Ion Heat Flux Research Articles

Three-dimensional transient modeling and simulation of high-current multi-component vacuum arc under transverse magnetic field

This paper established a three-dimensional transient MHD model of a high-current multi-component vacuum arc under a transverse magnetic field (TMF) to simulate the dynamic characteristics of plasma parameters in the uniform motion mode of a contracted arc under lower TMF. The model considered the ionization–recombination process among the multi-components and used the P1 model to calculate the thermal radiation losses. The simulation results show that the ion number density of The TMF arc is on the order 1024 m−3, and when the plasma temperature reaches 4.3 eV, the effects of thermal radiation cannot be ignored. The majority of the plasma from the cathode and anode undergo acceleration and then deceleration before finally intersecting at the center of the arc, creating an extreme value of the density and the pressure, where a large amount of kinetic energy is converted into internal energy. The arc will be bent and deflected under the action of the ampere force, and the deflection of Cu3+ is especially obvious. The TMF affects the collision strength of the jet in the intersection area and, thus, affects the ion density, in which the change of Cu2+ is dominant. The ionization–recombination process of ions is mainly determined by the electron temperature, which is affected by the arc current. As the current decreases, Cu1+ increases and Cu2+ and Cu3+ decrease, and the change in ionization rate is the main reason for the change in the proportion of each ionic component; the heat flux density to the anode and cathode is on the order of 1010 W/m2, which heats the front of the arc and ensures the stable movement of the arc. Meanwhile, due to the high ion number density, the ion heat flux accounts for the main part of the heat flux, and the anode exhibits a higher proportion of ion heat flux.

Recent advance progress of HL-3 experiments

Abstract Since the first plasma realized in 2020, a series of key systems on HL-3 (known as HL-2M before) tokamak have been equipped/upgraded, including in-vessel components (the first wall, lower divertor, and toroidal cryogenic/water-cooling/baking/glow discharge systems, etc.), auxiliary heating system of 11 MW, and 28 diagnostic systems (to measure the plasma density, electron temperature, radiation, magnetic field, etc.). Magnet field systems were commissioned firstly for divertor plasma discharges. During the 2nd experimental campaign of HL-3 tokamak, several great progresses have been achieved. Firstly, the successful operation with plasma current larger than 1 MA was achieved under a divertor configuration. Secondly, the advanced divertor concept with two distinct snowflake configurations was realized. It is found that the distribution of ion saturation current and heat flux on bottom plate becomes wide due to magnetic surface expansion, demonstrating the advantage of such configuration in the heat flux mitigation. In addition, using the combination of NBI, ECRH and LHCD, the standard sawtoothing high confinement mode of megampere plasma was firstly accessed on the HL-3. The successful commissioning of HL-3 is beneficial for the initial operation of ITER.

From L-mode to the L–H transition, experiments on ASDEX upgrade and related gyrokinetic simulations

This work combines experimental observations from the ASDEX Upgrade tokamak with related gyrokinetic simulations of the turbulence moving from L-mode toward, and beyond, the L–H transition. Dedicated experiments have been performed with slow steps of increasing electron cyclotron heating power. Gyrokinetic simulations of the edge turbulence of these plasmas highlight the key roles of the non-linear electromagnetic effects and the external flow shear (E × B shear), both related to the evolution of the plasma pressure profile with increasing heating power. The increase in the plasma βe destabilizes turbulence at low toroidal mode numbers, that, in turn, is strongly suppressed by the external flow shear. This allows the plasma pressure profiles to evolve without a sharp rise in the turbulent fluxes. When all the experimentally measured plasma parameters are consistently included as inputs of the local gyrokinetic simulations, both the experimental electron and ion heat fluxes are quantitatively reproduced on the whole L-mode phase of the selected discharge. Simulations carried out with edge parameters of an ELM-free H-mode phase still show the importance of the mechanisms discussed earlier while also indicating possible limitations of the local approach.

A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas

A reduced kinetic method (RKM) with a first-principles collision operator is introduced in a 1D2V planar geometry and implemented in a computationally inexpensive code to investigate non-local ion heat transport in multi-species plasmas. The RKM successfully reproduces local results for multi-species ion systems and the important features expected to arise due to non-local effects on the heat flux are captured. In addition to this, novel features associated with multi-species, as opposed to single species, cases are found. Effects of non-locality on the heat flux are investigated in mass and charge symmetric and asymmetric ion mixtures with temperature, pressure, and concentration gradients. In particular, the enthalpy flux associated with diffusion is found to be insensitive to sharp pressure and concentration gradients, increasing its significance in comparison to the conductive heat flux driven by temperature gradients in non-local scenarios. The RKM code can be used for investigating other kinetic and non-local effects in a broader plasma physics context. Due to its relatively low computational cost it can also serve as a practical non-local ion heat flux closure in hydrodynamic simulations or as a training tool for machine learning surrogates.

Ion kinetic effects on the formation of intense laser-driven shock waves

The ion kinetic effect on the formation of intense laser-driven collisional shock waves is investigated via hybrid fluid-particle-in-cell simulations. It is found that the ion heat flux dominates the shock formation, which is considerably larger than the electron heat flux in the shock region. The rise of the temperature due to the laser energy deposition drives a heatwave into the overdense plasma, creating an electron–ion energy exchange zone between the critical surface and heat wave front. The heated ions, which are generated at the electron–ion energy exchange zone via the friction force, are found to travel to the high-density region and cause a tail distribution gain. Despite the small quantity, the heated tail ions contribute most of the ion heat flux during the shock formation. Additionally, as the electron heat flux decreases, the population of the heated tail ions is reduced, leading to a fall in the ion heat flux. This results in the delay or even suppression of the shock formation, because the ions are in a non-equilibrium state in the vicinity of the shock region, the ratio of the downstream ion temperature to the upstream ion temperature tends to a modestly decrease in comparison to the theory. The study provides a clear picture of the formation process of laser-driven shock waves.

Ion heat transport in electron cyclotron resonance heated L-mode plasma on the T-10 tokamak

Anomalous ion heat transport is analyzed in the T-10 tokamak plasma heated with electron cyclotron resonance heating (ECRH) in second-harmonic extra-ordinary mode. Predictive modeling with empirical scaling for Ohmical heat conductivity shows that in ECRH plasmas the calculated ion temperature could be overestimated, so an increase of anomalous ion heat transport is required. To study this effect two scans are presented: over the EC resonance position and over the ECRH power. The EC resonance position varies from the high-field side to the low-field side by variation of the toroidal magnetic field. The scan over the heating power is presented with on-axis and mixed ECRH regimes. Discharges with high anomalous ion heat transport are obtained in all considered regimes. In these discharges the power balance ion heat conductivity exceeds the neoclassical level by up to 10 times. The high ion heat transport regimes are distinguished by three parameters: the ratio, the normalized electron density gradient , and the ion–ion collisionality . The combination of high , high , and −10 results in values of normalized anomalous ion heat fluxes up to 10 times higher than in the low transport scenario.

Real-time control of NBI fast ions, current-drive and heating properties

Conventionally, neutral beam injection (NBI) in tokamaks is controlled via engineering parameters such as injection voltage and power. Recently, the high-fidelity real-time NBI code RABBIT has been coupled to the discharge control system of ASDEX Upgrade. It allows to calculate the NBI fast-ion distribution and hence the properties of NBI in real-time, making it possible to control them directly. We successfully demonstrate control of driven current, ion heating and stored fast-ion energy by modifying the injected beam power. A combined ECRH and NBI controller is also successfully tested, which is able to adjust the heating mix between ECRH and NBI to match a certain desired ion heating fraction at given total power. Further experiments have been carried out towards control of the ion heat flux (i.e. ion heating plus collisional heat transfer between ions and electrons). They show good initial success, but also leave room for future improvements as the controller runs into instabilities at too high requests.

Local models of two-temperature accretion disc coronae – II. Ion thermal conduction and the absence of disc evaporation

ABSTRACT We use local stratified shearing-box simulations with magnetic field-aligned thermal conduction to study an idealized model of the coupling between a cold, radiatively efficient accretion disc, and an overlying, hot, two-temperature corona. Evaporation of a cold disc by conduction from the hot corona has been proposed as a means of mediating the soft-to-hard state transitions observed in X-ray binary systems. We model the coronal plasma in our local disc patch as an MHD fluid subject to both free-streaming ion conduction and a parametrized cooling function that captures the collisional transfer of energy from hot ions to colder, rapidly cooling leptons. In all of our models, independent of the initial net vertical magnetic flux (NF) threading the disc, we find no evidence of disc evaporation. The ion heat flux into the disc is radiated away before conduction can heat the disc’s surface layers. When an initial NF is present, steady-state temperature, density, and outflow velocities in our model coronae are unaffected by conduction. Instead of facilitating disc evaporation, thermal conduction is more likely to feed the disc with plasma condensing out of the corona, particularly in flows without NF. Our work indicates that uncertainties in the amount of NF threading the disc hold far greater influence over whether or not the disc will evaporate into a radiatively inefficient accretion flow compared to thermal conduction. We speculate that a change in net flux mediates disc truncation/evaporation.

Simultaneous reproduction of experimental profiles, fluxes, transport coefficients, and turbulence characteristics via nonlinear gyrokinetic profile predictions in a DIII-D ITER similar shape plasma

Experimental conditions obtained on the DIII-D tokamak in the ITER Similar Shape (ISS) have been compared extensively with nonlinear gyrokinetic simulation using the CGYRO code [Candy et al., J. Comput. Phys. 324, 73–93 (2016)] with comparisons spanning ion and electron heat fluxes, electron and impurity particle transport, and turbulent fluctuation levels and characteristics. Bayesian optimization techniques [Rodriguez-Fernandez et al., Nucl. Fusion 62(7), 076036 (2022)], combined with nonlinear gyrokinetics, have been used to obtain simultaneously Qi, Qe, and Γe flux-matched profiles that are found to be in good agreement with experimental profile measurements. Synthetic diagnostics were used to compare measured beam emission spectroscopy and correlation electron cyclotron emission turbulent fluctuations with nonlinear simulation. Although some disagreements exist, nonlinear simulations are found to be in generally good agreement with measured fluctuation levels, spectral shapes, and measured radial trends in low-k δne/ne and δTe/Te. Low (Li and C) and mid-Z (Ca) impurity transport was also compared with these flux-matched simulations. Fully stripped, low-Z impurities are well reproduced by the gyrokinetic modeling while clear disagreement exists in comparisons with mid-Z impurities. Nonlinear gyrokinetic investigation into the Z dependence of impurity transport in the ISS conditions is also performed, demonstrating clear trends of impurity diffusion with impurity Z (both D∝Z and D∝1/Z) that vary with the radial location studied. These trends are shown to result from the local dominance of ion temperature gradient or ∇n driven trapped electron mode turbulence and may contribute to the disagreement between simulation and experiment in mid-Z impurity transport. The results of this work represent one of the most complete validation studies of the gyrokinetic model performed to date and provide an example of new capabilities for predicting performance in future fusion devices.

A validation study of a bounce-averaged kinetic electron model in a KSTAR L-mode plasma

We extend the bounce-averaged kinetic (BK) electron model to be applicable in general tokamak magnetic geometries and implement it on the global δf particle-in-cell gyrokinetic code gKPSP. We perform a benchmark study of the updated BK model against the gyrokinetic electron model in flux-tube codes, CGYRO and GENE. From the comparisons among the simulations based on the local parameters of a KSTAR L-mode plasma, we confirm a reasonable agreement among the linear results from the different codes. In the nonlinear gKPSP simulation with a narrow plasma gradient region whose width comparable to the mode correlation length, ion and electron heat fluxes are compatible with those calculated by CGYRO. However, with an unstable region sufficiently wider than the mode correlation length, gKPSP predicts 2–3 times larger turbulent heat fluxes. Taking into account the differences between the flux-tube and global simulations, the overall agreement is encouraging for further validation and development of the BK electron model. In global simulations using a wide range of the experimental plasma profiles, we find an intricate coupling of turbulence spreading and a zonal flow in determining the radial profiles of turbulent heat fluxes, which has not been reported to date.

Analysis of the Energy Flux Density near Electron Diffusion Region of Asymmetric Magnetic Field Reconnection

Magnetic reconnection is a crucial energy conversion process in plasmas, and it is important to study the forms of energy conversion and their distribution in this process. Previous research has focused mainly on the energy fluxes in symmetric reconnection, while the study of asymmetric reconnection at the Earth’s magnetopause, especially in terms of statistical analysis of multiple events, has not been reported before. Therefore, 10 magnetic reconnection events at the magnetopause observed by MMS (Magnetospheric Multiscale) satellite that passed through the electron diffusion region were used for analysis. Although the contribution of different energy flux varies case by case, our results show that in most events, the ion enthalpy flux is dominant, followed by the Poynting flux. The ion heat flux is slightly smaller than the Poynting flux, while the sum of ion kinetic energy flux, electron enthalpy flux and electron heat flux only accounts for less than 10% of the total energy flux. By projecting the normalized energy flux of all events into BL−V(i,L) plane (in LMN coordinate), we find that the energy flux in M direction is comparable to the energy flux in L direction and also there is an “anti-correlated” relationship between the ion velocity and ion heat flux around reconnection diffusion region, consistent with previous studies.

Mechanism of enhanced ion temperature by impurity seeding in EAST H-mode plasma

Ion temperature (T i) profiles are commonly observed to increase in peaking, leading to higher central T i, after impurity seeding in the EAST H-mode plasma. Argon can be more efficient at raising T i than neon. Toroidal rotation can also be enhanced in scenarios with NBI heating. A more significant increase in toroidal rotation is brought about by seeding argon than seeding neon. Turbulence is experimentally observed to be suppressed. Extensive modeling using the quasilinear gyrokinetic code QuaLiKiz is performed to explain the above observations. It is found that the enhanced T i can always be explained by the turbulence stabilization. However, the mechanism of turbulence stabilization is related to heating methods and the seeding impurity species. In the pure RF (ECRH + LHW) heating scenarios, where only the trapped electron mode (TEM) exists, argon can stabilize the TEM more significantly than neon due to its higher charge and heavier mass. In scenarios with increasing NBI power, the ion heat flux can be dominated by the ion temperature gradient (ITG), thus the enhanced T i is mainly attributed to ITG stabilization. In these cases, except argon’s ability to more efficiently stabilize TEM, more evident increased toroidal rotation brought about by argon seeding can also be beneficial to stabilize turbulence.

Complex structure of turbulence across the ASDEX Upgrade pedestal

The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to the pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma $\beta$ values. The turbulent transport is found to exhibit a multi-channel, multi-scale character throughout the pedestal with the dominant contribution transitioning from ion-scale trapped electron modes/micro-tearing modes at the pedestal top to electron-scale electron temperature gradient modes in the steep gradient region. Consequently, the turbulent electron heat flux changes from ion to electron scales and the ion heat flux reduces to almost neoclassic values in the pedestal centre. $E\times B$ shear is found to strongly reduce heat flux levels in all channels (electron, ion, electrostatic, electromagnetic) and the interplay of magnetic shear and pressure gradient is found to locally stabilise ion-scale instabilities.

A self-sustaining mechanism for internal transport barrier formation in HL-2A tokamak plasmas

The formation of Internal Transport Barrier (ITB) is studied in HL-2A plasmas by means of nonlinear gyrokinetic simulations. A new paradigm for the ITB formation is proposed in which different physics mechanisms play a different role depending on the ITB formation stage. In the early stage, fast ions, introduced by Neutral Beam Injection ion system, are found to stabilize the thermal-ion-driven instability by dilution, thus reducing the ion heat fluxes and finally triggering the ITB. Such dilution effects, however, play a minor role after the ITB is triggered as electromagnetic (EM) effects are dominant in the presence of established high pressure gradients. We define the concept of ITB self-sustainment, as the low turbulence levels found within the fully formed ITB are consequences of large scale zonal flows, which in turn are fed by a non-linear interplay with large scale high frequency EM perturbations destabilized by the ITB itself.

Determining the access to H–mode in the ITER pre–fusion and fusion power operation phases at low plasma current with full–radius TGLF–SAT2 simulations of L–mode plasmas

The pre–fusion power operation 1 phase of ITER is planned to be characterized by electron cyclotron resonance heating only. Under the assumption that the access to H–mode is determined by a critical ion heat flux at the plasma edge, full–radius ASTRA simulations with the TGLF–SAT2 transport model are performed in order to compute the ion heat flux produced by the thermal exchange between electrons and ions in different operational conditions. Both hydrogen and deuterium plasmas at 5 MA are considered, respectively at 1.8 T and 2.65 T, corresponding to one third and half of the nominal maximum magnetic field. Different levels of electron cyclotron heating power are considered in sets of simulations with increasing values of the electron line averaged density. The predictions are compared with the currently available scaling of the critical ion heat flux. In hydrogen, 20 MW of electron heating power are predicted to allow H–mode access in a vanishingly small density window, whereas 30 MW and 40 MW would allow more substantial H–mode operational windows. Despite the fact that in deuterium plasmas the thermal exchange between electrons and ions is smaller by the hydrogen to deuterium mass ratio compared to hydrogen plasmas, the lower H–mode power threshold in deuterium leads to the prediction that an even broader and more robust domain to access H–mode is obtained at half field at 40 MW in deuterium as compared to operation in hydrogen at one third of the maximum magnetic field, even at the same power.

Resonance in radio frequency sheath admittance and enhanced impurity emission near the ion cyclotron frequency

Ion cyclotron resonance heating (ICRH) is of considerable interest among all auxiliary heating techniques, because it transfers power directly to ions, targets the high-density core, and involves the cheapest radio-frequency (RF) components. During ICRH operation, RF sheaths form on the ICRH antenna itself, nearby hardware, and far-field surfaces. These sheaths are associated with large hot-spot formation and impurity emissions. This work presents high-resolution numerical modelling of RF sheaths in nuclear fusion scenarios using hPIC2, a Debye-scale particle-in-cell code. The modelling reveals a new RF sheath phenomenon which occurs when the RF is resonant with a species ion cyclotron frequency or harmonic in an oblique magnetic field. This resonance of the RF sheath causes modifications of the energy-angle distributions of the ions impacting on the walls, with consequent increase in wall impurity emission. Due to the 1/R scaling of the magnetic field in a tokamak, such cases are possible on divertor or vacuum chamber surfaces, depending on the geometry of the tokamak and the RF heating scenario. A simple physics interpretation using a driven damped harmonic oscillator is proposed, where the ion sheath transit time plays the role of damping the RF sheath admittance. Critically, the resonance leads to increased ion heat flux at the wall as well as increased physical sputtering, despite a lack of increase in RF rectified sheath potential.

Comparison of momentum transport in matched hydrogen and deuterium H-mode plasmas in ASDEX Upgrade

Advanced momentum transport analysis is used to study matched hydrogen (H) and deuterium (D) plasmas in the core of ASDEX Upgrade. The aim is to validate gyrokinetic theory and assess a possible isotope dependence. The methodology extracts momentum diffusion, convection, and intrinsic torque as a function of time from experiments employing neutral beam injection (NBI) modulation. H and D plasma scenarios with comparable ion heat fluxes, NBI torque, electron densities, and several dimensionless parameters were designed to highlight any mass dependency. Linear gyrokinetic simulations predict that, for similar background gradients, the Prandtl and pinch numbers should be similar for H and D. This was confirmed by the experimental momentum transport analyses. The assessed intrinsic torques were found to be similar between H and D, co-current directed and located near the outermost region of the plasma core. The strength of the intrinsic torque is correlated with the amplitude of the plasma pressure gradient in the pedestal. Finally, a robust error analysis demonstrates the uniqueness of the parameters obtained together with their uncertainties. Neglecting the intrinsic torque, or its time dependence, systematically distorts the assessed momentum diffusion and convection. This is the first method to separate all three transport mechanisms from experimental data by retaining their time dependencies, that is found to match, quantitatively, the gyrokinetic predictions for Prandtl and pinch numbers, within experimental uncertainties.

Isotope effects on energy transport in the core of ASDEX-Upgrade tokamak plasmas: Turbulence measurements and model validation

Design and operation of future tokamak fusion reactors using a deuterium–tritium 50:50 mix requires a solid understanding of how energy confinement properties change with ion mass. This study looks at how turbulence and energy transport change in L-mode plasmas in the ASDEX Upgrade tokamak when changing ion species between hydrogen and deuterium. For this purpose, both experimental turbulence measurements and modeling are employed. Local measurements of ion-scale (with wavevector of fluctuations perpendicular to the B-field k⊥< 2 cm−1, k⊥ρs< 0.2, where ρs is the ion sound Larmor radius using the deuterium ion mass) electron temperature fluctuations have been performed in the outer core (normalized toroidal flux ρTor=0.65−0.8) using a multi-channel correlation electron cyclotron emission diagnostic. Lower root mean square perpendicular fluctuation amplitudes and radial correlation lengths have been measured in hydrogen vs deuterium. Measurements of the cross-phase angle between a normal-incidence reflectometer and an ECE signal were made to infer the cross-phase angle between density and temperature fluctuations. The magnitude of the cross-phase angle was found larger (more out-of-phase) in hydrogen than in deuterium. TRANSP power balance simulations show a larger ion heat flux in hydrogen where the electron-ion heat exchange term is found to play an important role. These experimental observations were used as the basis of a validation study of both quasilinear gyrofluid trapped gyro-Landau fluid-SAT2 and nonlinear gyrokinetic GENE codes. Linear solvers indicate that, at long wavelengths (k⊥ρs<1), energy transport in the deuterium discharge is dominated by a mixed ion-temperature-gradient (ITG) and trapped-electron mode turbulence while in hydrogen transport is exclusively and more strongly driven by ITG turbulence. The Ricci validation metric has been used to quantify the agreement between experiments and simulations taking into account both experimental and simulation uncertainties as well as four different observables across different levels of the primacy hierarchy.

Global gyrokinetic simulation for toroidal impurity mode turbulence

In this study, global gyrokinetic simulations of the toroidal impurity mode (tIM) turbulence are performed. A linear analysis shows that the tIM is an instability that occurs in the bad curvature region when the density gradients of bulk ions and impurities are in opposite directions. The tIM can be unstable even when the temperature profiles are flat. In the presence of temperature gradients, the tIM and toroidal ion temperature gradient (tITG) mode could coexist. For the small temperature gradient, the tIM is found to be dominant. The tIM turbulence drives the large inward impurity and outward ion particle transports. Furthermore, the inward ion heat flux driven by the tIM turbulence causes the ion temperature profile to be more peaked than the initial one. For the large temperature gradient, while such inward ion heat flux does not occur because of the dominant tITG mode, the large inward impurity and outward ion particle fluxes are still observed due to the subdominant tIM. These results indicate that the tIM plays an important role in turbulent heat and particle transport when impurities are injected.

High heat flux reduction to materials using current filaments

Reducing high electron and ion heat fluxes is one of the critical issues for shielding satellites and spacecraft. One of the ideas for shielding high particle and heat fluxes is to apply an external magnetic field generated by injecting current filaments. In this work, we model a flow of plasma, which includes electrons and ions in a small region, by using two spatial dimensions and three coordinates for velocities (2D3V) Particle-In-Cell (PIC) code to study the effects of the injected current filaments on particle and heat fluxes to the wall. The plasma enters the simulation domain from the source region at the left boundary and is fully absorbed in the conductor wall at the right boundary. Current filaments are injected to change the magnetic field structure of the system. We compare particle density, particle flux, and heat flux with and without injecting the current filaments into the domain in two dimensions. Based on the simulation results, we found that injecting current filaments can reduce the peak fluxes to the wall and transfer some of those fluxes along the wall. Therefore, injecting the current filaments is a good candidate for shielding satellites and spacecraft from high-energy ion and electron fluxes.