Heat Transport In Tokamaks Research Articles

Nonlocal self-organization of a dissipative system

We study the self-organization process induced by a nonlocal critical field, in analogy with the electric field that is derived from the global spatial profile of electric charge density during a discharge. In this nontrivial extension of standard sandpilelike models of intermittent dissipation, the charges move in a similar manner to grains of sand when the threshold condition on the field is achieved. Here we focus our attention on the long term statistics of events, so that we consider an extremely simplified model in close similarity with sandpiles, avoiding some of the extremely interesting complexities that occur in three-dimensional electric discharges. For the observed avalanches (discharges in this case) we analyze four characteristic quantities: current, charge discharged, energy discharged, and duration of the discharge. We have run several simulations to explore the parameter space and found in general that they exhibit well defined power law event statistics spanning for one to three decades in general. For some parameter values we observe the existence of large or global events, in addition to the power law statistics, some of which may be related to finite size effects due to the size of the simulation box. This is the first step in understanding the long term statistics of systems with avalanches or discharges, when the criticality is controlled by nonlocality, as there are a number systems, such as lightning discharges or heat transport in tokamaks, where this type of dynamics is expected to occur.

Analysis of Materials for Heat Transport in Tokamaks

Every nuclear power reactor, whether of fusion or fission, is essentially a thermal system that generates electricity. In this sense, there are several problems in relation to this heat transport. The model of plasma confinement by magnetic force, in the nuclear fusion (sterellator and tokamak), has only been 20 years and recently some success in the quality of the generated plasma has been achieved. However, due to the large amount of energy coming from the plasma, the choice of the material that will carry the generated energy is quite troublesome, due to the need to handle a very high temperature for the nuclear fission standards. Solutions are explored by the scientific community to transport the energy generated in the case of the primary circuit, after exceeding breakeven temperature and models that are based on the fission reactors of the fourth generation and those currently in operation, to search for solutions regarding the transport of heat generated for the generation of electric energy. Several materials such as pressurized water, sodium, helium and boron have been considered and studied to form the primary heat transfer circuit for the exchanger. A thorough analysis of these materials is necessary. This research looked at some of these materials for heat transport and power generation. Lithium and helium were found to be the probable materials for conveying heat and cooling in the blanket. The results show that research on blanket materials needs more attention. The quality of these materials needs to be improved by material research, with the ODS EUROFER alloy and other research to reduce material erosion by helium nano bubbles. Plasma quality needs to be improved to keep constant and free of impurities when using lithium in liquid form.

Investigation of the role of electron temperature gradient modes in electron heat transport in TCV plasmas

Electron-scale micro-turbulence driven by the electron temperature gradient (ETG) instability has recently been shown to impact the electron heat transport in tokamaks. Given the relevance of these mechanisms for ITER scenarios, a new study has been carried out on the TCV tokamak at the Swiss Plasma Center, which is equipped with both electron cyclotron heating (ECH) and neutral beam injection (NBI) heating, allowing investigation of the relevance of ETG transport. Dedicated L-mode TCV discharges have been performed and the experimental measurements have been compared with gyrokinetic simulations. The results indicate that ETGs should contribute to electron heat transport from mid-radius to the edge when NBI and ECH are simultaneously applied, while the cases with pure ECH are dominated by ion-scale turbulence at mid-radius and show signs of possible ETG contribution only at outer radii.

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.

Role of the plasma interaction with magnetic field in the “missing power” problem

It is shown that, at rapid changes of the heating power, the magnetically confined equilibrium plasma almost completely absorbs the injected energy, so that its only small part goes to the magnetic field. The result is obtained within the standard MHD theory with use of exact consequences of the force-balance equations in toroidal geometry. It is assumed that, when heated, the plasma evolves from one equilibrium state to another with the magnetic field frozen-in. Another constraint is the conservation of the toroidal magnetic flux in the plasma-wall vacuum gap. It is shown that the plasma interaction with magnetic field (which is traditionally neglected in the analysis of heat transport in tokamaks and stellarators) is the natural mechanism of fast redistribution of energy in the plasma, observed in some experiments in these devices at switchon of powerful heat sources.

Collisionless trapped-electron-mode turbulence and transport in fluid descriptions

AbstractA study of particle and electron heat transport in tokamaks due to trapped-electron-mode (TEM) turbulence is presented. The study is based on the Weiland fluid model for ion-temperature-gradient (ITG) modes and TEMs, complemented and compared with a trapped electron fluid treatment which retains contributions from the weakly trapped electrons. The dependence of the fluid transport coefficients on magnetic shear and other plasma parameters is discussed and compared with results obtained from nonlinear gyrokinetic simulations. Inward (pinch) flows of particles and heat, previously reported for the coupled ITG–TEM system, are also found in the TEM dominated regime.

On the use of critical gradient models in fusion plasma transport studies

Transport models for tokamak devices are often based on transport coefficients involving a critical threshold condition. In this paper, it is argued that the validation of such models against experimental data requires special care when the system profiles are close to this threshold (at some locations), due to the contribution of fluctuations to transport. The arguments presented here could have implications for the understanding and modeling of heat transport in tokamaks, since the large stiffness of the temperature profile observed in experimental points to a near-critical situation over much of the radius. The difficulties are illustrated by means of a simplified transport model, and a possible way to ameliorate this issue is proposed.

Application of the canonical profile theory to the problems of heat transport in tokamaks

A transport model for describing electron and ion plasmatemperatures is developed on the basis of the canonical profile theory for a tokamak with an arbitrary cross section. A comparison with the data from experiments on eight different tokamaks shows that the model is capable of adequately simulating plasma discharges. A scaling for the behavior of the relative temperature gradient at half the plasma minor radius is constructed based on both an analysis of the experimental data and the results of numerical calculations.

A continuum one-dimensional SOC model for thermal transport in tokamaks

Based on the now well-known and experimentally observed critical gradient length (LTe) in tokamaks, we present a continuum one-dimensional model for explaining self organized heat transport in tokamaks. The key parameters of this model include a hysteresis parameter, which ensures that the switching of the heat transport coefficient χ upwards and downwards takes place at two different values of R/LTe. Extensive numerical simulations of this model reproduce many features of present day tokamaks, such as sub-marginal temperature profiles, intermittent transport events, 1/f scaling of the frequency spectra, propagating fronts, etc. This model utilizes a minimal set of phenomenological parameters, which may be determined from experiments and/or simulations. Analytical and physical understanding of the observed features has also been attempted.

Continuum Self-Organized-Criticality Model of Turbulent Heat Transport in Tokamaks

A simple generic one-dimensional continuum model of driven dissipative systems is proposed to explain self-organized bursty heat transport in tokamaks. Extensive numerical simulations of this model reproduce many features of present day tokamaks such as submarginal temperature profiles, intermittent transport events, 1/f scaling of the frequency spectra, propagating fronts, etc. This model utilizes a minimal set of phenomenological parameters, which may be determined from experiments and/or simulations. Analytical and physical understanding of the observed features has also been attempted.

Transport modelling of inward heat transport in tokamaks

The presence of inward heat flows in tokamaks is analysed using a transport model for turbulent transport based on temperature gradient driven drift waves. The conditions needed for inward (pinch) heat flows are discussed and the results are compared with some experimental observations. In particular, it is shown that the differences observed between the off-axis heated discharges at DIII-D, where nondiffusive transport was observed, and similar discharges at JET are consistent with the predictions of the transport model.

Predictive tests of ITG based models of tokamak heat transport on ITER database discharges

Three gyro-Bohm transport models are applied to the L mode discharges of the ITER profile database for predictive tests of plasma confinement. All three models are based on ion temperature gradient driven turbulence but emphasize different aspects of the resulting turbulent transport. It is found that the model using the long wavelength component of the turbulence for the radial correlation length yields the predictions with the lowest overall residual error for a given database. Extrapolations for the performance of ITER are given for the models used.

Similarity Invariance of Magnetic States and Nonlocal Transient Effects on Heat Transport in Tokamaks

States of stationary magnetic entropy are connected by a similarity transformation that describes a poloidal flux-conserving rearrangement of the equilibrium and a global invariance of the magnetic structure. It is conjectured that the only permissible states in the confinement zone of a tokamak are magnetically similar states of stationary entropy, and that the physical properties of transport in these states are the same, apart from a similarity transformation. This conjecture, which establishes a connection between transport and magnetic structure, allows one to write down a power balance equation in the confinement zone that describes the temperature evolution in transient processes driven by rapid changes of the magnetic equilibrium. In the present paper the following experimental facts are considered in the light of this equation: the sensitivity of the core temperature of the tokamak to edge perturbations of the current channel, the nonlocal, nondiffusive behaviour of heat pulses from the mixing zone observed in heat modulated experiments and the global temperature evolution observed immediately after the L-H transition.

Development of a non-local model for tokamak heat transport in L-mode, H-mode and transient regimes

Non-local effects have recently been observed in many transient experiments in different tokamaks. These effects have been modelled by introducing a non-local dependence in the Bohm part of a previously introduced model for L-mode, so that good simulations are obtained for L - H transitions, cold pulses, sawteeth and ELMs. This model also explains the improvement of core transport in the whole high-performance phase of H-mode ELM-free discharges.

Measurement of magnetic fluctuation-induced heat transport in tokamaks and RFP

The local electron energy flux produced by magnetic fluctuations has been measured directly in the edge plasma of the Madison symmetric torus (MST) reversed field pinch (RFP), continuous current tokamak (CCT), and the scrape-off layer of the TEXT-U tokamak. The flux produced by electrons travelling parallel to a fluctuating magnetic field is obtained from correlation between the fluctuations in the parallel heat flux and the radial magnetic field. The fluctuations in the parallel heat flux were measured with a fast insertable pyrobolometer. The measurements reveal fundamental differences in the nature of electron energy transport in the RFP and the tokamak. In the RFP the fluctuation-induced energy flux is large (, comparable to the total ohmic heating power) inside the reversal surface where the magnetic field is expected to be stochastic, and small in the edge. The magnetic fluctuation induced radial energy flux Q and radial particle flux (measured independently) are related by a `convective' formula . The electron heat transport is significantly lower than the value predicted by the Rechester - Rosenbluth transport model. This feature of the electron energy transport can be explained using self-consistent calculations that account for clumping of electrons streaming along the magnetic field. In the tokamak the magnetic fluctuations do not contribute to the total energy transport except in the vicinity of the q = 2 magnetic surface, where the transport is associated with large amplitude Mirnov oscillations.

Bounce averaged trapped electron fluid equations for plasma turbulence

A novel set of nonlinear fluid equations for mirror-trapped electrons is developed which differs from conventional fluid equations in two main respects: (1) the trapped-fluid moments average over only two of three velocity space dimensions, retaining the full pitch angle dependence of the trapped electron dynamics, and (2) closure approximations include the effects of collisionless wave-particle resonances with the toroidal precession drift. Collisional pitch angle scattering is also included. By speeding up calculations by at least √mi/me, these bounce averaged fluid equations make possible realistic nonlinear simulations of turbulent particle transport and electron heat transport in tokamaks and other magnetically confined plasmas.

Application of a Two-Fluid Theoretical Plasma Energy Confinement Scaling to Current Tokamak Reactor Designs

A two-fluid theoretical model of heat transport in tokamaks is developed based on microinstabilities. A tau/sub E/ scaling of the form tau/sub E/=1.832a/sup 2.45/R/sup 0.59/q/sub a//sup -2.07/ X B/sub T//sup 0.91//sup 0.46/Z/sup -0.09/P/sub T//sup -0.55//sub {Kappa}//sup 0.55/ has been determined from this transport model. The theoretical tau/sub E/ scaling is used to determine the smallest size tokamak fusion reactor for two cases, ignition and Q=5 steady state. Parameters are in good agreement with Tokamak Ignition/Burns Experimental Reactor II designs based on empirical Kaye-Goldston tau/sub E/ scaling.

Tokamak heat transport – a study of heat pulse propagation in JET

The propagation of heat pulses originating from sawtooth activity in JET has been investigated in a series of limiter discharges with the following parameters: plasma current, Ip ≃ 3 MA, toroidal magnetic field, BT ≃ 3 T and elongation, κ = 1.45. The auxiliary power was varied such that the total power ranged from 2 to 13.5 MW. Electron temperature perturbations in a 20 cm region around a minor radius of r = (2/3)a were recorded with high time resolution, using a 12 channel electron cyclotron emission polychromator. From these measurements the electron heat diffusivity was derived. Over the whole range of powers considered, was found to be independent of power and to lie in the range of 2.5 ± 0.5 m2·s−1. The quantity is compared to as derived from global power balance analysis. For Ohmic heating, the latter is lower than by a factor of 2.5. For increasing auxiliary power, approaches . A model for the dependence of the local χe n the temperature gradient is presented; it permits a unified description of the heat pulse behaviour, the deterioration of confinement and a certain degree of profile consistency. The model does not invoke non-local parameters such as the total power input. It is shown that the present heat pulse data, subject to this interpretation, contradict the τE scaling laws of the typical form τE ∝ P−0.5.

Linear stability of high-m drift-tearing modes

A new model for the electron parallel conductivity in a plasma of moderate collisionality is formulated using the Williamson collision operator. With this model, the linear stability of high-m drift-tearing modes (driven unstable by ∇Te) is studied as a function of the electron-ion collision frequency νc with no restriction placed on the ratio νc/ω. It is shown that the growth rate of this instability can be substantial for realistic tokamak parameters. The implication for understanding the observed magnetic turbulence and anomalous electron heat transport in tokamaks is discussed.

Tokamak Heat Transport Due to Tearing Modes

Magnetic field perturbations accompanying the tearing instability allow rapid heat transport across regions enclosing mode-rational equilibrium flux surfaces. The electron-energy transport equation for this process is derived, under the assumptions of cylindrical geometry, incompressible flow, and relatively weak density gradients. For the thermoelectric instability predicted by kinetic theory, a quasilinear description of local flattening of the temperatures profile is obtained. The self-consistent field perturbation is shown to be quite weak, $\frac{\ensuremath{\delta}B}{{B}_{0}}\ensuremath{\sim}{10}^{\ensuremath{-}4}$; yet it yields a localized heat flux far exceeding pseudoclassical estimates.