AI Plasma Shape Control (Tokamak) — 2D Poloidal Cross-Section

Target Shape

Controller

AI feedback gain (K_p) 3.0

Disturbance strength 0.40

Live Telemetry

● AI CONTROL ACTIVE

Shape error (RMS)

0.00

Vertical drift Z₀

0.00 m

Total coil current

0.0 kA

Stable time

0.0 s

Vertical-Mode Stability

Open-loop growth γ

0.00 /s

Closed-loop pole (Re)

0.00 /s

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How it works

This is the 2D companion to the 3D tokamak sim — and it is actually the more physically direct view: a poloidal (R,Z) cross-section, exactly the plane real tokamak equilibrium reconstructions (EFIT) are plotted in, with no toroidal revolve needed. The boundary uses the same Miller/D-shape parametrization:

R(θ) = R0 + dR + a·cos(θ + δ·sin θ)
Z(θ) = dZ + a·κ·sin θ

An elongated plasma (κ > 1) is vertically unstable: a small vertical displacement Z0 grows exponentially at open-loop rate γ = 1.4·(κ−1)², unless a feedback loop opposes it. A PD controller reads the shape error e = (κ,δ,dR,dZ) − target and commands a corrective coil-current term u = −K_p·e − K_d·ė. Linearizing the vertical channel around the target gives a clean 2nd-order ODE:

Z0'' + (1.5 + 4Kd)·Z0' + 4·(Kp − γ)·Z0 = 0

whose characteristic equation s² + (1.5+4K_d)s + 4(K_p−γ) = 0 has roots you can watch live in the "Vertical-Mode Stability" panel: when K_p > γ both roots have negative real part (stable, decaying oscillation); when K_p < γ the stiffness term goes negative and one root becomes a positive real growth rate — an open-loop runaway, exactly what real tokamak "disruptions" look like. Set the gain slider below γ to watch it happen.

Preset — sets the (κ, δ) target shape; higher κ raises γ and makes the control problem harder.
AI gain K_p — feedback strength; must exceed γ for the vertical mode to be stable.
Disturbance — random forcing on the shape state, standing in for turbulence and error fields.
Inject kick — a one-off large disturbance, like a real error-field event or ELM.
The strip-chart along the bottom scrolls Z0(t) in real time, so the growth or decay rate is directly visible, not just reported as a number.

Plasma boundary Target shape PF shaping coils