From Lawson to Burning Plasmas: a Multi-Fluid Approach

The Lawson criterion gives the value for the triple product of density, temperature and energy confinement time needed for the plasma to ignite. Lawson's work was improved, adding 1D geometry and multi-fluid (ions, electrons and alphas) physics to the model. Physical equilibration times and different energy confinement times between species were accounted for in steady-state (Lawson-like) and time-dependent calculations. At this time it is more meaningful to consider a finite gain factor Q. The plasma conditions needed to achieve any desired value of Q both in the 0D and the 1D multi-fluid plasma description can be evaluated through freely-available versatile Mathematica notebooks. Arbitrary density and temperature profiles can be assigned from input. Results are related with experimental pure-deuterium discharges defining a no-alpha pressure. Given the multi-fluid Lawson product needed for a desired Q the alpha heating is subtracted from the energy balance and the no-alpha equilibrium pressure is obtained. The model easily allows to introduce scalings for energy confinement times. Including the τ_E dependence on power only one thermal equilibrium point exists for a given heating power instead of the two predicted by Lawson-like calculations.