Parallel Heat Transport Research Articles

Reversed-direction 2-point modelling applied to divertor conditions in DIII-D *

A predictive form of the extended 2-point model known as the ‘reverse 2-point model’, Rev2PM, is applied to a range of detachment levels in the open lower divertor of DIII-D, showing that the experimentally measured electron temperature (Te ) and pressure (pe ) at the divertor entrance can be calculated within 50% from target measurements, if and only if a posteriori corrections for convective heat flux are included in the model. Unlike the standard 2-point model, the Rev2PM calculates upstream scrape-off layer (SOL) quantities (such as separatrix Te and pe ) from target conditions (such as Te and parallel heat flux), with volumetric power and momentum losses depending solely on target Te . The Rev2PM is tested against a database of DIII-D inter-ELM divertor Thomson scattering measurements, built from a series of 6 MW, 1.3 MA, LSN H-mode discharges with varied main ion density, drift direction, and nitrogen puffing rate. Measured target Te ranged from 0.4–25 eV over this database, and upstream Te ranged from 5–60 eV. Poor agreement is found between upstream measurements and Rev2PM calculations that assume purely conductive parallel heat transport. However, introducing a posteriori corrections to account for convective heat transport brings the Rev2PM calculations within 50% of the measured upstream values across the dataset. These corrections imply that up to 99% of the parallel heat flux is carried by convection in detached conditions in the DIII-D open lower divertor, though further work is required to assess any potential dependencies on device size or divertor closure.

Evaluation of Relationship between Heat Transport and Flow Pattern of Parallel Tube Heat Transport Devices under Heat Flux Heating Conditions

Evaluation of Relationship between Heat Transport and Flow Pattern of Parallel Tube Heat Transport Devices under Heat Flux Heating Conditions

Enhanced preconditioner for JOREK MHD solver

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation tool for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. The code is usually run with a fully implicit time integration allowing to use large time steps independent of a CFL criterion. This is particularly important due to the strong scale separation between transport processes and slowly growing resistive modes in contrast to fast time scales associated with MHD waves and fast parallel heat transport. For solving the resulting large sparse-matrix system iteratively in each time step, a preconditioner based on the assumption of weak coupling between the toroidal harmonics is applied. The solution for each harmonic matrix is determined independently in this preconditioner using a direct solver. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. The developments include the implementation of a complex solver interface for the preconditioner leading to the general reduction of memory consumption. The most significant development presented consists in a generalization of the physics based preconditioner to ‘mode groups’, which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps, and thus improving the overall time performance by more than a factor of 3.

Kinetic model of the COMPASS tokamak SOL

Abstract In this work we report on results of full size kinetic modelling of the COMPASS tokamak SOL. Presented simulations indicate, that i. kinetic effects are significant in the inner divertor (ID) plasma; ii. normalized power loads to the ID are above the classical values and are caused by non-Maxwellian super-thermal electrons; iii. different divertor current regimes do not influence overall SOL parameters, except those of the divertor sheath; iv. ions at the divertors plasma are colder than the electrons; v. parallel heat transport is strongly non-local. Modelling results are in a reasonable agreement with the experimental measurements.

Runaway electron seed formation at reactor-relevant temperature

Systematic variation of the pre-disruption core electron temperature (Te) from 1 to 12 keV using an internal transport barrier scenario reveals a dramatic increase in the production of ‘seed’ runaway electrons (REs), ultimately accessing near-complete conversion of the pre-disruption current into sub-MeV RE current. Injected Ar pellets are observed to ablate more intensely and promptly as Te rises. At high Te, the observed ablation exceeds predictions from published thermal ablation models. Simultaneously, the thermal quench (TQ) is observed to significantly shorten with increasing Te—a surprising result. While the reason for the shorter TQ is not yet understood, candidate mechanisms include: insufficiently accurate thermal ablation models, enhanced ablation driven by the seed RE population, or significant parallel heat transport along stochastic fields. Kinetic modeling that self-consistently treats the plasma cooling via radiation, the induced electric field, and the formation of the seed RE is performed. Including the combined effect of the inherent dependence of hot-tail RE seeding on Te together with the shortened TQ, modeling recovers the progression towards near-complete conversion of the pre-disruption current to RE current as Te rises. Measurement of the HXR spectrum during the early current quench (CQ) reveals a trend of decreasing energy with pre-disruption Te. At the very highest Te (≈ 12 keV), ≈ 100% conversion of the thermal current to runaway current is found. The energy of this peculiar RE beam is inferred to be sub-MeV as it emits vanishingly few MeV hard x-rays (HXRs). These measurements demonstrate novel TQ dynamics as Te is varied and illustrate the limitations of treating the RE seed formation problem without considering the inter-related dependencies of the pellet ablation, radiative energy loss, and resultant variations of the TQ duration. If the observed shortening of the TQ with increasing Te extends to fusion-grade plasmas, than their propensity to form large quantities of RE seeds at high Te may be far worse than previously thought. Positively, the high Te scenario in DIII-D produces REs so prodigiously that it can serve as a meaningful new platform for demonstrating RE avoidance techniques.

Heat Transport Characteristics Of Thin Plate Type Parallel Tube Heat Transport Device with Low Surface Tension Solution

Heat Transport Characteristics Of Thin Plate Type Parallel Tube Heat Transport Device with Low Surface Tension Solution

Heat Transport Characteristics of Parallel Tube Heat Transport Device with Low Environmental Impact Refrigerants

Heat Transport Characteristics of Parallel Tube Heat Transport Device with Low Environmental Impact Refrigerants

Spontaneous Ion Temperature Gradient in Inhomogeneous Magnetic Fields and Its Effect on the Parallel Heat Transport

Spontaneous Ion Temperature Gradient in Inhomogeneous Magnetic Fields and Its Effect on the Parallel Heat Transport

Evaluation of Heat Transport Characteristics in Parallel Tube Heat Transport Device with HFC/HFO Refrigerant

Evaluation of Heat Transport Characteristics in Parallel Tube Heat Transport Device with HFC/HFO Refrigerant

Effects of Alcoholic Solution Concentration on Heat Transport Characteristics in Thin Plate Type Parallel Tube Heat Transport Device

Effects of Alcoholic Solution Concentration on Heat Transport Characteristics in Thin Plate Type Parallel Tube Heat Transport Device

Evaluation of Heat Transport Characteristics In Thin Plate Type Parallel Tube Heat Transport Device with Aqueous Alcoholic Solution

Evaluation of Heat Transport Characteristics In Thin Plate Type Parallel Tube Heat Transport Device with Aqueous Alcoholic Solution

Effect of Filling Ratio on Heat Transport Characteristics of Parallel Tube Heat Transport Device with HFO Refrigerant (R1234yf)

Effect of Filling Ratio on Heat Transport Characteristics of Parallel Tube Heat Transport Device with HFO Refrigerant (R1234yf)

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in 3-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands and remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in LHD and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.

Turbulent transport regimes and the scrape-off layer heat flux width

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments.

Thermal conductivity of multi-walled carbon nanotubes: Molecular dynamics simulations

Heat conduction in single-walled carbon nanotubes (SWCNTs) has been investigated by using various methods, while less work has been focused on multi-walled carbon nanotubes (MWCNTs). The thermal conductivities of the double-walled carbon nanotubes (DWCNTs) with two different temperature control methods are studied by using molecular dynamics (MD) simulations. One case is that the heat baths (HBs) are imposed only on the outer wall, while the other is that the HBs are imposed on both the two walls. The results show that the ratio of the thermal conductivity of DWCNTs in the first case to that in the second case is inversely proportional to the ratio of the cross-sectional area of the DWCNT to that of its outer wall. In order to interpret the results and explore the heat conduction mechanisms, the inter-wall thermal transport of DWCNTs is simulated. Analyses of the temperature profiles of a DWCNT and its two walls in the two cases and the inter-wall thermal resistance show that in the first case heat is almost transported only along the outer wall, while in the second case a DWCNT behaves like parallel heat transport channels in which heat is transported along each wall independently. This gives a good explanation of our results and presents the heat conduction mechanisms of MWCNTs.

Inboard and outboard radial electric field wells in the H- and I-mode pedestal of Alcator C-Mod and poloidal variations of impurity temperature

We present inboard (HFS) and outboard (LFS) radial electric field (Er) and impurity temperature (Tz) measurements in the I-mode and H-mode pedestal of Alcator C-Mod. These measurements reveal strong Er wells at the HFS and the LFS midplane in both regimes and clear pedestals in Tz, which are of similar shape and height for the HFS and LFS. While the H-mode Er well has a radially symmetric structure, the Er well in I-mode is asymmetric, with a stronger ExB shear layer at the outer edge of the Er well, near the separatrix. Comparison of HFS and LFS profiles indicates that impurity temperature and plasma potential are not simultaneously flux functions. Uncertainties in radial alignment after mapping HFS measurements along flux surfaces to the LFS do not, however, allow direct determination as to which quantity varies poloidally and to what extent. Radially aligning HFS and LFS measurements based on the Tz profiles would result in substantial inboard-outboard variations of plasma potential and electron density. Aligning HFS and LFS Er wells instead also approximately aligns the impurity poloidal flow profiles, while resulting in a LFS impurity temperature exceeding the HFS values in the region of steepest gradients by up to 70%. Considerations based on a simplified form of total parallel momentum balance and estimates of parallel and perpendicular heat transport time scales seem to favor an approximate alignment of the Er wells and a substantial poloidal asymmetry in impurity temperature.

Heat pulse propagation in chaotic three-dimensional magnetic fields

Heat pulse propagation in three-dimensional chaotic magnetic fields is studied by solving numerically the parallel heat transport equation using a Lagrangian Green's function (LG) method. The LG method provides an efficient and accurate technique that circumvents known limitations of finite elements and finite difference methods. The main two problems addressed are (i) the dependence of the radial transport of heat pulses on the level of magnetic field stochasticity (controlled by the amplitude of the magnetic field perturbation, ϵ), and (ii) the role of reversed shear magnetic field configurations on heat pulse propagation. In all the cases considered there are no magnetic flux surfaces. However, the radial transport of heat pulses is observed to depend strongly on ϵ due to the presence of high-order magnetic islands and Cantori. These structures act as quasi-transport barriers which can actually preclude the radial penetration of heat pulses within physically relevant time scales. The dependence of the magnetic field connection length, ℓB, on ϵ is studied in detail. Regions where ℓB is large, correlate with regions where the radial propagation of the heat pulse slows down or stops. The decay rate of the temperature maximum, 〈T〉max(t), the time delay of the temperature response as function of the radius, τ, and the radial heat flux , are also studied as functions of the magnetic field stochasticity and ℓB. In all cases it is observed that the scaling of 〈T〉max with t transitions from sub-diffusive, 〈T〉max ∼ t−1/4, at short times (χ∥t < 105) to a significantly slower, almost flat scaling at longer times (χ∥t > 105). A strong dependence on ϵ is also observed on τ and . Even in the case when there are no flux surfaces nor magnetic field islands, reversed shear magnetic field configurations exhibit unique transport properties. The radial propagation of heat pulses in fully chaotic fields considerably slows down in the shear reversal region and, as a result, the delay time of the temperature response in reversed shear configurations is about an order of magnitude longer than the one observed in monotonic q-profiles. The role of separatrix reconnection of resonant modes in the shear reversal region, and the role of shearless Cantori in the observed phenomena are also discussed.

Local and nonlocal anisotropic transport in reversed shear magnetic fields: Shearless Cantori and nondiffusive transport

A study of anisotropic heat transport in reversed shear (nonmonotonic q-profile) magnetic fields is presented. The approach is based on a recently proposed Lagrangian-Green's function method that allows an efficient and accurate integration of the parallel (i.e., along the magnetic field) heat transport equation. The magnetic field lines are described by a nontwist Hamiltonian system, known to exhibit separatrix reconnection and robust shearless (dq/dr=0) transport barriers. The changes in the magnetic field topology due to separatrix reconnection lead to bifurcations in the equilibrium temperature distribution. For perturbations of moderate amplitudes, magnetic chaos is restricted to bands flanking the shearless region. As a result, the temperature flattens in the chaotic bands and develops a very sharp radial gradient at the shearless region. For perturbations with larger amplitude, shearless Cantori (i.e., critical magnetic surfaces located at the minimum of the q profile) give rise to anomalous temperature relaxation involving widely different time scales. The first stage consists of the relatively fast flattening of the radial temperature profile in the chaotic bands with negligible flux across the shearless region that, for practical purposes, on a short time scale acts as an effective transport barrier despite the lack of magnetic flux surfaces. In the long-time scale, heat starts to flow across the shearless region, albeit at a comparatively low rate. The transport of a narrow temperature pulse centered at the reversed shear region exhibits weak self-similar scaling with non-Gaussian scaling functions indicating that transport at this scale cannot be modeled as a diffusive process with a constant diffusivity. Evidence of nonlocal effective radial transport is provided by the existence of regionswith nonzero heat flux and zero temperature gradient. Parametric flux-gradient plots exhibit multivalued loops that question the applicability of the Fourier-Fick's prescription even in the presence of a finite pinch velocity.

Parallel heat transport in magnetized plasma

A code that solves the coupled electron drift kinetic and temperature equations has been written to study the effects of collisionality and particle trapping on temperature equilibration along magnetic field lines. A Chapman-Enskog-like approach is adopted with the time-dependent distribution function written as the sum of a dynamic Maxwellian and a kinetic distortion expanded in Legendre polynomials. The drift kinetic equation is solved on a discrete grid in normalized speed, and an FFT algorithm is used to treat the onedimensional spatial domain along the magnetic field. The dependence of the steady-state temperature on collisionality and magnetic well depths is discussed in detail. As collisionality decreases (increasing background temperature), temperature variations decrease. As magnetic well depth increases (at fixed collisionality), temperature variations along the field line increase.

The effect of anisotropic heat transport on magnetic islands in 3-D configurations

An analytic theory of nonlinear pressure-induced magnetic island formation using a boundary layer analysis is presented. This theory extends previous work by including the effects of finite parallel heat transport and is applicable to general three dimensional magnetic configurations. In this work, particular attention is paid to the role of finite parallel heat conduction in the context of pressure-induced island physics. It is found that localized currents that require self-consistent deformation of the pressure profile, such as resistive interchange and bootstrap currents, are attenuated by finite parallel heat conduction when the magnetic islands are sufficiently small. However, these anisotropic effects do not change saturated island widths caused by Pfirsch-Schlüter current effects. Implications for finite pressure-induced island healing are discussed.