Toroidal Plasma Research Articles

Main-ion intrinsic toroidal rotation across the ITG/TEM boundary in DIII-D discharges during ohmic and electron cyclotron heating

Direct measurements of deuterium main-ion toroidal rotation spanning the linear ohmic to saturated ohmic confinement (LOC-SOC) regime and with additional electron cyclotron heating (ECH) are presented and compared with the more commonly measured impurity (carbon) ion rotation in DIII-D. Main ions carry the bulk of the plasma toroidal momentum, and hence, the shape of the main-ion rotation is more relevant to the study of angular momentum transport in tokamaks. Both in the LOC regime and with ECH, the main-ion toroidal rotation frequency is flat across the profile from the sawtooth region to the plasma separatrix. However, the impurity rotation profile possesses a rotation gradient, with the rotation frequency being lower near the plasma edge, implying a momentum pinch or negative residual stress inferred from the impurity rotation that differs from the main-ion rotation. In the SOC regime, both the main-ion and impurity rotation profiles develop a deeply hollow feature near the midradius while maintaining the offset in the edge rotation, both implying a positive core residual stress. In the radial region where the rotation gradient changes most dramatically, turbulence measurements show that density fluctuations near the trapped electron mode (TEM) scale are higher when the rotation profile is flat and drop significantly when the plasma density is raised and the rotation profile hollows, consistent with instabilities damped by collisions. Linear initial value gyrokinetic simulations with GYRO indicate that the transition from LOC-SOC in DIII-D occurs as TEMs are replaced by ion temperature gradient (ITG) driven modes from the outer radii inwards as the plasma collisionality increases, Zeff decreases, and the power flow through the ion channel progressively increases due to the electron-ion energy exchange. Gyrofluid modeling with trap gyro-Landau fluid (TGLF) successfully reproduces the plasma profiles at key times in the discharge and in time dependent simulations with predictive TRANSP. TGLF indicates that in the LOC and SOC regimes as well as with ECH, subdominant modes are present and that the plasma is not in a pure TEM or ITG binary state, but rather a more subtle mixed state. Predictions of the main-ion rotation profiles are performed with global nonlinear gyrokinetic simulations using GTS and reveal that the flat rotation is due to oscillatory variation of the turbulent residual stress across the profile, whereas the deeply hollow rotation profile is due to a larger-scale, dipole-like stress profile. In these cases, the predicted and observed main-ion rotation profile is consistent with the balance of turbulent residual stress and momentum diffusion.

Physics affecting heavy impurity migration in tokamaks: Benchmarking test-ion code ASCOT against TEXTOR tracer experiment

Abstract Erosion, transport and deposition of wall impurities are major concerns in future magnetic fusion devices, both from the perspective of the fusion plasma and the machine wall. An extensive study on molybdenum transport and deposition performed in the TEXTOR tokamak yielded a detailed deposition map that is ideal for benchmark deposition studies. A qualitative benchmark is attempted in this article with the ASCOT code. We set up a full 3D model of the TEXTOR tokamak and studied the influence of different physical mechanisms and their strengths on molybdenum deposition patterns on the simulated plasma-facing components: atomic processes, Coulomb collisions, scrape-off layer (SOL) profiles, source distribution, marker starting energy, radial electric field strength, SOL flow and toroidal plasma rotation. The outcome comprises 13 simulations, each with 100,000 markers. The findings are: • Toroidal plasma movement, either within the LCFS or as SOL flow, is negligible. • SOL profile and marker starting energy have modest impact on deposition. • Source distribution has a large impact in combination with radial electric field profiles. • The E ⇀ × B ⇀ drift has the highest impact on the deposition profiles.

Direct Measurement of a Toroidally Directed Zonal Flow in a Toroidal Plasma.

Zonal flow appears in toroidal, magnetically confined plasmas as part of the self-regulated interaction of turbulence and transport processes. For toroidal plasmas having a strong toroidal magnetic field, the zonal flow is predominately poloidally directed. This Letter reports the first observation of a zonal flow that is toroidally directed. The measurements are made just inside the last closed flux surface of reversed field pinch plasmas that have a dominant poloidal magnetic field. A limit cycle oscillation between the strength of the zonal flow and the amplitude of plasma potential fluctuations is observed, which provides evidence for the self-regulation characteristic of drift-wave-type plasma turbulence. The measurements help advance understanding and gyrokinetic modeling of toroidal plasmas in the pursuit of fusion energy.

Analysis of neutron streaming through penetrations in the JET biological shielding

In the present work neutron streaming through large ducts and labyrinths of the Joint European Torus (JET) biological shielding was evaluated. Neutron fluence and ambient dose equivalent were calculated along the total length of the ducts. Monte Carlo calculations using the MCNP code were performed for both Deuterium-Deuterium (D-D) and Deuterium-Tritium (D-T) toroidal plasma discharge sources. The results of the calculations were compared against measurements performed using thermoluminescence detectors. This work contributes to the operational radiation protection effort to minimize collective radiation dose to personnel at JET and, moreover, provides important information from JET experience that may assist in the optimization and validation of the radiation shielding design methodology used in future fusion plants, such as ITER and DEMO.

Edge plasma measurements on the OP 1.2a divertor plasmas at W7-X using the combined probe

During its second operational campaign (OP 1.2a) W7-X operated with an edge island divertor. Much higher densities (1020m−3) than in to the previous, limiter campaign were achieved. In order to asses this improved performance and the nature of transport with regard to the expected higher densities and other parameters such as the electron and ion temperature, the electric field and plasma flow, measurements at the plasma edge were conducted with reciprocating probe, mounted on a Manipulator. The probe contains a set of Langmuir pins, Mach probes, compensation coils and a set of 3D pick up coils for the measurement of the local magnetic field and fluctuations, and an ion sensitive probe. It has been observed, in addition to differences due to the magnetic configurations, that the magnetic topology is sensitive to the plasma conditions, especially to changes due to a evolving toroidal plasma current. Measurements from divertor cameras showed that an increasing toroidal current in the standard configuration broadened the heat flux and shifted the strike line considerably. These down-stream observation can be complemented with the measurements at the mid-plane with the manipulator mounted probes. During the experiments the edge island remnant was identified with the measured edge plasma profiles and compared with the predictions from the field line tracing code. Those electron densities and temperatures have been used as an input for understanding edge transport with the EMC3-EIRENE modeling. The results from EMC3-EIRENE also help improve the caculated density profiles, since the modelling provides a profile of the effective charge Zeff.

Finite ion orbit width effect on the neoclassical tearing mode threshold in a tokamak plasma

A new drift kinetic theory for the response of ions to small magnetic islands in toroidal plasma is presented. Islands whose width w is comparable to the ion poloidal Larmor radius are considered, expanding the ion response solution in terms of , where r is the minor radius. In this limit, the ion distribution can be represented as a function of toroidal canonical momentum, . With effects of grad-B and curvature drifts taken into account, the ion distribution function is a constant on a ‘drift island’ structure, which is identical to the magnetic island but radially shifted by . The distribution is then flattened across the drift island, rather than the magnetic island. For small islands , the pressure gradient is maintained across the magnetic island, suppressing the bootstrap current drive for the neoclassical tearing mode (NTM) growth. As , the ions are largely unperturbed. However, the electrons respond to the electrostatic potential required for quasi-neutrality and this provides a stabilizing contribution to the NTM evolution. This gives a new physical understanding of the NTM threshold mechanism, with implications for the design of NTM control systems for future tokamaks such as ITER.

Analysis of motor oils using an «Ékspress» spectrometer and microwave plasma source

It is known that the working properties of motor oil are determined by the presence of some elements of the periodic table. The properties of oil can vary significantly over time due to exposure to both high and extremely low pressures and temperatures. To ensure uninterrupted long-term operation of equipment, it is necessary to monitor various indicators of oil, including the determination of wear metals on a regular basis. Two methods of determining wear metals are most widely used: an electric arc with a rotating graphite disk and inductively coupled plasma. The goal of the work was to determine wear metals in oil using a microwave nitrogen plasma source and an «Ékspress» spectrometer according to ASTM D5185-09 method. Microwave plasma was produced using an industrial magnetron with a frequency of 2.5 GHz and a microwave resonator which provided toroidal plasma shape. Nitrogen (purity of 99.6%) was used as a plasma-forming gas. In accordance with the mentioned procedure, a series of wear metal samples was prepared by adding metal oxides to the base oil for comparison with the control experiment. After that, the solutions were diluted 1:10 by weight with kerosene to eliminate the difference in viscosity of the samples and ensure their spraying using a pneumatic spray. The spectrometer allows simultaneous recording of spectra in the region of 190 – 360 and 390 – 540 nm with an integration time of 70 msec. The intensity of C2and CN molecular bands was reduced by introducing air into the intermediate flame of the burner. The constructed calibration graphs for determination of Al, Pb, Fe, Cu, Cr, Cn were used in analysis of the control sample. It is shown that wear metals in oil can be determined using microwave plasma as a source of spectrum excitation.

On the induced azimuthal electric field in the current drive of an odd-parity rotating magnetic field

The azimuthal electric field Eθω, which is induced by the axial oscillating magnetic field Bzω of the odd-parity Rotating Magnetic Field (RMF) scheme, is experimentally found to play an important role in driving the toroidal plasma current. In the odd-parity RMF scheme, Eθω at the middle plane of the field reversed configuration can generate the so-called punctuated betatron-orbital electrons to drive the toroidal current in addition to the current driven by the transverse component of RMF Brω, whereas Brω is the only driving mechanism in the even-parity scheme. In this work, Eθω (or Bzω) and Brω are each studied to account for different current driving mechanisms. We report that Eθω accounts for the more efficient current driving in our experiments.

Influence of resonant magnetic perturbations and induced islands on plasma rotations and turbulence properties in the J-TEXT tokamak

Dedicated experiments have been carried out at the J-TEXT tokamak for investigating plasma responses to the externally applied resonant magnetic perturbation (RMP) field with various RMP currents under four different toroidal phases. After its penetration, the dominant component of the RMP resonated at q = 2 surface and excited an m/n = 2/1 magnetic island, which rotated poloidally when changing the toroidal phase of the RMP. The experimental results show significant influence of the RMP on plasma toroidal and perpendicular rotations, density fluctuations and geodesic acoustic modes (GAMs) as well as nonlinear interaction of ambient turbulence. Whereas the plasma rotations do not show big difference at the RMP-induced island O- and X-point, the turbulence level is substantially lower at the island O-point due to reduced local temperature gradient. The GAM zonal flows outside the island area are profoundly affected by the RMP in various RMP phases. Moreover, it was found that under certain RMP currents the nonlinear coupling of ambient turbulence was considerably enhanced, no matter of at the island O- or X-point. The results suggest a possible controlling role of the RMP in regulating the nonlinear interplay of electrostatic turbulence.

Spontaneous magnetic field multipolar structure in toroidal plasmas based on 2D equilibrium

The multipolar magnetic field structure is investigated by the momentum conservation equation with self-consistent 3D sheared flows during transition of plasma properties from local paramagnetic to diamagnetic fields. Numerical results show that the traditional poloidal magnetic field () is one part of equilibrium magnetic fields. The non-zero-order quantities are originated from the higher-order terms of 2D equilibrium treatment based on a Fourier expansion of ψ (r, θ). The distributions of magnetic field vectors of the order of 1, 2, and 3 terms are presented respectively in two, four, and six polar fields with the local vortex structures (spontaneous magnetic connection). The excitation mechanisms of the magnetic vortices are the coupling effects of the magnetic fluid structure pattern and the toroidal effects. These results can help us understand the physical mechanism of the interaction between the external perturbation fields and control tearing modes, as well as the radial plasma flow and magnetic vortices.

The scale-to-scale energy transfers correlated with the development of turbulence in toroidal plasmas

Two different directions of scale-to-scale energy transfer that corresponds to forward and inverse energy cascades, respectively, were clarified in toroidal plasma turbulence by means of experimental analysis. In the present work we first report the evidence that the turbulence dominated by broad wavenumber spectrum was developed under the action of forward (direct) energy cascade in a reversed field pinch (RFP) plasma, while the generation of GAM zonal flow (ZF) was related with the energy concentrating into low frequency region from higher frequency region due to inverse energy cascade in a tokamak plasma. The two evidences are compared. The results indicate a modulation mechanism in turbulence which is relative to the generation or development of specific turbulent flows. This hints a correlation between energy transfer and the development of toroidal plasma turbulence.

Radial energy channels may account for unexpected plasma losses

Alfvén modes in toroidal plasmas are capable of carrying away energy from a plasma’s hot core.

Nonlinear saturation of kinetic ballooning modes by zonal fields in toroidal plasmas

Kinetic ballooning modes (KBMs) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in magnetic fusion and space plasmas. While the nonlinear evolution of the ballooning modes has been proposed as a mechanism for “detonation” in various scenarios such as the edge localized modes in tokamaks, the role of the kinetic effects in such nonlinear dynamics remains largely unexplored. In this work, global gyrokinetic simulation results of KBM nonlinear behavior are presented. Instead of the finite-time singularity predicted by ideal magnetohydrodynamic theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. In the intermediate nonlinear regime, rapid growth of localized current sheets, which can induce magnetic reconnection, is observed.

Multipolar Structure of Equilibrium Shear Flow Field in Toroidal Plasmas**Supported by National Natural Science Foundation of China under Grant No. 11575066 and Domestic ITER under Grant No. 2009GB105003

The multipolar velocity field structures are investigated by 2D momentum conservation equation with 3D equilibrium sheared flows in the full toroidal system. Numerical results show that the non-existence of radial velocity field in equilibrium surfaces is suitable only for the zero-order term of our 2D simulation. The non-zero-order radial velocity field is still preserved, even when converted to conventional magnetic surface coordinates. The distribution of velocity field vectors of the order of 1, 2, and 3 are presented respectively in 2, 4, and 6 polar fields with the local vortex structure. The excitation mechanisms of these velocity vortices are the coupling effects of the magneto-fluid structure patterns and the toroidal effects. These results can help us understand the complexity of core physics, the transverse transport across magnetic field by the radial plasma flow and the formation of velocity vortices.

Fixed boundary Grad-Shafranov solver using finite difference method in nonhomogeneous meshgrid

In this work we present a numerical scheme to solve the Grad-Shafranov equation which correspond to magnetohydrodynamic equilibrium equation for a two-dimensional plasma. A typical case are the toroidal plasma in magnetic confinement devices used in thermonuclear fusion well known as Tokamaks. The proposed numerical scheme is based on the finite-difference method in nonhomogeneous meshgrid, which is adjusted to the fixed plasma boundary with “D-shape”. The solution of the Grad-Shafranov equation is obtained using the successive over-relaxation method, usually applied to solve Poisson equation’s problems. The values of the total plasma current and pressure in the magnetic axis are conserved in each iteration of the convergence process. The scheme is validated by direct comparison with the analytical result obtained by Soloviev.

Physics design for a lithium vapor box divertor experiment on magnum PSI

The lithium vapor box divertor is a potential solution for power exhaust in toroidal confinement devices. The divertor plasma interacts with a localized, dense cloud of lithium vapor, leading to volumetric radiation, cooling, recombination, and detachment. To minimize contamination of the core plasma, lithium vapor is condensed on cool (300–400°C) baffles upstream of the detachment point. Before implementing this in a toroidal plasma device with a slot divertor geometry, we consider an experiment with a scaled baffled-pipe geometry in the high-power linear plasma device Magnum-PSI. Three 15 cm-scale open cylinders joined by 6 cm diameter ‘nozzles’ are positioned on the plasma beam axis upstream of a target. The central box may be loaded with several tens of grams of lithium, which can be evaporated at 650°C to produce a vapor predicted, using a simple plasma-neutral interaction model, to be dense enough to cause volumetric detachment in the plasma. The power delivered to the target and box walls as measured by increases in their temperatures after a 10 s plasma pulse can be compared to determine the effectiveness of the vapor in detaching the plasma. Direct Simulation Monte Carlo simulations are performed to estimate the flow rates of lithium vapor between the boxes and to estimate the trapping of H2 delivered by the plasma in the boxes, which could inadvertently lead to detachment. Details of the geometry, simulations, and possible diagnostic techniques are presented.

Decomposing magnetic field measurements into internally and externally sourced components in toroidal plasma devices

The magnetic field on any closed surface can be separated into the component produced by currents in the volume enclosed by the surface and the component produced by currents external to the surface. This decomposition was first discovered by Gauss in 1839, and “Gauss' Algorithm” was used to show that the terrestrial field is sourced from inside the Earth. This magnetic source-decomposition can be used in magnetic confinement fusion to distinguish plasma fields from the fields of external sources using standard magnetic measurements, when no conductors reside in the region between the plasma and the magnetic sensors (otherwise, the internal source is not the plasma alone). Here, Gauss' Algorithm is extended from spherical geometry to cylindrical geometry to decompose fields in the cylindrical tokamak. Demonstrations of the decomposition on DIII-D discharges include the measurement of a rotating tearing mode separate from the induced wall eddy currents and the recovery of a vacuum measurement in the presence of an externally applied 3D field. Anticipated axisymmetric and non-axisymmetric applications, and the requisite diagnostics, are discussed. It is concluded that the ITER magnetic diagnostic design is well suited for many important axisymmetric and non-axisymmetric applications. Future work will extend this decomposition to include fields from halo currents and to generalize it to arbitrary toroidal geometries.

Toroidal modeling of resistive wall mode stability and control in HL-2M tokamak

Effects of toroidal plasma flow, magnetic drift kinetic damping as well as feedback control, on the resistive wall mode instability in HL-2M tokamak are numerically investigated, using the linear stability codes MARS-F/K (Liu et al 2000 Phys. Plasmas 7 3681, Liu et al 2008 Phys. Plasmas 15 112503). It is found that the precession drift resonance damping due to trapped thermal particles ensures a robust passive stabilization of the n = 1 (n is the toroidal mode number) RWM in the 2 MA double-null advanced plasma scenario designed for HL-2M, provided that the toroidal flow speed is not too fast: . With two rows of magnetic control coils designed for HL-2M, the optimal poloidal location for the RWM stabilization is found to be . Toroidal modeling also shows that the plasma flow damping, drift kinetic damping and magnetic feedback can be arranged to synergistically stabilize the RWM in HL-2M, by tuning the feedback gain phase and/or including derivative actions in the control loop. The numerical results obtained by MARS-F/K are qualitatively well re-produced by an analytic single-pole model.

Nonlocal transport in toroidal plasma devices

Collisional particle transport is examined in several toroidal plasma devices in the presence of perturbations typical of modes leading up to a disruption, of saturated tearing modes, or of unstable Alfvén modes. The existence of subdiffusive transport for electrons is found to occur in some cases at very low mode amplitudes and to also exist even for ions of high energy. Orbit resonances can produce long time correlations and traps for particle trajectories at perturbation amplitudes much too small for the orbits to be represented as uniformly chaotic. The existence and nature of subdiffusive transport is found to depend on the nature of the mode spectrum and frequency as well as the mode amplitudes.

Mechanisms of the energy transfer across the magnetic field by Alfvén waves in toroidal plasmas

Physics of the transverse energy transfer by Alfvén waves in toroidal plasmas is elucidated. It is found that, in contrast to the classical Alfvén waves in infinite plasmas, the Alfvén waves in toroidal systems produce plasma compression due to coupling with fast magnetoacoustic waves, which provides the energy transfer. The radial group velocities of the traveling waves constituting the Global Alfvén Eigenmodes and Toroidicity-induced Alfvén Eigenmodes are calculated. It is shown that equations for Alfvén eigenmodes derived in the approximation of vanishing wave field along the equilibrium magnetic field reproduce the longitudinal magnetic field of the wave and lead to correct transverse energy flux. The obtained results explain how Alfvén eigenmodes can provide the spatial energy channeling—the transfer of the energy by these modes from the unstable plasma region to the region where the mode damping dominates.