Average #betta# value of axially symmetric plasma

A useful expression for an average #betta# value is derived by using the Grad-Shafranov equation. The plasma is assumed to be confined in a finite region and to be in an axially symmetric magnetohydrodynamic equilibrium. The magnetic flux function psi is assumed to vanish on the plasma surface. The average beta value <#betta#> is defined by 8π∫pdV/∫B2dV, where p is the kinetic pressure, B is the strength of the magnetic field, and the integrations are carried out over the whole plasma region. When p is proportional to psi sup(α) (α is a positive number) and the toroidal magnetic field is absent, the value of <#betta#> is shown to be 2/α. This value is independent of the shape of the plasma. (author)