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.