E.Chudakov
Last updated: 31 May 2018 by gen@jlab.org
Magnet model
The 2-dimensional program
Poisson/Superfish
is used to simulate the Hall D superconducting solenoid. The geometry of the coils and iron
is an interpretation of the post-installation measurements from 2013 and 2014,
outlined in the
Technical Report on the solenoid. The model
included certain simplifications, in order to adapt it to
the 2-D POISSON program and to finite mesh size:
Thin layers (shims) were attached to one of the adjacent iron pieces
covering the full cross section (in fact the shims are plates of a
smaller surface).
The structure of the conductor was ignored. The subcoils' cross sections
were simulated by rectangular areas with uniform current densities.
Some filler plates between the yoke rings are not uniform in φ.
These plated are presented as azimuthally-symmetric rings of the same
volume as the filler plates and of the same thickness, however
of a different radial dimensions, depending on the actual volume.
Components
18 subcoils (combined into 4 coils). The current through each subcoil is
defined by the full number of turns in the subcoil.
4 barrel iron rings, 2 iron endcaps and several filler plates.
2 cladding rings around the yoke. The gap in the cladding at the
bottom of the magnet was ignored.
The geometry is shown in the following pictures:
The full area used for the Poisson simulation. The mesh is of a variable size.
A pdf picture (large!) is available.
The central area used for the Poisson simulation. The mesh triangles are not drawn.
The picture shows the iron, the conductor and the field/potential lines calculated for 1300A.
The vacuum boxes drawn around the 4 coils are added just for viewing and play no role
in the magnetic calculations.
A pdf picture is available.
The full area selection
The Dirichlet conditions were used on the boundaries (no field perpendicular
to the boundary). The field drops to about 0.1 mT at a ≈10 m
distance:
The field contour plots, calculated for 1350A.
A pdf picture is available.
A large full area requires more nodes on the mesh and longer calculations.
A smaller area is less accurate far outside of the magnet but
may be more accurate inside since a finer mesh can be used.
Z -900cm:1300cm; R 0:1380cm (large area)
Z -500cm: 800cm; R 0:400cm (small area)
The mesh
Poisson allows several areas in Z (and, independently, in R)
with different steps. However, in each projection there could
be not more than 8 areas. It is recommended that the steps in the
adjacent areas differ by a factor not greater than 2-2.5.
The results may depend strongly both on the number of nodes and
on the configurations of the mesh.
The following cases have been observed:
Good result: the calculations converge and the solution is reasonably
smooth.
Fair result: the calculations converge, the full energy estimate
is correct, but there are large point-to-point
fluctuations of the field in some areas.
Poor result: the calculations failed to converge reaching the used limit
for the number of iterations (200000), the full energy estimate
is incorrect and there are very large point-to-point
fluctuations of the field.
No result: POISSON.EXE crashes with a kind of a segmentation fault error.
The Poisson program prints warnings if the conversion speed is low,
suggesting to modify the "relaxation parameter" rhogam in a range
of 0.0005 - 0.08. I found that using a smaller parameter 0.08->0.0005
could improve the convergence and the number of iterations needed,
but would not improve the point-to-point fluctuations
(converting a case #3 to a case #2).
In order to simulate the effects of a small conductor motion I tried to
use as fine mesh as possible, at least in the areas around the conductor.
The full area used was -500cm:800cm in Z and 0:400cm in R. The smallest
steps producing a smooth solution were of 2.5mm in R and 5.0mm in Z,
in the area around the conductor.
The field "fluctuations" were checked in the areas where they were most
noticeable and where the field dependence on the radius
could be approximated with a 2-nd order polynomial function.
The deviations from the fitted functions was calculated along the lines:
line #1 Z1,R1->Z2,R2 (in cm): 30,165->30,180 in iron
line #2 Z1,R1->Z2,R2 (in cm): 30,115->30,130 in air outside of the coils
.am file Min steps: 2.5mm in R and 2.5mm in Z (small area)
.am file Min steps: 2.5mm in R and 2.5mm in Z (larger area)
.am file Min steps: 2.5mm in R and 1.25mm in Z (small area)
The mesh structure is given in the following table
(the units are cm):
The results are shown in the next table. The calculated RMS of BZ
are shown in the last two columns. Although in all 4 cases the calculations converged
after about 20000 iterations, only the first case produced a relatively small
fluctuations along the line #2 - about 20 Gauss. Decreasing the step size
in Z from 0.5cm to 0.25cm, even in a small area around Coil#2, increases the
field RMS to about 200 Gauss. A 0.125cm step in Z leads to strong fluctuations
of about 2000 Gauss.
The field plots for the cases #1-2 and #4 are shown on the following plots:
Case #1: The fields BZ, BR (Gauss) interpolated with a 1mm step
along a Z=30cm line are shown. No significant field fluctuations are seen.
A pdf picture is available.
Case #2: The fields BZ, BR (Gauss) interpolated with a 1mm step
along a Z=30cm line are shown. Some field fluctuations are seen.
A pdf picture is available.
Case #4: The fields BZ, BR (Gauss) interpolated with a 1mm step
along a Z=30cm line are shown. Strong field fluctuations are seen.
A pdf picture is available.
I checked if a finer mesh could be used for a simplified conductor geometry. The motivation
was to simulate the effect of a small motion of a a part of the coil, for example a pancake.
Assuming no saturation effects in steel one could simulate just the field generated by one
pancake at different locations, without the other conductor.
Simulation of the field produced by one pancake, at 3 different locations.
This plot presents the results for the central pancake at a 1500A current
(the pancakes at the sides are at zero current).
A pdf picture is available.
With a 0.5mm step in Z the field curve is smooth. However, if a 0.25cm step is used
in a range of 36<Z<68cm the fluctuations emerge again:
One pancake simulation at 750A: The fields BZ, BR (Gauss) interpolated with a 1mm step
along a Z=48.5cm line are shown. Field fluctuations are seen.
A pdf picture is available.
In summary, one can use a 0.25cm mesh step in R in the area of the conductor,
but only a 0.5cm step in Z.