Beta

Plasma performance is often expressed in terms of beta (β), defined as:

$\beta ={\frac {\left\langle p\right\rangle }{B^{2}/2\mu _{0}}}$

i.e., the ratio of the plasma pressure to the magnetic pressure. Here, <p> is the mean plasma pressure, and B the mean total field strength. It is customary to introduce also the poloidal β (β_p) and the toroidal β (β_t), in which B is replaced by the poloidal and toroidal magnetic field component, respectively. One has:

${\frac {1}{\beta }}={\frac {1}{\beta _{p}}}+{\frac {1}{\beta _{t}}}$

Normalized beta

The normalized beta (or Troyon factor) is an operational parameter indicating how close the plasma is to reaching the Greenwald limit. Its definition is (for tokamaks):

$\beta _{N}=\beta {\frac {aB}{I_{p}}}$

where B is in T, a in m, and I_p in MA.