Error field, torque, and plasma rotation

By calculating the torque on the error field coil structure, which is opposite to the torque exerting on the plasma, we find that the error-field-induced torque ($\tau_\phi$) can be expressed explicitly as the imaginary part of $ {\bf j}^\dag{\cal F}_1^{-1} (\delta W_b/\delta W_\infty) {\cal F}_2{\bf j}$, where ${\bf j}$ specifies the strength of the error field, $\delta W_b$ and $\delta W_\infty$ represent, respectively, the energy integrals with perfectly conducting wall and without wall, and ${\cal F}_1$ and ${\cal F}_2$ are regular equilibrium matrices. The kinetic version of the AEGIS code is being developed to calculate the torque in the numerically constructed equilibria. Experimental observations from DIII-D, JET, and C-Mod are examined and compared to our theoretical prediction based on the above torque expression. We will clarify the relationship between error field, torque, and plasma rotation.