Superconducting Magnet Current Ramps
Bringing a superconducting coil to field means ramping current slowly enough that induced losses and stresses stay within safe limits.
Why ramps are slow
A superconducting magnet stores energy in its magnetic field, E = (1/2) L I squared, where L is inductance and I is coil current. Changing current at rate dI/dt induces a voltage V = L dI/dt across the winding and drives eddy and hysteresis losses in the conductor and structure. Because the coil sits near its critical temperature, any excess heat can drive a normal zone, so ramps are deliberately gradual.
Rate limits
The controller enforces a maximum dI/dt set by three constraints: the terminal voltage the power supply and insulation can tolerate, the AC loss the cryoplant can remove, and the Lorentz stress the structure can carry as field rises. In large tokamak-class coils, ramp times to full field are minutes to tens of minutes, not seconds.
Control structure
Ramp control is usually feedforward: the desired current profile I(t) is a smooth trapezoid or S-curve with bounded first and second derivatives, and a fast inner loop regulates the power-supply output to track it. A measured current signal (DC current transducer) closes the loop, while a separate quench-detection channel watches for resistive voltage that a healthy ramp would not produce.
Kronos context
The Hyperion breeder is a spherical tokamak with a 16.84 T peak field on the toroidal-field structure and roughly 8 T on axis. Its coil set is a design and simulation target, not built hardware; ramp schedules in the model stage field before plasma initiation so equilibrium and vertical-control coils have headroom when the plasma forms.
- Ramp I(t) with bounded dI/dt and d2I/dt2
- Regulate supply voltage to track the reference
- Hold quench detection armed throughout
- Coordinate multiple coils so net force stays bounded
A clean ramp ends in a steady flat-top current held by the supply, or in persistent mode where a superconducting switch closes the circuit and the leads carry little current.