Electron Heat Diffusivity Research Articles

Inter-discharge optimization for fast, reliable access to ASDEX Upgrade advanced tokamak scenario

Rapid inter-discharge simulation and optimization using the RAPTOR code have allowed the development of a reliable and reproducible early heating strategy for an advanced tokamak (AT) scenario on ASDEX Upgrade. Solving for electron heat and current diffusion in RAPTOR with ad-hoc formulas for heat transport and electron cyclotron current drive (ECCD) efficiency is found to robustly recover the coupled dynamics of Te and q, while maintaining model parameters fixed for all discharges. The pedestal top boundary condition in pre-shot simulations is set by a newly derived scaling law for the electron pressure at ρ = 0.8, using a data set of previous AT discharges. RAPTOR simulations have allowed to develop an understanding of the onset of 3/2 tearing modes, which were observed to have a detrimental impact on confinement when low magnetic shear conditions are present at the rational surface during the high-β phase. Delaying the NBI heating, by a specific time interval found via simulations, has led to avoiding these modes. A non-linear optimization scheme has been applied to optimize the ECCD deposition radii to reach a stationary state with qmin>1 at the beginning of the flat-top phase, while ensuring a non-zero magnetic shear at q = 1.5 throughout the high-β phase, and has been successfully tested in experiment. However, further experiments, aiming for qmin>1.5 , have highlighted limitations of the present feedforward control approach in the presence of shot-to-shot variations that are not included in the applied model. Application of real-time model-based control is proposed to overcome model-reality mismatches in future work.

Micro-tearing mode dominated electron heat transport in DIII-D H-mode pedestal

A new, comprehensive set of evidence reveals that Micro-Tearing Modes (MTMs) dominate pedestal electron heat transport in an H-mode experiment in the DIII-D tokamak. The experiment investigates the role of MTMs by scanning pedestal collisionality, a main drive of MTM instability, from 0.43 to 0.84 on the pedestal top. Broadband (150–800 kHz) magnetic and density fluctuations originating from the pedestal gradient region and highly consistent with MTMs are observed, with amplitude increasing during the scan. The higher magnetic fluctuation amplitude correlates with a lower pedestal electron temperature gradient, implying MTMs may regulate the pedestal electron heat transport. The collisionality scan results in profile and transport changes consistent with predicted transport capability of MTMs: (1) experimentally-determined electron heat diffusivity increases ∼40% at the location where the broadband density fluctuations peak; (2) ion heat diffusivity has less increase (<20%); and (3) a locally flattened region in the electron temperature pedestal is observed at high collisionality. A local, linear gyrokinetic simulation finds MTMs as the most unstable mode in the pedestal gradient region. In addition, local, nonlinear simulations suggest MTMs can dominate and drive experimentally-relevant, megawatt-level electron heat flux. This result establishes MTMs as an effective transport mechanism in the H-mode pedestal, in particular at high collisionality.

On the impact of electric field fluctuations on microtearing turbulence

The magnetic drift and the electric potential play an important role in microtearing destabilization by increasing the growth rate of this instability in the presence of collisions, while in electrostatic plasma micro-turbulence, zonal electric potentials can have a strong impact on turbulent saturation. A reduced model has been developed, showing that the Rechester–Rosenbluth model is a good model for the prediction of electron heat diffusivity by microtearing turbulence. Here, nonlinear gyrokinetic flux-tube simulations are performed in order to compute the characteristics of microtearing turbulence and the associated heat fluxes in tokamak plasmas and to assess how zonal flows and zonal fields affect saturation. This is consistent with a change in saturation mechanism from temperature corrugations to zonal field- and zonal flow-based energy transfer. It is found that removing the electrostatic potential causes a flux increase, while linearly stabilization is observed.

Role of magnetohydrodynamic activity in sawtooth induced heat pulse propagation in ADITYA tokamak

Fast propagation of sawtooth induced heat pulse is observed in the magnetohydrodynamic (MHD) active plasmas of ADITYA tokamak. The sawtooth crash deposits heat beyond the inversion radius, which gets transported to the edge region of the plasma, and is reflected as inverted sawtooth modulation in the edge channels of electron cyclotron emission (ECE) and spectral line emission. The time-lag analysis on ECE signal reveals the propagation time from plasma core to edge of ∼150 µs. From this analysis, the estimated transient electron heat diffusivity is found to be ∼50–60 m2 s−1, which is ten times higher than that of power balance heat diffusivity , in the MHD active discharges of ADITYA. It has been observed that the presence of MHD (m/n = 2/1, 3/1) activity in the intermediate region between the q = 1 and the edge radii, significantly influences the heat transport from the plasma core to the edge region. Stochastic magnetic field region formation with overlapping m/n = 2/1 and 3/1 MHD islands facilitates the fast heat-pulse propagation during a sawtooth crash in ADITYA tokamak. The disparity between the measured and the power-balance estimated diffusivity is significantly reduced by considering the electron heat diffusivity due to stochastization of magnetic field in the intermediate region.

Electron temperature gradient driven transport model for tokamak plasmas

A new model for electron temperature gradient (ETG) modes is developed as a component of the multi-mode anomalous transport module [Rafiq et al., Phys Plasmas 20, 032506 (2013)] to predict a time-dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, β and gradient of β (β′), collisionality, safety factor, and toroidicity, where β is the ratio of the plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.

Study of Electron Anomalous Heat Diffusion Affected by Mode Number of Perturbed Magnetic Island in Tokamak Plasmas

Anomalous electron heat diffusion across high mode magnetic islands and the nonlocal high mode stochastic magnetic field are researched and compared with earlier low mode research work. The work in this paper uses two typical magnetic islands and a high mode stochastic magnetic field that are aroused by five incompact high mode perturbed magnetic islands. It is found that the mode number of the perturbed magnetic island is another key factor of anomalous electron heat diffusion across the minor radius in tokamak plasmas, besides the ratio of the parallel heat diffusion coefficient to the perpendicular coefficient and the width of diffusive layers.

Modeling and measurement of energetic particle slowing down in Wendelstein 7-X

The energetic particle slowing down model in the BEAMS3D stellarator neutral beam code is compared to analytic models and experimental data from the Wendelstein 7-X experiment (W7-X). Recently, the first neutral beam experiments were performed in W7-X, providing validation of neutral beam deposition codes (Lazerson S.A. et al 2020 Nucl. Fusion 60 076020). This work builds upon that work, and follows the gyro-center orbits of the neutral-beam-generated fast ions to the plasma boundary. Slowing down times based on measurements of diamagnetic energy changes are compared to simulation data. A discharge solely heated by neutral beam injection is used to compare neoclassical heat flux estimates to neutral beam fueling, heating, and current drive. Experimental estimates of electron heat diffusivity suggest that electron turbulence is destabilized by density peaking in the discharge. Neutral beam current drive dominates over bootstrap current, resulting in a reversal of the toroidal current, as seen experimentally. Particle losses and heat flux through the equilibrium boundary are described. The effects of the magnetic configuration and plasma density on such parameters are also assessed. Benchmarking based on analytic estimates and other energetic particle codes is presented.

Experimental investigation of a partial collapse during the sawtooth instability in EAST

ABSTRACT In this article, partial and full collapses of sawtooth activity are investigated with the high-resolution two-dimensional electron cyclotron emission (ECE) Imaging diagnostic in EAST. The partial collapse in normal sawtooth behavior is detected during the precursor phase of an L-mode plasma heated by ICRF. The electron heat diffusivity is determined with the time-to-peak analysis. The experimental results revealed that heat diffusivity suppresses at the time of the partial collapse. As a result, the partial collapse process interrupts and the small amount of heat releases outward. The hot core survives and is enclosed by the cold magnetic island. The inversion radii are estimated with the help of sawtooth and the only single inversion radius is found during the entire collapse process.

First demonstration of real-time kinetic equilibrium reconstruction on TCV by coupling LIUQE and RAPTOR

Kinetic equilibrium reconstruction (KER) in tokamaks is the solution of the free-boundary MHD equilibrium that best fits the external magnetic measurements and the internal plasma profiles as imposed from modeling and/or available internal measurements. In this paper, for the first time, the KER has been performed in real-time by coupling the free-boundary equilibrium code LIUQE to the 1.5D transport code RAPTOR, during a TCV discharge. The transport code is used as a dynamic state observer evolving the current diffusion equation, the electron heat and particle diffusion equations and correcting the prediction with the measurements available in real-time, making use of the extended Kalman filter (EKF) method. The simple coupling strategy, based on a matching of the free functions ( and ) on the right-hand-side of the Grad Shafranov equation, is shown to be effective in providing consistency of pressure and current density profiles between the two codes. We also show that, despite this highly non-linear system, this technique does not require significant additional computational time with respect to the running times of the two independent codes and does not require a tight coupling of the two codes allowing therefore their independent development. The KER is compared to standard real-time equilibrium reconstruction, performed routinely in TCV, where only the external magnetic measurements are taken into account. The following cases are considered: flat central ne, current density broadening due to applied electron cyclotron current drive and neoclassical tearing mode causing a temperature drop. The KER reproduces the expected changes of the internal profiles, tracking their dynamic evolution in their physical timescales.

Transport characteristics of deuterium and hydrogen plasmas with ion internal transport barrier in the Large Helical Device

A remarkable extension of the high-ion-temperature (high-Ti) regime was obtained in deuterium plasma experiments in the Large Helical Device. In order to clarify transport characteristics in the ion internal transport barrier (ITB) formation with an isotope effect, a dataset of pure deuterium (nD/ne > 0.8) and pure hydrogen (nH/ne > 0.8) plasmas in the high-Ti regime were analyzed, and two mechanisms of transport improvement were characterized. A significant reduction of ion heat transport in the core of both deuterium and hydrogen plasmas was observed, indicating ion ITB formation. The dependence of the ion heat diffusivity on temperature ratio (Te/Ti) and normalized Ti-gradient (R/LTi = −(R/Ti)(dTi/dr)) was investigated in the core region, in which gyrokinetic simulations with the GKV code predict the destabilization of ion temperature gradient (ITG) modes. The Te/Ti dependence shows ITG-like property, while a significant deviation from the ITG-like property is found in the R/ dependence, indicating suppression of the ITG mode in the large R/ regime and resultant ion ITB formation. In the comparison between deuterium plasma and hydrogen plasma, the lower transport in the deuterium plasma is observed in both ion and electron heat diffusivities, indicating a significant isotope effect. It was found with the nonlinear turbulent transport simulation with GKV that the zonal flow enhancement contributes to the ITG suppression in the deuterium plasma.

Modeling of turbulent particle and heat transport in helical plasmas based on gyrokinetic analysis

The particle and heat transport driven by the ion temperature gradient instability in helical plasmas is investigated by the gyrokinetic analysis taking into account the kinetic electron response. High and low ion temperature plasma cases for the discharge in the Large Helical Device (LHD) are studied. Two types of transport models with a lower computational cost to reproduce the nonlinear gyrokinetic simulation results within allowable errors are presented for application in quick transport analyses. The turbulent electron and ion heat diffusivity models are given in terms of the linear growth rate and the characteristic quantity for the linear response of zonal flows, while the model of the effective particle diffusivity is not obtained for the flattened density profile observed in the LHD. The quasilinear flux model is also shown for the heat transport. The quasilinear flux models for the energy fluxes are found to reproduce the nonlinear simulation results at the accuracy similar to that of the heat diffusivity models. In addition, the quasilinear particle flux model, which is applicable to the transport analysis for LHD plasmas, is constructed. These turbulent reduced models enable coupling to the other simulation in the integrated codes for the LHD.

Analysis of performance degradation in an electron heating dominant H-mode plasma after ECRH termination in EAST

In recent EAST experiments, significant performance degradation accompanied by a decrease of internal inductance is observed in an electron heating dominant H-mode plasma after the electron cyclotron resonance heating termination. The lower hybrid wave (LHW) deposition and effective electron heat diffusivity are calculated to explain this phenomenon. Analysis shows that the changes of LHW heating deposition rather than the increase of transport are responsible for the significant decrease in energy confinement (). The reason why the confinement degradation occurred on a long time scale could be attributed to both good local energy confinement in the core and also the dependence of LHW deposition on the magnetic shear. The electron temperature profile shows weaker stiffness in near axis region where electron heating is dominant, compared to that in large radius region. Unstable electron modes from low to high k in the core plasma have been calculated in the linear GYRO simulations, which qualitatively agree with the experimental observation. This understanding of the plasma performance degradation mechanism will help to find ways of improving the global confinement in the radio-frequency dominant scenario in EAST.

Ion heat transport dynamics during edge localized mode cycles at ASDEX Upgrade

The edge ion heat transport is analyzed in ASDEX Upgrade (AUG) by combining a comprehensive set of pedestal measurements with both interpretive and predictive modelling. The experimentally determined ion heat diffusivities, , are compared with neoclassical theory and the impact of edge localized modes (ELMs) on the edge ion heat transport level is studied in detail. Pedestal matching experiments in deuterium and hydrogen plasmas show that the inter-ELM pedestal remains close to the neoclassical value. The additional power needed in hydrogen to get similar pedestal temperatures as in deuterium plasmas mostly affects the electron heat channel, i.e. the electron heat diffusivity increases while the ion heat diffusivity stays at the same level within the uncertainties. Sub-ms measurements of the edge ion temperature allows us to extend the analysis to the entire ELM cycle. During the ELM crash, the ion heat transport is increased by an order of magnitude. The perturbed heat flux increases first at the separatrix, i.e. first the separatrix ion temperature increases, leading to a flatter ion temperature gradient, followed by a decrease of the whole pedestal profile. The ion heat transport returns to its pre-ELM neoclassical level 3–4 ms after the ELM crash.

Electron heat diffusivity in radially-bounded ergodic region of toroidal plasma

Drift-kinetic simulations are performed to investigate effect of ergodic field lines caused by resonant magnetic perturbations (RMPs) on radial heat diffusivity of electrons in the edge region of toroidal plasma of collisionality . The following is assumed in the simulations. The ergodic region is bounded radially on both sides by closed magnetic surfaces. The pressure gradient remains nonzero in the ergodic region because of an incomplete flattening of the pressure profile, and the characteristic scale length of the pressure gradient is of larger order than the overlapping width of the neighbouring magnetic islands. It is found in the quasi-steady state of that the electron heat diffusivity is of smaller order than the theoretical estimate derived by the Rechester–Rosenbluth model (Rechester and Rosenbluth 1978 Phys. Rev. Lett. 40 38). The radial heat conduction is dominated not only by parallel motions along the ergodic field lines, but also by trapped particle motions generated by the RMP field. The contribution of the trapped particles reduces the radial heat conduction enhanced by the parallel motions.

Observations of compound sawteeth in ion cyclotron resonant heating plasma using ECE imaging on experimental advanced superconducting tokamak

The spatial and temporal evolutions of compound sawteeth were directly observed using 2D electron cyclotron emission imaging on experimental advanced superconducting tokamak. The compound sawtooth consists of partial and full collapses. After partial collapse, the hot core survives as only a small amount of heat disperses outwards, whereas in the following full collapse a large amount of heat is released and the hot core dissipates. The presence of two q = 1 surfaces was not observed. Instead, the compound sawtooth occurs mainly at the beginning of an ion cyclotron resonant frequency heating pulse and during the L-H transition phase, which may be related to heat transport suppression caused by a decrease in electron heat diffusivity.

Parameter estimation for a nonlinear control-oriented tokamak profile evolution model

A control-oriented tokamak profile evolution model is crucial for the development and testing of control schemes for a fusion plasma. The RAPTOR (RApid Plasma Transport simulatOR) code was developed with this aim in mind (Felici 2011 Nucl. Fusion 51 083052). The performance of the control system strongly depends on the quality of the control-oriented model predictions. In RAPTOR a semi-empirical transport model is used, instead of a first-principles physics model, to describe the electron heat diffusivity in view of computational speed. The structure of the empirical model is given by the physics knowledge, and only some unknown physics of , which is more complicated and less well understood, is captured in its model parameters. Additionally, time-averaged sawtooth behavior is modeled by an ad hoc addition to the neoclassical conductivity and electron heat diffusivity. As a result, RAPTOR contains parameters that need to be estimated for a tokamak plasma to make reliable predictions. In this paper a generic parameter estimation method, based on the nonlinear least-squares theory, was developed to estimate these model parameters. For the TCV tokamak, interpretative transport simulations that used measured profiles were performed and it was shown that the developed method is capable of finding the model parameters such that RAPTOR’s predictions agree within ten percent with the simulated q profile and twenty percent with the measured profile. The newly developed model-parameter estimation procedure now results in a better description of a fusion plasma and allows for a less ad hoc and more automated method to implement RAPTOR on a variety of tokamaks.

Effects of toroidal rotation shear and magnetic shear on thermal and particle transport in plasmas with electron cyclotron heating on JT-60U

Increases in thermal and particle transport with electron cyclotron heating (ECH) that are observed in many tokamaks can be a critical issue in establishing ITER operational scenarios with electron heating. To address the issues, conditions with no increase in the thermal and particle transport with ECH have been experimentally investigated in positive magnetic shear, weak magnetic shear (WS) and reversed magnetic shear plasmas with internal transport barrier in the ion channel. The ion heat diffusivity (χi) around the internal transport barrier in the ion temperature remains constant with ECH when a large negative toroidal rotation shear (|dVφ/dr| > 4 × 105 s−1) is formed before the ECH. On the other hand, χi increases on the condition that the toroidal rotation shear is small or positive. The characteristics do not depend on magnetic shear, the electron to ion temperature ratio (Te/Ti) and ECH power. The electron heat diffusivity stays constant with ECH when the magnetic shear is negative. Effective particle transport remains constant or reduces during ECH under the condition of negative magnetic shear. An observation indicates that there is no threshold of the negative magnetic shear or a very small one for the electron channel sustainment; the electron thermal and particle confinement is maintained during ECH with a small negative magnetic shear in the WS operation.

Theoretical and Numerical Study of Electron Transport Through Magnetic Island

We investigate electron heat diffusion across a low mode magnetic island numerically in cylindrical geometry and compare with the theory in tokomak plasma physics. In order to keep the simulation results reliable, a modified simulation code, TM8P, was used in our simulation work. The correlation of the effective radial heat conductivity, χr, and several high ratio of parallel magnetic field heat diffusion coefficient to the perpendicular coefficient, \( {{\chi_{\parallel } } \mathord{\left/ {\vphantom {{\chi_{\parallel } } {\chi_{ \bot } }}} \right. \kern-0pt} {\chi_{ \bot } }} \), is studied in this article. It’s found that the theoretical prediction by Yu conform with the numerical results of TM8P when \( {{\chi_{\parallel } } \mathord{\left/ {\vphantom {{\chi_{\parallel } } {\chi_{ \bot } }}} \right. \kern-0pt} {\chi_{ \bot } }} \) is not bigger than 1012, i.e. the value of width of magnetic island to the width of diffusive layer, w/wc, is a small number.

Characterization of divertor footprints and the pedestal plasmas in the presence of applied n = 3 fields for the attached and detached conditions in NSTX

Recent progress in the study of 3D field effects on the divertor and pedestal plasmas is reported with the use of a new set of diagnostics. A wide angle visible camera provides 2D data of lower divertor surface covering almost the full range of radius (r) and toroidal angle (Φ), a significant advantage over the conventional 1D radial profile in examining non-axisymmetric effects of 3D fields on the divertor footprints. The spatial distribution of connection lengths (Lc) calculated by vacuum field line tracing in the presence of 3D fields (n = 3) agrees with the footprint pattern observed in the 2D wide angle camera images. The full (r, Φ) image data with high temporal resolution revealed that the spatial structure of modified divertor footprints is maintained even during the edge-localized modes (ELMs) triggered by applied n = 3 fields, when the ELM size is sufficiently small, i.e. the ELMs are ‘phase locked’ to the imposed perturbation field structure. This phase-lock is lost during the ELM rise time for ELMs with large energy loss, e.g. ΔWELM/WMHD > 4–5%. Divertor gas puff was used to create detached divertor condition and the effect of 3D fields on the detachment was investigated. The divertor remains partially detached with the 3D field application when a sufficient amount of gas is injected into the divertor region, which is accompanied by a noticeable drop of pedestal electron temperature (Te). However, with a lower gas puff, the divertor plasma re-attaches, when 3D fields were applied to the detached plasma, and the pedestal Te rises back up. There observed no other change in the pedestal profile associated with the re-attachment, indicating that this is likely to be dominated by a change in the electron thermal transport processes. A TRANSP analysis shows that the drop of pedestal electron heat diffusivity (χe) is responsible for this change but the source of this reduction is yet unclear.

Ablation Dynamics of Silicon by Femtosecond Laser and the Role of Early Plasma

In this paper, the femtosecond laser ablation of silicon is investigated by a two-dimensional hydrodynamic model. The ablation depth of the silicon wafer ablated in air at different laser intensities is calculated, and the corresponding experimental measurements are carried out for validation. Two different ablation regimes have been identified by varying the laser fluence. While two-photon absorption dominates in the low fluence regime (&lt;2 J/cm2), electron heat diffusion is a major energy transport mechanism at higher laser fluences (&gt;2 J/cm2). The ablation efficiency first increases with the laser fluence, and reaches the peak value at the laser fluence around 8 J/cm2. It starts to drop when the laser fluence further increases, because of the early plasma absorption of the laser beam energy.