Vertical Displacement Arrest

An elongated negative-triangularity plasma is vertically unstable; the position loop must catch a growing displacement faster than it can run away.

Catching a runaway before it runs

The breeder plasma is shaped with negative triangularity (δ = −0.30) and is vertically elongated, which makes it vertically unstable: a small vertical displacement grows exponentially unless actively opposed. The vertical position loop drives the fast poloidal-field coils to arrest the displacement, and it must have enough bandwidth and enough control authority to win the race against the growth rate.

import math
def controllable(gamma_s, loop_bw_hz, u_available, u_needed):
    # need both fast enough loop AND enough control authority
    fast_enough = loop_bw_hz >= 5.0 * (gamma_s / (2*math.pi))
    strong_enough = u_available >= u_needed
    return fast_enough and strong_enough

# growth rate gamma sets the minimum loop bandwidth
assert controllable(gamma_s=700.0, loop_bw_hz=1200.0,
                    u_available=1.0, u_needed=0.7)

Two failure modes, two guards

• Too slow: the loop bandwidth is below the growth rate; the displacement wins. Guarded by the timing budget.
• Saturated: the coils hit their current or voltage limit; authority runs out. Guarded by envelope headroom.
• If arrest fails, the event becomes a vertical displacement event (VDE) and hands off to disruption mitigation.

The loop is designed with explicit reserve authority so that a routine disturbance never runs the coils to saturation; the reserve exists specifically for the off-nominal kick. When both the bandwidth and the authority reserve are consumed, the design does not chase a lost cause — it recognizes the incipient displacement event and hands off to mitigation while a controlled termination is still possible, converting a failed catch into a mitigated shutdown rather than a full disruption.

The loop period is derived from the growth rate in control-loop timing math, and the authority margin is part of stability margins and control headroom. When both margins are exhausted, the failsafe recognizes an imminent VDE and arms the disruption mitigation reflex before the plasma is lost, so a failed catch degrades to a mitigated shutdown rather than an uncontrolled one.