Nonlinear State ofm=1Instability in Tokamaks with NonmonotonicqProfiles

The nonlinear saturated state of the $m=1\mathrm{}$, $n=1\mathrm{}$ ideal MHD instability is calculated for a large-aspect-ratio tokamak. When the $q\left(r\right)\mathrm{}$ profile is nonmonotonic with $\Delta q=q_{min}-1>0\mathrm{}$, the amplitude $\xi$ of the nonlinear state is given by $\frac{{\xi }^2{q}^{\prime \prime }}{\Delta q}=7.9[{\left(\frac{\Delta q_c}{\Delta q}\right)}^{\frac{3}{2}}-1]$, where $\Delta q_c$ is the critical value of $\Delta q$ at which the system is marginally stable. This nonlinear state is similar to that seen during the sawtooth crash in large tokamaks and may be related to the steady-state oscillations seen when sawteeth are suppressed by lower-hybrid current drive.