x". If the permeability were infinite, the field per ampere-turn would be constant at about 0.83 gauss/amp-turn. The figure shows that the saturation effects are significant at the operating field of 15 kG.
If you look at the "fine" plots of B/NI versus z, you will note that the saturation effects are not uniform through the magnet. For B>15 kG, the field at the ends of the magnet (z = ±300 cm) is slightly higher than the field at the center (z=0), while at lower fields the z-dependence is negligible.
Below are the files I extracted from Yang’s calculations, together with some plots and the Excel spreadsheets I used to produce them.