M IND Field Calculations Bob Wands April 27, 2011 1 Overview of M - PowerPoint PPT Presentation

M IND Field Calculations Bob Wands April 27, 2011 1

Overview of M IND Toroids • The M IND toroids are octagonal planes with a 14 meter span across the flats • There are two layers of 1.5 cm thick iron per plane • Layers are plug-welded to each other • Each layer consists of seven 2-meter wide plates • Orientation of seams (slots) is rotated 90 degrees between layers • Assembled plane is supported by ears • M agnetization is provided by 100 kA current in 10 cm diameter central hole 2

Plate Pattern – Slots in both layers are shown 10 cm dia hole for current Note: All 3-d plots shown in this presentation have the slots on the visible face running from the upper left to the lower right 3

Detail of slots and gaps in M IND plane Slot width of 3 mm and gap width of 0.5 mm were chosen based on plate tolerances and M inos Layer 2 3 mm slot experience Layer 1 0.5 mm gap 4

• The LDJ , M S10360, and KJS curves were measured for the M inos experiment. • The CM S Endcap curve was measured by PSL-Wisc for the CM S endcap iron • The CM S Endcap curve was used in the analyses presented here, as it is the most “conservative” of the curves. BH Curves 2.5 2 1.5 B - T LDJ 1 MS10360 KJS CMS Endcap 0.5 0 0 5000 10000 15000 20000 25000 30000 H - At/m 5

2-d M odel 1. Element is 8 node quadrilateral, ANSYS Plane53 – superb element 2. Formulation is magnetic vector potential 3. M odel is incapable of generating a z-component of field 4. M odel is assumed to represent a region far from ends of magnet 5. Current is applied as a current density to a circular region of elements at the model center 10 cm in diameter 6. Element size in the iron plane is 2.5 cm 7. Total degrees of freedom is 1.1 million 3-d M odel 1. Element is 8 node brick, ANSYS solid96 2. Formulation is magnetic scalar potential 3. M odel will generate a z-component of field if necessary 4. M odel is assumed to represent region far from ends of magnet 5. Current is applied as a total NI in a Biot-Savart primitive with a square (0.0707 m x 0.0707 m) cross section 6. Element size in the iron plane is 2.5 cm 7. Total degrees of freedom is 4.7 million – very fine for 3-d, but we could go finer 6

Approach to Verification of the Analysis • The 2-d and 3-d ANSYS magnetic models are compared for the case of homogeneous iron. With homogeneous iron, the two models are simulating precisely the same toroid. • It will be shown that the two models – which differ in formulation, dimensionality, and element order – produce very similar results • This exercise is necessary because the true 3-d configuration with slots and gaps cannot be simulated satisfactorily in 2-d, and therefore confidence in the 3-d model is imperative. Note: Neither the 2-d nor 3-d model includes the current return bus. When the location of this bus is specified, it can be easily added to the models 7

Flux Lines from 2-d Analysis – homogeneous iron 8

ANSYS results for azimuthal B-field – homogeneous iron Comparison of 2-d and 3-d results 2-d model 3-d model 9

Note: Results for 2d and 3d model with homogeneous iron are essentially identical on scale of plot Azimuthal B-field along line A-B - from 3d Model 2.6 2.5 B 2.4 2.3 2.2 A B-field - T 2.1 2 1.9 1.8 1.7 1.6 1.5 0 1 2 3 4 5 6 7 Distance along line A-B - m 10

2d and 3d Azimuthal B-field Comparison – Homogeneous Iron 0.5 0 B -0.5 Percent difference -1 A -1.5 -2 -2.5 0 1 2 3 4 5 6 7 Distance along line A-B - m 11

Azimuthal B-field from 3-d M odel with slots and gaps With homogeneous iron With slots and gaps 12

Note: path is in the middle of layer 1, i.e., 7.5 mm below the surface of layer 1 Azimuthal B-field along line A-B from 3-d Model 3 B with slots and gaps 2.5 with homogeneous iron A 2 B-field - T 1.5 1 0.5 0 0 1 2 3 4 5 6 7 Distance along line A-B - m 13

Through-the-Thickness Variation of Field in a Layer • To examine the through-the-thickness variation of field in a layer, five circular paths with radius 4.15 m were created at five different z-depths in layer 1. Depths were 0, 0.375 cm, 0.75 cm, 1.125 cm, and 1.5 cm. • The azimuthal b-field was calculated around each path at 25000 points (about 1 mm spacing to ensure hitting slots) • The azimuthal b-fields at the five points through the thickness were averaged and plotted • The maximum deviation of the five through-the-thickness values from the average value was plotted Note: Radius of 4.15 m was chosen to have the paths pass directly through four regions where the layer 1 and layer 2 slots cross. In these regions, there is a 3x3 mm hole through both layers of iron 14

Average B-azimuth through thickness at R = 4.15 m 2.5 slots- layer 2 slots - layer 2 x A x x 2 x 1.5 B-field - T 1 0.5 slot - layer 1 slot - layer 1 slots - layer 1 slot crossings - layer 1/ layer 2 slot crossings - layer 1/ layer 2 0 0 5 10 15 20 25 Distance along path from point A - m 15

M aximum deviation from average field through thickness 45 x A 40 x x slot crossings - layer 1/ layer 2 35 x 30 % deviation 25 slot crossings- layer 1/ layer 2 20 15 10 slots - layer 2 slots - layer 2 5 0 0 5 10 15 20 25 Distance along path from point A - m 16

Current Status • A 3-d field map on a 5 cm grid has been generated for the mid-layer z- positions of layer 1 and layer 2 for preliminary evaluation by the collaboration • The field map can be produced in any arbitrary z-plane through a given plane of iron. • Smaller grid sizes are possible; files grow very large • Slot and gap sizes can be varied in future work; M inos assumed a variation of slot size based on observation of actual assemblies. 17