Mode coupling and aspect ratio effects on low and high-nplasma instabilities

Abstract

In magnetically confined toroidal plasmas such as tokamaks, magnetohydrodynamic (MHD) instabilities experience strong toroidal and nonlinear mode coupling effects. Resistive MHD simulations with the M3D code show the importance of mode coupling and compressible MHD effects, which contribute to stronger mode coupling. For the m/n = 1/1 internal kink mode and sawtooth crash and for the edge localized mode (ELM) at higher n, MHD reproduces many features of the experimental observations, including the fast sawtooth crash and the moderate n ∼ 10 toroidal harmonics of the ELM. A general property of the perpendicular momentum equation in toroidal fusion plasmas is that the unbalanced radial forces remain relatively small, so that the terms that are lowest order in small inverse aspect ratio mostly cancel. The higher order terms then have significant effects, even at small r/Ro and small amplitude. Effects are strongest for the lowest toroidal harmonics n ≃ 1 and the most strongly driven ones with highest amplitude. Unlike the n = 1 internal kink mode, the small amplitude ELM ballooning/peeling-type mode, and thus ELM MHD marginal stability, may be reasonably described by the lowest order in aspect ratio, for moderate and large n ≳ 10. The ELM crash, however, depends on higher order.

H-mode plasmas at very low aspect ratio on the Pegasus Toroidal Experiment

“…Mode spectra are derived from cross-phase spectral analysis of a toroidal Mirnov coil array placed ~2 cm exterior to the plasma boundary [22]. Multiple n are observed during ELMs [26], consistent with the theoretical expectation of the simultaneous presence of multiple unstable peeling-ballooning modes [45][46][47][48]. Small ELMs have low ⩽ n 4, whereas large ELMs have intermediate < < n 5 15 present.…”

Solitary perturbations in the steep boundary of magnetized toroidal plasma

“…The observed SPs may be compared to nonlinear growth of a low- n mode reported in numerical simulations of the ELM crash phase252627. In those numerical studies, the energy of the low- n mode (typically n  = 1) rapidly grows and becomes comparable to the energies of the linearly dominant high- n modes in the nonlinear phase due to the nonlinear mode coupling.…”

Toroidal mode number transition of the edge localized modes in the KSTAR plasmas

“…The linear analysis is useful but has limited applicability in interpretation of several common features of the ELM dynamics observed on the KSTAR [8,10] such as saturation of the mode amplitude instead of exponential growth and rapid change of the mode structure much faster than the energy transport time scale. In particular, the change of the toroidal mode number spectrum near the crash phase is recently found in a number of nonlinear numerical simulations of ELMs [11][12][13][14]. Changes of the toroidal mode number were also observed during the inter-ELM-crash period without major changes in the global plasma parameters in the JET tokamak [15].…”