Electron Temperature Profiles Research Articles

Neural network approximation of Bayesian models for the inference of ion and electron temperature profiles at W7-X

In this paper, we describe a method for training a neural network (NN) to approximate the full model Bayesian inference of plasma profiles from x-ray imaging diagnostic measurements. The modeling is carried out within the Minerva Bayesian modeling framework where models are defined as a set of assumptions, prior beliefs on parameter values and physics knowledge. The goal is to use NNs for fast ion and electron temperature profile inversion from measured image data. The NN is trained solely on artificial data generated by sampling from the joint distribution of the free parameters and model predictions. The training is carried out in such a way that the mapping learned by the network constitutes an approximation of the full model Bayesian inference. The analysis is carried out on images constituted of 20 × 195 pixels corresponding to binned lines of sight and spectral channels, respectively. Through the full model inference, it is possible to infer electron and ion temperature profiles as well as impurity density profiles. When the network is used for the inference of the temperature profiles, the analysis time can be reduced down to a few tens of microseconds for a single time point, which is a drastic improvement if compared to the ≈4 h long Bayesian inference. The procedure developed for the generation of the training set does not rely on diagnostic-specific features, and therefore it is in principle applicable to any other model developed within the Minerva framework. The trained NN has been tested on data collected during the first operational campaign at W7-X, and compared to the full model Bayesian inference results.

Safety factor profile control with reduced central solenoid flux consumption during plasma current ramp-up phase using a reinforcement learning technique

Safety factor profile control via active feedback control of electron temperature profile during a plasma current ramp-up phase of a DEMO reactor is investigated to minimize the magnetic flux consumption of a central solenoid (CS) for wide range of q profiles. It is shown that q profiles with positive, weak and reversed magnetic shear can be obtained with the resistive flux consumption less than 60% of the empirical estimation which is calculated using the Ejima constant of 0.45. For the optimization of the target electron temperature profile and feedback gain to control electron heating power, reinforcement learning technique is introduced. One important feature of the system trained by reinforcement learning is that it can optimize the target electron temperature adaptive to the present status of a plasma. This adaptive feature of the reinforcement learning enables to control q profiles even in the case that an effective charge profile is randomly modified and it is not measured directly.

First modeling of strongly radiating WEST plasmas with SOLEDGE-EIRENE

Abstract We present first results of SOLEDGE-EIRENE modeling a strongly radiating plasma in the WEST tokamak. Using measurements from a reciprocating Langmuir probe we have determined the SOLEDGE input parameters, i.e. separatrix density at outboard midplane and radial transport coefficients typical of L-mode plasma. We have performed deuterium plasma simulations with presence of oxygen, injected from the core boundary into the simulation domain. The comparison between the radiated power measured from the bolometry in the divertor region and the one computed from SOLEDGE simulations seems to indicate a concentration of oxygen of about 2%. Moreover we have obtained good agreement between simulation results and experimental measurements on electron density and electron temperature profiles at the outer strike point. First qualitative analysis of spectroscopic synthetic diagnostic on Dα signals is also presented.

Comparison of a 2D nonlocal transport model to ECRH experiments in LHD

A recently developed model of nonlocal transport in two dimensions (2D), the “iterative method” [J. E. Maggs and G. J. Morales, Phys. Rev. E 99, 013307 (2019)], is applied to the published results of ECRH experiments [Takahashi et al. AIP Conf. Proc. 1580, 145 (2014)] performed in the Large Helical Device. It is found from the temperature profiles obtained from the 2D model that the sharply peaked electron temperature profiles observed in such experiments, and previously associated with local transport and “internal transport barriers” or Core Electron-Root Confinement, are also consistent with nonlocal transport. It is shown that the iterative method is suited to handling both scenarios.

Investigation of recombination front region in detached plasmas in a linear divertor plasma simulator

Abstract We have investigated detailed plasma structure around the recombination front region (RFR), where volume electron-ion recombination (EIR) strongly occurs in detached plasmas, by using two-dimensional (2D) movable probe system as well as laser Thomson scattering diagnostics. The 2D distribution of electron density, electron temperature, and plasma potential around the RFR, has been revealed for the first time. The spatial distribution of the particle loss rate due to EIR estimated from electron temperature and electron density profiles indicated that the three-dimensional structure of the RFR adopts a cone structure. Furthermore, in the peripheral region of the RFR, the radial profile of the electron density was widened locally with increasing cross-field transport caused by plasma fluctuation. From the heat transport analysis of electrons, it was found that the thermal relaxation process between electrons and ions is important for the cooling of electrons, and that the convection of electrons regulates electron heat transport near the RFR.

Actuator management development on ASDEX-Upgrade

In future tokamak devices, the control system will have to handle several control goals simultaneously with a limited number of actuators in long and high performance discharges. One of the critical roles of the future control systems will be the management of actuators, which would assign the most convenient available actuators primarily to the control goals of the highest importance at the time. Such a system would consist of a discharge program defining the experiment, a discharge supervisor making automatic high level decisions in real time and a component handling the actuators at a lower level: The virtual actuator, which is a software object responsible for distributing the controller commands to a set of selected actuators. This paper describes the implementation of a virtual actuator for all 8 gyrotrons of ASDEX-Upgrade. We also describe the intended use of the virtual actuator for three experiments: β control using ECRH, a disruption avoidance strategy, and electron temperature profile control. The paper also gives an overview of future actuator management developments at ASDEX-Upgrade: extension to all heating sources, inclusion of mirrors for ECRH, and intelligent real time distribution of the actuators between the control goals.

Sensitivity of Thomson Scattering Measurements on Electron Distribution Modeling in Low-Density RFP Plasmas

A numerical method which relies on Thomson scattering data for the identification and analysis of electron distributions is presented and discussed; the method is developed within the framework of Bayes probability theory. Use of this method on Reversed Field eXperiment (RFX)-mod low-density data supports the proposition that suprathermal tails cause systematic asymmetries in electron temperature profiles. In the limits of signal and spectral resolution of the diagnostic, a semiquantitative analysis is carried on; the presence of nonthermal (NT) populations is found to be consistent with runaway/slideaway plasma conditions. In low-density discharges NT $e^{-}$ presence is compatible with the presence of kinetic dynamo and can contribute to configuration sustainment.

Helical core formation and evolution during current ramp-up in the high-field tokamak Alcator C-Mod

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 results in a reversed shear q-profile. The onset and early development of a helical core in C-Mod were simulated using a new 3D time-dependent equilibrium reconstruction, based on the ideal MHD equilibrium code VMEC. The reconstruction used the experimental density, temperature, and soft-X-ray fluctuations. The pressure profile can become hollow due to an inverted, hollow electron temperature profile caused by molybdenum radiation in the plasma core during the current ramp-up phase before the onset of sawteeth, which may also occur in ITER with tungsten. Based on modeling, it is found that a reverse shear q-profile combined with a hollow pressure profile reduces the onset condition threshold, enabling helical core formation from an otherwise axisymmetric equilibrium.

Self-consistent simulation of transport and turbulence in tokamak edge plasma by coupling SOLPS-ITER and BOUT++

The status of coupling the fluid plasma/neutral 2D transport code SOLPS-ITER and the fluid 3D turbulence code BOUT++ is reported. Both codes simulated the same region, which is from several cm inside the magnetic separatrix to the far scrape-off layer (SOL). Compared to the profile evolution time scale, the characteristic time scale of the turbulence is quite short. For the turbulence code BOUT++, the time scale is around 10−6 s. However, for the transport code SOLPS-ITER, the time scale is around 10−3–10−2 s. An iterative scheme is used that each system is evolved on its own characteristic time scale. SOLPS-ITER can provide the background profiles of density, ion, and electron temperature to BOUT++. In turn, BOUT++ can provide the corresponding radial transport coefficients to SOLPS-ITER. The coupling has involved the ion density, ion temperature, and electron temperature. After several steps of iteration, the profiles of density, ion, and electron temperature show fluctuations, and the differences of the changes between two consecutive profiles are getting smaller and smaller. Finally, the self-consistent solutions of turbulence and transport can be obtained.

Fast evaluation of the current drive efficiency by electron cyclotron waves for reactor studies

The determination of the current driven by electron cyclotron waves is usually performed employing ray/beam tracing codes, which require as an input the magnetic equilibrium, the electron density and the electron temperature profiles on one side and the beam injection parameters on the other. In the frame of systems-code applications, however, a different approach is needed, as some of the required input quantities are not available. Here, a procedure to evaluate the achievable ECCD efficiency for given global reactor parameters is proposed. It relies on a single numerical evaluation of the current drive efficiency (based on the adjoint method and including momentum-conserving corrections) for suitably chosen input values. The results are shown to be in good agreement with the full numerical optimization of the ECCD efficiency for a number of reactor-relevant scenarios. As described in this paper, this approach does not include the effect of parasitic absorption from higher cyclotron harmonics, which becomes important starting from electron temperatures of the order of 30 keV.

Investigation of Optically Grey Electron Cyclotron Harmonics in Wendelstein 7-X

For a magnetic field of 2.5T, the electron cyclotron harmonics are spectrally well separated in W7-X as it has a large aspect ratio. Because of this advantage from the geometry of W7-X stellarator, it is easier to scan these higher harmonics (70,140,210…..GHz) compared to tokamaks with small aspect ratio. For confinement reasons, W7-X is planned to work at high plasma densities applying O2 electron cyclotron resonance heating (ECRH). For such plasmas, which already have been demonstrated in experimental campaign OP1.2a of W7-X, electron cyclotron emission (ECE) from second harmonic extraordinary mode (X2) is in cutoff. In that case, optically grey higher harmonics provide the only access to ECE signal and hence electron temperature profiles. A Michelson interferometer will be used in the next operational campaign of W7-X for broadband (50-500 GHz) ECE scan and that will be compared to modeling of ECE emission at different plasma parameters from radiation transport calculations (TRAVIS). The strong stray radiation from non-absorbed ECRH is a major concern in scanning these higher harmonics using an interferometer because this stray radiation will dominate the spectra thus masking the ECE signal. For this purpose, a multimode notch filter design based on a multilayer dielectric structure is constructed to attenuate the stray radiation at 140GHz by 50dB.

Development of ECE/ECEI diagnostics and MHD-related studies on HL-2A tokamak

A novel 60-channel electron cyclotron emission (ECE) radiometer has been designed and tested for the measurement of electron temperature profiles on the HL-2A tokamak. This system is based on the intermediate frequency division technique, and has the features of wide working frequency range (60−90 GHz) and high temporal-spatial resolution (3 µs, 1 cm), which covers almost the entire plasma region. Also, an electron cyclotron emission imaging (ECEI) system has been developed for studying two dimensional electron temperature fluctuations. It is comprised of several front-end quasi-optical lenses, a 24 channel heterodyne imaging array with a tunable RF frequency range spanning 60−135 GHz, and a set of back-end ECEI electronics that together generate two 24×8 array images of the 2nd harmonic X-mode electron cyclotron emission from the HL-2A plasma. The measurement region can be flexibly shifted due to two independent local oscillator sources, and the field of view can be adjusted easily by changing the position of the zoom lenses as well. The temporal resolution is about 2.5 µs and the achievable spatial resolution is 1 cm. The ECE/ECEI diagnostics have been demonstrated to be powerful tools to study MHD-related physics including the multi-scale interaction between macro-scale MHD and micro-scale turbulence on the HL-2A tokamak.

Comparison between Theoretical and Experimental Radial Electron Temperature Profiles in a Low Density Weakly Ionized Plasma

Experimental and theoretical studies of the radial distribution function of the electron temperature (RDFT) in a low-density plasma and weakly ionized gas for the abnormal glow region are presented. Experimentally, the electron temperatures and densities are measured by a Langmuir probe moved radially from the center to the edge of the cathode electrode for helium gas at different pressures in the low-pressure glow discharge. The comparison of the final experimental data for the radial distribution of electron temperatures and densities for different low pressures ranging from 0.2 to 1.2 torr, with the final proved equation of RDFT confirms that the electron temperatures decrease with increasing product of radial distance and gas pressures, showing a radial decrement dependence of the electron temperature from the center to the edge of the electrode. This is attributed to the increase of the number of electron-atom collisions at higher gas pressures and consequently of the rate of ionization. For the axial distance (L) from the tip of the probe to cathode electrode and the cathode electrode radius (R), a theoretical and experimental comparison for the two conditions L R, for both cases the produced plasma temperatures decrease and densities increase. It is concluded that the RDFT accurately shows a dramatic decrease for L R similar as for conditions of magnetized and unmagnetized effect for DC plasma. This means that the rate of plasma loss by diffusion decreased for L < R, agrees well with the applied of magnetic field behavior

Electron-cyclotron-resonance heating in Wendelstein 7-X: A versatile heating and current-drive method and a tool for in-depth physics studies

For stellarators, which need no or only small amounts of current drive, electron-cyclotron-resonance heating (ECRH) is a promising heating method even for the envisaged application in a fusion power plant. Wendelstein 7-X (W7-X) is equipped with a steady-state capable ECRH system, operating at 140 GHz, which corresponds to the 2nd cyclotron harmonic of the electrons at a magnetic field of 2.5 T. Ten gyrotrons are operational and already delivered 7 MW to W7-X plasmas. Combined with pellet injection, the highest triple product (0.68 × 1020 keV m−3 s), observed up to now in stellarators, was achieved (Sunn Pedersen et al 2018 Plasma Phys. Control. Fusion 61 014035). For the first time, W7-X plasmas were sustained by 2nd harmonic O-mode heating, approaching the collisionality regime for which W7-X was optimized. Power deposition scans did not show any indication of electron temperature profile resilience. In low-density, low-power plasmas a compensation of the bootstrap current with electron-cyclotron current drive (ECCD) was demonstrated. Sufficiently strong ECCD close to the plasma centre produced periodic internal plasma-crash events, which coincide with the appearance of low order rationals of the rotational transform.

Fast and pervasive heat transport induced by multiple locked modes in DIII-D

This work presents the impact that multiple island chains co-existent across a tokamak plasma profile have on the heat transport and final temperature of that plasma. Numerical studies using the TM1 code show that error fields (EFs) with multiple poloidal components accelerate the core field penetration compared to pure m/ n = 2/1 EF penetration (here m and n are the poloidal and toroidal mode numbers respectively). After field penetration, locked magnetic islands of 2/1, 3/1 and 4/1 flatten the temperature at the corresponding rational surfaces. The co-existence of these islands significantly enhances the plasma heat transport throughout a wide swath of plasma from the core 2/1 rational surface to plasma edge. The electron temperature profile from 2/1 to 4/1 rational surfaces can be nearly flattened even if there is no island overlap, and the temperature inside each island is determined by the boundary temperature at the outboard separatrix of the island. The resulting central decreases by more than 50%, in good agreement with experimental observations and much lower than modeling with only a single 2/1 locked island. Further comparisons of the profile between numerical modeling and DIII-D experiment indicates that the observed reduction in the edge temperature requires edge island overlap and stochasticity. Numerical scans reveal the profile decreases further when large EF amplitudes create larger islands, wider edge stochastic regions and secondary island structures. Scans of the relative phase between EF harmonics reveal that the 3/1 island width is most sensitive to the island phase and the central changes with the 3/1 island width. These results indicate that the coexistence of multiple LMs in tokamak plasmas deteriorate thermal confinement more than the sum of their isolated impacts would and that this may be responsible for the fast thermal quench observed prior to major disruptions.

Upgrade of the multi-energy soft x-ray diagnostic system for studies of ELM dynamics in the EAST tokamak

The multi-energy soft x-ray (ME-SXR) diagnostic system has been calibrated to study the evolution of the edge electron temperature profile during the edge localized mode (ELM) events. The electronic bandwidth of the Mazet MTi04 multi-channel variable gain trans-impedance amplifier measured in the laboratory is consistent with the nominal value. As the gain of the preamplifier is increased from 105 to 2 × 107, the bandwidth is decreased from 100 kHz to 10 kHz. The relative gain errors for different channels (5 arrays ×20 channels) were also calibrated in situ after the system was installed on the EAST tokamak. The results showed that the relative gain error (RGE) in each array was less than 10% compared to the reference channel of the array, and was insensitive to the preamplifier gains. A feedback loop was designed to automatically adjust the programmable gains of the preamplifiers based on the signal amplitudes measured in the previous discharge. The reconstructed edge electron temperature (Te) profile was also uploaded automatically to the MDSplus server between discharges. Utilizing the fast temporal resolution of Te (∼5 kHz), the dynamics of edge electron temperature evolution during Type I and high frequency ELM (HF-ELM) events were compared. The results showed that the edge Te profile collapsed during Type I ELMs, while for the HF-ELM regime, the edge Te profile pedestal structure sustains stiffness.

A Scanning SXR Spectrometer Used in Experiments on ECR Plasma Heating at the L-2M Stellarator

Abstract—A diagnostic complex that is based on a scanning soft X-ray spectrometer has been developed at the Prokhorov General Physics Institute. The diagnostic complex is intended to measure the radial profiles of the plasma electron temperature in the L-2M stellarator. The maximum counting rate of the spectrometer is 2.0 × 105 pulses/s. It allows measuring of SXR spectra in the energy range of γ-photons of 1–80 keV. The spectral resolution of the spectrometer measured using a source of radioactive radiation with energy of E = 5.89 keV (55Fe) was ΔE = 320 eV (FWHM). The scanning system makes it possible to measure SXR spectra along the chords lying in the angular range from –13.5° to +26.5°. Negative and positive angles correspond to chords below and above the equatorial plane of the facility, respectively. The radial resolution of the spectrometer at the plasma axis is ~1.7 cm. The first results of spectral measurements in experiments at electron cyclotron resonance plasma heating at the L-2M stellarator are presented.

Experimental investigation of the compression and heating of an MHD-driven jet impacting a target cloud

Adiabatic compression has been investigated by having an MHD-driven plasma jet impact a gas target cloud. Compression and heating of the jet upon impact were observed and compared to theoretical predictions. Diagnostics for comprehensive measurements included a Thomson scattering system, a fast movie camera, a translatable fiber-coupled interferometer, a monochromator, a visible-light photodiode, and a magnetic probe array. Measurements using these diagnostics provided the time-dependent electron density, electron temperature, continuum emission, line emission, and magnetic field profile. Increases in density and magnetic field and a decrease in jet velocity were observed during the compression. The electron temperature had a complicated time dependence, increasing at first, but then rapidly declining in less than 1 μs which is less than the total compression time. Analysis indicates that this sudden temperature drop is a consequence of radiative loss from hydrogen atoms spontaneously generated via three-body recombination in the high-density compressed plasma. A criterion for how fast compression must be to outrun radiative loss is discussed not only for the Caltech experiment but also for fusion-grade regimes. In addition, the results are analyzed in the context of shocks the effects of which are compared to adiabatic compression.

A model for the basic plasma parameter profiles and the force exerted by fireballs with non-isothermal electrons

As discovered in recent work, plasma fireballs have the ability to exert considerable force onto ions and neutrals and, hence, induce macroscopic gas flows. This property makes them interesting objects for fundamental scientific research. Furthermore, there are also the possibilities for applications in the field space propulsion. As there is a lack of fundamental understanding of these plasma phenomena, this article aims to enhance the physical knowledge of fireballs by presenting a mathematical model for the calculation of the force that can be provided by them. It will be shown that all the main plasma parameters such as the plasma potential and the electron density can be derived completely with the knowledge of the potential of the electrode and the radial electron temperature profile. The calculations show very good agreement with the experimental data if two species of electrons (i.e., fast and slow) are considered. Both electron populations have different temperature profiles as is shown with measurements. Furthermore, it will be demonstrated that the potential drop throughout the fireball is much larger than previously thought and that this larger potential drop can considerably contribute to the acceleration of ions in the double layer. This mechanism makes it more likely that the force exerted by the fireball is rather caused by heating of the neutrals via collisions with those accelerated ions and the high energetic ions themselves than by collisions between fast electrons and neutrals.

Core plasma confinement during detachment transition with RMP application in LHD

The core plasma confinement during detachment phase is investigated in the discharges with application of resonant magnetic perturbation (RMP) field in LHD. The RMP application creates a remnant magnetic island in the edge stochastic layer, which largely changes the plasma parameter profiles including impurity radiation. The electron temperature and pressure profiles are flattened at the island, while the electron density is slightly peaked at the edge of the island. The estimated impurity radiation profile is enhanced and fixed around the magnetic island during the detached phase, where the discharge is stably sustained with controlled level of radiation. Without RMP, the radiation penetrates the confinement region, leading to radiation collapse. It is found that in the case of the RMP application the plasma stored energy increases discontinuously at the detachment transition. In spite of the reduced effective plasma volume caused by the edge magnetic island and by the enhanced radiation there, the central plasma pressure finally exceeds the case without RMP. This is caused by the pressure profile peaking at the central region in the case with RMP. These results indicate clear change of core plasma confinement during the detached phase with RMP.