Early internal detection of MHD by Faraday-effect polarimetry in high-$q_{min}$ DIII-D plasmas and correlation with ideal-wall beta limit*

Faraday-effect polarimetry via the Radial Interferometer Polarimeter (RIP) detects internal magnetic fluctuations in high-$q_{min}$ DIII-D plasmas up to 300 ms before the magnetic sensing coils. The first mode detected by the coils often has $n$ = 2 or $n$ = 1, but the first mode detected by RIP has $n$ = 3, consistent with stability calculations using the DCON code. These plasmas, with $q_{min} > 1.4$, are designed to achieve high $\beta_N$, but $\beta_N$ is commonly limited by tearing modes, the onset of which is difficult to predict. The RIP diagnostic measures the line integral of magnetic fluctuations across the center of the plasma. The detected $n$ = 3 mode appears at the lowest-$m/n$ rational surface available for $n$ = 3, with $m$ = 6, 7, or 8, depending on $q_{min}$. The DCON code calculates the ideal-wall kink-mode  $\beta_N$ limits for modes with $n$ = 1 - 3, and these limits are used as a proxy for linear tearing mode stability. For these plasmas, the  $\beta_N$ limit for $n$ = 3 is generally the lowest. Hence, as  $\beta_N$ increases, DCON predicts the onset of an $n$ = 3 mode first, and sampling different shots, RIP detects n = 3 instability with  $\beta_N \sim 50 - 75\%$ of the $n$ = 3 ideal-wall limit. The 6/3 mode, resonant at the $q$ = 2 surface, occurs initially without a 4/2 or 2/1 mode, consistent with the DCON calculation, but the 4/2 and 2/1 modes do appear later in time, and their amplitudes increase as the 6/3 mode amplitude decreases. In other cases, the appearance of an $n$ = 2 mode coincides with the disappearance of $n$ = 3. The narrow eigenfunctions of higher-$n$, core-resonant modes render them challenging to detect with sensing coils.  With its unique ability to probe the core, RIP has improved understanding of MHD stability and evolution, and its early detection of MHD will allow application of tearing control tools before modes can grow to large amplitude.