Scrape-off Layer Width Research Articles

Theoretical aspects and practical implications of the heuristic drift SOL model

The heuristic drift (HD) model for the tokamak power scrape-off layer width provides remarkable agreement in both absolute magnitude and scalings with the measured width of the exponential component of the heat flux at divertors targets, in low gas-puff H-Mode tokamaks. This motivates further exploration of its theoretical aspects and practical implications. The HD model requires a small non-ambipolar electron particle diffusivity ∼10−2m2/s. It also implies large parallel heat flux in ITER and suggests that more radical approaches will be needed to handle the ∼20 GW/m2 parallel heat flux expected in Demo. Remarkably, the HD model is also in good agreement with recent near-SOL heat flux profiles measured in a number of limiter L-Mode experiments, implying ubiquity of the underlying mechanism. Finally, the HD model suggests that the H-Mode and more generally Greenwald density limit may be caused by MHD instability in the SOL, rather than originating in the core plasma or pedestal. If the SOL width in stellarators is set by magnetic topology rather than by drifts, this would be consistent with the absence of the Greenwald density limit in stellarators.

Intrinsic instabilities in X-point geometry: A tool to understand and predict the Scrape Off Layer transport in standard and advanced divertors

Intrinsic Scrape Off Layer (SOL) instabilities are studied using flute approximation and incorporating the appropriate sheath boundary conditions at the target. The linear growth rate and the structure of the modes are obtained. The associated diffusion is estimated using a γ/k⊥2 approach for the fastest growing modes. The model used includes curvature and sheath drives, finite Larmor radius effects and partial line tying at the target. The magnetic geometry is obtained using current carrying wires, representing the plasma current and the divertor coils, and naturally generates X-point geometry and magnetic shear effects. The calculation is performed for ITER relevant parameters and scans in SOL width and distance from the separatrix are presented. In addition to a standard Lower Single Null, Super-X and Snowflake configurations are examined in order to assess the importance of the geometry on the stability of the boundary plasma.

Effect of the limiter position on the scrape-off layer width, radial electric field and intrinsic flows

The effect of the limiter position on the scrape-off layer (SOL) width, radial electric field and intrinsic flows is investigated via global, three-dimensional turbulence simulations in four different limiter configurations. The limiter position affects the SOL dynamics in a number of ways, for example by changing the effective connection length or by modifying the unstable modes present in the system. The simulations show that the SOL width is much smaller and less poloidally asymmetric when the plasma is limited on the low-field side than on the high-field side, which can be explained by a change in the turbulence regime between the two configurations. The radial electric field is determined by the combined effect of the sheath physics and the electron adiabaticity condition, and its poloidal structure depends on the limiter position, as it can be fairly well explained through an analytical model. Intrinsic parallel flows established in the SOL, typically leading to co-current toroidal rotation with a magnitude that strongly depends on the limiter position, can also be fairly well reproduced analytically for each limiter configuration.

3D Properties of Edge Turbulent Transport in Full‐Torus Simulations and their Impact on Poloidal Asymmetries

AbstractThe 3D fluid turbulence code TOKAM3X is used to investigate the 3D properties of edge turbulent transport and their impact on poloidal asymmetries. Simulations are run in circular limited plasmas in a domain covering both closed and open flux surfaces. Turbulence characteristics exhibit large inhomogeneities both in the radial and poloidal directions reminiscent of experimental observations. The low field side mid‐plane in particular is found to be locally more fluctuating and intermittent than the rest of the Scrape‐Off‐Layer (SOL). As a consequence of this asymmetry, radial turbulent transport, that represents 80 to 90% of the total radial flux, is strongly ballooned, with 75% of the flux flowing through LFS. The equilibrium of the edge plasma is impacted by this asymmetry through the existence of large amplitude asymmetric parallel flows as well as through the development of poloidally asymmetric radial decay lengths making it impossible to define a single SOL width. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Scaling of the scrape-off layer width during inter-ELM H modes on MAST as measured by infrared thermography

The power load to the divertor surfaces is a key concern for future devices such as ITER, due to the thermal limits on the material surface. One factor that characterizes the heat flux to the divertor is the fall off length in the scrape-off layer (SOL), which recent empirical scalings have shown could be as small as 1 mm. These predictions are based on a multi-machine scaling of the heat flux width fitted using an expression for the divertor heat flux profile which includes a term for the exponential decay in the SOL and diffusion about the last closed flux surface (LCFS) in the private flux region. This expression has been used to fit a database of inter-ELM H mode profiles at the upper divertor and extract the fall off length, λq, for a range of different plasma parameters in double null plasmas. The midplane separation between the primary and secondary LCFS (δrsep) of the double null plasma used in the study are in the range 2 ⩽ δrsep ⩽ 7 mm and no correlation is seen between the fall off length and the δrsep. The MAST data shows good agreement with the formula, with the fitted fall off length spanning a range of 5–11 mm in the data base generated. Regression of this data has shown that the fall off length has the strongest dependence on the plasma current (or equivalently, the poloidal magnetic field at the outboard midplane) to the power −0.71. The scaling with the smallest χ2 error utilizes the poloidal magnetic field at the outboard midplane (Bpol,omp) and the power crossing the SOL in the relation with χ2 = 3.46 and R2 = 0.56 as a goodness of fit. The equivalent scaling with plasma current is with χ2 = 3.84 and R2 = 0.55. The moderate goodness of fit suggests that additional plasma parameters are required to accurately reproduce the observed variation in λq.

Theory of the scrape-off layer width in inner-wall limited tokamak plasmas

We develop a predictive theory applicable to the scrape-off layer (SOL) of inner-wall limited plasmas. Using the non-linear flattening of the pressure profile as a saturation mechanism for resistive ballooning modes, we are able to demonstrate and quantify the increase of the SOL width with plasma size, connection length, plasma β, and collisionality. Individual aspects of the theory, such as saturation physics, parallel dynamics, and system size scaling, are tested and verified using non-linear, 3D flux-driven SOL turbulence simulations. Altogether, very good agreement between theory and simulation is found.

Theory-based scaling of the SOL width in circular limited tokamak plasmas

A theory-based scaling for the characteristic length of a circular, limited tokamak scrape-off layer (SOL) is obtained by considering the balance between parallel losses and non-linearly saturated resistive ballooning mode turbulence driving anomalous perpendicular transport. The SOL size increases with plasma size, resistivity, and safety factor q. The scaling is verified against flux-driven non-linear turbulence simulations, which reveal good agreement within a wide range of dimensionless parameters, including parameters closely matching the TCV tokamak. An initial comparison of the theory against experimental data from several tokamaks also yields good agreement.

Role of ion temperature on scrape-off layer plasma turbulence

Turbulence in Scrape-off layer (SOL) of tokamak plasma has been studied numerically using interchange modes with the help of electron continuity, quasineutrality, and ion energy equations. Electron temperature is assumed uniform. We have studied dynamics of seeded plasma blob and plasma turbulence to identify the role of ion temperature and its gradient. The ion temperature elongates the blob poloidally and reduces its radial velocity. Initial dipole nature of the plasma blob potential breaks and generates few more dipoles during its propagation in the SOL. Plasma turbulence simulation shows poloidally elongated density and ion temperature structures that are similar to the seeded blob simulation studies. Fluctuations of the density and ion temperature have been presented as function of scale lengths of the density and ion temperature. Reduction of the SOL width and increase of radial electric field have been measured in the presence of the ion temperature. Particle and energy transports have been also presented as the function of the density and ion temperature scale lengths.

Snowflake divertor configuration studies in National Spherical Torus Experiment

Experimental results from NSTX indicate that the snowflake divertor (D. Ryutov, Phys. Plasmas 14, 064502 (2007)) may be a viable solution for outstanding tokamak plasma-material interface issues. Steady-state handling of divertor heat flux and divertor plate erosion remains to be critical issues for ITER and future concept devices based on conventional and spherical tokamak geometry with high power density divertors. Experiments conducted in 4–6 MW NBI-heated H-mode plasmas in NSTX demonstrated that the snowflake divertor is compatible with high-confinement core plasma operation, while being very effective in steady-state divertor heat flux mitigation and impurity reduction. A steady-state snowflake divertor was obtained in recent NSTX experiments for up to 600 ms using three divertor magnetic coils. The high magnetic flux expansion region of the scrape-off layer (SOL) spanning up to 50% of the SOL width λq was partially detached in the snowflake divertor. In the detached zone, the heat flux profile flattened and decreased to 0.5–1 MW/m2 (from 4–7 MW/m2 in the standard divertor) indicative of radiative heating. An up to 50% increase in divertor, Prad in the snowflake divertor was accompanied by broadening of the intrinsic C III and C IV radiation zones, and a nearly order of magnitude increase in divertor high-n Balmer line emission indicative of volumetric recombination onset. Magnetic reconstructions showed that the x-point connection length, divertor plasma-wetted area and divertor volume, all critical parameters for geometric reduction of deposited heat flux, and increased volumetric divertor losses were significantly increased in the snowflake divertor, as expected from theory.

Numerical investigation of edge plasma phenomena in an enhanced D-alpha discharge at Alcator C-Mod: Parallel heat flux and quasi-coherent edge oscillations

Reduced-model scrape-off layer turbulence (SOLT) simulations of an enhanced D-alpha (EDA) H-mode shot observed in the Alcator C-Mod tokamak were conducted to compare with observed variations in the scrape-off-layer (SOL) width of the parallel heat flux profile. In particular, the role of the competition between sheath- and conduction-limited parallel heat fluxes in determining that width was studied for the turbulent SOL plasma that emerged from the simulations. The SOL width decreases with increasing input power and with increasing separatrix temperature in both the experiment and the simulation, consistent with the strong temperature dependence of the parallel heat flux in balance with the perpendicular transport by turbulence and blobs. The particularly strong temperature dependence observed in the case analyzed is attributed to the fact that these simulations produce SOL plasmas which are in the conduction-limited regime for the parallel heat flux. A persistent quasi-coherent (QC) mode dominates the SOLT simulations and bears considerable resemblance to the QC mode observed in C-Mod EDA operation. The SOLT QC mode consists of nonlinearly saturated wave-fronts located just inside the separatrix that are convected poloidally by the mean flow, continuously transporting particles and energy and intermittently emitting blobs into the SOL.

Diffusive–convective transition for scrape-off layer transport and the heat-flux width

Transport of plasma from the edge pedestal gradient region into the scrape-off layer (SOL) forms the heat exhaust channel. The properties of this channel are critical for future tokamak devices. The SOL heat-flux width is believed to be set by a competition between classical parallel transport and turbulent cross-field transport. In previous work, (Myra et al 2011 J. Nucl. Mat. 415 S605) focusing on modeling of the heat-flux width in the National Spherical Torus Experiment (NSTX), the possibility of a transition from quasi-diffusive to convective transport in the SOL was noticed. This transition, and the scaling of the heat-flux width, is explored here through additional SOL turbulence simulations using the SOLT code (Russell et al 2009 Phys. Plasmas 16 122304). At the transition, the transport becomes intermittent, and the SOL width is broadened due to blob emission. Critical parameters for the transition are investigated, including the power flux into the SOL, the field line pitch, the connection length and the plasma collisionality. An inverse dependence of the heat-flux width on the poloidal field, also seen routinely in experiments, is noted and explained qualitatively.

Heuristic drift-based model of the power scrape-off width in low-gas-puff H-mode tokamaks

A heuristic model for the plasma scrape-off width in low-gas-puff tokamak H-mode plasmas is introduced. Grad B and curv B drifts into the scrape-off layer (SOL) are balanced against near-sonic parallel flows out of the SOL, to the divertor plates. The overall particle flow pattern posited is a modification for open field lines of Pfirsch–Schlüter flows to include order-unity sinks to the divertors. These assumptions result in an estimated SOL width of ∼2aρp/R. They also result in a first-principles calculation of the particle confinement time of H-mode plasmas, qualitatively consistent with experimental observations. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL width, derived above, with heat from the main plasma. The separatrix temperature is calculated based on a two-point model balancing power input to the SOL with Spitzer–Härm parallel thermal conduction losses to the divertor. This results in a heuristic closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and in scaling with recent experimental data. Further work should include full numerical calculations, including all magnetic and electric drifts, as well as more thorough comparison with experimental data.

Study of Scrape-Off-Layer Width in Ohmic and Lower Hybrid Wave Heated Double-Null Divertor Plasma in EAST

Edge profiles in Ohmic and lower hybrid (LH) wave heated discharges in EAST are presented. A comparison of the measured profiles is made with those from the theoretical prediction for the scrape-off-layer (SOL) width. The edge plasma parameters are diagnosed by a triple probe divertor diagnostic system and fast reciprocating probes at the outer mid-plane. The experimental results show that the SOL width of double-null (DN) divertor plasmas in EAST appears to exhibit a negative dependence on the power crossing the separatrix, which is consistent with the collisional SOL scalings of JET and Alcator C-Mod. This will provide useful information for extrapolation to the ITER SOL width scaling for power deposition.

Reduced model simulations of the scrape-off-layer heat-flux width and comparison with experiment

Reduced model simulations of turbulence in the edge and scrape-off-layer (SOL) region of a spherical torus or tokamak plasma are employed to address the physics of the scrape-off-layer heat-flux width. The simulation model is an electrostatic two-dimensional fluid turbulence model, applied in the plane perpendicular to the magnetic field at the outboard midplane of the torus. The model contains curvature-driven-interchange modes, sheath losses, and both perpendicular turbulent diffusive and convective (blob) transport. These transport processes compete with classical parallel transport to set the SOL width. Midplane SOL profiles of density, temperature, and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment [S. M. Kaye et al., Phys. Plasmas 8, 1977 (2001)] to study the scaling of the heat-flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL heat-flux width for the low power H-mode discharges studied, while additional physics is required to fully explain the plasma current scaling of the SOL heat-flux width observed experimentally in higher power discharges. Intermittent separatrix-spanning convective cells are found to be the main mechanism that sets the near-SOL width in the simulations. The roles of sheared flows and blob trapping versus emission are discussed.

SOL width in limited versus diverted discharges in DIII-D

An experiment aimed at benchmarking the ITER scrape-off layer (SOL) power width scaling in limited L-mode discharges has been conducted on DIII-D. Scans of the main scaling parameters were performed in an inner-wall-limited (IWL) magnetic configuration. Using the near-SOL density and temperature e-folding lengths, λn, λT, determined from reciprocating Langmuir probe measurements, SOL power flux density e-folding lengths, λq, are derived. A few lower single null (LSN) discharges were also run for comparison. The results are generally in agreement with the ITER design assumptions, finding that λn and λT are correlated (λT∼1.2λn) and both λn and λT are on average 2.1–2.5 times larger in IWL configurations than in LSN. In moderate elongation (κ∼1.4) IWL discharges, λq is largest and agrees with the assumed ITER scaling within the estimated uncertainty (a factor of ∼2). In IWL discharges λq measurements are consistent with the expectations of SOL power balance.

Turbulent transport and the scrape-off-layer width

The two-dimensional fluid turbulence code SOLT is employed to study the role of midplane turbulence on the scrape-off-layer (SOL) heat flux width of tokamak plasmas. The physics simulated includes curvature-driven-interchange modes, sheath losses, and perpendicular turbulent diffusive and convective (blob) transport. Midplane SOL profiles of density, temperature and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment (NSTX) to study the scaling of the heat flux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL width for the low power ELM-free H-mode discharges studied, while additional physics is required to explain the plasma current scaling of the SOL width observed experimentally in higher power discharges. Additional simulations predict a transition to a convectively-dominated SOL at critical values of power and connection length.

Overview of results from the National Spherical Torus Experiment (NSTX)

The mission of the National Spherical Torus Experiment (NSTX) is the demonstration of the physics basis required to extrapolate to the next steps for the spherical torus (ST), such as a plasma facing component test facility (NHTX) or an ST based component test facility (ST-CTF), and to support ITER. Key issues for the ST are transport, and steady state high β operation. To better understand electron transport, a new high-k scattering diagnostic was used extensively to investigate electron gyro-scale fluctuations with varying electron temperature gradient scale length. Results from n = 3 braking studies are consistent with the flow shear dependence of ion transport. New results from electron Bernstein wave emission measurements from plasmas with lithium wall coating applied indicate transmission efficiencies near 70% in H-mode as a result of reduced collisionality. Improved coupling of high harmonic fast-waves has been achieved by reducing the edge density relative to the critical density for surface wave coupling. In order to achieve high bootstrap current fraction, future ST designs envision running at very high elongation. Plasmas have been maintained on NSTX at very low internal inductance li ∼ 0.4 with strong shaping (κ ∼ 2.7, δ ∼ 0.8) with βN approaching the with-wall β-limit for several energy confinement times. By operating at lower collisionality in this regime, NSTX has achieved record non-inductive current drive fraction fNI ∼ 71%. Instabilities driven by super-Alfvénic ions will be an important issue for all burning plasmas, including ITER. Fast ions from NBI on NSTX are super-Alfvénic. Linear toroidal Alfvén eigenmode thresholds and appreciable fast ion loss during multi-mode bursts are measured and these results are compared with theory. The impact of n > 1 error fields on stability is an important result for ITER. Resistive wall mode/resonant field amplification feedback combined with n = 3 error field control was used on NSTX to maintain plasma rotation with β above the no-wall limit. Other highlights are results of lithium coating experiments, momentum confinement studies, scrape-off layer width scaling, demonstration of divertor heat load mitigation in strongly shaped plasmas and coupling of coaxial helicity injection plasmas to ohmic heating ramp-up. These results advance the ST towards next step fusion energy devices such as NHTX and ST-CTF.

The role of parallel heat transport in the relation between upstream scrape-off layer widths and target heat flux width in H-mode plasmas of the National Spherical Torus Experiment

The physics of parallel heat transport was tested in the scrape-off layer (SOL) plasma of the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000); S. M. Kaye et al., Nucl. Fusion 45, S168 (2005)] tokamak by comparing the upstream electron temperature (Te) and density (ne) profiles measured by the midplane reciprocating probe to the heat flux (q⊥) profile at the divertor plate measured by an infrared camera. It is found that electron conduction explains the near SOL width data reasonably well while the far SOL, which is in the sheath limited regime, requires an ion heat flux profile broader than the electron one to be consistent with the experimental data. The measured plasma parameters indicate that the SOL energy transport should be in the conduction-limited regime for R−Rsep (radial distance from the separatrix location) <2–3cm. The SOL energy transport should transition to the sheath-limited regime for R−Rsep>2–3cm. The Te, ne, and q⊥ profiles are better described by an offset exponential function instead of a simple exponential. The conventional relation between midplane electron temperature decay length (λTe) and target heat flux decay length (λq) is λTe=7∕2λq, whereas the newly derived relation, assuming offset exponential functional forms, implies λTe=(2–2.5)λq. The measured values of λTe∕λq differ from the new prediction by 25%–30%. The measured λq values in the far SOL (R−Rsep>2–3cm) are 9–10cm, while the expected values are 2.7<λq<4.9cm (for the sheath-limited regime). We propose that the ion heat flux profile is substantially broader than the electron heat flux profile as an explanation for this discrepancy in the far SOL.

Numerical investigations of edge plasma flows in the Tore Supra tokamak

The 2D boundary layer code TECXY has been used to simulate edge plasma parameters in the Tore Supra tokamak. Experimental situations have been analysed when the plasma contact point is shifted to different poloidal positions (limiter at bottom, top, outboard and inboard midplane) as well as the edge plasma conditions during lower hybrid RF power scan experiments. With the results of the calculations it was possible to reproduce experimentally observed changes to the flow pattern in the scrape-off-layer (SOL) for different plasma positions. These changes can be associated with the dependence of the radial electric field and the corresponding E × B drift velocity on the limiter position as well as to the poloidal asymmetries of the input particle flux. However, the code results with ‘standard radial transport’ did not show the large changes to the SOL widths as observed in the experiment. In order to reproduce in the calculations the observed differences in the SOL width, it was necessary to assume strong convective (or diffusive) radial plasma flow localized at the outboard midplane.

Integrated plasma physics modelling for the Culham steady state spherical tokamak fusion power plant

Integrated modelling of important plasma physics issues related to the design of a steady-state spherical tokamak (ST) fusion power plant is described. The key is a steady-state current drive, and 92% of this is provided by a combination of bootstrap and diamagnetic currents, both of which have a substantial toroidal component in a ST. The remaining current is to be provided by either neutral beam injection or radio-frequency waves, and various schemes for providing this are discussed and quantified. The desire to achieve a high bootstrap current drives the design to high plasma pressure, β (normalized to the magnetic field pressure), and high elongation. Both these requirements have implications for ideal magneto-hydrodynamic instability which are discussed. Confinement is addressed both through comparison with the recent scaling laws developed from the conventional tokamak database and self-consistent one-dimensional modelling of the transport processes. This modelling shows that the power required for the current drive (∼50 MW) is sufficient to heat the plasma to a regime where more than 3 GW of fusion power is produced, taking into account the dilution due to He ash and prompt α-particle losses, which are small. A preliminary study of the micro-instabilities, which may be responsible for the turbulent transport is provided. Given assumptions about the particle confinement, we make estimates of the fuelling requirements to maintain the steady state. Finally, the power loading due to the exhaust is derived using theory-based scalings for the scrape-off layer width.