Beta

Plasma performance is often expressed in terms of beta ($\beta$), 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, $\left\langle p\right\rangle$ is the mean plasma pressure, and $B$ the mean total field strength. It is customary to introduce also the poloidal beta $\beta _{p}$ and the toroidal beta $\beta _{t}$, 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):

$\beta _{N}=\beta _{t}{\frac {aB_{0}}{I_{p}}}$

where $B_{0}$ is the external magnetic field in T, $a$ is the minor radius in m, and $I_{p}$ is the plasma current in MA. Typically, the maximum value of $\beta _{N}$ before the onset of deleterious instability is 3.5, although significantly higher values have been achieved.

See also

• Internal inductance
• Wikipedia:Beta_(plasma_physics)