Parallel Heat Conduction Research Articles

Tokamak edge-SOL turbulence in H-mode conditions simulated with a global, electromagnetic, transcollisional drift-fluid model

Abstract The design of commercially feasible magnetic confinement fusion reactors strongly relies on the reduced turbulent transport in the plasma edge during operation in the high confinement mode (H-mode). We present first global turbulence simulations of the ASDEX Upgrade tokamak edge and scrape-off layer in ITER baseline H-mode conditions. Reasonable agreement with the experiment is obtained for outboard mid-plane measurements of plasma density, electron and ion temperature, as well as the radial electric field. The radial heat transport is underpredicted by roughly 1/3. These results were obtained with the GRILLIX code implementing a transcollisional, electromagnetic, global drift-fluid plasma model, coupled to diffusive neutrals. The transcollisional extensions include neoclassical corrections for the ion viscosity, as well as either a Landau-fluid or free-streaming limited model for the parallel heat conduction. Electromagnetic fluctuations are found to play a critical role in H-mode conditions. We investigate the structure of the significant E × B flow shear, finding both neoclassical components as well as zonal flows. But unlike in L-mode, geodesic acoustic modes are not observed. The turbulence mode structure is mostly that of drift-Alfvén waves. However, in the upper part of the pedestal, it is very weak and overshadowed by neoclassical transport. At the pedestal foot, on the other hand, we find instead the (electromagnetic) kinetic ballooning mode, most clearly just inside the separatrix. Our results pave the way towards predictive simulations of fusion reactors.

Ion heating/transport characteristics of the merging startup plasma scenario in the TS-6 spherical tokamak

Here we report the ion heating/transport characteristics of the merging startup scenario in the TS-6 spherical tokamak. In addition to the previously investigated impulsive heating process during magnetic reconnection, here we also focus on a longer time scale response of the ion temperature profile both during and after merging, including the semi-steady plasma confinement phase. During magnetic reconnection, (i) the ion temperature profile forms a poloidally asymmetric profile around the X-point in the initiation phase and (ii) radially asymmetric higher deposition is obtained at the high field side. After merging, (iii) the radially asymmetric double-peak structure is affected by parallel heat conduction and is aligned with field lines, but it does not simply become a flux function on a microsecond time scale—inboard/outboard asymmetry lasts even in the semi-steady confinement phase. (iv) Under the influence of the low-aspect-ratio configuration, there is a two to three times higher toroidal field on the high-field side on the same closed flux surface: characteristic asymmetry of inboard/outboard ion temperature has been found experimentally for the first time.

The thermal conductivity of graphite composite insulation boards: A theoretical and experimental study

Graphite composite insulation boards (GCIB) have emerged as a promising solution in the construction industry, offering a combination of fire resistance, high temperature stability, and excellent insulation properties. As their usage continues to increase, it is crucial to develop and validate a more accurate theoretical model for the effective design and optimization of building insulation systems. Traditional models including series and parallel models are employed for estimating the thermal conductivity of GCIB but revealed higher relative errors and lower theoretical calculation accuracy. Therefore, the primary objective is to design and validate a more efficient theoretical model for thermal conductivity prediction in GCIB. This paper investigates the thermal conductivity of GCIB under varying composition ratios by designing a novel Parallel-Series Parallel (PSP) approach. The PSP model is designed based on a single basic cell where the graphite polystyrene particles are employed as the matrix material while cement, vitrified microspheres, and silica fume are used as inclusion materials. Then, the thermal conductivity unit is divided into three parallel heat conduction subunits where the matrix materials and inclusion materials in the three subunits are integrated in a series-parallel manner to provide a more realistic representation of the heat transfer mechanisms within the composite. For a comprehensive assessment, the study encompasses theoretical analysis, empirical assessment, and finite element (FE) simulations to illustrate its thermal properties. The predicted thermal conductivity reveals perfect consensus in comparison with the FE and experimental test outcomes by achieving lower relative errors of 2.7 %∼3.8 % and 1.9 %∼ 3.0 % respectively. The model validated through numerical simulations and sample experiments illustrates a significant improvement in accuracy of about 76.4 %∼94.3 % when compared to traditional series and parallel methods. Prominently, the findings indicate that the thermal conductivity of GCIBs declines considerably as the volumetric ratio of graphite polystyrene particles (Ф1/Ф3) increases and stabilizes when the proportion reaches 10, emphasizing the importance of optimizing material composition to enhance the thermal performance of GCIB. Overall, the validated PSP model by accurately determining the thermal conductivity of GCIB serves as a reliable tool for designing and optimizing high-performance insulation materials, contributing to energy efficiency and sustainability in building and construction industries.

Amorphous-like thermal conductivity and high mechanical stability of cyclopentane clathrate hydrate.

The thermal conductivity κ of cyclopentane clathrate hydrate (CP CH) of type II was measured at temperatures down to 100 K and at pressures up to 1.3 GPa. The results show that CP CH displays amorphous-like κ characteristic of many crystalline clathrate hydrates, e.g., tetrahydrofuran (THF) CH. The magnitude of κ is 0.47 W m-1 K-1 near the melting point of 280 K at atmospheric pressure, and it is almost independent of pressure and temperature T: ln κ = -0.621-40.1/T at atmospheric pressure (in SI-units). This is slightly less than κ of type II CHs of water-miscible solvents such as THF. Intriguingly, unlike other water-rich type II clathrate hydrates of water-miscible molecules M (M·17 H2O), CP CH does not amorphize at pressures up to 1.3 GPa at 130 K and also remains stable up to 0.5 GPa at 240 K. This shows that CP CH is mechanically more stable than the previously studied water-rich type II CHs, and suggests that repulsive forces between CP and the H2O cages increase the mechanical stability of crystalline CP CH. Moreover, we show that κ of an ice-CH mixture, which often arises for CHs that form naturally, is described by the average of the parallel and series heat conduction models to within 5% for ice contents up to 22 wt%. The findings provide a better understanding of the thermal and stability properties of clathrate hydrates for their applications such as gas storage compounds.

Microscopic thermal characteristics of parallelly arranged nanowires in a liquid: the role of interface thermal resistance, solid-like liquid layer, and the restricted phonon transport

Nanofluids based on extended nanostructures, such as nanowires, have been demonstrated improved thermal conductivities (κ). However, the lack of a complete understanding at the microscopic level hinders the development of such nanofluids towards practical applications. We aim to provide it by investigating how the interface thermal resistance (R b ), ballistic phonon transport, and the solid-like liquid layer affect the heat conduction in nanowire-based nanofluids. By employing Non-Equilibrium Molecular Dynamics (NEMD), it is found that the heat conduction in the parallelly arranged liquid and the nanowires exhibit a coupled thermal behavior owing to the R b . This contradicts the predictions of the classical parallel heat conduction model, therefore, a novel model is proposed taking this coupled behavior into account. Using this model, it is shown that the high κ of the solid phase has a limited contribution to the effective κ of nanofluids having short nanowires due to the dominant R b effect. For the case of long nanowires, however, the individual nanowire κ becomes a vital parameter defining the effective κ. Further, NEMD calculations reveal that the κ of suspended nanowires in a liquid is markedly reduced, questioning the validity of classical effective medium theories which use the bulk parameters. This reduction is attributed to surface atoms’ restricted vibrational freedom and the nanowire’s phonon-boundary scattering. By substituting this reduced κ of the solid phase into the new mathematical model, the theoretical predictions align closely with the NEMD calculations, exhibiting deviations below 10%. The sole contribution from the solid-like liquid layer to the κ enhancement lies between 20%–30% in the nanofluids presently considered. Therefore, the findings of this study highlight the important roles play by the identified microscopic thermal characteristics in defining the effective κ of nanofluids based on nanowires.

Effect of magnetic geometry on the energy partition between ions and electrons in the scrape-off layer of magnetic fusion devices

A universal energy partition mechanism between ions and electrons has been confirmed to exist in the scrape-off layer of both the WEST tokamak and the W7-X stellarator. A peaked plasma density structure induced by an infinite magnetic connection length structure is observed to destroy this dependence and enhance the local ion and electron temperature ratio in the stellarator. A theoretical analysis reveals that the ratio of ion and electron parallel heat conduction is predominant in determining this universality, while electrons would further be cooled in the density-peaked region.

Assessment of the impact of the kinetic effect of ion parallel heat conduction on DEMO-relevant SOL plasma using integrated SOL-divertor code SONIC

In plasmas of lower collisionality, such as the scrape-off layer (SOL) of a fusion tokamak device, the parallel heat conductivity of ions becomes smaller than the classical Spitzer–Harm model due to a nonlocal kinetic effect. We have assessed, by simulation, the impact and role of the kinetic effect of ion heat conductivity (abbreviated as ion KE in this paper) on DEMO-relevant tokamak SOL plasma, using the Japanese demonstration tokamak reactor concept JA DEMO. A series of test simulations, where the ion KE is modeled by a widely used free-streaming energy (FSE)-limited model, has demonstrated: (a) the ion KE decreases the ion parallel heat flux density in JA DEMO SOL (at the baseline operation scenario) around the X-point and further upstream of the low-field side (LFS) area along the separatrix, where the parallel collisionality is smaller. Up to 40%–60% decrease is observed, compared to the case without (w/o) ion KE, among the test cases where the ion KE level is scanned over the possible range (i.e. parameter α i of the FSE-limited model is varied over ); (b) the ion KE leads to significant increase in the ion temperature T i (up to 600% increase) and significant decrease in the ion density n i (up to −80%) over wide area of the SOL upstream. Energy balance analysis has suggested that the ion KE affects the upstream n i and T i by the power of 0.4 and −0.4, respectively, of the flux limiting factor, as long as spatial changes in plasma parameters are moderate. The results of this study serve as a fundamental assessment of the ion KE for DEMO- relevant SOL plasma, clarifying the need for further sophistication of the model toward more quantitative prediction.

A Study on the Various Modes of Parallel Heat Conduction in the Coronal Loops of Small and Large Solar Flares Using Scaling Laws

A Study on the Various Modes of Parallel Heat Conduction in the Coronal Loops of Small and Large Solar Flares Using Scaling Laws

Dual-pace transient heat conduction in vertically aligned carbon nanotube arrays induced by structure separation

Vertically aligned arrays of carbon nanotubes (CNTs) are attractive for a wide range of macroscopic applications which can exploit the remarkable properties of individual nanotubes. In this work, an abnormal behavior of CNT bundles in heat conduction is discovered under the transient electro-thermal characterization. The measured voltage change over the sample shows a dual-pace thermal response (DTR), which could not be fitted using a single thermal diffusivity heat transfer model. Instead, two thermal diffusivities are determined from the DTR phenomenon. Three rounds of cryogenic experiments are conducted to investigate the physics behind DTR phenomenon. It starts to emerge when the temperature is reduced to a certain level. After two rounds of cryogenic experiments, the DTR phenomenon becomes permanent from 295 K to 10 K. The nano-scale structure separation induced by the increased thermal strain leads to macroscale structure separation, which results in two parallel heat conduction paths responsible for the DTR phenomenon. By building a new parallel heat transfer model taking both the transient and steady-state electrical and thermal response into consideration, the area ratio of separated CNTs is determined. This result uncovers the existence of coiled morphology and nano-structure evolution of CNTs under cryogenic state and its effect on thermal and electrical transport, especially on their transient behaviors. Knowledge of the thermal transport in these CNTs arrays is important considering the fact that transient thermal response strongly affects their mechanical, optical, and electrical behaviors.

Understanding detachment of the W7-X island divertor

The fundamental behavior of the W7-X island divertor under detached conditions, which has been theoretically predicted with the EMC3-Eirene code, is re-examined here under the experimental conditions achieved so far and compared with the first experimental results. Both simulations and experiments cover a range of divertor configurations and plasma parameters, and show the following common trends: (1) with rising impurity radiation, the target heat load decreases ‘uniformly’ over the entire target surface in the sense that both the peak and average heat loads can drop by an order of magnitude. Impurity radiation (mainly from intrinsic carbon) occurs primarily at the plasma edge and the resulting negative impact on the stored energy is less than 10%. (2) When the total radiation exceeds a critical level, the target particle flux (the recycling flux Γrecy) begins to fall and can drop by a factor of 3–5 at high radiation levels without an obvious indication of significant volume recombination. (3) While Γrecy decreases, the divertor neutral pressure continues to build up and reaches a maximum, at which point Γrecy has declined significantly. (4) During detachment, the electron temperature at the last closed flux surface falls in a way that is not quantitatively understandable from parallel classical heat conduction processes. This paper presents a physical explanation of the numerical/experimental results described above. Furthermore, using the EMC3-Eirene code as a diagnostic tool, we are able, apparently for the first time, to provide a full quantitative analysis of each transport channel in the island divertor, aiming to clarify how the island divertor plasma self-regulates to maintain particle, energy, and momentum balance under detached conditions.

Electric field and turbulence in global Braginskii simulations across the ASDEX Upgrade edge and scrape-off layer

Turbulence simulations in diverted geometry across the edge and scrape-off layer (SOL) of ASDEX Upgrade are performed with the GRILLIX code (Stegmeir et al 2019 Phys. Plasmas 26 052517). The underlying global (full-f) drift-reduced Braginskii model allows to concurrently study the self-consistent dynamics of the turbulence and the background as well as the evolution of toroidal and zonal flows. Different contributions to the radial electric field are identified. The dominant contribution on closed flux surfaces comes from the ion pressure gradient, due to the diamagnetic drift in the curved magnetic field. Large deviations can be induced, in particular, by the polarization particle flux, leading to zonal flows. The latter are driven by small-scale eddies, but do not exhibit much impact on the overall transport which is driven by ballooning modes at larger scales. Ion viscosity is found to be important in damping poloidal rotation through adjusting of the parallel velocity profile, but not via direct vorticity damping. The zonal flow drive peaks at the separatrix, where a strong shear layer forms due to the sheath-induced counter-propagating SOL flow, allowing for the formation of a transport barrier. The temperature profile across the separatrix is determined by the competition between cross-field transport and outflow in the SOL, the latter being largely controlled by the parallel heat conductivity.

Turbulence driven widening of the near-SOL power width in ASDEX Upgrade H-Mode discharges

Divertor heat flux data from infra red (IR) from various tokamaks in H-Mode regime show that the power width, , scales approximately like 1.6 (R/a) ρs,pol. However, the IR based scaling comes with the restriction that only discharges were considered with attached divertor conditions. Here we set up a new data base covering low edge density data but also including high density plasmas reaching the H-mode density limit. We use Thomson-scattering to measure the electron temperature decay length which will set the near-SOL power width through parallel heat conduction. We present scaling results for the density, temperature and pressure separatrix fall-off lengths. As the principal result we derive a generalized power width scaling which reads as where describes a normalized collisionality (). The parameter describes the relative importance of the interchange effect on drift-wave turbulence as proposed by Scott and is found to be closely linked to the diamagnetic parameter αd introduced by Rogers, Drake and Zeiler (RDZ). The edge operational space for ASDEX Upgrade displays a boundary qualitatively in agreement with the region labelled as density limit in the edge plasma phase space proposed by RDZ. The data base shows in the limit of low edge densities () accurate agreement to the IR based power width scaling. At elevated separatrix densities () the power width is broadened by a factor of up to about three accompanied by a reduction of the H98,y2 confinement factor. Plasmas with higher triangularity show higher values for H98,y2 in the same range of normalized collisionality.

Thermal dynamics in the flux‐coordinate independent turbulence code GRILLIX

AbstractGRILLIX employs the flux‐coordinate independent approach (FCI), which allows us to study boundary plasma turbulence in realistic diverted configurations. Recently, the physical model in GRILLIX has been extended to a global drift‐reduced Braginskii model, without any separation between background and fluctuations. It includes electromagnetic and thermal dynamics with hot ions, relaxation of the Boussinesq approximation and non‐linear parametric dependencies. This contribution presents solutions to associated issues, that is, the ion diamagnetic polarization and the stiff parallel heat conduction. Simulations based on parameters characteristic for the Alcator C‐Mod tokamak were carried out. In circular geometry, the self‐consistent electric field contains zonal flows and geodesic acoustic modes in the confined region. In the scrape‐off layer, the electron parallel heat conduction and its boundary condition determine the temperature and electric field, leading to sheared flows at the last closed flux surface.

Coronal Loop Scaling Laws for Various Forms of Parallel Heat Conduction

Abstract The solar atmosphere is dominated by loops of magnetic fluxes that connect the multi-million degree corona to the much cooler chromosphere. The temperature and density structure of quasi-static loops are determined by the continuous flow of energy from the hot corona to the lower solar atmosphere. Loop scaling laws provide relationships between global properties of the loop (such as the peak temperature, pressure, and length); they follow from the physical variable dependencies of various terms in the energy equation, and, hence, the form of the loop scaling law provides insight into the key physics that control the loop structure. Traditionally, scaling laws have been derived under the assumption of collision-dominated thermal conduction. Here, we examine the impact of different regimes of thermal conduction—collision-dominated, turbulence-dominated, and free-streaming—on the form of the scaling laws relating the loop temperature and heating rate to its pressure and half-length. We show that the scaling laws for turbulence-dominated conduction are fundamentally different than those for collision-dominated and free-streaming conduction, inasmuch as the form of the scaling laws now depend primarily on conditions at the low-temperature, rather than high-temperature, part of the loop. We also establish regimes in the temperature and density space in which each of the applicable scaling laws prevail.

Investigation of fine structure formation of guide field reconnection during merging plasma startup of spherical tokamak in TS-3U

Ion heating/transport and its fine structure formation process through magnetic reconnection have been investigated by high guide field tokamak merging experiments in TS-3 and TS-3U. In addition to the previously reported demonstration of high-temperature plasma startup without center solenoid, the detailed fine structure formation process of reconnection heating has been revealed using new 96CH/320CH ultra-high-resolution 2D ion Doppler tomography diagnostics. By identifying the double-axis field configuration with the X-point on the midplane using in situ magnetic probe diagnostics, the detailed measurement successfully revealed that the ion temperature profile forms two types of characteristic heating structure, both around the X-point and downstream. The former is affected by the Hall effect to form a tilted heating profile, while the latter is affected by the transport process which a forms a poloidal double-ring-like structure. The achieved ion heating mostly depends on the reconnecting component of the magnetic field, and the contribution of the guide field to decrease the heating efficiency tends to be saturated in the high guide field regime. Under the influence of better toroidal confinement with higher guide field, the downstream ion heating is transported vertically, mostly by parallel heat conduction, and finally forms a poloidal ring-like hollow distribution aligned with the closed flux surface at the end of merging.

On the role of finite grid extent in SOLPS-ITER edge plasma simulations for JET H-mode discharges with metallic wall

The impact of the finite grid size in SOLPS-ITER edge plasma simulations is assessed for JET H-mode discharges with a metal wall. For a semi-horizontal divertor configuration it is shown that the separatrix density is at least 30% higher when a narrow scrape-off layer (SOL) grid width is chosen in SOLPS-ITER compared to the case for which the SOL grid width is maximised. The density increase is caused by kinetic neutrals being not confined inside the divertor region because of the reduced extent of the plasma grid. In this case, an enhanced level of reflections of energetic neutrals at the low-field side (LFS) metal divertor wall is observed. This leads to a shift of the ionisation source further upstream which must be accounted for as a numerical artefact. An overestimate in the cooling at the divertor entrance is observed in this case, identified by a reduced heat flux decay parameters λqdiv. Otherwise and further upstream the mid-plane heat decay length λq parameter is not affected by any change in divertor dissipation. This confirms the assumptions made for the ITER divertor design studies, i.e. that λq upstream is essentially set by the assumptions for the ratio radial to parallel heat conductivity. It is also shown that even for attached conditions the decay length relations λne > λTe > λq hold in the near-SOL upstream. Thus for interpretative edge plasma simulations one must take the (experimental) value of λne into account, rather than λq, as the former actually defines the required minimum upstream SOL grid extent.

Heating and Cooling of Coronal Loops with Turbulent Suppression of Parallel Heat Conduction.

Using the "enthalpy-based thermal evolution of loops" (EBTEL) model, we investigate the hydrodynamics of the plasma in a flaring coronal loop in which heat conduction is limited by turbulent scattering of the electrons that transport the thermal heat flux. The EBTEL equations are solved analytically in each of the two (conduction-dominated and radiation-dominated) cooling phases. Comparison of the results with typical observed cooling times in solar flares shows that the turbulent mean free path λT lies in a range corresponding to a regime in which classical (collision-dominated) conduction plays at most a limited role. We also consider the magnitude and duration of the heat input that is necessary to account for the enhanced values of temperature and density at the beginning of the cooling phase and for the observed cooling times. We find through numerical modeling that in order to produce a peak temperature ≃1.5 × 107 K and a 200 s cooling time consistent with observations, the flare-heating profile must extend over a significant period of time; in particular, its lingering role must be taken into consideration in any description of the cooling phase. Comparison with observationally inferred values of post-flare loop temperatures, densities, and cooling times thus leads to useful constraints on both the magnitude and duration of the magnetic energy release in the loop, as well as on the value of the turbulent mean free path λT .

Simulation of self-generated magnetic fields in an inertial fusion hohlraum environment

We present radiation-hydrodynamic simulations of self-generated magnetic field in a hohlraum, which show an increased temperature in large regions of the underdense fill. Non-parallel gradients in electron density and temperature in a laser-heated plasma give rise to a self-generated field by the “Biermann battery” mechanism. Here, HYDRA simulations of three hohlraum designs on the National Ignition Facility are reported, which use a partial magnetohydrodynamic (MHD) description that includes the self-generated source term, resistive dissipation, and advection of the field due to both the plasma flow and the Nernst term. Anisotropic electron heat conduction parallel and perpendicular to the field is included, but not the Righi-Leduc heat flux. The field strength is too small to compete significantly with plasma pressure, but affects plasma conditions by reducing electron heat conduction perpendicular to the field. Significant reductions in heat flux can occur, especially for high Z plasma, at modest values of the Hall parameter, Ωeτei≲1, where Ωe=eB/mec and τei is the electron-ion collision time. The inclusion of MHD in the simulations leads to 1 keV hotter electron temperatures in the laser entrance hole and high-Z wall blowoff, which reduces inverse-bremsstrahlung absorption of the laser beam. This improves propagation of the inner beams pointed at the hohlraum equator, resulting in a symmetry shift of the resulting capsule implosion towards a more prolate shape. The time of peak x-ray production in the capsule shifts later by only 70 ps (within experimental uncertainty), but a decomposition of the hotspot shape into Legendre moments indicates a shift of P2/P0 by ∼20%. This indicates that MHD cannot explain why simulated x-ray drive exceeds measured levels, but may be partially responsible for failures to correctly model the symmetry.

ANOMALOUS COOLING OF CORONAL LOOPS WITH TURBULENT SUPPRESSION OF THERMAL CONDUCTION

ABSTRACT We investigate the impact of turbulent suppression of parallel heat conduction on the cooling of post-flare coronal loops. Depending on the value of the mean free path associated with the turbulent scattering process, we identify four main cooling scenarios. The overall temperature evolution, from an initial temperature in excess of 107 K, is modeled in each case, highlighting the evolution of the dominant cooling mechanism throughout the cooling process. Comparison with observed cooling times allows the value of to be constrained, and interestingly this range corresponds to situations where collision-dominated conduction plays a very limited role, or even no role at all, in the cooling of post-flare coronal loops.

Two-fluid description of wave-particle interactions in strong Buneman turbulence

To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation while a plasma is unstable to the Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. We show that both energy dissipation and momentum transport along electric current in the current layer are locally quasi-static, but globally dynamic and irreversible. Turbulent drag dissipates both the streaming energy of the current sheet and the associated magnetic energy. The net loss of streaming energy is converted into the electron component heat conduction parallel to the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that relates the turbulence-induced convective momentum transport and thermal momentum transport. Electron trapping and de-trapping drive local momentum transports, while phase mixing converts convective momentum into thermal momentum. The drag acts like a micro-macro link in the anomalous heating processes. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons, but most of the magnetic energy is dissipated and converted into the component heat of electrons perpendicular to the magnetic field. This heating process is decoupled from the heating of Buneman instability in the current sheets. Ion heating is weak but ions play an important role in assisting energy exchanges between waves and electrons. Cold ion fluid equations together with our electron fluid equations form a complete set of equations that describes the occurrence, growth, saturation and decay of the Buneman instability.