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BELFEM 0.9.3
Berkeley Lab Finite Element Framework
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BELFEM 0.9.3
Berkeley Lab Finite Element Framework
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Date: 2026-09-18 Purpose: REBCO tapes wound around a flat Rutherford-type core, with a Python-generated mesh.
This deck models the flat, flexible REBCO cable of Romancew (2026): REBCO tape wrapped helically around a Rutherford-type copper core. The core is a flat bar with rounded edges, a stadium in cross-section, and the tapes follow it at a constant lay angle measured from the cable axis. The deck winds five 4 mm tapes at 30 degrees, the most that fit on the core, covering 89 % of its surface; the reference study wraps a single tape (numTapes = 1). A translated periodic condition represents a fifth of a pitch of an infinite cable, after which every tape continues into its neighbor. A 30 A ramp over 10 s drives the model for 15 s with Newton, Anderson stabilization, MUMPS, and GMRES. The copper core is not modeled: its section is meshed as air, so the deck is about the tape alone.
python/main.py generates the mesh, writes rutherford.msh, and prints the matching topology section in rutherford_topology.conf. The parameters follow the reference study: tape width 2, 4 or 6 mm (default 4), lay angle 30 or 45 degrees (default 30), edge radius 0.9 mm (a 1.8 mm thick core). The core width is not documented there; 12 mm is a placeholder.
The cable axis is z. The core cross-section is a stadium of width cableWidth along x and thickness 2 edgeRadius along y: two flat faces joined by semicircles of radius edgeRadius. Its perimeter is
P = 2 (cableWidth - 2 edgeRadius) + 2 pi edgeRadius
The extruded core is a developable surface, so a tape at lay angle θ is a straight band in the unrolled (arc length, z) plane, advancing tan θ of perimeter per unit z. One turn takes the pitch L = P / tan θ along z, the tape covers tapeWidth / cos θ of perimeter at any z, and the tape is only bent, never stretched, in this idealization. On the round edges the tape crosses the curvature obliquely: its centerline sees the bending radius edgeRadius / sin² θ and the twist rate sin θ cos θ / edgeRadius (Euler's theorem on the cylinder), so a 30 degree lay bends the tape half as much as a 45 degree lay. The generator prints both numbers.
Multiple tapes per layer sit at equal perimeter spacing. Stacked layers are counter-wound (criss-cross) at the same pitch, which makes their lay angles differ slightly because the outer stadium has the longer perimeter; layAngle is the layer-0 value. The end planes are pure translations of each other, so numPitches * numTapes must be a whole number (a third of a pitch with three tapes closes with the tapes permuted). The half-pitch closure by a 180 degree rotation about the axis, which the stadium's symmetry would allow, is not implemented.
The closure decides how many conductors the model has. Because tape k continues into tape k + q across the periodic planes, with q the number of tape positions advanced over the model length, a layer of n tapes is gcd(q, n) galvanically separate conductors. With five tapes over a fifth of a pitch that is one conductor: a single tape of five times the length, crossing each end plane five times. Every conductor is one current condition and consumes one cohomology generator, and a periodic model spends a further generator on the free axial loop. The condition is defined on one crossing of the conductor, the back-plane and front-plane curves of its first tape ([1] and [2]), with the tape current as amplitude: the current is the same on every crossing, so one crossing fixes it, exactly as corc_periodic_bc does. Listing several crossings of one conductor in one bracket group is a different condition (the group chain links the conductor once per crossing) and is not what is wanted here.
The tape strips are built from rows at constant z, spaced so the step along the tape equals tapeResolution; the slots across the tape are the same size. A strip quad is therefore a parallelogram with one side along the perimeter and one along the tape, and the periodic cut planes are rows of the mesh rather than slices through elements. Split along the short diagonal, the quads give near-equilateral triangles at 30 degrees. The bare core between the tape turns is meshed at gapResolution. The flat/round junctions cross these elements; the chord error is a few micrometers at the default resolution. End caps are meshed once in the plane through the exact ring positions and instantiated at both ends, so the periodic pairs match node for node. With the defaults, the mesh has about 15 000 nodes and 74 000 tetrahedra and takes twenty seconds to build.
| file | role |
|---|---|
| python/main.py | mesh generator; run it from this directory |
| python/rutherford/, python/mesh/ | packages the generator uses |
| python/rutherford/tests/ | unit and end-to-end tests for the generator |
| input.conf | deck |
This deck ships no .geo. The mesh is built by a Python tool, which also prints the matching topology section for input.conf:
Run it from this directory so the mesh lands where input.conf expects it. The tool needs numpy and calls the gmsh executable. The tests run from python/:
Romancew, E. (2026). Development and Characterization of Flat and Flexible REBCO Cables for High-Field Accelerator Magnets. M.S. thesis, Northern Illinois University. Tape widths, lay angles and the bending study; the core cross-section is not given there.
1.18.0