Large Aspect Ratio Tokamaks Research Articles

RETRACTED: High temperature plasma equilibrium analysis by remote magnetic diagnostics in large aspect ratio tokamaks

In this contribution we have reviewed on remote magnetic techniques for determination of plasma displacement based on poloidal flux in large aspect ratio tokamaks. This instrument consists of a two semicircle loops which installed toroidally on inner and outer sides of tokamak chamber and connected with each other. Really, this instrument detects the difference of poloidal flux on the High Field Side (HFS) and Low Field Side (LFS) of tokamak chamber, which we needed in calculating of the Plasma displacement. Main benefit of our proposed instrument is its simplicity. Based on this technique we determined the plasma position, and to compare the result obtained using this technique, an array of four magnetic probes and two flux loops are also designed, constructed and installed on outer surface of the IR-T1 tokamak and plasma position obtained from them. Results are in good agreement with analytical solution of equilibrium problem.

Snowflake Divertor Experiments in the DIII-D, NSTX, and NSTX-U Tokamaks Aimed at the Development of the Divertor Power Exhaust Solution

Experimental results from the National Spherical Torus Experiment (NSTX), a medium-size spherical tokamak with a compact divertor, and DIII-D, a large conventional aspect ratio tokamak, demonstrate that the snowflake (SF) divertor configuration may provide a promising solution for mitigating divertor heat loads and target plate erosion compatible with core H-mode confinement in the future fusion devices, where the standard radiative divertor solution may be inadequate. In NSTX, where the initial high-power SF experiment was performed, the SF divertor was compatible with H-mode confinement, and led to the destabilization of large Edge Localized Modes (ELMs). However, a stable partial detachment of the outer strike point was also achieved where inter-ELM peak heat flux was reduced by factors 3–5, and peak ELM heat flux was reduced by up to 80% (see standard divertor). The DIII-D studies show the SF divertor enables significant power spreading in attached and radiative divertor conditions. Results include: compatibility with the core and pedestal, peak inter-ELM divertor heat flux reduction due to geometry at lower $n_{e}$ , and ELM energy and divertor peak heat flux reduction, especially prominent in radiative $D_{2}$ -seeded SF divertor, and nearly complete power detachment and broader radiated power distribution in the radiative $D_{2}$ -seeded SF divertor at $P_{\text {SOL}}=3-4$ MW. A variety of SF configurations can be supported by the divertor coil set in NSTX Upgrade. Edge transport modeling with the multifluid edge transport code UEDGE shows that the radiative SF divertor can successfully reduce peak divertor heat flux for the projected $P_{\text {SOL}} \simeq 9$ MW case. The radiative SF divertor with carbon impurity provides a wider $n_{e}$ operating window, 50% less argon is needed in the impurity-seeded SF configuration to achieve similar $q_{\text {peak}}$ reduction factors (see standard divertor).

RETRACTED: Semi-emprical techniques for the specification of Shafranov shift in the large aspect ratio tokamaks

Equilibrium reconstruction consists in identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this research, we have reviewed six techniques for determination of the plasma position in IR-T1 tokamak and the effects of superconducting coils and chamber: an optical, flux loops, magnetic probes, multipole moments techniques, and two methods based on the vertical field coil characteristics and analytical solution of Grad–Shafranov equation. In the first method an image processing technique used for the output signal of CCD camera and plasma emission intensity profile and then plasma position obtained. To compare the plasma position obtained using this method, flux loop method, magnetic probe method, multipole moments method, analytical solution of Grad–Shafranov equation, and a sensor-less method based on vertical field coil characteristics are also experimented on the IR-T1 tokamak. Results were compared and discussed.

A New Perspective on Protection of Nuclear Reactor Surfaces From High Energy Plasma Irradiation by Equilibrium Reconstruction

Ignition is the point at which a nuclear fusion of hydrogen isotopes reaction becomes self-sustaining. This occurs when the energy being given off by the fusion reactions heats the fuel mass more rapidly than various loss mechanisms cool it. At this point, the external energy needed to heat the fuel to fusion temperatures is no longer needed. As the rate of fusion varies with temperature, the point of ignition for any given machine is typically expressed as a temperature. On the other hand, energy confinement time is expressed by an equilibrium state. Analytical solutions of Grad-Shafranov equation (GSE) can be used for theoretical studies of plasma equilibrium, transport and Magnetohydrodynamic stability of tokamaks. In this paper we have presented two families of exact solutions. With applying these solutions to IR-T1 tokamak, a small, air core, low beta and large aspect ratio tokamak with a circular cross section, we calculated poloidal magnetic flux. Due to the generality and high accuracy of the second exact solution for all of the magnetic configurations of interest, the result of this solution for IR-T1 tokamak is good (tokamak-relevant) equilibrium compare to the first exact solution for this tokamak. We intend to use these analytical solutions as benchmark of numerical equilibrium codes.

Plasma turbulence in the scrape-off layer of the ISTTOK tokamak

The properties of plasma turbulence in a poloidally limited scrape-off layer (SOL) are addressed, with focus on ISTTOK, a large aspect ratio tokamak with a circular cross section. Theoretical investigations based on the drift-reduced Braginskii equations are carried out through linear calculations and non-linear simulations, in two- and three-dimensional geometries. The linear instabilities driving turbulence and the mechanisms that set the amplitude of turbulence as well as the SOL width are identified. A clear asymmetry is shown to exist between the low-field and the high-field sides of the machine. While the comparison between experimental measurements and simulation results shows good agreement in the far SOL, large intermittent events in the near SOL, detected in the experiments, are not captured by the simulations.

Early evolution of electron cyclotron driven current during suppression of tearing modes in a circular tokamak

When electron cyclotron (EC) driven current is first applied to the inside of a magnetic island, the current spreads throughout the island and after a short period achieves a steady level. Using a two equation fluid model for the EC current that allows us to examine this early evolution in detail, we analyze high-resolution simulations of a 2/1 classical tearing mode in a low-beta large aspect-ratio circular tokamak. These simulations use a nonlinear 3D reduced-MHD fluid model and the JOREK code. During the initial period where the EC driven current grows and spreads throughout the magnetic island, it is not a function of the magnetic flux. However, once it has reached a steady-state, it should be a flux function. We demonstrate numerically that if sufficiently resolved toroidally, the steady-state EC driven current becomes approximately a flux function. We discuss the physics of this early period of EC evolution and its impact on the size of the magnetic island.

Nonlinear tearing modes stabilization by oscillating the resonant surface

The stabilization of the nonlinear tearing mode by rapidly oscillating the resonant surface has been investigated numerically in a large aspect ratio tokamak with a circular cross-section. By means of the radio frequency current drive, the plasma current can be modulated to make the resonant surface (rs) oscillate in time near its mean position. Previous results show that the linear tearing mode can be suppressed by oscillating the resonant surface with a suitable frequency and amplitude. At the nonlinear stage, the tearing mode stabilization shows different properties. The suppression effects not only depend on the modulation frequency and the oscillation width of the resonant surface but also depend on the relative size of χ0 to δ (here, χ0 is the oscillation width of the resonant surface and δ is the width of tearing layer) and the relative width of χ0 to the magnetic island width W.

RETRACTED: Plasma equilibrium reconstruction for the nuclear fusion of magnetically confined hydrogen isotopes

Analytical solutions of electromagnetism driven Grad-Shafranov equation (GSE) can be used for theoretical studies of plasma equilibrium, transport and Magnetohydrodynamic stability of tokamaks. In this research, an extended analytic solution to the Grad-Shafranov equation was presented. The solution describes standard tokamaks configurations. It allows the simulation magnetic surfaces of plasmas with elongation and triangularity, with an independent choice of pressure and plasma current. We have determined equilibrium magnetic surfaces in IR-T1 tokamak. With applying these solutions to IR-T1 tokamak, a small, air core, low beta and large aspect ratio tokamak with a circular cross section, we have calculated poloidal magnetic flux. Due to the generality and high accuracy of the first exact solution for all of the magnetic configurations of interest, the result of this solution for IR-T1 tokamak is acceptable equilibrium compare to the second one for this tokamak. These analytical solutions can be used as an input of feedback control system.

Shearless bifurcation on symplectic maps of magnetic field lines in tokamaks with reversed current

We introduce two-dimensional symplectic maps to describe the Poincaré maps of magnetic field lines in large aspect ratio tokamak equilibria with reversed non-monotonic plasma current density profiles. For these maps, we investigate the effect of the symmetry breaking due to the toroidal correction with a peculiar invariant, namely, a magnetic surface with a null rotation number, enclosing a vanishing current. We find that this rotationless invariant surface is surrounded by many small island chains. Furthermore, near such invariant, the symmetry breaking gives rise to two magnetic shearless invariants surrounded by twin island chains. We also find chaotic lines adjacent to all the observed islands created by the considered structurally unstable equilibria.

RETRACTED ARTICLE: Prevention of Plasma–Surface Interactions by Control of Plasma Equilibrium in Large Aspect Ratio Tokamaks

In tokamak plasma, impurities present a number of problems. One is the radiative power loss, principally due to line radiation from partially stripped ions. Another is fuel dilution. This arises because impurity atoms produce many electrons and, for a given plasma pressure, these electrons lake the place of fuel particles. At high concentrations impurities prevent the plasma being heated. This is particularly a problem during the plasma start-up phase since impurities radiate most strongly at low temperatures before they become highly ionized. Impurities can also lead to disruptions as a result of edge cooling and consequent current profile modification. On the other hand, these problems can be prevented by control of plasma equilibrium (which is defined by Grad–Shafranov (GS) equation). Numerous methods exist to solve the GS equation, describing the equilibrium of plasma confined by an axisymmetric magnetic field. In this paper, we have proposed a new numerical solution to the GS equation of an axisymmetric, transformed in cylindrical coordinates solved with the Chebyshev collocation method, when the source term (current density function) on the right hand side is linear. The Chebyshev collocation method is a method for computing highly accurate numerical solutions of deferential equations. We describe a circular cross section of tokamak and present numerical result of magnetic surfaces on the IR-T1 tokamak and then compare the results with an analytical solution.

Particle transport induced by electrostatic wave fluctuations

Particle transport driven by electrostatic waves at the plasma edge is numerically investigated, for large aspect ratio tokamaks, by considering a kinetic model derived from guiding-center equations of motion. Initially, the transport is estimated for trajectories obtained from differential equations for a wave spectrum generated by a dominant spatial mode and three time modes. Then, in case of infinite time modes, the differential equations of motion are used to introduce a symplectic map that allows to analyze the particle transport. The particle transport barriers are observed for spatial localized dominant perturbation and infinite modes. In presence of infinite spatial modes, periodic islands arise in between chaotic trajectories at the plasma edge.

Collisionless microtearing modes in hot tokamaks: Effect of trapped electrons

Collisionless microtearing modes have recently been found linearly unstable in sharp temperature gradient regions of large aspect ratio tokamaks. The magnetic drift resonance of passing electrons has been found to be sufficient to destabilise these modes above a threshold plasma β. A global gyrokinetic study, including both passing electrons as well as trapped electrons, shows that the non-adiabatic contribution of the trapped electrons provides a resonant destabilization, especially at large toroidal mode numbers, for a given aspect ratio. The global 2D mode structures show important changes to the destabilising electrostatic potential. The β threshold for the onset of the instability is found to be generally downshifted by the inclusion of trapped electrons. A scan in the aspect ratio of the tokamak configuration, from medium to large but finite values, clearly indicates a significant destabilizing contribution from trapped electrons at small aspect ratio, with a diminishing role at larger aspect ratios.

Doppler backscattering for spherical tokamaks and measurement of high-k density fluctuation wavenumber spectrum in MAST

The high-k () wavenumber spectrum of density fluctuations has been measured for the first time in MAST (Lloyd et al 2003 Nucl. Fusion 43 1665). This was accomplished with the first implementation of Doppler backscattering (DBS) for core measurements in a spherical tokamak. DBS has become a well-established and versatile diagnostic technique for the measurement of intermediate- k (, and higher) density fluctuations and flows in magnetically confined fusion experiments. Previous implementations of DBS for core measurements have been in standard, large aspect ratio tokamaks. A novel implementation with two-dimensional (2D) steering was necessary to enable DBS measurements in MAST, where the large variation of the magnetic field pitch angle presents a challenge. We report on the scattering considerations and ray tracing calculations used to optimize the design and present data demonstrating measurement capabilities. Initial results confirm the applicability of the design and implementation approaches, showing the strong dependence of scattering alignment on the toroidal launch angle and demonstrating that DBS is sensitive to the local magnetic field pitch angle. We also present comparisons of DBS plasma velocity measurements with charge exchange recombination and beam emission spectroscopy measurements, which show reasonable agreement over most of the minor radius, but imply large poloidal flows approaching the magnetic axis in a discharge with an internal transport barrier. The 2D steering is shown to enable high-k measurements with DBS, at cm () for launch frequencies less than 75 GHz; this capability is used to measure the wavenumber spectrum of turbulence and we find for –11, which is similar to the expectation for the turbulent kinetic cascade of .

Impact of punctual flat magnetic shear on the field line transport

We investigate the magnetic field line transport for tokamak equilibria with monotonic magnetic shear perturbed by resonant fields. We show that when the local profile is flat at the plasma edge a transport barrier can be created leading to a field line transport reduction. This transport reduction is due to the field lines topological modifications, caused by a local flattened profile that reduces the global field lines escape pattern. The results are obtained by applying a symplectic map that describes perturbed magnetic field lines in large aspect ratio tokamaks.

Role of Trapped Electrons on Global Gyrokinetic Linear Stability of Collisionless Microtearing Modes

Unstable collisional MicroTearing Mode (MTMs) have been found in experiments of high-β Spherical Tokamaks and are believed to be driven by drift resonance of trapped electrons. It has been recently shown that at large aspect ratio, the magnetic drift resonance of highly passing electrons is a minimal mechanism to drive the collisionless MTM unstable. In this work, a preliminary study of inclusion of trapped electrons in large aspect ratio tokamaks indicate that for the reference parameters investigated, the collisionless MTM retain their essential mode structures, while growth rates are only moderately affected.

Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient ηe. Scans at different β values show an inverse relationship between the ηe threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.

Influence of the electric and magnetic shears on tokamak transport

We applied a non-integrable drift-kinetic model, valid for large aspect ratio tokamaks, to investigate plasma edge particle transport driven by drift waves. Particle transport is obtained from the chaotic trajectories obtained by numerically integrating the canonical equations of motion, for the total flow formed by the equilibrium sheared flow and few dominant resonant drift waves propagating in the sheared equilibrium magnetic field. Thus, we investigate the transport dependence on the radial profiles of the electric and magnetic fields and show that radial particle transport at the plasma edge can be reduced by properly modifying the electric and magnetic shear profiles. For non-monotonic radial electric fields, we also observe non-twist transport barriers with shearless invariants identified by extremum values of the rotation number profiles of the invariant curves. The observed non-twist barriers are modified by the magnetic shear and persist for magnetic shear variations expected in present tokamaks.

Quick asymptotic expansion aided by a variational principle

It is shown how expanding asymptotically a variational functional can yield the asymptotic expansion of its Euler equation. The procedure is simple but novel and requires taking the variation of the expanded functional with respect to the leading order of the originally unknown function, even though the leading order of this function has already been determined in a previous order. An example is worked out that of a large aspect ratio tokamak plasma equilibrium state with relatively strong flows and high plasma beta.

A computational approach to continuum damping of Alfvén waves in two and three-dimensional geometry

While the usual way of calculating continuum damping of global Alfvén modes is the introduction of a small artificial resistivity, we present a computational approach to the problem based on a suitable path of integration in the complex plane. This approach is implemented by the Riccati shooting method and it is shown that it can be transferred to the Galerkin method used in three-dimensional ideal magneto-hydrodynamics (MHD) codes. The new approach turns out to be less expensive with respect to resolution and computation time than the usual one. We present an application to large aspect ratio tokamak and stellarator equilibria retaining a few Fourier harmonics only and calculate eigenfunctions and continuum damping rates. These may serve as an input for kinetic MHD hybrid models making it possible to bypass the problem of having singularities on the path of integration on one hand and considering continuum damping on the other.

Plasma Equilibrium in Presence of the Poloidal Flow in Tokamaks

Main purposes of this contribution are analysis of dynamic equilibrium properties of a large aspect ratio and low beta tokamaks, in particular deriving a modified relation for the Shafranov shift in the presence of poloidal flow, and demonstrate it experimentally. Poloidal flow can produce modifications in the equilibrium properties. By increasing Alfvenic Mach number from zero, flow produce outward force, and plasma shifted in outward direction. If the poloidal Alfvenic Mach number equal to one, singularity will observe in the solution of generalized Grad-Shafranov equation. Also inversion of Shafranov shift in the transition of flow speed between sub-Alfvenic to super-Alfvenic speeds can be observed due to inward force produced by flow.