Andreas Wingen

• Dr. rer. nat.
• Researcher at Oak Ridge National Laboratory

This paper describes the extensive progress that has been made in the understanding of tokamak pedestal physics since the 2007 publication of ‘Progress in the ITER Physics Basis’ (Ikeda 2007 Nucl. Fusion 47 E01–S500). It serves as Chapter 3 of the 2025 Nuclear Fusion Special Issue titled ‘On the Path to Tokamak Burning Plasma Operation’ (Campbell e...

Evidence of a MHD dynamo brought about by intrinsic helical core structures in negative triangularity (NT) and ITER baseline scenario (IBS) plasmas demonstrates paths to operating tokamaks without seeds for deleterious global MHD modes. A stationary sawtooth- and edge localized mode-free state maintains high performance for long durations in a stro...

A novel multicode workflow to interpret collector probe deposition patterns in DIII-D has been developed. The components of the workflow consist of a detailed computer-aided-design file of the vessel wall and the scrape-off-layer (SOL) codes MAFOT, OSM, DIVIMP, and 3DLIM. A special-purpose toolkit enables passing the output of these codes among eac...

The engineering limits of plasma-facing components (PFCs) constrain the allowable operational space of tokamaks. Poorly managed heat fluxes that push the PFCs beyond their limits not only degrade core plasma performance via elevated impurities, but can also result in PFC failure due to thermal stresses or melting. Simple axisymmetric assumptions fa...

Edge localized modes (ELMs) are triggered using deuterium pellets injected into plasmas with ITER-relevant low collisionality pedestals, and the resulting peak ELM energy fluence is reduced by approximately 25-50% relative to natural ELMs destabilized at similar pedestal pressures. Cryogenically frozen deuterium pellets are injected from the low-fi...

3D nonlinear, as well as 2D linear M3D-C1 simulations are used to model ELM triggering by small pellets in DIII-D discharges in the ITER relevant, peeling-limited pedestal stability regime. A critical pellet size threshold is found in both experiment and modeling depending on pedestal conditions, pellet velocity and injection direction. Using radia...

A convective heat flux model for perturbed plasmas, based on guiding center ion drift in vacuum fields (Wingen, et al 2014 Phys. Plasmas 21 012509), has been updated. The old model only considered ion heat flux, while here also electron heat flux is included. The updated model predicts divertor heat flux distributions in non-axisymmetric (3D) plasm...

Large, spontaneous m/n = 1/1 helical cores are predicted in tokamaks with extended regions of low- or reversed-magnetic shear profiles in a region within the q = 1 surface and an onset condition determined by constant (dp/dρ)/Bt2 along the threshold. These 3D modes occurred frequently in Alcator C-Mod during ramp-up when slow current penetration re...

We report measurements of a+/− 5 mm toroidal variation of the outer strike point radial position using an array of three identical Langmuir probes distributed at 90° intervals around the torus (90°, 180°, 270°). The strike point radial location is determined from the profiles of floating potential (Vf) measured by the three 6 mm diameter domed Lang...

In DIII-D, large currents flowing into the divertor floor during edge-localized modes (ELMs) have been measured by an array of shunt current resistors before an increase of heat flux is measured by IR thermography. The diagnostic consists of 40 tiles distributed in five concentric circles in the lower divertor with sampling rates range between 50 a...

Small 3D perturbations to the magnetic field in DIII-D (δB/B∼2×10−4) result in large modulations of density fluctuation amplitudes in the pedestal, which are shown using Doppler backscattering measurements to vary by a factor of 2. Helical perturbations of equilibrium density within flux surfaces have previously been observed in the pedestal of DII...

Large, spontaneous m/n = 1/1 helical cores are shown to be expected in tokamaks such as ITER with extended regions of low- or reversed- magnetic shear profiles and q near 1 in the core. The threshold for this spontaneous symmetry breaking is determined using VMEC scans, beginning with reconstructed 3D equilibria from DIII-D and Alcator C-Mod based...

The Small Angle Slot (SAS) was recently installed on DIII-D as an advanced divertor, promising easier plasma detachment and lower temperatures across the whole target. A twofold study of the SAS magnetic geometry and topology is presented in this paper. On one hand, a two-dimensional uncertainty quantification analysis is carried out through a Mont...

This paper presents the first fully 3-dimensional (3D) equilibrium reconstruction of a helical core in a tokamak device. Using a new parallel implementation of the Variational Moments Equilibrium Code (PARVMEC) coupled to V3FIT, 3D reconstructions can be performed at resolutions necessary to produce helical states in nominally axisymmetric tokamak...

Recent experimental observations have found turbulent fluctuation structures that are non-axisymmetric in a tokamak with applied 3D fields. In this paper, two fluid resistive effects are shown to produce changes relevant to turbulent transport in the modeled 3D magnetohydrodynamic (MHD) equilibrium of tokamak pedestals with these 3D fields applied....

Stationary 3D equilibria can form in fusion plasmas via saturation of magnetohydrodynamic (MHD) instabilities or stimulated by external 3D fields. In these cases the current profile is anomalously broad due to magnetic flux pumping produced by the MHD modes. Flux pumping plays an important role in hybrid tokamak plasmas, maintaining the minimum saf...

In this work, single- and two-fluid resistive magnetohydrodynamic calculations of the plasma response to n = 3 magnetic perturbations in single-null (SN) and snowflake (SF) divertor configurations are compared with those based on the vacuum approach. The calculations are performed using the code M3D-C¹ and are based on simulated NSTX-U plasmas. Sig...

In order to understand the effect of rotation on the response of a plasma to three-dimensional magnetic perturbations, we perform a systematic scan of the zero-crossing of the rotation profile in a DIII-D ITER-similar shape equilibrium using linear, time-independent modeling with the M3D-C1 extended magnetohydrodynamics code. We confirm that the lo...

Here, a technique for tokamak equilibrium reconstructions is used for multiple DIII-D discharges, including L-mode and H-mode cases when weakly 3D fields $$\left(\delta B/B\sim { {10}^{-3}}\right)$$ are applied. The technique couples diagnostics to the non-linear, ideal MHD equilibrium solver VMEC, using the V3FIT code, to find the most likely 3D e...

The hybrid scenario is a candidate for stationary high-fusion gain tokamak operation in ITER and DEMO. To obtain such performance, the energy confinement and the normalized pressure βN must be maximized, which requires operating near or above ideal MHD no-wall limits. New experimental findings show how these limits can affect hybrid operation. Even...

Vacuum resonant magnetic perturbations (RMP) applied to otherwise axisymmetric tokamak plasmas produce in general a combination of non-resonant effects that preserve closed flux surfaces (kink response) and resonant effects that introduce magnetic islands and/or stochasticity (tearing response). The effect of the plasma kink response on the linear...

Recent experiments on DIII-D have demonstrated that having a toroidally-monochromatic spectral content of edge-resonant magnetic perturbations (RMPs) is not a necessary condition for suppression of edge localized modes (ELMs). Robust ELM suppression has been reproducibly obtained on DIII-D during experiments in which various non-axisymmetric coil l...

Calculations of the plasma response to applied non-axisymmetric fields in several DIII-D discharges show that predicted displacements depend strongly on the edge current density. This result is found using both a linear two-fluid-MHD model (M3D-C1) and a nonlinear ideal-MHD model (VMEC). Furthermore, it is observed that the probability of a dischar...

Measurements show fast ion losses correlated with applied three-dimensional (3D) fields in a variety of plasmas ranging from L-mode to resonant magnetic perturbation (RMP) edge localized mode (ELM) suppressed H-mode discharges. In DIII-D L-mode discharges with a slowly rotating n = 2 magnetic perturbation, scintillator detector loss signals synchro...

An image inversion scheme for the soft-X-ray imaging system (SXRIS) diagnostic at the DIII-D tokamak is developed to obtain the local soft-X-ray emission at a poloidal cross-section from the spatially line-integrated image taken by the SXRIS camera. The scheme uses the Tikhonov regularization method since the inversion problem is generally ill-pose...

Recent experiments on DIII-D have increased confidence in the ability to suppress edge-localized modes (ELMs) using edge-resonant magnetic perturbations (RMPs) in ITER, including an improved physics basis for the edge response to RMPs as well as expansion of RMP ELM suppression to more ITER-like conditions. Complete ELM suppression has been achieve...

Recent observations on DIII-D have advanced the understanding of plasma response to applied resonant magnetic perturbations (RMPs) in both H-mode and L-mode plasmas. Three distinct 3D features localized in minor radius are imaged via filtered soft x-ray emission: (i) the formation of lobes extending from the unperturbed separatrix in the X-point re...

Numerical modelling of the plasma boundary position and its displacement due to external magnetic perturbations in DIII-D low-collisionality H-mode discharges is presented. The results of the vacuum model are compared to the experimental measurements for boundary displacements including Thomson scattering electron temperature Te, charge exchange re...

Significant changes in the edge localized mode (ELM) crash heat load deposition patterns compared to typical ELMs are seen via infra-red observations during resonant magnetic perturbation experiments at the Joint European Torus (JET). These modifications result from the changed magnetic topology of the plasma, caused by the perturbations. Dependenc...

The lower hybrid wave (LHW) heating experiments at the Experimental Advanced Superconducting Tokamak (EAST) show a wide range of similarities to effects known from applied resonant magnetic perturbations (RMPs) by in-vessel or external magnetic perturbation coils. These observations suggest a current flow understood to be along scrape-off layer (SO...

The effects of applied 3D resonant magnetic perturbations are modelled with and without self-consistent plasma response. The plasma response is calculated using a linear two-fluid model. A synthetic diagnostic is used to simulate soft x-ray (SXR) emission within the steep gradient region of the pedestal, 0.98 > ψ > 0.94. Two methods for simulating...

Resonant magnetic perturbation experiments at JET with the ITER-like wall have shown the formation of radially propagating pre-ELM structures in the heat flux profile on the outer divertor. These appear a few milliseconds before the major divertor heat load, caused by type-I edge-localized modes (ELMs). The formation of the pre-ELM structures is ac...

Progress in the definition of the requirements for edge localized mode (ELM) control and the application of ELM control methods both for high fusion performance DT operation and non-active low-current operation in ITER is described. Evaluation of the power fluxes for low plasma current H-modes in ITER shows that uncontrolled ELMs will not lead to d...

Extremely low density operation free of error field penetration supports the excitation of trace-level quiescent runaway electron (RE) populations during the flat-top of DIII-D Ohmic discharges. Operation in the quiescent regime allows accurate measurement of all key parameters important to RE excitation, including the internal broadband magnetic f...

The heat flux patterns measured in low-collisionality DIII-D H-mode plasmas strongly deviate from simultaneously measured CII emission patterns, used as indicator of particle flux, during applied resonant magnetic perturbations. While the CII emission clearly shows typical striations, which are similar to magnetic footprint patterns obtained from v...

In-vessel, non-axisymmetric, control coils have proven to be an important option for mitigating and suppressing edge-localized modes (ELMs) in high performance operating regimes on a growing number of tokamaks. Additionally, an in-vessel non-axisymmetric ELM control coil is being considered in the ITER baseline design. In preparing for the initial...

Linear, two-fluid, resistive modelling of the plasma response to applied non-axisymmetric fields shows significant displacement of edge temperature and density profiles. The calculated displacements, often of 2 cm or more in H-mode pedestals with parameters appropriate to DIII-D, are due to the helical distortions resulting from stable edge modes b...

Strong mitigation of edge-localized modes has been observed on Experimental Advanced Superconducting Tokamak, when lower hybrid waves (LHWs) are applied to H-mode plasmas with ion cyclotron resonant heating. This has been demonstrated to be due to the formation of helical current filaments flowing along field lines in the scrape-off layer induced b...

Strong mitigation of edge-localized modes has been observed on Experimental Advanced Superconducting Tokamak, when lower hybrid waves (LHWs) are applied to H-mode plasmas with ion cyclotron resonant heating. This has been demonstrated to be due to the formation of helical current filaments flowing along field lines in the scrape-off layer induced b...

Imaging beam emission spectroscopy has been used to study the displacement of the plasma boundary in ELMing H-mode discharges with a 10 Hz rotating n = 2 external magnetic field perturbation in DIII-D. The rotating magnetic field creates a helical displacement of the beam emission profile of ~2 cm on the low-field-side (LFS) midplane which rotates...

Perturbations in the plasma boundary due to the application of non-axisymmetric n = 3 fields (δB/B ~ 10−4−10−3) were measured in the X-point region in DIII-D by tangential imaging of extreme ultra-violet and soft x-ray emission. Vacuum-field calculations show that these perturbations take the form of lobes extending outwards from the unperturbed se...

In this work we validate vacuum model predictions for the displacement of the separatrix due to applied resonant magnetic perturbations (RMPs) against experimental measurements. It is often assumed that plasma screening of RMP may be weak in the region of low rotation, high resistivity and high magnetic shear near the plasma separatrix and in the s...

A synthetic soft x-ray diagnostic is applied to DIII-D plasmas to model experimental measurements of soft x-ray emissions from the lower X-point and divertor region during applied resonant magnetic perturbations (RMPs). The synthetic soft x-ray diagnostic takes into account the modeled magnetic topology in DIII-D using the full soft x-ray emission...

A tangential 2-D soft x-ray (SXR) imaging system is installed on DIII-D to directly measure the 3-D magnetic topology at the plasma edge. This diagnostic allows the study of the plasma SXR emissivity at time resolutions >=,0 ms and spatial resolutions ˜1 cm. Extracting 3-D structure from the 2-D image requires the inversion of large ill-posed matri...

Three-dimensional (3D) perturbations in the edge plasma due to the application of non-axisymmetric fields are measured in the X-point region in DIII-D by tangential imaging of Ultra-Soft (USXR) and Soft X-Ray (SXR) emission in an effort to understand the internal plasma response. To date, 3D structures are resolved by performing a differential meas...

A recently developed numerical model, describing a self-amplification and structure formation process which is used to model the initial non-linear growth phase of edge-localized modes (ELMs), is applied to the JET tokamak. Connection length simulations of the magnetic topology, including only error fields, for JET reveal the existence of small, so...

Test particle evaluation of the diffusion coefficient in the presence of magnetic field fluctuations and binary collisions is presented. Chaotic magnetic field lines originate from resonant magnetic perturbations (RMPs). To lowest order, charged particles follow magnetic field lines. Drifts and interaction (collisions) with other particles decorrel...

The numerical model of the non-linear evolution of edge-localized modes (ELMs) in tokamaks being used in this paper assumes that thermoelectric currents flow in short connection length flux tubes, initially established by error fields or other non-axisymmetric magnetic perturbations. The additional magnetic perturbation of the current filaments cha...

An extended model is proposed to describe the magnetic topology during appearance of edge localized modes (ELMs). It is applied to an ELMing H-mode in a lower single null discharge at DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)]. The process of flux tube formation is discussed based on a previously proposed two-step model. Large currents, as f...

Edge localized modes (ELMs) are qualitatively and quantitatively modeled in tokamaks using current bursts which have been observed in the scrape-off-layer (SOL) during an ELM crash. During the initial phase of an ELM, a heat pulse causes thermoelectric currents. They first flow in short connection length flux tubes which are initially established b...

The influences of resonant magnetic perturbations (RMPs) on the poloidal rotation at the edge of a tokamak are investigated. Specific results are displayed for the tokamak TEXTOR with the dynamic ergodic divertor (DED). The latter can be operated in three different base mode configurations, namely 12/4, 6/2 and 3/1. The base mode configurations dis...

A conceptual model describing the nonlinear gowth of type-I ELMs in high performance tokamak plasmas has been presented along with a numerical simulation of the separatrix evolution, described by the model, during an ELM in a typical DIII-D H-mode plasma. The

A model describing the 3D nonlinear evolution of ELMs in DIII-D has been developed. The model invokes field-aligned currents flowing through short flux tubes embedded in the pedestal plasma that connect the outer to the inner target plate. These flux tubes are initially formed by field-errors and a field-error correction coil. Magnetic perturbation...

Edge localized modes (ELMs) are predicted to be a significant problem for ITER due to impulse heating of the divertor target plates. During low collisionality experiments on DIII-D where ELMs were suppressed using resonant magnetic perturbations (RMP), target plate profiles of particle flux (Jsat), electron temperature (Te), and floating potential...

It is shown that resonant magnetic perturbations generate sheared flow velocities in magnetized plasmas. Stochastic magnetic fields in incomplete chaos influence the drift motion of electrons and ions differently. Using a fast mapping technique, it is demonstrated that a radial electric field is generated due to the different behavior of passing pa...

In DIII-D the splitting and deformation of the separatrix due to externally applied resonant magnetic perturbations is calculated using a vacuum field line integration code (TRIP3D–MAFOT). The resulting footprint pattern on the divertor target plates is shown in high resolution by contour plots of the connection lengths and penetration depths of th...

Numerical modeling of the typical footprint structures on the target plates of a divertor tokamak is presented. In the tokamak DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] toroidal mode number n=3 resonant magnetic perturbations are responsible for characteristic footprint stripes. The numerics can resolve substructures within each footprint s...

A numerical model of the nonlinear evolution of edge localized modes (ELMs) in tokmaks is presented. In the model discussed here it is assumed that thermoelectric currents flow in short connection length flux tubes, initially established by error fields or other non-axisymmetric magnetic perturbations. Magnetic perturbations resulting from the curr...

A study of three-dimensional (3D) perturbed magnetic field structures and transport for edge localized mode control experiments with resonant magnetic perturbations at DIII-D is presented. We focus on ITER-Similar Shape plasmas at ITER relevant electron pedestal collisionalities . This study is performed in comparison with results from TEXTOR-Dynam...

The motion of electrons and ions in stochastic magnetic fields is considered. The analysis starts from a Hamiltonian formulation of the drift motion including electric fields. For an efficient statistical evaluation of the resulting particle transport, a symplectic mapping technique is applied. Compared to previous considerations, the ion and elect...

A fine structure of open chaotic field lines, namely, a heteroclinic tangle, in the ergodic divertor has been observed by measurements of heat deposition pattern on the divertor plates at TEXTOR. Calculations show that magnetic footprints on the divertor plates are formed by open field lines coming from the plasma along narrow stripe regions called...

Experimental observations of heat fluxes on divertor plates of tokamaks show typical structures boomerang wings for varying edge safety factors. The heat flux patterns follow from general principles of nonlinear dynamics. The pattern selection is due to the unstable and stable manifolds of the hyperbolic fixed points of the last intact island chain...

The ergodization of the magnetic field lines imposed by the dynamic ergodic diverter (DED) in TEXTOR can lead both to confinement improvement and to confinement deterioration. The cases of substantial improvement are in resonant ways related to particular conditions in which magnetic flux tubes starting at the X points of induced islands are connec...

New results from the generation of runaways and the loss of runaway electrons in an ergodized magnetic field are presented. For the generation process, a clear difference between a 'normal' and a clean, freshly boronized wall condition has been found. Under clean wall conditions, one observes at low densities not only the runaway electrons with ene...

Heat ‡uxes on divertor plates of tokamaks show typical structures being related to the topology of large connection lengths of magnetic …eld lines. The selection of those areas of large connection lengths which ultimately determine the heat ‡ux pattern is due to the unstable and stable manifolds of the hyperbolic …xed points of the last intact isla...

The relativistic motion of test particles in stochastic magnetic fields is investigated. Guiding-centre motion is analysed in relativistic invariant form for toroidal geometry. Including stochastic magnetic field components, a symmetric Hamiltonian mapping technique, leading to a 4-dimensional iteration procedure, is developed. In general, an exter...

Drift orbits of test particles are studied using a recently proposed Hamiltonian theory of guiding-center motion in toroidal systems. A symplectic mapping procedure in symmetric form is developed which allows a fast and accurate characterization of the Poincare plots in poloidal cross sections. It is shown that the stochastic magnetic field acts di...

The topological structure and the statistical properties of stochastic magnetic fields are investigated on the basis of the so called tokamap. First, a monotonic safety factor (q-profile) is assumed. As it is demonstrated, the transition from the continuous model to the discrete mapping in its symmetric form is essential, not only for the symplecti...

A nonlinear Schrödinger equation with periodic coefficients, as it appears, e.g., in nonlinear optics, is considered. The high-frequency, variable part of the dispersion may be even much larger than the mean value. The ratio of the length of the dispersion map to the period of a solution is assumed as one small parameter. The second one corresponds...

The dynamic ergodic divertor in TEXTOR provides an ergodized edge of the plasma in order to control heat and particle exhaust. The sixteen perturbation coils are mounted on the inner side of the tokamak vessel and are parallel to the field lines at a resonant flux surface (1). De- pending on the currents distribution in the coils, a helical magneti...

Auf der Basis der symmetrischen Hamiltonschen Mapping Technik [S. Abdullaev, J. Phys. A: Math. Gen. 35, 2811, (2002)] werden die Transport Mechanismen für Wärme und Teilchen in stochastischen Fusionsplasmen untersucht. Sowohl die chaotischen Bewegungen im Plasma als auch die Wandstrukturen, die in offenen chaotischen Systemen wie dem DED am TEXTOR...