Scenario and Trajectory Optimization
Scenario optimization searches for an actuator trajectory that reaches a target plasma state while respecting every operational and stability limit.
What a scenario is
A discharge scenario is the full time history of the controlled quantities and the actuator waveforms that produce them: how current ramps, when heating turns on, how density is built, and how the plasma is shaped. Optimizing a scenario means choosing this history to reach a goal, such as a stable high-performance phase, at least cost in stress and risk.
As an optimization problem
The problem is posed with a cost function (for example, time to target or actuator effort), a dynamics model, and constraints. Constraints encode physics limits such as the density limit, the beta limit, and the safety factor staying above unity, plus engineering limits such as coil current and heating power. The optimizer finds a feasible trajectory that minimizes cost.
# Sketch of a trajectory optimization statement
minimize J(x, u) # cost over states x and actuators u
subject to x[k+1] = f(x[k], u[k]) # plasma dynamics model
g(x[k]) <= 0 # stability limits (q>1, beta, density)
u_min <= u[k] <= u_max # actuator limits
x[0] = x_init, x[N] in X_targetFeedforward and feedback together
The optimized trajectory becomes the feedforward plan. Feedback controllers then correct for the difference between plan and reality. A good scenario keeps the plasma close enough to the plan that feedback only has to make small corrections, which keeps actuators away from their saturation limits.
In the Kronos program
For the Hyperion breeder, scenario optimization must respect the negative-triangularity shape and drive toward the design operating point without crossing stability boundaries during the ramp. Because the machine is not yet built, these trajectories are developed against validated models and rehearsed in the flight simulator so that the first hardware discharges follow a well-understood plan.