Cylindrical Tokamak Equilibrium
Consider a low, large aspectratio, tokamak plasma equilibrium whose magnetic fluxsurfaces map out (almost) concentric circles in the poloidal plane. Such an equilibrium can be approximated as a periodic cylinder [4,14].
Let us employ a conventional set of righthanded cylindrical coordinates, , , . The
equilibrium magnetic fluxsurfaces lie on surfaces of constant . The system is
assumed to be periodic in the (“toroidal”) direction, with periodicity length ,
where is the simulated major radius of the plasma. Let be the minor radius of the plasma. The equilibrium magnetic
field is written

(3.1) 
where
is the poloidal magnetic fieldstrength, and the toroidal magnetic fieldstrength.
Here,
and
. The safetyfactor profile takes the form

(3.2) 
[See Equation (1.76).] It is assumed that
.
The equilibrium current density is written

(3.3) 
where
the poloidal and toroidal current densities
take the respective forms
and denotes . The plasma equilibrium satisfies the force balance criterion [see Equation (2.377)],

(3.6) 
where is the total plasma pressure. It follows from Equations (3.1) and (3.3)–(3.5) that

(3.7) 