Modification of Rotation Frequency

The reconnected magnetic flux at the rational surface is assumed to convected by the local plasma flow. (See Section 3.11.) Hence, changes in the plasma flow at the rational surface induced by the electromagnetic torques that develop in the vicinity of this surface will modify the convection velocity. Consequently, the tearing mode's rotation frequency can be written

$\displaystyle \omega(t) = \omega_{0} + ({\bf k}\cdot {\mit\Delta}{\bf V}_i)_{r=...
...ega_{0} + m\,{\mit\Delta\Omega}_\theta(r_s,t) - n\,{\mit\Delta\Omega}_z(r_s,t),$ (3.185)

where $\omega_{0}$ is the natural frequency of the tearing mode. The natural frequency is defined as the rotation frequency of tearing mode that develops spontaneously, and does not interact with any external structure (such as a resistive wall or an error-field). The previous expression is known as the no-slip constraint [4], and has been verified experimentally [12]. It follows from Equations (3.170) and (3.171) that

$\displaystyle \omega(t) = \omega_{0} - \sum_{p=1,\infty}\left[\alpha_p(t)+\beta_p(t)\right].$ (3.186)