Strong-coupling expansion and effective hamiltonians

When looking for analytical approaches to treat frustrated quantum magnets, it is often very useful to start from a limit where the ground state is highly degenerate. This chapter discusses several ways of deriving {effective Hamiltonians} around such limits, starting from standard {degenerate perturbation theory} and proceeding to modern approaches more appropriate for the derivation of high-order effective Hamiltonians, such as the perturbative continuous unitary transformations or contractor renormalization. In the course of this exposition, a number of examples taken from the recent literature are discussed, including frustrated ladders and other dimer-based Heisenberg models in a field, as well as the mapping between frustrated Ising models in a transverse field and quantum dimer models.Comment: To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil

Confinement physics of H-mode discharges in DIII-D

The authors' data indicate that the L-mode to H-mode transition in the DIII-D tokamak is associated with the sudden reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. In addition to the reduction in edge density and magnetic fluctuations observed at the transition, the edge radial electric field becomes more negative after the transition. They have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase with plasma density and toroidal field are particularly significant. Control of the ELM frequency and duration by adjusting neutral beam input power has allowed us to produce H-mode plasmas with constant impurity levels and durations up to 5 s. Energy confinement time in ohmic H-mode plasmas and in deuterium H-mode plasmas with deuterium beam injection can exceed saturated ohmic confinement times by at least a factor of two. Energy confinement times above 0.3 s have been achieved in these beam-heated plasmas with plasma currents in the range of 2.0 to 2.5 MA. Local transport studies have shown that electron and ion thermal diffusivities and angular momentum diffusivity are comparable in magnitude and all decrease with increasing plasma current

Confinement physics of H-mode discharges in DIII-D

The authors' data indicate that the L-mode to H-mode transition in the DIII-D tokamak is associated with the sudden reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. In addition to the reduction in edge density and magnetic fluctuations observed at the transition, the edge radial electric field becomes more negative after the transition. They have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase with plasma density and toroidal field are particularly significant. Control of the ELM frequency and duration by adjusting neutral beam input power has allowed us to produce H-mode plasmas with constant impurity levels and durations up to 5 s. Energy confinement time in ohmic H-mode plasmas and in deuterium H-mode plasmas with deuterium beam injection can exceed saturated ohmic confinement times by at least a factor of two. Energy confinement times above 0.3 s have been achieved in these beam-heated plasmas with plasma currents in the range of 2.0 to 2.5 MA. Local transport studies have shown that electron and ion thermal diffusivities and angular momentum diffusivity are comparable in magnitude and all decrease with increasing plasma current

Recent results from DIII-D and their implications for next generation tokamaks

Recent results from the DIII-D tokamak have provided significant contributions to the understanding of many of the elements of tokamak physics and the application of this understanding to the design of next generation devices including ITER and CIT. The limitations of magnetohydrodynamic stability on the values of plasma beta (the ratio of kinetic pressure to the containing pressure of the magnetic field) that can be attained has been experimentally demonstrated and found to be described by existing theory. Values of beta (10.7%) well in excess of those required for proposed devices (ITER and CIT) have been demonstrated. Regimes of confinement (H-mode) have been established that scale favorably to proposed next generation devices, and experiments demonstrating the dependence of the energy confinement on plasma size have been completed. Understanding of confinement is rapidly developing especially in the areas of bulk transport and the role of turbulence in the plasma edge. Key experimental results in areas of plasma transport and edge plasma phenomena are in agreement with theories based on short wavelength turbulence. Control of the divertor heat loads and impurity influx has been demonstrated, and new progress has been made in the understanding of plasma edge phenomena. Experiments with ion Bernstein wave heating have not found regimes in which these waves can produce effective central ion heating. Electron cyclotron current drive experiments have demonstrated 70 kA of driven current in 400 kA discharges

Overview of the JET results

Since the last IAEA Conference JET has been in operation for one year with a programmatic focus on the qualification of ITER operating scenarios, the consolidation of ITER design choices and preparation for plasma operation with the ITER-like wall presently being installed in JET. Good progress has been achieved, including stationary ELMy H-mode operation at 4.5 MA. The high confinement hybrid scenario has been extended to high triangularity, lower ρ*and to pulse lengths comparable to the resistive time. The steady-state scenario has also been extended to lower ρ*and ν*and optimized to simultaneously achieve, under stationary conditions, ITER-like values of all other relevant normalized parameters. A dedicated helium campaign has allowed key aspects of plasma control and H-mode operation for the ITER non-activated phase to be evaluated. Effective sawtooth control by fast ions has been demonstrated with3He minority ICRH, a scenario with negligible minority current drive. Edge localized mode (ELM) control studies using external n = 1 and n = 2 perturbation fields have found a resonance effect in ELM frequency for specific q95values. Complete ELM suppression has, however, not been observed, even with an edge Chirikov parameter larger than 1. Pellet ELM pacing has been demonstrated and the minimum pellet size needed to trigger an ELM has been estimated. For both natural and mitigated ELMs a broadening of the divertor ELM-wetted area with increasing ELM size has been found. In disruption studies with massive gas injection up to 50% of the thermal energy could be radiated before, and 20% during, the thermal quench. Halo currents could be reduced by 60% and, using argon/deuterium and neon/deuterium gas mixtures, runaway electron generation could be avoided. Most objectives of the ITER-like ICRH antenna have been demonstrated; matching with closely packed straps, ELM resilience, scattering matrix arc detection and operation at high power density (6.2 MW m-2) and antenna strap voltages (42 kV). Coupling measurements are in very good agreement with TOPICA modelling. \ua9 2011 IAEA, Vienna

Overview of the JET results

Since the last IAEA Conference JET has been in operation for one year with a programmatic focus on the qualification of ITER operating scenarios, the consolidation of ITER design choices and preparation for plasma operation with the ITER-like wall presently being installed in JET. Good progress has been achieved, including stationary ELMy H-mode operation at 4.5 MA. The high confinement hybrid scenario has been extended to high triangularity, lower ρ*and to pulse lengths comparable to the resistive time. The steady-state scenario has also been extended to lower ρ*and ν*and optimized to simultaneously achieve, under stationary conditions, ITER-like values of all other relevant normalized parameters. A dedicated helium campaign has allowed key aspects of plasma control and H-mode operation for the ITER non-activated phase to be evaluated. Effective sawtooth control by fast ions has been demonstrated with3He minority ICRH, a scenario with negligible minority current drive. Edge localized mode (ELM) control studies using external n = 1 and n = 2 perturbation fields have found a resonance effect in ELM frequency for specific q95values. Complete ELM suppression has, however, not been observed, even with an edge Chirikov parameter larger than 1. Pellet ELM pacing has been demonstrated and the minimum pellet size needed to trigger an ELM has been estimated. For both natural and mitigated ELMs a broadening of the divertor ELM-wetted area with increasing ELM size has been found. In disruption studies with massive gas injection up to 50% of the thermal energy could be radiated before, and 20% during, the thermal quench. Halo currents could be reduced by 60% and, using argon/deuterium and neon/deuterium gas mixtures, runaway electron generation could be avoided. Most objectives of the ITER-like ICRH antenna have been demonstrated; matching with closely packed straps, ELM resilience, scattering matrix arc detection and operation at high power density (6.2 MW m-2) and antenna strap voltages (42 kV). Coupling measurements are in very good agreement with TOPICA modelling. \ua9 2011 IAEA, Vienna

Overview of the JET results

Since the last IAEA Conference JET has been in operation for one year with a programmatic focus on the qualification of ITER operating scenarios, the consolidation of ITER design choices and preparation for plasma operation with the ITER-like wall presently being installed in JET. Good progress has been achieved, including stationary ELMy H-mode operation at 4.5 MA. The high confinement hybrid scenario has been extended to high triangularity, lower ρ*and to pulse lengths comparable to the resistive time. The steady-state scenario has also been extended to lower ρ*and ν*and optimized to simultaneously achieve, under stationary conditions, ITER-like values of all other relevant normalized parameters. A dedicated helium campaign has allowed key aspects of plasma control and H-mode operation for the ITER non-activated phase to be evaluated. Effective sawtooth control by fast ions has been demonstrated with3He minority ICRH, a scenario with negligible minority current drive. Edge localized mode (ELM) control studies using external n = 1 and n = 2 perturbation fields have found a resonance effect in ELM frequency for specific q95values. Complete ELM suppression has, however, not been observed, even with an edge Chirikov parameter larger than 1. Pellet ELM pacing has been demonstrated and the minimum pellet size needed to trigger an ELM has been estimated. For both natural and mitigated ELMs a broadening of the divertor ELM-wetted area with increasing ELM size has been found. In disruption studies with massive gas injection up to 50% of the thermal energy could be radiated before, and 20% during, the thermal quench. Halo currents could be reduced by 60% and, using argon/deuterium and neon/deuterium gas mixtures, runaway electron generation could be avoided. Most objectives of the ITER-like ICRH antenna have been demonstrated; matching with closely packed straps, ELM resilience, scattering matrix arc detection and operation at high power density (6.2 MW m-2) and antenna strap voltages (42 kV). Coupling measurements are in very good agreement with TOPICA modelling. \ua9 2011 IAEA, Vienna

Simulation of neutron emission in neutral beam injection heated plasmas with the real-time code RABBIT

In plasmas heated with deuterium beams a deficit of the expected fusion neutron rate is an indicator of the deterioration of the fast-ion confinement, caused, for instance, by magnetohydrodynamic instabilities. The capability of predicting this deficit during the discharge relies on the availability of real-time estimates of the neutron rate from NBI codes which must be fast and accurate at the same time. Therefore, the recently developed real-time RABBIT code for neutral beam injection (NBI) simulations has been extended to output the distribution function and calculate the neutron emission. After the description of this newly installed diagnostics in RABBIT, benchmarks with NUBEAM, a massively used and validated Monte Carlo NBI solver, are discussed on ASDEX-Upgrade and JET cases. A first application for control-room intershot analysis on DIII-D is presented, and the results are compared on a large database with a slower NUBEAM analysis. Further application possibilities, e.g. for real-time control of Alfven eigenmodes, are outlined

Overview of the JET results with the ITER-like wall

Following the completion in May 2011 of the shutdown for the installation of the beryllium wall and the tungsten divertor, the first set of JET campaigns have addressed the investigation of the retention properties and the development of operational scenarios with the new plasma-facing materials. The large reduction in the carbon content (more than a factor ten) led to a much lower Z(eff) (1.2-1.4) during L- and H-mode plasmas, and radiation during the burn-through phase of the plasma initiation with the consequence that breakdown failures are almost absent. Gas balance experiments have shown that the fuel retention rate with the new wall is substantially reduced with respect to the C wall. The re-establishment of the baseline H-mode and hybrid scenarios compatible with the new wall has required an optimization of the control of metallic impurity sources and heat loads. Stable type-I ELMy H-mode regimes with H-98,H-y2 close to 1 and beta(N) similar to 1.6 have been achieved using gas injection. ELM frequency is a key factor for the control of the metallic impurity accumulation. Pedestal temperatures tend to be lower with the new wall, leading to reduced confinement, but nitrogen seeding restores high pedestal temperatures and confinement. Compared with the carbon wall, major disruptions with the new wall show a lower radiated power and a slower current quench. The higher heat loads on Be wall plasma-facing components due to lower radiation made the routine use of massive gas injection for disruption mitigation essential