The Greenwald Density Limit

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The Greenwald limit is an empirical ceiling on tokamak plasma density. Negative-triangularity operation lets Kronos run above the conventional fraction.

Definition

n_GW = I_p / (π a²)

MetroVolt Greenwald fraction

f_GW = 1.33 (Mode D; design ceiling 1.35)

Density

n̄_e = 2.2 × 10²⁰ m⁻³

Anchor

non-disruptive NT operation to 1.8 × n_GW

The Greenwald density limit is an empirical rule for how much plasma density a tokamak can hold before disruptions become likely. It scales with plasma current and inversely with the square of the minor radius: n_GW = I_p / (π a²). Fusion power rises with the square of density, so operating close to — or above — this limit is valuable, but risky in conventional plasmas.

Kronos MetroVolt runs at a Greenwald fraction of f_GW = 1.33 (line-averaged density n̄_e = 2.2 × 10²⁰ m⁻³) at the frozen Mode-D point, well above the nominal limit and inside the design's 1.35 ceiling. This is anchored on the demonstrated record that negative-triangularity plasmas sustain non-disruptive operation up to 1.8× the Greenwald density — headroom that a positive-triangularity H-mode plasma does not reliably have.

Running with density headroom rather than at the ragged edge of a disruption is part of what makes the negative-triangularity choice a stability decision as much as a confinement one.