Large Aspect Ratio Tokamaks Research Articles

Plasma self-driven current in tokamaks with magnetic islands

Abstract Magnetic island perturbations may cause a reduction in plasma self-driven current that is needed for tokamak operation.
 A novel effect on tokamak self-driven current revealed by global gyrokinetic simulations is due to magnetic-island-induced
3D electric potential structures, which have the same dominant mode numbers as that of the magnetic island,
whereas centered at both the inner and outer edge of the island. The non-resonant potential islands
are shown to drive a current through an efficient nonlinear parallel acceleration of electrons.
In large aspect ratio (large-A) tokamak devices, this new effect can result in a significant
global reduction of the electron bootstrap current when the island size is sufficiently large,
in addition to the local current loss across the island region due to the pressure profile flattening.
It is shown that there exists a critical magnetic island width for large-A tokamaks beyond which
the electron bootstrap current loss is global and increases rapidly with the island size.
As such, this process may introduce a size limit for tolerable magnetic islands in large-A tokamak
devices in the context of steady state operation. On the other hand, the current loss caused by magnetic islands in
low-A tokamaks such as spherical tokamak (ST) NSTX/U is minor.
The reduction of the axisymmetric current by magnetic islands scales with the square of island width.
However, the loss of the current is mainly local to the island region, and the pace of current
loss as the island size increases is substantially slower compared to large-A tokamaks.
In particular, the bootstrap current reduction in STs is even smaller in the reactor-relevant
high-$\beta_p$ regime where neoclassical tearing modes are more likely to develop.

Drift kinetic theory of neoclassical tearing modes in tokamak plasmas: polarisation current and its effect on magnetic island threshold physics

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

Retraction Note to: Prevention of Plasma–Surface Interactions by Control of Plasma Equilibrium in Large Aspect Ratio Tokamaks

Retraction Note to: Prevention of Plasma–Surface Interactions by Control of Plasma Equilibrium in Large Aspect Ratio Tokamaks

Design and implementation of a prototype infrared video bolometer (IRVB) in MAST Upgrade.

A prototype infrared video bolometer (IRVB) was successfully deployed in the Mega Ampere Spherical Tokamak Upgrade (MAST Upgrade or MAST-U), the first deployment of such a diagnostic in a spherical tokamak. The IRVB was designed to study the radiation around the lower x-point, another first in tokamaks, and has the potential to estimate emissivity profiles with spatial resolution beyond what is achievable with resistive bolometry. The system was fully characterized prior to installation on MAST-U, and the results are summarized here. After installation, it was verified that the actual measurement geometry in the tokamak qualitatively matches the design; this is a particularly difficult process for bolometers and was done using specific features of the plasma itself. The installed IRVB measurements are consistent both with observations from other diagnostics, including magnetic reconstruction, visible light cameras, and resistive bolometry, as well as with the IRVB-designed view. Early results show that with conventional divertor geometry and only intrinsic impurities (for example, C and He), the progression of radiative detachment follows a similar path to that observed for large aspect ratio tokamaks: The peak of the radiation moves along the separatrix from the targets to the x-point and high-field side midplane with a toroidally symmetric structure that can eventually lead to strong effects on the core plasma inside the separatrix.

Drift kinetic theory of the NTM magnetic islands in a finite beta general geometry tokamak plasma

In (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) a new 4D drift kinetic nonlinear theory, valid in the limit of a low beta, small inverse aspect ratio, circular cross section, toroidal geometry, to describe the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is derived. In (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) this theory is reduced in a low collisionality limit, which allows a dimensionality reduction to a 3D problem to efficiently resolve the collisional dissipation layer in the vicinity of the trapped-passing boundary. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) adopts an improved model for the magnetic drift frequency, which reduces the threshold magnetic island half-width from , where is the trapped ion banana orbit width, to , making it in closer agreement with experimental observations for the large aspect ratio tokamak equilibrium. In the present paper, the theory is extended to a high beta, arbitrary tokamak geometry to capture the plasma shaping effects on the NTM threshold physics with the focus on the non-zero triangularity discharges that are known to have a strong impact on the plasma MHD stability. First, it is found that the higher triangularity plasma is more prone to NTMs which is in agreement with the tearing mode onset relative frequency measurements in DIII-D. Second, the NTM threshold dependence on the tokamak inverse aspect ratio obtained in (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) is refined and extended to a finite aspect ratio limit. Third, the NTM threshold dependence on poloidal beta is obtained and benchmarked against the EAST threshold island width measurements.

Influence of anomalous perpendicular transport on linear tearing mode dynamics in tokamak plasmas

The analysis of a previous paper [A. Cole and R. Fitzpatrick, Phys. Plasmas 13, 032503 (2006)] that maps out all of the two-fluid response regimes of a linear tearing layer interacting with an externally generated resonant magnetic perturbation, in a large aspect-ratio tokamak plasma, is generalized to take into account realistic levels of perpendicular particle transport. A new response-regime map is obtained that differs substantially, in many respects, from the old one. The improved analysis is first employed to find all of the two-fluid growth-rate regimes of a non-interacting low-mode-number tearing mode in a large aspect-ratio tokamak plasma. The analysis is then used to determine the scaling of the error-field penetration threshold with machine parameters in large aspect-ratio tokamak plasmas.

Edge harmonic oscillations in plasmas with a separatrix and the effect of edge magnetic shear

This work presents an extension of exfernal mode theory, where the effects of edge magnetic shear and plasma separatrix are investigated and applied to edge harmonic oscillations (EHOs). Linear analytical modelling is performed on a large aspect ratio tokamak with circular cross section, from which a set of three coupled differential equations describing the dispersion relation are derived. To correctly assess the effect of edge shear on exfernal modes, higher order corrections need to be retained in the expansion of the safety factor around the rational surface. The equations are solved numerically for equilibrium pressure and safety factor profiles containing the key features for the excitation of exfernal modes, including a model of a plasma separatrix. The current-driven branch of the instability is significantly reduced by the inclusion of the separatrix, but the mode remains unstable through coupling with the pressure-driven infernal drive. The obtained parameter space for the instability without the effect of the separatrix is compared with the growth rates calculated using the KINX code, and with the nonlinear plasma displacement calculated using the VMEC free-boundary code. From the comparison it was found that the edge shear can be of order unity and still excite exfernal modes, implying that EHOs can be excited even with weak flattening of the local safety factor at the edge, which is in line with some current experimental observations, but contrary to previous simpler analytic theory.

On similarity scaling of tokamak fusion plasmas with different aspect ratio

Previously, tokamak research has been focused mainly on large aspect ratio devices where the vessel/plasma major radius is about a factor three larger than the plasma radius. This research culminated in the design and construction of the international thermonuclear experimental reactor, ITER. Spherical tokamaks (ST), with aspect ratio below two, represent an attractive alternative to large aspect ratio tokamaks as, in our opinion, provide a faster, more economical and compact solution on the path to a fusion reactor. STs are the focus of research at Tokamak Energy Ltd with its present device ST40 in operation and the first ST reactor being designed, taking advantage of the high temperature superconductor (HTS) technology. HTS allow to design a ST with magnetic field/comparable or exceeding that of present-day large aspect ratio tokamaks. However, plasma studies carried out so far on compact, low aspect ratio tokamaks have been limited to small, low magnetic field, low plasma-current devices and therefore the data available for extrapolating to large scale ST plasmas is limited. This paper addresses the problem of scaling the results of large aspect ratio tokamak and existing ST plasmas to a high field ST reactor using plasma-similarity arguments in order to mitigate its design and operational risks. The role of the plasma aspect ratio in scaling burning plasmas as well as conventional experiments in deuterium is highlighted. We find that the scaling for fusion-reactor plasmas exhibit a stronger dependence on the magnetic field and aspect ratio than the one of conventional non-burning plasmas. The parameters of a ST having the same fusion gain Q fus of ITER under different confinement assumptions and for different aspect ratios are presented and discussed.

Tokamak research at the Ioffe Institute

Recent research at three small tokamaks with different parameters located at the Ioffe Institute—the spherical tokamak Globus-M, the large aspect ratio tokamak FT-2 and the compact tokamak TUMAN-3M—are reviewed. This overview covers energy confinement (Globus-M and FT-2), L–H transition (TUMAN-3M and FT-2), Alfvén waves (Globus-M and TUMAN-3M), ion cyclotron emission (TUMAN-3M), major plasma discharge disruption (Globus-M) and scrape-off layer (Globus-M) studies. A full-f global gyrokinetic modeling benchmark using synthetic diagnostics in FT-2 is described. Anomalous absorption and emission in electron cyclotron resonance heating experiments due to the parametric excitation of localized upper hybrid waves are analyzed theoretically. Progress in the development of the neutral particle analysis, gamma-ray spectrometry and divertor Thomson scattering combined with laser-induced fluorescence diagnostics for ITER is discussed. The status of the new Globus-M2 spherical tokamak is reported.

On the energy confinement time in spherical tokamaks: implications for the design of pilot plants and fusion reactors

Experiments on NSTX and MAST have shown the thermal energy confinement time in spherical tokmaks (STs), , to have a stronger toroidal field and weaker plasma current dependence than in conventional large aspect ratio tokamaks. These scalings were derived for single machines both of which are similarly sized, consequently the NSTX and MAST scaling laws do not include a size dependence, and so cannot be used to extrapolate the performance of future STs. Using physics-based dimensional arguments we extend the NSTX scaling to include a size scaling. We also resolve a colinearity problem specific to NSTX data by assuming core transport is gyro-Bohm like. The resulting scaling has approximately zero beta dependence, a typical collisionality dependence, and a relatively weak safety factor dependence: . With the exception of the safety factor, all exponents are consistent with recent experiments in large aspect ratio tokamaks. This apparent difference between STs and large aspect ratio tokamaks is consistent with MAST and NSTX results. We have considered the implications of the scaling for pilot plants and reactors and find it may be possible to develop more compact reactors based on the ST approach.

Low-frequency magnetohydrodynamic spectra of plasmas with anisotropic pressure in axisymmetric toroidal systems

The low-frequency ideal magnetohydrodynamic (MHD) spectra of anisotropic pressure plasmas in axisymmetric toroidal systems are analyzed. In the framework of the Chew-Goldberger-Low model, the continuum spectrum equations for the coupled localized Alfvén and slow magnetosonic modes are derived. The equations are applied to study the continuous spectra for low-pressure plasmas in large aspect ratio tokamaks. It is shown that for some classes of plasma equilibria the pressure anisotropy results in instability of continuous modes. Such an instability is due to anisotropic plasma stratification over poloidal angle on the magnetic surfaces. It takes place for both the zonal flow modes with (m, n) = 0 and the general electromagnetic modes with (m, n) ≠ 0. The latter are unstable only if they are localized near the rational magnetic surface. A stabilization of this instability due to the Alfvén effect is shown for the modes localized away from the rational magnetic surface.

Comparative study of Fisch-Boozer and Ohkawa current drive mechanisms for electron cyclotron waves

Localized current drive by electron cyclotron (EC) waves is of significant importance in the outer half region of tokamak plasmas. Using the coupled GENRAY/CQL3D suite codes, a systematic comparative study between Ohkawa current drive (OKCD) and electron cyclotron current drive (ECCD) is performed. The results show that OKCD has more advantages than ECCD for far off-axis localized current drive in tokamaks with large inverse aspect ratios, while ECCD is more efficient than OKCD in tokamaks with low inverse aspect ratios. The results of local current driving on the q = 2 rational surface show that both OKCD and ECCD are effective for control of the m = 2/n = 1 tearing mode or neoclassical tearing mode (NTM). It seems that efficient Ohkawa current can be driven in a specific far off-axis radial position as long as the local inverse aspect ratio is large enough. The effect of collisionality imposes a significant impact on OKCD and results in reduction of the net current driven by unit EC power. The dimensionless current drive efficiency of OKCD increases with increasing electron beta βe in a medium range. The results further confirm that OKCD can be a valuable alternative localized current drive method to replace ECCD in large inverse aspect ratio tokamaks or in the radial position where the local inverse aspect ratio is large enough.

Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.

Non-isomorphic radial wavenumber dependencies of residual zonal flows in ion and electron Larmor radius scales, and effects of initial parallel flow and electromagnetic potentials in a circular tokamak

Radial wavenumber dependencies of the residual zonal potential for E × B flow in a circular, large aspect ratio tokamak is investigated by means of the collisionless gyrokinetic simulations of Rosenbluth–Hinton (RH) test and the semi-analytic approach using an analytic solution of the gyrokinetic equation Rosenbluth and Hinton (1998 Phys. Rev. Lett. 80 724). By increasing the radial wavenumber from an ion Larmor radius scale to an electron Larmor radius scale , the well-known level is retained, while the level remains O(1) when the wavenumber is decreased from the electron to the ion Larmor radius scale, if physically same adiabatic assumption is presumed for species other than the main species that is treated kinetically. The conclusion is not modified by treating both species kinetically, so that in the intermediate scale between the ion and electron Larmor radius scale it seems difficult to determine the level uniquely. The toroidal momentum conservation property in the RH test is also investigated by including an initial parallel flow in addition to the perpendicular flow. It is shown that by taking a balance between the initial parallel flow and perpendicular flows which include both E × B flow and diamagnetic flow in the initial condition, the mechanical toroidal angular momentum is approximately conserved despite the toroidal symmetry breaking due to the finite radial wavenumber zonal modes. Effect of electromagnetic potentials is also investigated. When the electromagnetic potentials are applied initially, fast oscillations which are faster than the geodesic acoustic modes are introduced in the decay phase of the zonal modes. Although the residual level in the long time limit is not modified, this can make the time required to reach the stationary zonal flows longer and may weaken the effectiveness of the turbulent transport suppression by the zonal flows.

On current drive by Ohkawa mechanism of electron cyclotron wave in large inverse aspect ratio tokamaks

A localized and efficient current drive method in the outer-half region of the tokamak with a large inverse aspect ratio is proposed via the Ohkawa mechanism of electron cyclotron (EC) waves. Further off-axis Ohkawa current drive (OKCD) via EC waves was investigated in high electron beta βe HL-2M-like tokamaks with a large inverse aspect ratio, and in EAST-like tokamaks with a low inverse aspect ratio. OKCD can be driven efficiently, and the driven current profile is spatially localized in the radial region, ranging from 0.62 to 0.85, where the large fraction of trapped electrons provides an excellent advantage for OKCD. Furthermore, the current drive efficiency increases with an increase in minor radius, and then drops when the minor radius beyond a certain value. The effect of trapped electrons greatly enhances the current driving capability of the OKCD mechanism. The highest current drive efficiency can reach 0.183 by adjusting the steering mirror to change the toroidal and poloidal incident angle, and the total driven current by OKCD can reach 20–32 kA MW−1 in HL-2M-like tokamaks. The current drive is less efficient for the EAST-like scenario due to the lower inverse aspect ratio. The results show that OKCD may be a valuable alternative current drive method in large inverse aspect ratio tokamaks, and the potential capabilities of OKCD can be used to suppress some important magnetohydrodynamics instabilities in the far off-axis region.

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. It is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

Plasma Response to Resonant Magnetic Perturbations in Large Aspect Ratio Tokamaks

In this paper, a plasma response model is investigated for large aspect ratio tokamaks, on the presence of external nonaxisymmetric resonant magnetic perturbations. To control plasma confinement, the plasma is perturbed by external resonant helical windings, similar to those introduced by an ergodic magnetic limiter. The plasma response to the perturbation is modeled as an additional magnetic perturbation, created by a current sheet on the main perturbed resonant surface, vanishing the radial component of the total magnetic field in the considered resonant surface. In order to show the influence of the plasma response on the field line topology, the field line differential equations are integrated numerically, showing the reduction of magnetic island sizes and the regularization of chaotic regions around the resonant surface where the response was introduced, in agreement with results observed in sophisticated simulation codes. Finally, the connection lengths indicate that, regarding their distribution, the plasma response introduces a homogenization effect which may affect the deposition patterns at the tokamak wall.

Remote diagnostics for determination of plasma shift in large aspect ratio tokamaks

Remote diagnostics for determination of plasma shift in large aspect ratio tokamaks

Sub-Alfvénic reduced magnetohydrodynamic equations for tokamaks

A reduced set of magnetohydrodynamic (MHD) equations is derived, applicable to large aspect ratio tokamaks and relevant for dynamics that is sub-Alfvénic with respect to ideal ballooning modes. This ordering optimally allows sound waves, Mercier modes, drift modes, geodesic-acoustic modes (GAM), zonal flows and shear Alfvén waves. Wavelengths long compared to the gyroradius but comparable to the minor radius of a typical tokamak are considered. With the inclusion of resistivity, tearing modes, resistive ballooning modes, Pfirsch–Schluter cells and the Stringer spin-up are also included. A major advantage is that the resulting system is two-dimensional in space, and the system incorporates self-consistent and dynamic Shafranov shifts. A limitation is that the system is valid only in radial domains where the tokamak safety factor, $q$, is close to rational. In the tokamak core, the system is well suited to study the sawtooth discharge in the presence of Mercier modes. The systematic ordering scheme and methodology developed are versatile enough to reduce the more general collisional two-fluid equations or possibly the Vlasov–Maxwell system in the MHD ordering.