Heat Transport In Plasmas Research Articles

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

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

Retraction statement: Adaptive distributed parameter and input estimation in linear parabolic PDEs

Summary In this paper, we discuss the on-line estimation of distributed source term, diffusion, and reaction coefficients of a linear parabolic partial differential equation using both distributed and interior-point measurements. First, new sufficient identifiability conditions of the input and the parameter simultaneous estimation are stated. Then, by means of Lyapunov-based design, an adaptive estimator is derived in the infinite-dimensional framework. It consists of a state observer and gradient-based parameter and input adaptation laws. The parameter convergence depends on the plant signal richness assumption, whereas the state convergence is established using a Lyapunov approach. The results of the paper are illustrated by simulation on tokamak plasma heat transport model using simulated data. Copyright © 2016 John Wiley & Sons, Ltd.

Estimation of Heat Source Term and Thermal Diffusion in Tokamak Plasmas Using a Kalman Filtering Method in the Early Lumping Approach

In this paper, early lumping estimation of space-time varying diffusion coefficient and source term for a nonhomogeneous linear parabolic partial differential equation (PDE) describing tokamak plasma heat transport is considered. The analysis of this PDE is achieved in a finite-dimensional framework using the cubic b-splines finite element method with the Galerkin formulation. This leads to a finite-dimensional linear time-varying state-space model with unknown parameters and inputs. The extended Kalman filter with unknown inputs without direct feedthrough (EKF-UI-WDF) is applied to simultaneously estimate the unknown parameters and inputs and an adaptive fading memory coefficient is introduced in the EKF-UI-WDF, to deal with time varying parameters. Conditions under which the direct problem is well posed and the reduced order model converges to the initial one are established. In silico and real data simulations are provided to evaluate the performances of the proposed technique.

Adaptive Distributed Parameter and Input Estimation in Plasma Tokamak Heat Transport

: In this paper, the adaptive estimation of spatially varying diffusion and source term coefficients for a linear parabolic partial differential equation describing tokamak plasma heat transport is considered. An estimator is defined in the infinite-dimensional framework having the system state and the parameters’ estimate as its states. Our scheme allows to estimate constant, spatially distributed and spatio-temporally distributed parameters as well as input with known upper bounds in time. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the Galerkin finite-dimensional technique is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.

Finite Volume schemes on unstructured grids for non-local models: Application to the simulation of heat transport in plasmas

In the so-called Spitzer–Härm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer–Härm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.

Simultaneous analysis of ion and electron heat transport by power modulation in JET

Heating power modulation experiments using ion cyclotron resonance heating (ICRH) in the 3He minority scheme have been performed in the JET tokamak to investigate heat transport properties. This RF scheme provides a dominant localized ion heating, but also some electron heating, and therefore both ion and electron heat channels were modulated. This allows us to carry out a simultaneous transport analysis of ion and electron heat transport channels, including transient transport phenomena. This also provides an experimental assessment of the ICRH heat sources of the 3He scheme. The modulation approach, so far widely used for electron transport studies, has been validated for ion heat transport in these experiments and yields results on stiffness and threshold of the ion temperature gradient (ITG)-driven ion heat transport. The results for the electron channel demonstrate the importance of the ITG-driven, off-diagonal, contribution to electron heat transport in plasmas with significant ion heating.

Interplay between Particle Momentum and Heat Transport

The interlinkage of particle, momentum, and heat transport in plasmas appears as a nondiffusive term of each transport equation. The physical mechanisms determining the diffusive and nondiffusive terms of particle, momentum, and heat transports are described. The nondiffusive term in the particle transport and impurity transport, which causes an inward pinch or outward flux, is driven by the temperature gradient and the magnetic field curvature. One significant piece of evidence of the nondiffusive term of particle transport is observed in the impurity transport as an impurity hole, where the impurity profiles become extremely hollow and the inward flow due to the density gradient is balanced with the outward flow driven by the ion temperature gradients. The outward convection of impurity observed contradicts the neoclassical prediction but is expected to contribute to the purity of plasma in the ion root even if the radial electric field is negative. The nondiffusive term in the momentum transport, which drives spontaneous toroidal rotation, is also observed in the plasmas in the Large Helical Device (LHD). The spontaneous rotations are driven by the electric field near the plasma edge and the ion temperature gradient at the midradius in the plasma. In the heat transport, no clear nondiffusive term is observed, and it is considered to be diffusive. The temperature and temperature gradient dependences of the diffusive terms are studied with the perturbation transport study and the slow transition between two transport branches that have a weak and a strong temperature dependence of thermal diffusivity.

Impact of nonlocal electron heat transport on the high temperature plasmas of LHD

Edge cooling experiments with a tracer-encapsulated solid pellet in the large helical device (LHD) show a significant rise in core electron temperature (the maximum rise is around 1 keV) as well as in many tokamaks. This experimental result indicates the possible presence of the nonlocality of electron heat transport in plasmas where turbulence as a cause of anomalous transport dominates. The nonlocal electron temperature rise in the LHD takes place in almost the same parametric domain (e.g. in a low density) as in the tokamaks. Meanwhile, the experimental results of LHD show some new aspects of nonlocal electron temperature rise, for example the delay in the nonlocal rise of core electron temperature relative to the pellet penetration time increases with the increase both in the collisionality in the core plasma and the electron temperature gradient scale length in the outer region of the plasma.

3D study of energy transport and role of stochasticity in the W7-X edge

The magnetic structures of W7-X edge configurations typically exhibit ergodic regions of different radial extent, where the radial plasma heat transport might be expected to be a combined effect of intrinsic anomalous diffusion and stochastic transport due to radially diffusing magnetic field lines. This question has been investigated by a dedicated numerical study of the energy transport performed with the EMC3 edge plasma transport code applied to three W7-X configurations of major interest. Both the calculated temperature profiles and heat load distributions on the divertor plates show that, contrary to simple collisionless estimates predicting a significant stochastic transport, the heat transport is dominated by intrinsic anomalous diffusion even for very small values of the transport coefficient. This behavior could be explained using an improved estimate including collisional transport.

Nonlocal electron heat transport and electron–ion energy transfer in the presence of strong collisional heating

Nonlocal electron heat transport in plasmas heated by a high-intensity laser field is investigated. We show how the heat transport is strongly modified by the super-Gaussian character of the energy distribution caused by the strong collisional heating. The change in the collisional electron–ion energy exchange due to this modification of the shape of the electron distribution function is also studied.

Influence of low-order rational magnetic surfaces on heat transport in TJ-II heliac ECRH plasmas

We study the effect of low-order rational surfaces on electron heat transport in plasmas confined in the TJ-II stellarator (Alejaldre et al 1990 Fusion Technol. 17 131) and heated by electron cyclotron waves. Enhancement of core electron heat confinement is observed when the rational surface is placed in the vicinity of the power deposition zone, either by performing a magnetic configuration scan or by inducing Ohmic current in a single discharge. The key to improving heat confinement seems to be a locally strong positive radial electric field, which is made possible by a synergistic effect between enhanced electron heat fluxes through radial positions around low-order rationals and pump out mechanisms in the heat deposition zone.

Nonlocal heat transport in plasmas down steep temperature gradients

An analytic solution to the problem of nonlocal heat transport in plasmas by electrons whose range is not short compared to the temperature scale length is presented. The formalism extends the results of Albritton et al. [Phys. Rev. Lett. 57, 1887 (1986)] to an arbitrary ionization state Z. This simple transport scheme is checked against recent experiments in the AURORA device [Phys. Fluids B 1, 741 (1989)]. The agreement, both for the measured cold electron temperature profile and the plasma potential, is very good and comparable to the result of full kinetic calculations.