Coordinate Systems in the Model
How the toroidal frame of the breeder and the axial frame of the burner are set up so measurements are unambiguous.
Two natural frames
The two machines have different symmetries, so the model uses two coordinate conventions. Getting these right matters because every measurement callout is expressed in one of them.
Hyperion: cylindrical toroidal frame
Hyperion is nearly axisymmetric about its vertical centerline, so it uses a cylindrical frame with three coordinates: major radius R measured outward from the centerline, height Z measured up and down from the midplane, and toroidal angle phi around the machine. Plasma shape parameters, triangularity and elongation, live in the R-Z plane, which is why the poloidal cutaway is the canonical shape view.
The burner: axial frame
The burner is a long linear device, so it uses an axial frame: distance s along the mirror axis, radius r from that axis, and azimuth theta around it. Components are located by their s-position, so the callout for a plug throat reports where along the axis it sits and how tightly the field lines pinch there.
Origin choices
- Hyperion's origin sits on the centerline at the plasma midplane, so Z is symmetric about zero.
- The burner's origin sits at the center of the central cell, so the two plugs are symmetric in positive and negative s.
Why it is stated
Publishing the frame is part of keeping the model a usable engineering record. A reader who wants to check a coil position against the design paper needs to know exactly what R, Z, or s a callout refers to. See Units and Scale for how those coordinates are dimensioned.