Cylindrical Tearing Mode Equation
The magnetic structure of a tearing perturbation is determined by the so-called cylindrical tearing mode equation, (3.35), which can be written in the form [4,14]
![$\displaystyle \frac{\partial^2\delta\psi}{\partial r^2} + \frac{1}{r}\,\frac{\p...
...tial r}-\frac{m^2}{r^2}\,\delta\psi - \frac{J_z'\,\delta\psi}{r\,(1/q-n/m)}= 0,$](img1523.png) |
(3.60) |
where
![$\displaystyle J_z(r)= \frac{R_0\,\mu_0\,j_z(r)}{B_z}$](img1524.png) |
(3.61) |
is a dimensionless measure of the toroidal current density profile.
Note that Equation (3.60) is singular at the so-called rational magnetic flux-surface, radius
, at which
![$\displaystyle q(r_s) = \frac{m}{n}.$](img427.png) |
(3.62) |
At the rational surface,
, where
is the equilibrium magnetic field, and
the wavevector of the tearing perturbation.