The Lawson Criterion & Triple Product
The Lawson criterion sets the density-temperature-confinement product a plasma must reach to sustain net fusion. Here is how it frames the Kronos design.
- Triple product
- n · T · τ_E
- Required confinement
- H₉₈ = 2.28 (profile basis, Mode D; 2.38 banking)
- Operating gain
- Q_eng = 3.9 (exhaust-honest); hot-ion ceiling ledgers labeled history
- Radiation losses
- bremsstrahlung 718 MW, synchrotron 158 MW at R_wall = 0.90
The Lawson criterion states the condition a fusion plasma must meet for the energy released to exceed the energy needed to keep it hot. In practice it is expressed as the triple product of density, temperature, and energy confinement time (n · T · τE). A plasma below the threshold loses more than it makes; above it, fusion self-heating can dominate.
For the Kronos MetroVolt design, the Lawson analysis is done with radiation losses included — bremsstrahlung (718 MW, on the corrected relativistic basis) and synchrotron (158 MW at a wall reflectivity of 0.90) — because a high-field, high-density plasma radiates strongly. The required confinement multiplier that falls out of this chain is H98 = 2.28 on a profile basis at the Mode-D operating point (2.38 on the banking leg; the Mode-C-era 1.84 figure is labeled history).
The MetroVolt operating point is described honestly as a driven system, not an igniting one: the frozen Mode-D point closes at an engineering gain Qeng = 3.9 on the exhaust-honest ledger (the retired hot-ion ceiling ledgers are kept as labeled history). The design does not claim ignition.