High Beta Tokamak Research Articles

Resistive wall mode and neoclassical tearing mode coupling in rotating tokamak plasmas

A model system of equations has been derived to describe a toroidally rotating tokamak plasma, unstable to resistive wall modes (RWMs) and metastable to neoclassical tearing modes (NTMs), using a linear RWM model and a nonlinear NTM model. If no wall is present, the NTM growth shows the typical threshold/saturation island widths, whereas a linearly unstable kink mode grows exponentially in this model plasma system. When a resistive wall is present, the growth of the linearly unstable RWM is accelerated by an unstable island: a form of coupled RWM–NTM mode. Crucially, this coupled system has no threshold island width, giving the impression of a triggerless NTM, observed in high beta tokamak discharges. Increasing plasma rotation at the island location can mitigate its growth, decoupling the modes to yield a conventional RWM with no threshold width.

Analytic Equilibria of High-Beta Tokamaks with Toroidal and Poloidal Flows and Pressure Anisotropy Associated with Parallel Heat Flux

Analytic solutions for a reduced set of magnetohydrodynamic equilibrium equations for high-beta tokamaks with toroidal and poloidal flow velocities comparable to the poloidal sound velocity as well as with pressure anisotropy associated with parallel heat flux are presented. The equations for the parallel heat flux are closed with a fluid closure model. Equilibrium profiles including anisotropic ion and electron pressures are self-consistently obtained and their properties are analytically examined. The solution indicates a qualitatively different behavior in the region around the poloidal sound velocity from those for adiabatic pressure [A. Ito and N. Nakajima: Plasma Phys. Control. Fusion 51 (2009) 035007] and the Chew–Goldberger–Low (CGL) double adiabatic pressure for ions since the parallel heat flux modifies the characteristics of sound waves.

Gyrokinetic turbulence simulations of high-beta tokamak and helical plasmas with full-kinetic and hybrid models

Turbulent transport in high-beta toroidal plasmas is investigated by means of an electromagnetic gyrokinetic model and a newly developed electromagnetic hybrid model consisting of the gyrokinetic equation for ions and drift-Landau-fluid equations for electrons. Full gyrokinetic simulation results for Cyclone base case tokamak and for Large Helical Device (LHD) plasmas are quickly and accurately reproduced by the hybrid simulation. In the kinetic ballooning mode (KBM)-driven turbulence the ion heat and particle fluxes are mainly caused by electrostatic perturbation, and the contribution of magnetic perturbation is small and negative. The electron heat flux is caused by both electrostatic and magnetic perturbations. The numerical solutions satisfy the entropy balance equation, and the entropy is transferred from ions to electrons through electrostatic and magnetic perturbations. An analysis based on the entropy balance equation shows that the zonal structure is produced by magnetic nonlinearity corresponding to the Maxwell stress in the fluid limit but is weakened by the electrostatic one related to the Reynolds stress. A linear analysis on the standard configuration of LHD plasmas shows the suppression of the ion temperature gradient mode by finite-beta effects and the destabilization of KBM at high beta.

Simulation of feedback control system for NTM stabilisation in ASDEX Upgrade

Neoclassical Tearing Modes (NTMs) are a class of MHD instability in high beta tokamak plasmas which significantly increase radial transport, thus capping the performance of fusion plasmas. More importantly, NTMs can lead to disruptions which compromise the lifetime of structural components. Several tokamaks have demonstrated that Electron Cyclotron Resonant Heating (ECRH) can stabilise NTMs if the power deposition is aligned with the mode location. The deposition location depends on the toroidal magnetic field, flux and density profiles, and can be controlled by tilting the mirror in the ECRH launcher. Until recently, the mirror angle was set by feedforward control at ASDEX Upgrade.In order to adapt automatically to different discharge scenarios, the system at ASDEX Upgrade has been extended to steer the mirror using feedback control. The mirror must react on the current diffusion time scale, on the order of 100ms. This is within the capabilities of the mechanical subsystem and real-time plasma diagnostics, but requires careful interfacing between these components. For example, asynchronous data transfer and non-linearities make it difficult to design an analytically optimal controller. Therefore a simulation has been used to test and tune different controller architectures. This simulation is the subject of the current contribution. Performing the optimisation process offline saves valuable experiment time and allows risk-free experimentation with novel designs. Settings which were optimised in the simulation led to considerable improvement of the system performance.

Nonlinear Simulation of Energetic Particle Modes in High-Beta Tokamak Plasma

Nonlinear Simulation of Energetic Particle Modes in High-Beta Tokamak Plasma

Equilibria of toroidal plasmas with toroidal and poloidal flow in high-beta reduced magnetohydrodynamic models

A reduced set of magnetohydrodynamic equilibrium equations for high-beta tokamaks is derived from the fluid moment equations for collisionless, magnetized plasmas. Effects of toroidal and poloidal flow comparable to the poloidal-sound velocity, two-fluid, ion finite Larmor radius (FLR), pressure anisotropy and parallel heat fluxes are incorporated into the Grad–Shafranov equation by means of asymptotic expansions in terms of the inverse aspect ratio of a torus. The two-fluid effects induce the diamagnetic flows, which result in asymmetry of the equilibria with respect to the sign of the E × B flow. The gyroviscosity and other FLR effects cause the so-called gyroviscous cancellation of the convection due to the ion diamagnetic flow. The qualitative difference between the equilibria with and without the parallel heat fluxes is shown to stem from characteristics of the sound waves. Higher order terms of quantities like the pressures and the stream functions show the shift of their isosurfaces from the magnetic surfaces due to effects of flow, two-fluid and pressure anisotropy. The reduced form of the diamagnetic current associated with pressure anisotropy is also obtained.

Global and Kinetic MHD Simulation by the Gpic-MHD Code

In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC (particle-in-cell) code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic (MHD) simulation]. In the new algorithm, the vorticity equation and the generalized Ohm's law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. The basic algorithm is equivalent to solving the reduced-MHD-type equations with kinetic corrections, in which MHD physics related to Alfven modes are well described. The estimation of perturbed electron pressure from particle dynamics is dominant, while the effects of other moments are negligible. Another advantage of the algorithm is that the longitudinal induced electric field, ETz = −∂Az/∂t, is explicitly estimated by the generalized Ohm's law and used in the equations of motion. Furthermore, the particle velocities along the magnetic field are used (vz-formulation) instead of generalized momentums (pz-formulation), hence there is no problem of ‘cancellation', which would otherwise appear when Az is estimated from the Ampere's law in the pz-formulation. The successful simulation of the collisionless internal kink mode by the new Gpic-MHD with realistic values of the large-scale and high-beta tokamaks revealed the usefulness of the new algorithm.

Evidence for the Importance of Trapped Particle Resonances for Resistive Wall Mode Stability in High Beta Tokamak Plasmas

Active measurements of the plasma stability in tokamak plasmas reveal the importance of kinetic resonances for resistive wall mode stability. The rotation dependence of the magnetic plasma response to externally applied quasistatic n=1 magnetic fields clearly shows the signatures of an interaction between the resistive wall mode and the precession and bounce motions of trapped thermal ions, as predicted by a perturbative model of plasma stability including kinetic effects. The identification of the stabilization mechanism is an essential step towards quantitative predictions for the prospects of "passive" resistive wall mode stabilization, i.e., without the use of an "active" feedback system, in fusion-alpha heated plasmas.

Numerical calculation of equilibria with poloidal-sonic flow and finite Larmor radius effects in large aspect-ratio tokamaks

A code has been developed for calculating magnetohydrodynamic equilibria with poloidal-sonic flow and finite Larmor radius effects in high-beta tokamaks using an inverse aspect-ratio expansion and a reduced two-fluid model. The Grad–Shafranov equations governing the first- and second-order poloidal fluxes can be expressed in terms of five free profiles of the first-order poloidal flux. Sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces, and the criteria for the presence of the “poloidal-sonic singularity” are presented.

Diagnostics for Lab and Astrophysical Plasmas

To monitor effects of vacuum conditioning, three radiation diagnostics are being built: a Helium–Neon (HeNe) heterodyne interferometer, a Bolometer, and a Hydrogen-alpha (Hα) detector. The interferometer will measure the line-average refractive index of the plasma, enabling us to obtain the line average density. The bolometer is a soft X-ray/UV detector (similar to those used on the Sustained Spheromak Physics Experiment (McLean et al. in Rev. Sci. Instruments 72(1):556–561, 2001) and the High-Beta Tokamak Experiment (Xiao and Navratil. in Rev. Sci. Instrument 67(9):3334–3335, 1996) and is used to directly measure the radiation loss from photons. The Hα detector will detect the amount of Hα being emitted by the plasma as a function of time, thus gauging the neutral density. These same concepts are also applied to astrophysical plasmas, with slightly different approaches. A brief overlap between diagnostics/detectors for laboratory and astrophysical plasmas is discussed.

The role of kinetic effects, including plasma rotation and energetic particles, in resistive wall mode stability

The resistive wall mode (RWM) instability in high-beta tokamaks is stabilized by energy dissipation mechanisms that depend on plasma rotation and kinetic effects. Kinetic modification of ideal stability calculated with the “MISK” code [B. Hu et al., Phys. Plasmas 12, 057301 (2005)] is outlined. For an advanced scenario ITER [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)] plasma, the present calculation finds that alpha particles are required for RWM stability at presently expected levels of plasma rotation. Kinetic stabilization theory is tested in an experiment in the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] that produced marginally stable plasmas with various energetic particle contents. Plasmas with the highest and lowest energetic particle content agree with calculations predicting that increased energetic particle pressure is stabilizing but does not alter the nonmonotonic dependence of stability on plasma rotation due to thermal particle resonances. Presently, the full MISK model, including thermal particles and an isotropic slowing-down distribution function for energetic particles, overpredicts stability in NSTX experiments. Minor alteration of either effect in the theory may yield agreement; several possibilities are discussed.

Self-Consistent Pressure and Current Profiles in High-Beta D-3He Tokamak Reactors

D-3He reactor has a great advantage of neutron-poor operation, but it requires higher-beta value and higher bootstrap current fraction than D-T reactor. In this paper, we investigated self-consistent plasma pressure and current profiles in the case of a positive magnetic shear mode (parabolic temperature profile) and a negative magnetic shear mode (ITB temperature profile) using TOTAL-T code including Cytran module. In a negative magnetic shear mode, toroidal beta value βT ∼ 52.4 % and bootstrap current fraction fbs ∼ 0.93 was obtained in a plasma with aspect ratio 1.77, plasma major radius 6.2 m, toroidal field 4.2 T and plasma current 49.3 MA.

Pressure-gradient-induced Alfvén eigenmodes: I. Ideal MHD and finite ion Larmor radius effects

In the second magnetohydrodynamic (MHD) ballooning stable domain of a high-beta tokamak plasma, the Schrödinger equation for ideal MHD shear Alfvén waves has discrete solutions corresponding to standing waves trapped between pressure-gradient-induced potential wells. Our goal is to understand how these so-called α-induced toroidal Alfvén eigenmodes (αTAE) are modified by the effects of finite Larmor radii (FLR) and kinetic compression of thermal ions in the limit of massless electrons. In this paper, we neglect kinetic compression in order to isolate and examine in detail the effect of FLR terms. After a review of the physics of ideal MHD αTAE, the effect of FLR on the Schrödinger potential, eigenfunctions and eigenvalues is described with the use of parameter scans. The results are used in a companion paper to identify instabilities driven by wave–particle resonances in the second stable domain.

Dynamically stable, self-similarly evolving, and self-organized states of high beta tokamak and reversed pinch plasmas and advanced active control

Generalized simultaneous eigenvalue equations derived from a generalized theory of self-organization are applied to a set of simultaneous equations for two-fluid model plasmas. An advanced active control by using theoretical time constants is proposed by predicting quantities to be controlled. Typical high beta numerical configurations are presented for the ultra low q tokamak plasmas and the reversed-field pinch (RFP) ones in cylindrical geometry by solving the set of simultaneous eigenvalue equations. Improved confinement with no detectable saw-teeth oscillations in tokamak experiments is reasonably explained by the shortest time constant of ion flow. The shortest time constant of poloidal ion flow is shown to be a reasonable mechanism for suppression of magnetic fluctuations by pulsed poloidal current drives in RFP experiments. The bifurcation from basic eigenmodes to mixed ones deduced from stability conditions for eigenvalues is shown to be a good candidate for the experimental bifurcation from standard RFP plasmas to their improved confinement regimes.Generalized simultaneous eigenvalue equations derived from a generalized theory of self-organization are applied to a set of simultaneous equations for two-fluid model plasmas. An advanced active control by using theoretical time constants is proposed by predicting quantities to be controlled. Typical high beta numerical configurations are presented for the ultra low q tokamak plasmas and the reversed-field pinch (RFP) ones in cylindrical geometry by solving the set of simultaneous eigenvalue equations. Improved confinement with no detectable saw-teeth oscillations in tokamak experiments is reasonably explained by the shortest time constant of ion flow. The shortest time constant of poloidal ion flow is shown to be a reasonable mechanism for suppression of magnetic fluctuations by pulsed poloidal current drives in RFP experiments. The bifurcation from basic eigenmodes to mixed ones deduced from stability conditions for eigenvalues is shown to be a good candidate for the experimental bifurcation from stand...

Burning plasma simulation and environmental assessment of tokamak, spherical tokamak and helical reactors

Reference 1-GWe DT reactors (tokamak TR-1, spherical tokamak ST-1 and helical HR-1 reactors) are designed using physics, engineering and cost (PEC) code, and their plasma behaviours with internal transport barrier operations are analysed using toroidal transport analysis linkage (TOTAL) code, which clarifies the requirement of deep penetration of pellet fuelling to realize steady-state advanced burning operation. In addition, economical and environmental assessments were performed using extended PEC code, which shows the advantage of high beta tokamak reactors in the cost of electricity (COE) and the advantage of compact spherical tokamak in life-cycle CO2 emission reduction. Comparing with other electric power generation systems, the COE of the fusion reactor is higher than that of the fission reactor, but on the same level as the oil thermal power system. CO2 reduction can be achieved in fusion reactors the same as in the fission reactor. The energy payback ratio of the high-beta tokamak reactor TR-1 could be higher than that of other systems including the fission reactor.

Analytic high-beta tokamak equilibria with poloidal-sonic flow

A reduced set of equations for high-beta tokamak equilibria with flow comparable to the poloidal sound velocity is solved analytically. The solution includes higher-order terms of asymptotic expansions in terms of the inverse aspect ratio and indicates the modification of the magnetic structure and the departure of the pressure surfaces from the magnetic surfaces by sub- or super-poloidal-sonic flows. The analytical representation for the shift of the magnetic axis from the geometrical axis (the Shafranov shift) and that of the pressure maximum and the equilibrium beta limit are also obtained. The Shafranov shift is enhanced by a slightly super-poloidal-sonic flow and it produces a forbidden region of equilibrium by the poloidal-sonic flow. The physical mechanism of the shift of the pressure maximum from the magnetic axis due to the poloidal-sonic flow is discussed in analogy to those of the geodesic acoustic mode and the slow magnetosonic wave.

Imaging Measurement for Pressure-Driven Instability in Spherical Tokamak

The two dimensional images of pressure-driven instabilities were measured in high-beta spherical tokamak (ST) formed by their axial merging at TS-4 device. A blight line parallel to the magnetic field lines was identified for the first time when the edge magnetic surface was destabilized in s-alpha diagram for ballooning modes.

Burning plasma simulation of TR-1 tokamak and HR-1 helical reactors

For comparative assessment of tokamak and helical reactors, two base case reactor designs with 1 GW electric power output are introduced; high-field high-beta compact tokamak reactor TR-1 (major radius R = 5.2 m, magnetic field B = 7.1 T) and high-beta helical system HR-1 ( R = 12.1 m, B = 4.6 T). Operational boundaries of both reactors are compared by the zero-dimensional energy balance model, which clarifies the difference between the higher temperature operational regime of TR-1 and the lower temperature regime of HR-1. These operational scenarios are reconfirmed by the toroidal transport analysis linkage (TOTAL) code coupling with two-dimensional equilibrium in the TOTAL-T tokamak code and three-dimensional equilibrium in the TOTAL-H helical code. The beta effect on confinement degradation and the impurity radiation effect on energy balance are found to make the ignition difficult in both systems.

Simulation of saturated tearing modes in tokamaks

A quasi-linear model, which includes the effect of the neoclassical bootstrap current, is developed for saturated tearing modes in order to compute magnetic island widths in axisymmetric toroidal plasmas with arbitrary aspect ratio and cross-sectional shape. The model is tested in a simple stand-alone code and is implemented in the BALDUR [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1982)] predictive modeling code. It is found that the widths of tearing mode islands increase with decreasing aspect ratio and with increasing elongation. Also, the island widths increase when the gradient of the current density increases at the edge of the islands and when the current density inside the islands is suppressed, such as the suppression caused by the near absence of the bootstrap current within the islands. In simulations of tokamak discharges, it is found that tearing mode island widths oscillate in time in response to periodic sawtooth crashes. The local enhancements in the transport produced by magnetic islands have a noticeable effect on global plasma confinement in simulations of low aspect ratio, high beta tokamaks, where saturated tearing mode islands can occur with widths that are greater than 15% of the plasma minor radius.

Experimental and Theoretical Research about a Scenario to Produce High-Beta Spherical Tokamak by Merging Method

Experimental and Theoretical Research about a Scenario to Produce High-Beta Spherical Tokamak by Merging Method