Stored-Energy and Beta Feedback

Beta and stored-energy feedback keeps plasma pressure near its performance target while staying below the limit where pressure-driven instabilities appear.

What beta measures

Beta is the ratio of plasma pressure to magnetic pressure. It is a direct measure of how efficiently the magnetic field is being used to confine pressure. Higher beta means more fusion power for the same field, but beyond a limit the plasma becomes unstable to pressure-driven modes. Control aims to sit just below that limit.

Stored energy

Stored energy is the total thermal energy in the plasma, closely related to beta and to confinement quality. It is estimated in real time from magnetic measurements (a diamagnetic signal) and from profile diagnostics. Because stored energy sets both fusion output and the severity of a disruption, it is a primary controlled variable.

The feedback loop

The main actuator is heating power. A beta or stored-energy controller compares the estimate against a reference and modulates auxiliary heating to hold it. Fueling and current can also be trimmed. The loop must respect the beta limit as a hard constraint, backing heating off if the plasma approaches instability.

Interaction with the limit

The beta limit is not a fixed number; it depends on the current and pressure profiles. Operating near it is safe only if profile control keeps the plasma shape of the pressure and current favorable. This ties beta control to current-profile control, so the two loops are designed together rather than in isolation.

In the Kronos program

The Hyperion breeder's design operating point corresponds to 88.7 megawatts of fusion power at a gain of 3.424. Stored-energy control holds the plasma at the pressure that produces this output while profile control maintains the margin to the beta limit. Because the machine is in simulation ahead of construction, these loops are tuned against validated models rather than hardware.