Plug-Coil Overstress Protection

At the design bore the burner plug coil is stressed 3-3.9x beyond feasibility; the protection loop treats coil stress as a first-class safety limit, not a design detail.

A structural limit stated honestly

The burner's end-plug field of 26.49 T (with a 17 T throat) implies mechanical stresses on the plug coil that, at the design bore, exceed feasible material limits by a factor of about 3–3.9. As specified, the coil is infeasible — this is a documented design-and-simulation gate, not a solved problem. The overstress protection loop exists to make that limit inviolable in any built prototype: coil stress is monitored and enforced as a hard trip condition.

def stress_ratio(hoop_stress_MPa, allowable_MPa):
    return hoop_stress_MPa / allowable_MPa

def coil_permit(ratio, trip_at=1.0, warn_at=0.85):
    if ratio >= trip_at:
        return 'TRIP -> dump'      # never operate an overstressed coil
    if ratio >= warn_at:
        return 'WARN -> limit current'
    return 'permit'

# the design-point specification sits at ratio ~3-3.9: infeasible as-is
assert coil_permit(3.4) == 'TRIP -> dump'

What protection can and cannot do

• It CAN guarantee no built coil is driven past its real material limit — current is capped or dumped first.
• It CANNOT make the specified 26.49 T bore feasible; that requires a design change, not a control loop.
• It therefore bounds the achievable operating field to what the actual coil can survive, and reports the gap.

The protection loop is coupled to the magnet energy extraction path: an overstress trip drives the coil current into the dump rather than holding it. Coil stress is inferred from strain sensing and the structural model, cross-checked, and voted like any critical safety signal (see voting and redundancy).

The protection loop's honest consequence is a bounded operating field: it will cap current at whatever the real coil can survive and report the gap between that and the specified 26.49 T bore, rather than pretend the specification is achievable. That gap is a design finding, surfaced by the control system, that feeds back to the magnet engineers — the loop's job is to make the limit inviolable and the shortfall measurable, not to close a gap that only a design change can close.

Stating the 3–3.9× gate plainly is part of the design philosophy: the control system is honest about the physics it must respect. This gate is why the burner is presented as a design-and-simulation study, and it composes with the plug-stability supervisor.