Control of bootstrap current in the pedestal region of tokamaks
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Abstract:
The high confinement mode (H-mode) plasmas in the pedestal region of tokamaks are characterized by steep gradient of the radial electric field, and sonic poloidal Up,m flow that consists of poloidal components of the E×B flow and the plasma flow velocity that is parallel to the magnetic field B. Here, E is the electric field. The bootstrap current that is important for the equilibrium, and stability of the pedestal of H-mode plasmas is shown to have an expression different from that in the conventional theory. In the limit where |Up,m| ≫ 1, the bootstrap current is driven by the electron temperature gradient and inductive electric field fundamentally different from that in the conventional theory. The bootstrap current in the pedestal region can be controlled through manipulating Up,m and the gradient of the radial electric. This, in turn, can control plasma stability such as edge-localized modes. Quantitative evaluations of various coefficients are shown to illustrate that the bootstrap current remains finite when |Up,m| approaches infinite and to provide indications how to control the bootstrap current. Approximate analytic expressions for viscous coefficients that join results in the banana and plateau-Pfirsch-Schluter regimes are presented to facilitate bootstrap and neoclassical transport simulations in the pedestal region.Keywords:
Pedestal
Bootstrap current
Electric current
Pressure gradient
Plasma stability
The Tokamak simulation code (TSC) is used to provide initial conditions for predictive TRANSPort and integrated modeling code (PTRANSP) simulations of ITER target steady state scenarios. The PTRANSP simulations are carried out using the new multi-mode (MMM7.1) and the gyro-Landau-fluid (GLF23) transport models. It is found that there are circumstances under which the total fusion power decreases with increasing pedestal temperature height. When the total current (from magnetic axis to plasma edge) is fixed, an increased fraction of the current is concentrated in the pedestal region as the pedestal height is increased. As a consequence of the fixed total current, this results a smaller fraction of the current in the core plasma and, consequently, lower energy confinement. In previous simulations of ITER, in which the fusion power increased with increasing pedestal temperature height, the plasma current from the top of the pedestal to the magnetic axis was held fixed independent of the pedestal temperature. Simulations presented in this paper also indicate that improvement in fusion power production occurs when the lower hybrid current drive is replaced with electron cyclotron current drive. Again, the improvement results from the redistribution of plasma current since the lower hybrid power generally drives current closer to the plasma edge than does the electron cyclotron power. ITER simulation results obtained using the MMM7.1 transport model are compared with those using the GLF23 model. It is found that, in simulations of target steady state scenarios, momentum transport and flow-shear suppression features of the new MMM7.1 model can lead to predictions of internal transport barriers in temperature and rotation frequency.
Pedestal
Thermonuclear Fusion
Bootstrap current
Electron temperature
Fusion power
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Abstract The ‘Super H-Mode’ regime is predicted to enable pedestal height and fusion performance substantially higher than standard H-Mode operation. This regime exists due to a bifurcation of the pedestal pressure, as a function of density, that is predicted by the EPED model to occur in strongly shaped plasmas above a critical pedestal density. Experiments on Alcator C-Mod and DIII-D have achieved access to the Super H-Mode (and Near Super H) regime, and obtained very high pedestal pressure, including the highest achieved on a tokamak ( p ped ~ 80 kPa) in C-Mod experiments operating near the ITER magnetic field. DIII-D Super H experiments have demonstrated strong performance, including the highest stored energy in the present configuration of DIII-D ( W ~ 2.2–3.2 MJ), while utilizing only about half of the available heating power ( P heat ~ 7–12 MW). These DIII-D experiments have obtained the highest value of peak fusion gain, Q DT,equiv ~ 0.5, achieved on a medium scale ( R < 2 m) tokamak. Sustained high performance operation ( β N ~ 2.9, H 98 ~ 1.6) has been achieved utilizing n = 3 magnetic perturbations for density and impurity control. Pedestal and global confinement has been maintained in the presence of deuterium and nitrogen gas puffing, which enables a more radiative divertor condition. A pair of simple performance metrics is developed to assess and compare regimes. Super H-Mode access is predicted for ITER and expected, based on both theoretical prediction and observed normalized performance, to allow ITER to achieve its goals ( Q = 10) at I p < 15 MA, and to potentially enable more compact, cost effective pilot plant and reactor designs.
Pedestal
DIII-D
Alcator C-Mod
Fusion power
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High-beta, low-aspect-ratio (“compact”) stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks (2–4). They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A β=4% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment (NCSX). It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at β=4% have been evaluated for the Quasi-Omnigeneous Stellarator (QOS) experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described.
BETA (programming language)
Aspect ratio (aeronautics)
Bootstrap current
Ballooning
Plasma stability
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In the high confinement mode (H-mode) of tokamak operation, sharp gradients and the resulting high bootstrap current near the edge of a tokamak plasma (the pedestal) typically trigger eruptions called edge localised modes (ELMs). On the ITER scale, these have the potential to cause unacceptable erosion of materials. However, there exist scenarios, such as the quiescent H-mode (QH), where there are no ELMs. The ELITE code was originally developed to efficiently calculate the edge ideal MHD stability properties of tokamaks, optimised for the intermediate-high toroidal mode number, n, modes associated with ELMs. In QH-mode the limiting MHD is typically low n. Chapter 3 presents the extension of the ELITE code to arbitrary n. Chapter 4 presents successful benchmarks against the original ELITE code as well as GATO and MARG2D at low n. A first application of the new ELITE code was to study the stability of the QH-mode pedestal in DIII-D. Results from this study are presented in Chapter 5, which show the presence of low n phenomena.
Additionally, understanding the pedestal performance losses in JET ITER-like wall (ILW) plasmas is vital to the success of future JET and ITER experiments. Chapter 6 presents an inter-ELM pedestal stability study, which compares the pedestal evolution to the criteria of the pedestal structure model, EPED. These results suggest that maximising the region of plasma that has second stability access will lead to the highest pedestal heights and, therefore, best confinement - a key result for optimising the fusion performance of JET and future tokamaks, such as ITER.
Pedestal
Bootstrap current
DIII-D
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In a tokamak pedestal, radial scale lengths can become comparable to the ion orbit width, invalidating conventional neoclassical calculations of flow and bootstrap current. In this work we illustrate a non-local approach that allows strong radial density variation while maintaining small departures from a Maxwellian distribution. Non-local effects alter the magnitude and poloidal variation of the flow and current. The approach is implemented in a new global delta-f continuum code using the full linearized Fokker-Planck collision operator. Arbitrary collisionality and aspect ratio are allowed as long as the poloidal magnetic field is small compared to the total magnetic field. Strong radial electric fields, sufficient to electrostatically confine the ions, are also included. These effects may be important to consider in any comparison between experimental pedestal flow measurements and theory.
Pedestal
Bootstrap current
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Received 14 April 2011DOI:https://doi.org/10.1103/PhysRevLett.106.169903© 2011 American Physical Society
Pedestal
Bootstrap current
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Citations (2)
Simulations of three Joint European Torus [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)] type I ELMy high-confinement discharges in a power scan are carried out using the JETTO integrated modeling code [M. Erba et al., Plasma Phys. Controlled Fusion 39, 261 (1997)] with predictive core and pedestal models, which include the effect of edge localized modes (ELMs). It is found that current-driven peeling modes trigger the ELM crashes in these discharges and, as a result, yield an explanation of the experimentally observed increase in pedestal height with heating power. After each ELM crash, the pressure gradient and the related bootstrap current density at the edge of plasma rapidly increase with increasing heating power, while the total current density rises only slowly because the total current density is impeded by a back electromotive force. Hence, as the heating power is increased, the pedestal pressure can rise to higher values during an ELM cycle before the current density reaches the level required for destabilization of the current-driven peeling modes. In addition, a stability analysis using the HELENA and MISHKA codes [A. B. Mikhailovskii et al., Plasma Phys. Rep. 23, 713 (1997)] is carried out in conjunction with these simulations. The analysis includes infinite-n ideal ballooning, finite-n ballooning, and low-n kink/peeling modes.
Pedestal
Ballooning
Joint European Torus
Bootstrap current
Collisionality
Edge-localized mode
Pressure gradient
Electron temperature
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Citations (12)
High-beta, low-aspect-ratio (compact) stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady-state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks (2-4). They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A beta = 4% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment (NCSX). It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at beta = 4% have been evaluated for the Quasi-Omnigeneous Stellarator (QOS) experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described.
BETA (programming language)
Bootstrap current
Ballooning
Aspect ratio (aeronautics)
Plasma stability
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The strong radial electric field in a subsonic tokamak pedestal modifies the neoclassical ion parallel flow velocity, as well as the radial ion heat flux. Existing experimental evidence of the resulting alteration in the poloidal flow of a trace impurity is discussed. We then demonstrate that the modified parallel ion flow can noticeably enhance the pedestal bootstrap current when the background ions are in the banana regime. Only the coefficient of the ion temperature gradient drive term is affected. The revised expression for the pedestal bootstrap current is presented. The prescription for inserting the modification into any existing banana regime bootstrap current expression is given.
Pedestal
Bootstrap current
Ion current
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Citations (18)
The high confinement mode (H-mode) plasmas in the pedestal region of tokamaks are characterized by steep gradient of the radial electric field, and sonic poloidal Up,m flow that consists of poloidal components of the E×B flow and the plasma flow velocity that is parallel to the magnetic field B. Here, E is the electric field. The bootstrap current that is important for the equilibrium, and stability of the pedestal of H-mode plasmas is shown to have an expression different from that in the conventional theory. In the limit where |Up,m| ≫ 1, the bootstrap current is driven by the electron temperature gradient and inductive electric field fundamentally different from that in the conventional theory. The bootstrap current in the pedestal region can be controlled through manipulating Up,m and the gradient of the radial electric. This, in turn, can control plasma stability such as edge-localized modes. Quantitative evaluations of various coefficients are shown to illustrate that the bootstrap current remains finite when |Up,m| approaches infinite and to provide indications how to control the bootstrap current. Approximate analytic expressions for viscous coefficients that join results in the banana and plateau-Pfirsch-Schluter regimes are presented to facilitate bootstrap and neoclassical transport simulations in the pedestal region.
Pedestal
Bootstrap current
Electric current
Pressure gradient
Plasma stability
Cite
Citations (2)