Density limit of tokamak experiments

Neutral gas which penetrates into a hot plasma body, of characteristic dimension L b , average density n̄ and temperature T, consists mainly of a slow and a fast component, of densities n ns , n nf and temperatures T ns ≪T, T nf ≃T, respectively. These components have the penetration lengths L ns = l/σ cs n̄ and L nf = 1/σ cf n̄, corresponding to the critical densities n cs =1/σ cs L b and n cf =l/σ cf L b where l/σ cf ≃lOO/σ cs ≃5 × 10 18 m −2 for hydrogen in the range 10 6 < T < 10 7 K. Thus, hot plasmas can be divided into the classes of permeable dilute, permeable non-dilute, and impermeable systems defined by n̄⪅n cs ≪n cf , n cs ≪n̄⪅n cf , and n cs ≪ n cf ≪ n̄, respectively. Concerning tokamaks, an analysis of the plasma-neutral gas interaction leads to the following conclusions: So far, all reported tokamak experiments have been conducted in the permeable density range and have been limited by instabilities in the transition region close to n̄ = n cf . Full-scale tokamak reactors should, on the other hand, operate far inside the impermeable density range. The driving force of instabilities due to the pressure gradient is expected to reach its maximum value when n̄ approachesthe density limit ncf from below, i.e. at the transition to the impermeable state. The experimentally observed parameter values at the instability limit agree with those calculated from the theory on collisionless ballooning modes driven by the pressure gradient.