Ohmic Flux Research Articles

Integrated modeling of CFETR hybrid scenario plasmas

Demonstration of DEMO relevant fusion power (P fus) level and tritium self-sufficiency are two important goals of the China fusion engineering testing reactor (CFETR). In this work the integrated modeling including self-consistent core–pedestal coupling are used to design the hybrid scenario plasmas at flat-top phase for these goals. Such plasmas have been taken as the reference plasma for studying the compatibility of the hybrid scenario with CFETR engineering design in the past two years. The physics justification for the selection of plasma density, Z eff, safety factor profile, and in particular the choice of auxiliary heating and current drive is presented. According to a scan of plasma density and Z eff, the target of P fus ≈ 1 GW and finite ohmic flux consumption ∆Φohm (4 h) ⩽ 250 Vs can be met with Z eff = 1.9–2.2 and the density at the pedestal top set at 90% of the Greenwald limit. Turbulent transport analysis using the gyro-Landau-fluid model TGLF shows that the electromagnetic effects can enhance the energy confinement but reduce the particle confinement and thus P fus. A baseline hybrid scenario case matching the target in the concept design is built using a combination of neutral beams (NB) and electron cyclotron (EC) waves to flatten the safety factor profile in the deep core region (with the normalized plasma radius ρ ⩽ 0.4). Such profile can yield better particle and energy confinement than that with either higher magnetic shear in the deep core region or higher q value in outer core region (e.g., due to the addition of lower hybrid current drive). Switching a part of auxiliary heating from electron to ions, e.g., replacing a part of EC waves by waves in the ion cyclotron range of frequencies, reduces the particle confinement and thus P fus. Since high harmonic fast waves (HHFW) can drive current at the same location as ECCD with higher current drive efficiency than ECCD and yield more electron heating than NB, the case using HHFW to replace a part of EC waves and NB can yield higher P fus and lower ∆Φohm than the baseline case. A discussion is given on future simulations to explore the improvement in plasma performance and the broadening of the feasible design space.

Numerical study of natural convection and radiation exchange in an asymmetrically heated inclined channel

Introduction: In this paper, numerical study is carried out to investigate natural convection and radiation heat transfer in an asymmetrical heated inclined air channel with open ends. The Reynolds-averaged Navier–Stokes equations are solved using a commercial computational fluid dynamics solver ANSYS-FLUENT© in conjunction with the discrete ordinate radiation model. Simulations were run considering the channel with inclination angle to horizontal in the range 18° to 45° and a wall surface emissivity of 0.27–0.95. The channel length to channel space ratio was selected in the range 44–220. A uniform heat flux in the range 100–500 W/m2 was applied along the upper wall of the channel while the lower wall and side walls were assumed thermally insulated. Results: Temperature profiles along the upper and lower walls of the channel were obtained with variations in the channel length to space ratios, angles of inclination, radiation emissivity, and input Ohmic heat flux. The effect of various parameters on the maximum wall temperature and heat transfer was investigated. The numerical predictions are validated by comparison with the experimental data available in literature. Conclusion: The numerical results obtained are found in good agreement with the experimental measurements. From the numerical results, a correlation of local and average Nusselt number with modified channel Rayleigh number in the range of 101–105 is developed at asymmetric heat flux boundary conditions. Nu = 0.6851Ra” 0.2612

Superconductor Stability Against Quench and Its Correlation with Current Propagation and Limiting

This paper presents a numerical (finite element) analysis of superconductor stability and current propagation under random variations of critical superconductor parameters. Instead of using singular (homogeneous) values, random variations potentially are appropriate to take into account any conductor inhomogeneity that can be considered as an obstacle to current propagation. Traditional assumptions like homogeneous current distribution, critical temperature, critical current density and critical magnetic fields are not justified in general; a local disturbance (for example, release of mechanical stress energy), if not immediately distributed by solid conduction, would generate a transient increase of local conductor temperature. Local critical current density and magnetic field then will be reduced, and current distribution will change. Disturbances may arise also from transport currents that locally exceed the critical current of the superconductor. Disturbances of all kinds may increase the conductor temperature above its critical value. A local analysis of all superconductor states thus is mandatory to safely avoid a quench. As an extension of standard stability models, also flux flow resistive states are taken into account. We will try to find a possibly existing correlation between current propagation and superconductor stability. Fault current limiting is discussed as a special case of current propagation. The analysis is applied to a bundle of high-temperature superconductor (HTSC) filaments. As will be shown, temperature profiles in a superconductor do not allow a clear distinction between Ohmic resistive or flux flow resistive fault current limiting. Though frequently made in the literature, this separation is highly questionable, because Ohmic resistive and flux flow resistive states may locally coexist, side by side, but are not very stable in the superconductor volume.

Control of post-disruption runaway electron beams in DIII-D

Recent experiments in the DIII-D tokamak have demonstrated real-time control and dissipation of post-disruption runaway electron (RE) beams. In the event that disruption avoidance, control, and mitigation schemes fail to avoid or suppress RE generation, active control of the RE beam may be an important line of defense to prevent the rapid, localized deposition of RE beam energy onto vulnerable vessel sections. During and immediately after the current quench, excessive radial compression of the runaway beams is avoided by a combination of techniques, improving the likelihood of the beams surviving this dynamic period without a fast termination. Once stabilized, the runaway beams are held in a steady state (out to the ohmic flux limit) with the application of active plasma current and position controls. Beam interaction with the vessel wall is minimized by avoiding distinct thresholds for enhanced wall interaction at small and large radii, corresponding to inner wall and outer limiter interaction, respectively. Staying within the “safe zone” between those radial thresholds allows for the sustainment of long-lived, quiescent runaway beams. The total beam energy and runaway electron population are then dissipated gradually by a controlled ramp-down of the runaway current.

Calculation of Turn Skipping Losses in Helical Flux Compression Generators

In helical flux compression generators, the ohmic and intrinsic flux losses limit severely the performance of them. One of the sources of intrinsic flux losses is the turn skipping flux loss. This paper first introduces an accurate criterion for the prevention of the turn skipping phenomenon in these generators. Then, a novel method is presented to calculate the flux loss due to this phenomenon. In addition, an equivalent resistance is introduced to consider the effect of turn skipping flux loss on the generator performance. The calculation results show that, as soon as the turn skipping occurs, about 30% of a turn flux is lost and this value is increased rapidly with eccentricity increasing. Therefore, it is necessary to prevent this phenomenon as far as possible. The calculated output current of the simulated generator also shows that the maximum current when considering the turn skipping loss is about 15% of the maximum current in the case of ignoring it. Based on the authors' knowledge, quantification of the turn skipping flux losses has not been presented previously in the open literature.

Non-linear model-based optimization of actuator trajectories for tokamak plasma profile control

A computational method is presented to determine the tokamak actuator time evolution (trajectories) required to optimally reach a given point in the tokamak operating space while satisfying a set of constraints. Usually, trajectories of plasma auxiliary heating, current drive and plasma current required during the transient phases of a tokamak shot to reach a desired shape of the plasma temperature and safety factor (q) profiles are determined by trial-and-error by physics operators. In this paper, these trajectories are calculated by solving a non-linear, constrained, finite-time optimal control problem.The optimization problem contains a physics model of the non-linear plasma profile dynamics, a cost function to be minimized, and a set of constraints on the actuators and plasma quantities. The method is tested by optimizing the trajectories of Ip, heating and current drive power to obtain a typical hybrid plasma q profile at the end of the current ramp-up phase, while minimizing both the Ohmic flux swing and the distance from a stationary condition, and requiring q > 1 and edge Vloop > 0 at all times. The optimized trajectories feature an Ip overshoot similar to that used in existing experiments, and are shown to perform significantly better than a set of non-optimized trajectories, allowing stationary profiles to be obtained at the beginning of the flat-top phase. Additional information is obtained, including the parameter sensitivity of the optimal solution, a linear model describing the linearized dynamics of the profiles around the optimal trajectory, as well as a classification of the actuator trajectories based on the critical constraint which limits their value at a given time. This provides a solid basis for subsequent closed-loop feedback controller design. The tools presented in this paper could be useful to improve existing tokamak operational scenarios, to prepare operation of future machines and optimize their design.

A three-dimensional mathematical model of active signal processing in axons

Action potentials in neurons are generated on the plasma membrane through depolarization, i.e. exchange of charges through the membrane. Hodgkin and Huxley developed a mathematical model which describes the interaction of ions through an active plasma membrane. In Vossen et al. (Comput Visual Sci 10:107–121, 2007) we developed a passive three-dimensional (3D) model for signal propagation in dendrite. We now combine this model with a generalized Hodgkin-Huxley model to obtain a 3D-model that describes active signal processing on realistic cell morphologies. Time dependent changes of the neuron’s intra- and extracellular potential is regulated by the Ohmic flux of charges. These fluxes are balanced in membrane-near areas by the capacitory and Hodgkin-Huxley flux. The active model we present consists of five non-linear, coupled integro-differential equations which are solved numerically with a finite volume approach, implicit time stepping and Newton’s method for solving the underlying non-linear system of equations with multigrid solver methods. We present numerical results as well as axon behavior in a biological setting. This model can be considered as a three-dimensional expansion of existing state of the art one-dimensional models, with the significant advantage of being able to investigate the morphological influence of neuron cell types on their specific signaling properties.

Understanding and predicting the dynamics of tokamak discharges during startup and rampdown

Understanding the dynamics of plasma startup and termination is important for present tokamaks and for predictive modeling of future burning plasma devices such as ITER. We report on experiments in the DIII-D tokamak that explore the plasma startup and rampdown phases and on the benchmarking of transport models. Key issues have been examined such as plasma initiation and burnthrough with limited inductive voltage and achieving flattop and maximum burn within the technical limits of coil systems and their actuators while maintaining the desired q profile. Successful rampdown requires scenarios consistent with technical limits, including controlled H-L transitions, while avoiding vertical instabilities, additional Ohmic transformer flux consumption, and density limit disruptions. Discharges were typically initiated with an inductive electric field typical of ITER, 0.3 V/m, most with second harmonic electron cyclotron assist. A fast framing camera was used during breakdown and burnthrough of low Z impurity charge states to study the formation physics. An improved “large aperture” ITER startup scenario was developed, and aperture reduction in rampdown was found to be essential to avoid instabilities. Current evolution using neoclassical conductivity in the CORSICA code agrees with rampup experiments, but the prediction of the temperature and internal inductance evolution using the Coppi–Tang model for electron energy transport is not yet accurate enough to allow extrapolation to future devices.

Demonstration of Tokamak Ohmic Flux Saving by Transient Coaxial Helicity Injection in the National Spherical Torus Experiment

Transient coaxial helicity injection (CHI) started discharges in the National Spherical Torus Experiment (NSTX) have attained peak currents up to 300 kA and when coupled to induction, it has produced up to 200 kA additional current over inductive-only operation. CHI in NSTX has shown to be energetically quite efficient, producing a plasma current of about 10 A/J of capacitor bank energy. In addition, for the first time, the CHI-produced toroidal current that couples to induction continues to increase with the energy supplied by the CHI power supply at otherwise similar values of the injector flux, indicating the potential for substantial current generation capability by CHI in NSTX and in future toroidal devices.

Ramp-Up of CHI-Initiated Plasmas on NSTX

Ongoing experiments on the National Spherical Torus Experiment have demonstrated ohmic transformer flux savings by initiating the discharge with transient coaxial helicity injection (CHI). The combined use of discharge cleaning of the CHI electrodes and use of lithium evaporation, along with the use of poloidal field coils, to produce a buffer flux that prevents arcs at the top of the device has been shown to reduce the radiation from low-Z impurities. Without such impurity reduction, CHI-initiated discharges could not have their plasma current increased by ohmic ramp-up; however, the CHI-initiated discharges with reduced low-Z radiation can be ramped up by induction and exhibit higher plasma current than discharges without the benefit of CHI initiation.

Guiding of vortices and ratchet effect in superconducting films with asymmetric pinning potential

Two-dimensional vortex dynamics in a ratchet washboard planar pinning potential in the presence of thermal fluctuations is considered on the basis of a Fokker-Planck equation. Explicit expressions for two nonlinear anisotropic voltages (longitudinal and transverse with respect to the current direction) are derived and analyzed. The physical origin of these odd (with respect to magnetic field or transport current direction reversal) voltages is caused by the interplay between the even effect of vortex guiding and the ratchet asymmetry. Both voltages are going to zero in the linear regimes of the vortex motion [i.e., in the thermally activated flux flow (TAFF) and Ohmic flux flow (FF) regimes] and have a bumplike current or temperature dependence in the vicinity of the highly nonlinear resistive transition from the TAFF to the FF.

Lower hybrid assisted plasma current ramp-up in ITER

Lower hybrid (LH) assisted plasma current ramp-up in ITER is demonstrated using a free-boundary full tokamak discharge simulator which combines the DINA-CH and CRONOS codes. LH applied from the initial phase of the plasma current ramp-up increases the safety margins in operating the superconducting poloidal field coils both by reducing resistive ohmic flux consumption and by providing non-inductively driven plasma current. Loss of vertical control associated with high plasma internal inductance is avoided by tailoring the plasma current density profiles. Effects of early LH application on the plasma shape evolution are identified by the free-boundary plasma simulation.

Experimental Investigation of Opposing Mixed Convection in a Channel with an open Cavity Below

In this article, mixed convection in an open cavity with a heated wall bounded by a horizontal unheated plate is investigated experimentally. The heated wall is on the opposite side of the forced inflow. The results are reported in terms of wall temperature profiles of the heated wall and flow visualization. The range of pertinent parameters used in this experiment are Reynolds numbers (Re) from 100 to 2,000 and Richardson numbers (Ri) from 4.3 to 6,400. Also, the ratio between the length and the height of cavity (L/D) ranges from 0.5–2.0, and the ratio between the channel and cavity height (H/D) is equal to 1.0. The lack of experimental results on mixed convection in a channel with an open cavity below was an impetus for investigating this configuration when one cavity vertical wall is heated at uniform heat flux. The present results show that at the lowest investigated Reynolds number, the surface temperatures are lower than the corresponding surface temperatures for Re = 2,000 at the same ohmic heat flux. The flow visualization shows that for Re = 1,000, there are two nearly distinct fluid motions: a parallel forced flow in the channel and a recirculation flow inside the cavity. For Re = 100, the effect of a stronger buoyancy determines a penetration of thermal plumes from the heated plate wall into the upper channel. Moreover, the flow visualization shows that for lower Reynolds numbers, the forced motion penetrates inside the cavity, and a vortex structure is adjacent to the unheated vertical plate. At higher Reynolds numbers, the vortex structure has a larger extension while L/D is held constant.

Three-Dimensional Mathematical Models of Active Signal Processing in Dendrites and Subcellular Calcium Signaling

Event Abstract Back to Event Three-Dimensional Mathematical Models of Active Signal Processing in Dendrites and Subcellular Calcium Signaling Konstantinos Xylouris1*, Gillian Queisser2 and Gabriel Wittum2 1 University of Frankfurt, Germany 2 University of Heidelberg, Germany Action potentials in neurons are generated on the plasma membrane through depolarization, i.e. exchange of charges through the membrane. Hodgkin and Huxley developed a mathematical model which describes the interaction of ions through an active plasma membrane. We combined a passive three-dimensional (3D) model for signal propagation in dendrites with a generalized Hodgkin-Huxley model to obtain a 3D-model that describes active signal processing on realistic cell morphologies. Time dependent changes of the neuron's intra- and extracellular potential is regulated by the Ohmic flux of charges. These fluxes are balanced in membrane-near areas, by the capacitory and Hodgkin-Huxley flux. The active model we present consists of five non-linear, coupled integro-differential equations which are solved numerically with a finite volume approach, implicit time stepping and Newton's method for solving the underlying non-linear system of equations with multigrid solver methods. We present numerical results as well as axon behavior in a biological setting. This model can be considered as a three-dimensional expansion of existing state of the art one-dimensional models, with the significant advantage of being able to investigate the morphological influence of neuron cell types on their specific signaling properties. On a subcellular level we investigated the influence of the nuclear morphology on calcium signals. There we find two main types of nuclei, infolded and spherical. While spherical nuclei are observed to be "signal-integrators", infolded nuclei are adept at resolving high-frequency signals. Calcium acts as a key regulator in the nucleus for biochemical events that trigger gene transcription and is involved in processes such as memory formation and information storage. Recent research showed that the morphology of hippocampal neuron nuclei is regulated by the cell's NMDA receptors, which led us to investigate the morphological influence in a modeling environment. Similar to nerve cells the nucleus is able to dynamically change its form in response to the cell's activity and therefore influences the way calcium signals are interpreted in the nucleus. Especially the concept of high-frequency calcium signaling could be introduced by this model and has been further investigated experimentally in recent work. Conference: Bernstein Symposium 2008, Munich, Germany, 8 Oct - 10 Oct, 2008. Presentation Type: Oral Presentation Topic: All Abstracts Citation: Xylouris K, Queisser G and Wittum G (2008). Three-Dimensional Mathematical Models of Active Signal Processing in Dendrites and Subcellular Calcium Signaling. Front. Comput. Neurosci. Conference Abstract: Bernstein Symposium 2008. doi: 10.3389/conf.neuro.10.2008.01.071 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 17 Nov 2008; Published Online: 17 Nov 2008. * Correspondence: Konstantinos Xylouris, University of Frankfurt, Frankfurt, Germany, konstantinos.xylouris@gmail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Konstantinos Xylouris Gillian Queisser Gabriel Wittum Google Konstantinos Xylouris Gillian Queisser Gabriel Wittum Google Scholar Konstantinos Xylouris Gillian Queisser Gabriel Wittum PubMed Konstantinos Xylouris Gillian Queisser Gabriel Wittum Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

The upgraded Pegasus Toroidal Experiment

The Pegasus Toroidal Experiment was developed to explore the physics limits of plasma operation as the aspect ratio (A) approaches unity. Initial experiments on the device found that access to high normalized current and toroidal beta was limited by the presence of large-scale tearing modes. Major upgrades have been conducted of the facility to provide the control tools necessary to mitigate these resistive modes. The upgrades include new programmable power supplies, new poloidal field coils and increased, time-variable toroidal field. First ohmic operations with the upgraded system demonstrated position and current ramp-rate control, as well as improvement in ohmic flux consumption from 2.9 MA Wb−1 to 4.2 MA Wb−1. The upgraded experiment will be used to address three areas of physics interest. First, the kink and ballooning stability boundaries at low A and high normalized current will be investigated. Second, clean, high-current plasma sources will be studied as a helicity injection tool. Experiments with two such sources have produced toroidal currents three times greater than predicted by geometric field line following. Finally, the use of electron Bernstein waves to heat and drive current locally will be studied at the 1 MW level; initial modelling indicates that these experiments are feasible at a frequency of 2.45 GHz.

Quantification of Ohmic and Intrinsic Flux Losses in Helical Flux Compression Generators

Helical magnetic flux compression generators (MFCGs) are the most promising energy sources with respect to their current amplification and compactness. They are able of producing high current pulses required in many pulsed power applications with at least one order of magnitude higher energy density than capacitive storage with similar discharge characteristics. However, the main concern with MFCGs is their intrinsic flux loss that limits severely their performance and which is not yet well understood. In general, all flux losses have a differing degree of impact, depending on the generator's volume, current and energy amplification, size of the driven load, and angular frequency of armature-helix contact point. Although several computer models have been developed in the open literature, none of them truly quantify, starting from basic physics principles, the ohmic and intrinsic flux losses in helical MFCGs. This paper describes a novel method that provides a separate calculation of intrinsic flux losses (flux that is left behind in the conductors and lost for compression) and ohmic losses, being especially easy to implement and fast to calculate. We also provide a second method that uses a simple flux quantification, making a mathematical connection between the intrinsic flux losses, quantified by the first method, and the intrinsic flux losses observed in the generators. This second method can also be used to a priori estimate the MFCG performance. Further, we will show experimental and calculated data and discuss the physical efficiency limits and scaling of generator performance at small sizes.

Modelling of Ohmic discharges in ADITYA tokamak using the Tokamak Simulation Code

Several Ohmic discharges of the ADITYA tokamak are simulated using the Tokamak Simulation Code (TSC), similar to that done earlier for the TFTR tokamak. Unlike TFTR, the dominant radiation process in ADITYA is through impurity line radiation. TSC can follow the experimental plasma current and position to very good accuracy. The thermal transport model of TSC including impurity line radiation gives a good match of the simulated results with experimental data for the Ohmic flux consumption, electron temperature and Zeff. Even the simulated magnetic probe signals are in reasonably good agreement with the experimental values.

Performance and stability of near-unity aspect ratio plasmas in the Pegasus Toroidal Experiment

The Pegasus Toroidal Experiment [R. Fonck et al., Bull. Am. Phys. Soc. 41, 1400 (1996)] is a spherical torus designed to study the limits of plasma behavior as the aspect ratio A approaches unity. Access to near-unity A is achieved through the use of a novel high-stress reinforced solenoid magnet. High toroidal beta βt is obtained in ohmically-heated plasmas by operation at low field with densities up to the Greenwald limit. Values of βt up to 20% and normalized beta up to 5 have been obtained. The ratio of plasma current to toroidal field rod current, known as the toroidal field utilization, reaches values as large as 1 but appears to approach a “soft” boundary at that level related to both ohmic flux limitations and the onset of resistive magnetohydrodynamic (MHD) activity. The m/n=2/1 and 3/2 modes are most frequently observed, in agreement with the inferred safety factor profiles. Experiments are beginning to access the external kink stability boundary at edge safety factor q95=5, which is significantly higher than that observed in conventional tokamaks. Calculations using the DCON code [A. H. Glasser and M. S. Chance, Bull. Am. Phys. Soc. 42, 1848 (1997)] confirm instability to the ideal kink.

New Hall voltages in a planar pinning potential

Two-dimensional vortex dynamics in a planar pinning potential (PPP) created by uniaxial or bianisotropic pinning planes in the presence of thermal fluctuations is considered on the basis of a Fokker–Planck equation. Explicit expressions for two new nonlinear anisotropic Hall voltages (longitudinal and transverse with respect to the current direction) are derived and analyzed. The physical origin of these odd (with respect to magnetic field reversal) voltages is caused by the subtle interplay between even effect of vortex guiding along the PPP and the odd Hall effect. Both new voltages are going to zero in the linear regimes of the vortex motion (i.e. in the thermoactivated flux flow (TAFF) and ohmic flux flow (FF) regimes) and have a bumplike current j or temperature θ dependence in the vicinity of highly nonlinear resistive transition from the TAFF to FF. As new odd voltages arise due to the Hall effect their characteristic scale is proportional to the Hall constant as for ordinary “steplike” odd Hall voltage, investigated earlier by Mawatari.

Thermal design of symmetrically and asymmetrically heated channel–chimney systems in natural convection

In this paper, design charts for the evaluation of thermal parameters for natural convection with air in a channel–chimney system are proposed. In the thermal analysis of natural convection in channel–chimney systems, the variables that play an important role are: the ohmic heat flux, maximum wall temperatures and geometrical parameters such as the height of the heated channel, the channel spacing and the height and spacing of unheated extensions. A simple numerical procedure to obtain the thermal design charts, a thermal optimization of the system and an uncertainty analysis due to the thermophysical properties are presented. Results are carried out for symmetrically and asymmetrically heated channels with walls at uniform heat flux and a simple estimation procedure is proposed to evaluate the error in the relevant geometrical and thermal parameters due to a different value of the reference temperature. The estimated error, however, is less than the uncertainty of the experimental data employed. Some simple examples are given to show the use of the charts. The proposed results are obtained from experimental data in the following dimensionless parameter ranges: 5.0⩽ L h/ b⩽20; 1.5⩽ L/ L h⩽4; 1⩽ B/ b⩽4; 10 2⩽ Ra⩽10 6.