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 or destabilizing major MHD activity. 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. Typically, the maximum value of β_N before the onset of deleterious instability is 3.5, although significantly higher values have been achieved.