ELM triggering conditions for the integrated modeling of H-mode plasmas

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. Formation of the pedestal and the L-H transition is the direct result of ExB flow shear suppression of anomalous transport. The periodic ELM crashes are triggered by either the ballooning or peeling MHD instabilities. The BALOO, DCON, and ELITE ideal MHD stability codes are used to derive a new parametric expression for the peeling-ballooning threshold. The new dependence for the peeling-ballooning threshold is implemented in the ASTRA transport code. Results of integrated modeling of DIII-D like discharges are presented and compared with experimental observations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

BOUT++: a framework for parallel plasma fluid simulations

A new modular code called BOUT++ is presented, which simulates 3D fluid equations in curvilinear coordinates. Although aimed at simulating Edge Localised Modes (ELMs) in tokamak X-point geometry, the code is able to simulate a wide range of fluid models (magnetised and unmagnetised) involving an arbitrary number of scalar and vector fields, in a wide range of geometries. Time evolution is fully implicit, and 3rd-order WENO schemes are implemented. Benchmarks are presented for linear and non-linear problems (the Orszag-Tang vortex) showing good agreement. Performance of the code is tested by scaling with problem size and processor number, showing efficient scaling to thousands of processors. Linear initial-value simulations of ELMs using reduced ideal MHD are presented, and the results compared to the ELITE linear MHD eigenvalue code. The resulting mode-structures and growth-rate are found to be in good agreement (BOUT++ = 0.245, ELITE = 0.239). To our knowledge, this is the first time dissipationless, initial-value simulations of ELMs have been successfully demonstrated.Comment: Submitted to Computer Physics Communications. Revised to reduce page count. 18 pages, 16 figure

Peeling-ballooning stability of tokamak plasmas with applied 3D magnetic fields

The poloidal harmonics of the toroidal normal modes of an unstable axisymmetric tokamak plasma are employed as basis functions for the minimisation of the 3D energy functional. This approach presents a natural extension of the perturbative method considered in Anastopoulos Tzanis et al (2019 Nucl. Fusion 59 126028). This variational formulation is applied to the stability of tokamak plasmas subject to external non-axisymmetric magnetic fields. A comparison of the variational and perturbative methods shows that for D-shaped, high β N plasmas, the coupling of normal modes becomes strong at experimentally relevant applied 3D fields, leading to violation of the assumptions that justify a perturbative analysis. The variational analysis employed here addresses strong coupling, minimising energy with respect to both toroidal and poloidal Fourier coefficients. In general, it is observed that ballooning unstable modes are further destabilised by the applied 3D fields and field-aligned localisation of the perturbation takes place, as local ballooning theory suggests. For D-shaped high β N plasmas, relevant to experimental cases, it is observed that the existence of intermediate n unstable peeling-ballooning modes, where a maximum in the growth rate spectrum typically occurs, leads to a destabilising synergistic coupling that strongly degrades the stability of the 3D system

Noncommutative Topological Theories of Gravity

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler characteristic and the signature invariant are obtained. This gives us a way towards the description of noncommutative gravitational instantons as well as noncommutative local gravitational anomalies.Comment: 17+1 pages, LaTeX, no figures, some clarifications, comments and references added, style improve

Achieving a robust grassy-ELM operation regime in CFETR

We have identified a robust grassy-edge localized mode (ELM) operation regime for future tokamak reactors. The regime exists within a pedestal top electron collisionality (ν *) window at high global poloidal beta (β p). The existence of an upper ν * limit for grassy-ELMs is consistent with results previously reported in experiments (Oyama et al 2010 Nucl. Fusion 50 064014), while the existence of a lower ν * limit has not been reported previously. Using EPED and BOUT  +  +, a theoretical model that quantitatively explains the physics of the grassy-ELMs within the window, which distinguishes them from the small mixed-ELMs at lower ν *, is presented for the first time. A peeling-ballooning stability boundary is obtained by scanning the operating density space. The change in density corresponds to a change in ν * that affects the pedestal bootstrap current. High β p leads to a strong Shafranov shift, which affects the flux surface averaged pressure drive. The two effects combine to create a peeling-dominated window in intermediate ν * buffered by ballooning-dominated regimes. Only the peeling-dominated regime shows a cyclic behavior in the perturbed pressure during the nonlinear simulation of an ELM crash, reminiscent of grassy-ELM dynamics. Similarly, the energy released across the separatrix is demonstrated to be significantly smaller. The quick recovery of the ELM crash is explainable by the rapid rise of a low n kink-peeling instability when the pedestal current Iped exceeds a threshold at high β p. It minimizes the excursion beyond marginal stability and is absent in the ballooning-dominated regime. Comparison with recent experiments over a range of β p and ν * strongly supports the physical picture proposed by the modeling

Kinetic modeling of H-mode pedestal with effects from anomalous transport and MHD stability

Scaling of the H-mode pedestal in tokamak plasmas with type I ELMs and dependence of the pedestal properties and the resulting divertor head load width with the plasma elongation and plasma current are investigated using the kinetic neoclassical XGC0 code for DIII-D and Alcator C-Mod tokamaks. The simulations in this study use realistic diverted geometry and are self-consistent with the inclusion of kinetic neoclassical physics, theory-based anomalous transport models with the E×B flow shearing effects, as well as an MHD ELM triggering criterion. Scalings for the pedestal width and height are developed as a function of the scanned plasma parameters. The nonlinear interplay between anomalous and neoclassical effects motivates the development of a self-consistent simulation model that includes neoclassical and anomalous effects simultaneously. It is demonstrated that the divertor heat load width depend on the plasma currents. In the development of this dependence, effects of neutral collisions and anomalous transport are taken into account. Changes in the neoclassical divertor heat load fluxes associated with the introduction of the neutral collision and anomalous transport effects are described.За допомогою кінетичного неокласичного коду XGC0 для розрядів в токамаках DIII-D і Alcator C-Mod досліджено скейлінг п’єдесталу в плазмі, що перебуває в режимі поліпшеного утримання, з прикордонними локалізованими модами (ПЛМ) першого типу, властивості п’єдесталу і потоку тепла на дивертор в залежності від витягнутості плазми та струму плазми. У розрахунках використовуються: реалістична геометрія дивертора, кінетична модель для неокласичних ефектів, модель аномального транспорту, яка враховує ефекти шира (ExB)-потоків, і умови збудження ПЛМ-нестійкостей. У результаті розрахунків отримані скейлінгі для ширини і висоти п’єдесталу як функції параметрів плазми. Нелінійна взаємодія неокласичних ефектів і ефектів, пов'язаних з аномальним транспортом, є мотивацією для розробки самоузгодженої чисельної моделі, яка одночасно включає ефекти аномального і неокласичного транспорту. Показано, що потоки тепла на дивертор залежать від плазмових струмів. Також представлено результати дослідження залежності напівширини профілів тепла на дивертор від ефектів, пов'язаних з аномальним транспортом і зіткненнями з нейтральними частинками.С помощью кинетического неоклассического кода XGC0 для разрядов в токамаках DIII-D и Alcator C-Mod исследованы скэйлинг пьедестала в плазме, находящейся в режиме улучшенного удержания, с приграничными локализованными модами (ПЛМ) первого типа, и зависимость свойств пьедестала и потока тепла на дивертор от вытянутости плазмы и тока плазмы. В расчетах используются: реалистичная геометрия дивертора, кинетическая модель для неоклассических эффектов, модель аномального транспорта, которая учитывает эффекты шира (ExB)-потоков, и условия возбуждения ПЛМ-неустойчивостей. В результате расчетов получены скэйлинги для ширины и высоты пьедестала как функции параметров плазмы. Нелинейное взаимодействие неоклассических эффектов и эффектов, связанных с аномальным транспортом, является мотивацией разработки самосогласованной численной модели, которая одновременно включает эффекты аномального и неоклассического транспорта. Показано, что потоки тепла на дивертор зависят от плазменных токов. Также представлены результаты исследования зависимости полуширины профилей тепла на дивертор от эффектов, связанных с аномальным транспортом и столкновениями с нейтральными частицами

Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events

The $B^0$-$\bar B^0$ oscillation frequency has been measured with a sample of 23 million \B\bar B pairs collected with the BABAR detector at the PEP-II asymmetric B Factory at SLAC. In this sample, we select events in which both B mesons decay semileptonically and use the charge of the leptons to identify the flavor of each B meson. A simultaneous fit to the decay time difference distributions for opposite- and same-sign dilepton events gives $\Delta m_d = 0.493 \pm 0.012{(stat)}\pm 0.009{(syst)}$ ps$^{-1}$.Comment: 7 pages, 1 figure, submitted to Physical Review Letter