A one-dimensional tearing mode equation for pedestal stability studies in tokamaks

Starting from expressions in Connor et al. (Phys. Fluids, vol. 31, 1988, p. 577), we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna & Callen (Phys. Plasmas, vol. 1, 1994, p. 2308) and Nishimura et al. (Phys. Plasmas, vol. 5, 1998, p. 4292), but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. the Joint European Torus (JET). We discuss how this one-dimensional model for tearing modes, which assumes a single poloidal harmonic for the perturbed poloidal flux, compares with a model that includes poloidal coupling Fitzpatrick et al. (Nucl. Fusion, vol. 33, 1993, p. 1533).

A new solution to the plasma starved event horizon magnetosphere

Very Long Baseline Interferometry observations at 86 GHz reveal an almost hollow jet in M87 with a forked morphology. The detailed analysis presented here indicates that the spectral luminosity of the central spine of the jet in M87 is a few percent of that of the surrounding hollow jet 200–400 μ as from the central black hole. Furthermore, recent jet models indicate that a hollow “tubular” jet can explain a wide range of plausible broadband spectra originating from jetted plasma located within ~30 μ as of the central black hole, including the 230 GHz correlated flux detected by the Event Horizon Telescope. Most importantly, these hollow jets from the inner accretion flow have an intrinsic power capable of energizing the global jet out to kiloparsec scales. Thus motivated, this paper considers new models of the event horizon magnetosphere (EHM) in low luminosity accretion systems. Contrary to some models, the spine is not an invisible powerful jet. It is an intrinsically weak jet. In the new EHM solution, the accreted poloidal magnetic flux is weak and the background photon field is weak. It is shown how this accretion scenario naturally results in the dissipation of the accreted poloidal magnetic flux in the EHM not the accumulation of poloidal flux required for a powerful jet. The new solution indicates less large scale poloidal magnetic flux (and jet power) in the EHM than in the surrounding accretion flow and cannot support significant EHM driven jets.

The external kink mode in diverted tokamaks

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}<2$, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}<2$, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.