GlasserGreeneJohnson Parameters
It is convenient to add to this appendix a generalized calculation of the magnetic curvature length, , that appears in the Rutherford island width evolution
equation, (12.15).
Let
,
, and
.
Furthermore, let


(A.89) 


(A.90) 


(A.91) 


(A.92) 


(A.93) 


(A.94) 
It follows that [6]
where
, and is the equilibrium plasma pressure.
Finally,

(A.98) 
The value of the dimensionless parameter at a given rational magnetic fluxsurface is related to the magnetic curvature length, , introduced in Section 11.4, according to

(A.99) 
Here,
is a dimensionless measure of the plasma pressure at the rational surface [see Equations (4.65) and (4.66)],
the magnetic shearlength at the rational surface [see Equation (5.27)], and
the effective pressure gradient scalelength at the rational surface [see Equation (8.35)]. The previous equation is a generalization of Equation (11.57).
The latter equation only holds in a largeaspect ratio, low, tokamak plasma with magnetic fluxsurfaces of circular crosssection.