Density limit

The maximum density that can be obtained in stable plasma operations (without disruption) is empirically given by

$$n_e \approx 1.5 n_G,$$ (96)

where $n_G$ is the Greenwalt density, which is given by

$$n_G = 10^{20} \frac{I_p}{\pi a^2} \times 10^{- 6}$$ (97)

where $I_p$ is the plasma current, $a$ is the minor radius, all physical quantities are in SI units. The $1.5 n_G$ gives the density limit that can be achieved for a tokamak operation scenario with plasma current $I_p$ and plasma minor radius $a$. The Greenwalt density limit is an empirical one, which, like other empirical limits, can be exceeded in practice (for example, the density actually achieved in an experiment can be $n_e = 1.6 n_G$). Equation (97) indicates that the Greenwalt density is proportional to the current density. Therefore the ability to operate in large plasma current density means the ability to operate with high plasma density.

Note that neither the pressure limit nor the density limit is determined by the force-balance constraints. They are determined by the stability of the equilibrium. On the other hand, since the stability of the equilibrium is determined by the equilibrium itself, the pressure and density limit involves equilibrium quantities. For this reason, I decide to mention these contents (pressure and density limits) in these notes on equilibrium. Next, I will return to the discussions of equilibrium.