Consider a low-, large aspect-ratio, tokamak plasma equilibrium whose magnetic flux-surfaces 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 right-handed cylindrical coordinates, , , . The
equilibrium magnetic flux-surfaces 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
Cylindrical Tokamak Equilibrium
is the poloidal magnetic field-strength, and the toroidal magnetic field-strength.
. The safety-factor profile takes the form
[See Equation (1.76).] It is assumed that
The equilibrium current density is written
the poloidal and toroidal current densities
take the respective forms
and denotes . The plasma equilibrium satisfies the force balance criterion [see Equation (2.377)],
where is the total plasma pressure. It follows from Equations (3.1) and (3.3)–(3.5) that