Ion Heat Conductivity Research Articles

Effects of hydrogen isotope species on ITG microturbulence in LHD

The linear and nonlinear effects of hydrogen isotope species on ion temperature gradient (ITG) instability in the Large Helical Device (LHD) stellarator are studied using radially global gyrokinetic simulation. We found that the coupling range of linear toroidal harmonics depends on the ion mass of the hydrogen isotope. The growth rates of ITG mode are almost the same for H, D, and T plasmas, indicating a gyro-Bohm scaling of ion-mass dependence. The nonlinear electrostatic simulations show that the zonal flow breaks the radially elongated eigenmode structures and reduces the size of the turbulence eddies, which suppresses the turbulence and the ion heat transport in the LHD. The turbulence amplitude without the zonal flow is almost the same for H, D, and T plasmas, while it decreases with increasing ion mass of the hydrogen isotope when the zonal flow is present. The reduction of the turbulent transport with larger ion mass is mostly due to the enhancement of zonal flows by larger ion mass. The ion heat conductivity deviates from the gyro-Bohm scaling for both cases with and without the zonal flow.

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.

(Invited) On Non-equilibrium Thermodynamics in Electrochemical Systems

Much of our understanding of physical behavior of materials is based on the concept of equilibrium, which lies at the heart of classical thermodynamics, condensed matter physics, and modern reaction kinetics. If a thermodynamic system is in equilibrium conditions, which is the situation when an energy system (e.g., a fuel cell or a battery) is under open circuit voltage, the surface and bulk of the electrode are only subject to fluctuation of thermodynamic qualities. For the cases that are not at equilibrium, but are close to it, Onsager established linear reciprocal relationships between flux and thermodynamic force for a thermodynamic system in nonequilibrium states. These linear relationships are manifested in transport phenomena, which are non-equilibrium processes, such as ion diffusion and heat conduction.When an electrochemical reaction takes place at an electrode of a fuel cell, electrolyzer, or battery, the thermodynamic system is far away from equilibrium. Therefore, the thermodynamic states of the surface and bulk of an electrode are subject to external thermodynamic forces. As a result, in an active electrode, the electrochemical reaction on the surface causes all thermodynamic variables to change in both the surface and the bulk. In this talk, I will use solid oxide cells and lithium-ion batteries as an example to address three questions related to materials in non-equilibrium thermodynamic states: (i) how do fast kinetics and high current in an operating electrochemical cell affect the thermodynamic states of its material constituents, (ii) whether or not the state of non-equilibrium can remain stable with constant flow of matter and energy, and (iii) what is the origin that governs activity and stability in solid oxide cells?

The performance of equilibrium radial electric field shear on microturbulence with different magnetic shears in tokamak plasmas

Global gyrokinetic particle simulations show that equilibrium radial electric field (E r ) shear reduces the linear growth rate, ion heat conductivity, and nonlinear turbulence amplitude for both the ion temperature gradient (ITG) and kinetic ballooning mode (KBM) microturbulence by tilting the poloidal mode structure. The increase in the magnetic shear enhances the stabilizing performance of the E r shear on linear growth rate for the ITG case but has no effect on that for the KBM case. The radial correlation length of the ITG turbulence is decreased by increasing the magnetic shear in a weak ion diamagnetic flow shear condition with low β, leading to a reduction in the effective E × B shearing rate, which weakens the suppression performance of the E r shear on the ITG turbulence amplitude. In contrast, under a larger ion diamagnetic shear flow for higher β, an increase in magnetic shear strengthens the suppression performance of the E r shear on the KBM turbulence amplitude due to an increase in the effective shearing rate by increasing the radial correlation length of the turbulence.

Promoting ion and heat transfer of solid polymer electrolytes by tuning polymer chain length and salt concentration

ABSTRACT The heat and mass performance of solid polymer electrolytes (SPEs) directly affects their application in solid-state batteries (SSBs). However, high crystallinity and charged clusters hinder the transport of Li+ in SPEs, resulting in low ion diffusivities and thermal conductivities. Therefore, understanding the effects of SPE structure on ion transport and heat conduction is critical for SPE designing. In this work, the ion diffusivities and thermal conductivities of SPEs containing polyethylene oxide (PEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt with different PEO chain lengths and salt concentrations are studied and the structural properties are analyzed to determine the mechanisms of ion transport and heat conduction. The results show that the crystallinity and charged clusters decrease in SPEs with short-chain PEO and low salt concentration, thereby improving ion transfer and heat conduction. Moreover, phonon spectra shift to a higher-frequency domain when salt concentration increases, which induces a decrease in thermal conductivity. Decreased salt concentration and chain length increased conductivity by 350% and 176%, respectively, and thermal conductivity by 122% and 140%, respectively. These findings, which indicate that SPEs with short-chain PEO and low salt concentration have better ion and heat transfer, provide valuable insight into the design of PEO-LiTFSI electrolytes.

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.

Parametric dependencies of anomalous ion heat conductivity in T-10 plasma with Ohmic heating

Ion heat conductivity in deuterium plasma of the circular limiter tokamak T-10 is analyzed in more than 100 Ohmic shots. Four data scans: plasma density, effective charge, plasma current, and toroidal magnetic field are presented. Each scan is formed with the preservation of other parameters. It is shown that at the plasma periphery, r/a=0.6−0.8, the ion heat conductivity exceeds neoclassical values up to three to eight times. The anomalous part χian increases with plasma density and effective charge, while it decreases with plasma current and does not depend on the toroidal magnetic field. The highest value of χian is observed in high-density low-current regimes. More negative values of plasma electric potential correlate with higher values of χian. The empirical scaling of χian is derived. The transport model based on this scaling allows us to describe experimental profiles of ion temperature Ti(r) within experimental error ±15%.

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.

Validation of low-Z impurity transport theory using boron perturbation experiments at ASDEX upgrade

An experimental technique has been developed at ASDEX upgrade (AUG) to separately identify the diffusive and convective components of the boron particle flux. Using this technique a database of B transport coefficients has been assembled that shows that the normalized ion temperature gradient () is the strongest organizing parameter for both the B diffusion and convection and large is a necessary ingredient to obtain hollow B density profiles in AUG. This database also shows that large changes in the applied neutral beam injection (NBI) have a relatively small impact on impurity transport compared to similar changes in electron cyclotron resonance heating (ECRH). Even low levels of ECRH power dramatically increase both the diffusive and convective fluxes and lead to peaking of the impurity density profile. Comparisons to a combination of neoclassical and quasi-linear gyrokinetic simulations show good agreement in the measured and predicted diffusion coefficients. The outward convection measured in NBI dominated plasmas, however, is not well captured by the simulations, despite the inclusion of fast ions. In contrast, the convection is reasonably well reproduced for plasmas with flat or peaked boron density profiles. This dataset provides an excellent experimental validation of the non-monotonic, predicted, convective-particle-flux created by the combination of pure-pinch, thermo-diffusion, and roto-diffusion. In addition, this dataset demonstrates a non-monotonic dependence of the experimental particle diffusivity to ion heat conductivity (D/χ i) in qualitative agreement with theoretical predictions.

Improved neoclassical plasma confinement and turbulence suppression in a magnetic well in tokamak reactors

It has been known that the width of the trapped particles, i.e. bananas, is reduced or squeezed in a magnetic well in tokamaks. The magnetic squeezing factor S B depends on the energy and pitch angle of the particles. When ρ p/a ∼ 1, S B becomes appreciably larger than unity; it can be of the order of 2 for a parabolic well with B −1 d2 B/dr 2 ∼ 2a −2. Here, ρ p is the poloidal gyro-radius, B is the magnetic field strength, r is the local minor radius, and a is the minor radius. However, the real orbit width measured in terms of the poloidal magnetic flux is still less than a because of the magnetic squeezing; for S B = 2, it is a 30% reduction. The transport consequences of the squeezed bananas in a magnetic well are calculated by solving the drift kinetic equation utilizing the constants of motion in the large aspect ratio limit. Consequently, neoclassical ion heat conductivity χ h in the reactor relevant collisionality regime (i.e. banana regime) is reduced by a factor of ; for S B = 2, it is almost a factor of three reduction for the same temperature. The ion temperature scaling of χ h improves from the conventional, and weakly favorable scaling to the strongly favorable scaling for high temperature fusion grade tokamak plasmas; the scaling however does not take the temperature dependence of the magnetic well itself into account. Here, T i is the ion temperature. In addition, it is shown that plasma turbulence is suppressed in a magnetic well using the reduced decorrelation time argument and anomalous plasma confinement is improved. The combined improvements result in a favorable temperature scaling in the ion energy confinement time, and make burning aneutronic fuels feasible. The implications on a tokamak with a magnetic well as a fusion reactor are discussed.

Global gyrokinetic simulation of neoclassical ambipolar electric field and its effects on microturbulence in W7-X stellarator

Global neoclassical simulations of a model equilibrium of the W7-X stellarator find an ambipolar electric field with either an ion root or an electron root solution depending on the temperature ratio between electrons and ions. The ambipolar electric field is then used as an equilibrium field in the turbulence simulations of ion temperature gradient (ITG) instability. The shear of the ambipolar electric field has modest effects on the ITG linear instability, nonlinear saturation amplitude, and turbulent transport in the ion root case. However, in the electron root case, the ambipolar electric field significantly reduces the linear ITG growth rate, turbulence intensity, and radial correlation length, resulting in an ion heat conductivity comparable to the neoclassical transport level in the strong shear region.

Effects of equilibrium radial electric field on ion temperature gradient instability in the scrape-off layer of a field-reversed configuration

Linear and nonlinear effects of the equilibrium radial electric field on the ion temperature gradient (ITG) instability in the scrape-off layer (SOL) of a field-reversed configuration have been studied using gyrokinetic particle simulations for a single toroidal mode. Linear simulations with adiabatic electrons find that the flow shear reduces the growth rate and causes a radial tilting of the mode structure on the toroidal plane. Nonlinear simulations find that the flow shear significantly decreases ITG saturation amplitude and ion heat transport in the SOL by reducing both turbulence intensity and eddy size. The turbulence intensity is determined by fluid eddy rotation, which is the dominant saturation mechanism for the SOL ITG instability with a single toroidal mode number. On the other hand, parallel wave-particle decorrelation is the dominant mechanism for the SOL ITG turbulent transport. A random walk model using the guiding center radial excursion as the characteristic length scale and the eddy turnover time as the characteristic time scale fits very well to the scaling of ion heat conductivity with the flow shear.

A mechanism of ion temperature peaking by impurity pellet injection in a heliotron plasma

Experiments on the Large Helical Device with the injection of carbon pellets into discharges of low density have demonstrated a significant reduction of the ion heat conduction in the plasma core and an increase in the central ion temperature by a factor of up to 2. These results are interpreted in the framework of a transport model elaborated on the basis of those applied previously to explain the improvement in confinement by impurity seeding into the tokamak devices TEXTOR and JET. The calculations performed reproduce well the strong peaking of the ion temperature profile with increasing carbon density nZ and the consequent drop in the confinement as nZ exceeds a certain critical level. The importance of different elements in the model, such as braking of the main ion rotation by friction with impurity ones and the shape of the density profiles, are investigated. A qualitative assessment of the applicability under fusion reactor conditions, e.g. of much higher plasma density and heating power, is performed.

Ripple transport and neoclassical diffusion in IR-T1 tokamak

In tokamaks, small variations in the magnetic field create ripple. The discontinuous nature of the magnetic field coils in an axisymmetric torus conduces to additional particle trapping, and it is responsible for an additional neoclassical diffusion. Ripples also reduce the particle removal efficiency and disturb plasma confinement and cause constraints in the design of magnet of fusion reactor. Therefore, it is quite important to include the ripple for the design of plasma edge components. Herein, several considerations are taken into account to calculate and evaluate the diffusion coefficient and ion heat conductivity in ripple transport and also to compare it with neoclassical mode.

Synthetic edge and scrape-off layer diagnostics—a bridge between experiments and theory

The scrape off layer (SOL) plasma in a Tokamak device and its coupling with the edge dictate the performance of a discharge to a high degree—especially as all plasma has to go through the SOL, which is the main exhaust channel for the hot plasma. This contribution provides an introduction to the modelling efforts of the plasma dynamics in the SOL and the edge regions. We employ a fully dynamical fluid model, the HESEL code. HESEL is equipped with synthetic diagnostic tools as probe arrays, Li-beam spectroscopy, and Gas Puff Imaging. Using the synthetic probe arrays to measure the electron and ion heat advection and conduction we obtain the upstream power fall-off length for a broad range of plasma parameters and by applying non-linear fitting procedures we derive the scaling of the fall-off length. The obtained results are in agreement with recent experimental observations from L-mode ASDEX Upgrade data. A workflow for generating synthetic Lithium beam data, where the fluctuation data from HESEL are passed to the RENATE code are discussed using experimental results from ASDEX Upgrade.

Characteristics of trapped electron transport, zonal flow staircase, turbulence fluctuation spectra in elongated tokamak plasmas

The effects of plasma elongation on trapped electron mode (TEM) driven turbulence and transport are investigated with detailed analyses of fluctuation, zonal flow and zonal pressure. For the study, global nonlinear TEM simulations with different elongations () are performed by employing a bounce-averaged gyrokinetic code gKPSP. From the simulations, -scalings of the electron heat conductivity (), ion heat conductivity (), and particle diffusivity () are found as , and , respectively. Higher plasma elongation is found to enhance zonal flows and their shearing rate at short radial scales, which in turn reduce the radial correlation length of turbulence and limit avalanche-like large scale transport events. Radial corrugations of density and temperature profiles also emerge due to quasi-stationary zonal flows at short spatial scales. In addition, it is found that the Doppler shift caused by the quasi-stationary zonal flows can modify the phase velocity of fluctuation in the laboratory frame and result in turbulence spectra consisting of components propagating in both electron and ion diamagnetic directions, while the transport is mainly governed by TEM.

Ion heat transport in ohmic plasmas of the T-10 tokamak

Results of the investigation of ion heat transport processes in the T-10 tokamak are presented. Experiments are carried out in a wide range of ohmic plasma parameters (ne, Ipl, and Zeff). Variation of the effective ionic charge from 3.5–4 to 1 is performed by inserting a lithium limiter. Measurements of the ion and electron temperature and density profiles are presented. The power balance approach is used for the determination of the ion heat conductivity. Modeling is performed using the ASTRA transport code. It is shown that in ohmic plasmas in the region of r/a ~ 0.5, ion heat conductivity is close to the neoclassical values, which are calculated using the NCLASS code.

An improved and fully implicit multi-group non-local electron transport model and its validations

The combined effect of thermal flux inhibition and non-local electron heat flux in the radiation hydrodynamics (RHD) simulation of laser-driven systems can be accurately predicted by using non-local electron transport (NLET) models. These models can avoid commonly used space and time-independent ad-hoc flux-limiting procedures. However, the use of classical electron collision frequency in these models is rigorously valid for high temperature non-degenerate plasmas. In laser-driven systems, the electron thermal energy transport is important in regions between the critical density and ablation surface where the plasma is partially degenerate. Therefore, an improved model for electron collision frequency in this regime is required to accurately predict the thermal energy transport. Previously, we have reported an improved single group non-local electron transport model by using a wide-range electron collision frequency model valid from warm-dense matter (WDM) to fully ionized plasmas. In this work, we have extended this idea into a two-dimensional multi-group non-local electron transport (MG-NLET) model. Moreover, we have used a fully implicit numerical integration scheme in which the models for multi-group thermal radiation transport, laser absorption, electron-ion thermal energy relaxation and ion heat conduction are included in a single step. The performance of this improved MG-NLET model has been assessed by comparing the simulated foil trajectories with the reported experimental data for laser-driven plastic foils. The results indicate that the improved model yields results that are in better agreement with the experimental data.

Collisionality dependence and ion species effects on heat transport in He and H plasma, and the role of ion scale turbulence in LHD

Surveys of the ion and electron heat transports of neutral beam (NB) heating plasma were carried out by power balance analysis in He and H rich plasma at LHD. Collisionality was scanned by changing density and heating power. The characteristics of the transport vary depending on collisionality. In low collisionality, with low density and high heating power, an ion internal transport barrier (ITB) was formed. The ion heat conductivity (χi) is lower than electron heat conductivity (χe) in the core region at ρ < 0.7. On the other hand, in high collisionality, with high density and low heating power, χi is higher than χe across the entire range of plasma. These different confinement regimes are associated with different fluctuation characteristics. In ion ITB, fluctuation has a peak at ρ = 0.7, and in normal confinement, fluctuation has a peak at ρ = 1.0. The two confinement modes change gradually depending on the collisionality. Scans of concentration ratio between He and H were also performed. The ion confinement improvements were investigated using gyro-Bohm normalization, taking account of the effective mass and charge. The concentration ratio affected the normalized χi only in the edge region (ρ ~ 1.0). This indicates ion species effects vary depending on collisionality. Turbulence was modulated by the fast ion loss instability. The modulation of turbulence is higher in H rich than in He rich plasma.

Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

AbstractThe one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ0 ≤ 100ρs, where ρs is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 1019 W/cm2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ0 ≈ 1 g/cm2, and G &gt; 2000 at Hρ0 ≈ 5 g/cm2. To evaluate the ignition energy Eig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence Eig ~ ρ0−2 and gives Eig = 160 kJ for ρ0 = 100ρs ≈ 22 g/cm3.