Frontiers in Commercializing Fusion Development: the New Landscape of Companies Investing in Fusion Worldwide
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Magnetohydrodynamics - Overview
Center for Turbulence Research 361 Proceedings of the Summer Program 2006 Magnetohydrodynamics - overview Magnetohydrodynamics (MHD) is the study of the interaction of electrically conduct- ing fluids and electromagnetic forces. MHD problems arise in a wide variety of situations ranging from the explanation of the origin of Earth's magnetic field and the prediction of space weather to the damping of turbulent fluctuations in semiconductor melts dur- ing crystal growth and even the measurement of the flow rates of beverages in the food industry. The description of MHD flows involves both the equations of fluid dynamics - the Navier-Stokes equations - and the equations of electrodynamics - Maxwell's equa- tions - which are mutually coupled through the Lorentz force and Ohm's law for moving electrical conductors. Given the vast range of Reynolds numbers and magnetic Reynolds numbers characterising astrophysical, geophysical, and industrial MHD problems it is not feasible to devise an all-encompassing numerical code for the simulation of all MHD flows. The challenge in MHD is rather to combine a judicious application of analytical tools for the derivation of simplified equations with accurate numerical algorithms for the solution of the resulting mathematical models. The 2006 summer program provided a unique opportunity for scientists and engineers working in different sub-disciplines of MHD to interact with each other and benefit from the numerical capabilities available at the Center for Turbulence Research. In materials processing such as the growth of semiconductor crystals or the continuous casting of steel turbulent flows are often undesirable. The application of steady magnetic fields provides a convenient means for the contactless damping of turbulent fluctuations and for the laminarisation of flows. -
A Mathematical Introduction to Magnetohydrodynamics
Typeset in LATEX 2" July 26, 2017 A Mathematical Introduction to Magnetohydrodynamics Omar Maj Max Planck Institute for Plasma Physics, D-85748 Garching, Germany. e-mail: [email protected] 1 Contents Preamble 3 1 Basic elements of fluid dynamics 4 1.1 Kinematics of fluids. .4 1.2 Lagrangian trajectories and flow of a vector field. .5 1.3 Deformation tensor and vorticity. 14 1.4 Advective derivative and Reynolds transport theorem. 17 1.5 Dynamics of fluids. 20 1.6 Relation to kinetic theory and closure. 24 1.7 Incompressible flows . 32 1.8 Equations of state, isentropic flows and vorticity. 34 1.9 Effects of Euler-type nonlinearities. 35 2 Basic elements of classical electrodynamics 39 2.1 Maxwell's equations. 39 2.2 Lorentz force and motion of an electrically charged particle. 52 2.3 Basic mathematical results for electrodynamics. 57 3 From multi-fluid models to magnetohydrodynamics 69 3.1 A model for multiple electrically charged fluids. 69 3.2 Quasi-neutral limit. 74 3.3 From multi-fluid to a single-fluid model. 82 3.4 The Ohm's law for an electron-ion plasma. 86 3.5 The equations of magnetohydrodynamics. 90 4 Conservation laws in magnetohydrodynamics 95 4.1 Global conservation laws in resistive MHD. 95 4.2 Global conservation laws in ideal MHD. 98 4.3 Frozen-in law. 100 4.4 Flux conservation. 105 4.5 Topology of the magnetic field. 109 4.6 Analogy with the vorticity of isentropic flows. 117 5 Basic processes in magnetohydrodynamics 119 5.1 Linear MHD waves. -
Simultaneous Ultra-Fast Imaging and Neutron Emission from a Compact Dense Plasma Focus Fusion Device
instruments Article Simultaneous Ultra-Fast Imaging and Neutron Emission from a Compact Dense Plasma Focus Fusion Device Nathan Majernik, Seth Pree, Yusuke Sakai, Brian Naranjo, Seth Putterman and James Rosenzweig * ID Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095, USA; [email protected] (N.M.); [email protected] (S.P.); [email protected] (Y.S.); [email protected] (B.N.); [email protected] (S.P.) * Correspondence: [email protected]; Tel.: +310-206-4541 Received: 12 February 2018; Accepted: 5 April 2018; Published: 11 April 2018 Abstract: Recently, there has been intense interest in small dense plasma focus (DPF) devices for use as pulsed neutron and X-ray sources. Although DPFs have been studied for decades and scaling laws for neutron yield versus system discharge current and energy have been established (Milanese, M. et al., Eur. Phys. J. D 2003, 27, 77–81), there are notable deviations at low energies due to contributions from both thermonuclear and beam-target interactions (Schmidt, A. et al., Phys. Rev. Lett. 2012, 109, 1–4). For low energy DPFs (100 s of Joules), other empirical scaling laws have been found (Bures, B.L. et al., Phys. Plasmas 2012, 112702, 1–9). Although theoretical mechanisms to explain this change have been proposed, the cause of this reduced efficiency is not well understood. A new apparatus with advanced diagnostic capabilities allows us to probe this regime, including variants in which a piston gas is employed. Several complementary diagnostics of the pinch dynamics and resulting X-ray neutron production are employed to understand the underlying mechanisms involved. -
A European Success Story the Joint European Torus
EFDA JET JETJETJET LEAD ING DEVICE FOR FUSION STUDIES HOLDER OF THE WORLD RECORD OF FUSION POWER PRODUCTION EXPERIMENTS STRONGLY FOCUSSED ON THE PREPARATION FOR ITER EXPERIMENTAL DEVICE USED UNDER THE EUROPEAN FUSION DEVELOPEMENT AGREEMENT THE JOINT EUROPEAN TORUS A EUROPEAN SUCCESS STORY EFDA Fusion: the Energy of the Sun If the temperature of a gas is raised above 10,000 °C virtually all of the atoms become ionised and electrons separate from their nuclei. The result is a complete mix of electrons and ions with the sum of all charges being very close to zero as only small charge imbalance is allowed. Thus, the ionised gas remains almost neutral throughout. This constitutes a fourth state of matter called plasma, with a wide range of unique features. D Deuterium 3He Helium 3 The sun, and similar stars, are sphe- Fusion D T Tritium res of plasma composed mainly of Li Lithium hydrogen. The high temperature, 4He Helium 4 3He Energy U Uranium around 15 million °C, is necessary released for the pressure of the plasma to in Fusion T balance the inward gravitational for- ces. Under these conditions it is pos- Li Fission sible for hydrogen nuclei to fuse together and release energy. Nuclear binding energy In a terrestrial system the aim is to 4He U produce the ‘easiest’ fusion reaction Energy released using deuterium and tritium. Even in fission then the rate of fusion reactions becomes large enough only at high JG97.362/4c Atomic mass particle energy. Therefore, when the Dn required nuclear reactions result from the thermal motions of the nuclei, so-called thermonuclear fusion, it is necessary to achieve u • extremely high temperatures, of at least 100 million °C. -
Stability Study of the Cylindrical Tokamak--Thomas Scaffidi(2011)
Ecole´ normale sup erieure´ Princeton Plasma Physics Laboratory Stage long de recherche, FIP M1 Second semestre 2010-2011 Stability study of the cylindrical tokamak Etude´ de stabilit´edu tokamak cylindrique Author: Supervisor: Thomas Scaffidi Prof. Stephen C. Jardin Abstract Une des instabilit´es les plus probl´ematiques dans les plasmas de tokamak est appel´ee tearing mode . Elle est g´en´er´ee par les gradients de courant et de pression et implique une reconfiguration du champ magn´etique et du champ de vitesse localis´ee dans une fine r´egion autour d’une surface magn´etique r´esonante. Alors que les lignes de champ magn´etique sont `al’´equilibre situ´ees sur des surfaces toriques concentriques, l’instabilit´econduit `ala formation d’ˆıles magn´etiques dans lesquelles les lignes de champ passent d’un tube de flux `al’autre, rendant possible un trans- port thermique radial important et donc cr´eant une perte de confinement. Pour qu’il puisse y avoir une reconfiguration du champ magn´etique, il faut inclure la r´esistivit´edu plasma dans le mod`ele, et nous r´esolvons donc les ´equations de la magn´etohydrodynamique (MHD) r´esistive. On s’int´eresse `ala stabilit´ede configurations d’´equilibre vis-`a-vis de ces instabilit´es dans un syst`eme `ala g´eom´etrie simplifi´ee appel´ele tokamak cylindrique. L’´etude est `ala fois analytique et num´erique. La solution analytique est r´ealis´ee par une m´ethode de type “couche limite” qui tire profit de l’´etroitesse de la zone o`ula reconfiguration a lieu. -
Magnetohydrodynamics 1 19.1Overview
Contents 19 Magnetohydrodynamics 1 19.1Overview...................................... 1 19.2 BasicEquationsofMHD . 2 19.2.1 Maxwell’s Equations in the MHD Approximation . ..... 4 19.2.2 Momentum and Energy Conservation . .. 8 19.2.3 BoundaryConditions. 10 19.2.4 Magneticfieldandvorticity . .. 12 19.3 MagnetostaticEquilibria . ..... 13 19.3.1 Controlled thermonuclear fusion . ..... 13 19.3.2 Z-Pinch .................................. 15 19.3.3 Θ-Pinch .................................. 17 19.3.4 Tokamak.................................. 17 19.4 HydromagneticFlows. .. 18 19.5 Stability of Hydromagnetic Equilibria . ......... 22 19.5.1 LinearPerturbationTheory . .. 22 19.5.2 Z-Pinch: Sausage and Kink Instabilities . ...... 25 19.5.3 EnergyPrinciple ............................. 28 19.6 Dynamos and Reconnection of Magnetic Field Lines . ......... 29 19.6.1 Cowling’stheorem ............................ 30 19.6.2 Kinematicdynamos............................ 30 19.6.3 MagneticReconnection. 31 19.7 Magnetosonic Waves and the Scattering of Cosmic Rays . ......... 33 19.7.1 CosmicRays ............................... 33 19.7.2 Magnetosonic Dispersion Relation . ..... 34 19.7.3 ScatteringofCosmicRays . 36 0 Chapter 19 Magnetohydrodynamics Version 1219.1.K.pdf, 7 September 2012 Please send comments, suggestions, and errata via email to [email protected] or on paper to Kip Thorne, 350-17 Caltech, Pasadena CA 91125 Box 19.1 Reader’s Guide This chapter relies heavily on Chap. 13 and somewhat on the treatment of vorticity • transport in Sec. 14.2 Part VI, Plasma Physics (Chaps. 20-23) relies heavily on this chapter. • 19.1 Overview In preceding chapters, we have described the consequences of incorporating viscosity and thermal conductivity into the description of a fluid. We now turn to our final embellishment of fluid mechanics, in which the fluid is electrically conducting and moves in a magnetic field. -
Application of High Performance Computing for Fusion Research Shimpei Futatani
Application of high performance computing for fusion research Shimpei Futatani Department of Physics, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain The study of the alternative energy source is one of the absolutely imperative research topics in the world as our present energy sources such as fossil fuels are limited. This work is dedicated to the nuclear fusion physics research in close collaboration with existing experimental fusion devices and the ITER organization (www.iter.org) which is an huge international nuclear fusion R&D project. The goal of the ITER project is to demonstrate a clean and safe energy production by nuclear fusion which is the reaction that powers the sun. One of the ideas of the nuclear fusion on the earth is that the very high temperature ionized particles, forming a plasma can be controlled by a magnetic field, called magnetically confined plasma. This is essential, because no material can be sustained against such high temperature reached in a fusion reactor. Tokamak is a device which uses a powerful magnetic field to confine a hot plasma in the shape of a torus. It is a demanding task to achieve a sufficiently good confinement in a tokamak for a ‘burning plasma’ due to various kinds of plasma instabilities. One of the critical unsolved problems is MHD (MagnetoHydroDynamics) instabilities in the fusion plasmas. The MHD instabilities at the plasma boundary damages the plasma facing component of the fusion reactor. One of techniques to control the MHD instabilities is injection of pellets (small deuterium ice bodies). The physics of the interaction between pellet ablation and MHD dynamics is very complex, and uncertainties still remain regarding the theoretical physics as well as the numerical modelling point of view. -
UC San Diego Center for Energy Research, Lppfusion to Collaborate on Fusion Energy Research
Focus Fusion Report October 17, 2017 Summary: • UC San Diego CER to Collaborate • Two More DPF Groups Aim to Use pB11 in 2018 • IEEE Spectrum Reports on LPPFusion • Former Fusion Chief Advocates pB11 in Physics Today UC San Diego Center for Energy Research, LPPFusion to Collaborate on Fusion Energy Research The ideal energy source is the goal of a new collaboration between the Center for Energy Research (CER) at UC San Diego and LPPFusion, Inc. The collaboration, formalized with an agreement on October 2, aims at the development of the dense plasma focus (DPF) device for fusion energy. “The alternate fusion schemes offer a potential route to fusion energy that could be faster and much cheaper than other approaches," explains CER Director, Farhat N. Beg. “LPPFusion is a leader in this field and will make available to CER its research data and expertise to help us set up our own DPF facility at UC San Diego.” LPPFusion’s FF-1 device is one of only a few mega-ampere DPFs in the world. Our research in the coming year will involve the first experiments using hydrogen-boron fuel. This fuel produces energy in the form of charged particles only, not neutrons, which both eliminates radioactive waste and makes possible inexpensive direct conversion of energy to electricity. “The collaboration with the Center for Energy Research will help us to better analyze and understand our data,” said LPPFusion President and Chief Scientist Eric J. Lerner. “Their expertise in plasma simulation will aid our efforts in modeling our experiments. We also expect that, once their own DPF is functioning, we can perform joint experiments that will help demonstrate how the DPF energy output scales with energy input. -
Identification of the Sequence of Steps Intrinsic to Spheromak Formation
Identification of the Sequence of Steps Intrinsic to Spheromak Formation P.M. Bellan, S. You, and G. S. Yun California Institute of Technology Pasadena, CA 91125, USA Abstract. A planar coaxial electrostatic helicity source is used for studying the relaxation process intrinsic to spheromak formation. Experimental observations reveal that spheromak formation involves: (1) breakdown and creation of a number of distinct, arched, filamentary, plasma-filled flux loops that span from cathode to anode gas nozzles, (2) merging of these loops to form a central column, (3) jet-like expansion of the central column, (4) kink instability of the central column, (5) conversion of toroidal flux to poloidal flux by the kink instability. Steps 1 and 3 indicate that spheromak formation involves an MHD pumping of plasma from the gas nozzles into the magnetic flux tube linking the nozzles. In order to measure this pumping, the gas puffing system has been modified to permit simultaneous injection of different gas species into the two ends of the flux tube linking the wall. Gated CCD cameras with narrow-band optical filters are used to track the pumped flows. Keywords: spheromak, magnetohydrodynamics, kink, jet PACS: 52.55.Ip, 52.35.Py, 52.55.Wq, 52.59.Dk INTRODUCTION which is rich in toroidal field energy (typical poloidal currents are 100 kA) but poor in poloidal field energy. Spheromaks are toroidal MHD equilibria incorporating Spheromak formation involves conversion of toroidal nested poloidal magnetic flux surfaces suitable for magnetic flux into poloidal magnetic flux while confining a fusion plasma. Unlike tokamaks, conserving magnetic helicity (but not conserving spheromaks are a self-organizing, minimum-energy magnetic energy). -
Revamping Fusion Research Robert L. Hirsch
Revamping Fusion Research Robert L. Hirsch Journal of Fusion Energy ISSN 0164-0313 Volume 35 Number 2 J Fusion Energ (2016) 35:135-141 DOI 10.1007/s10894-015-0053-y 1 23 Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media New York. This e-offprint is for personal use only and shall not be self- archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com”. 1 23 Author's personal copy J Fusion Energ (2016) 35:135–141 DOI 10.1007/s10894-015-0053-y POLICY Revamping Fusion Research Robert L. Hirsch1 Published online: 28 January 2016 Ó Springer Science+Business Media New York 2016 Abstract A fundamental revamping of magnetic plasma Introduction fusion research is needed, because the current focus of world fusion research—the ITER-tokamak concept—is A practical fusion power system must be economical, virtually certain to be a commercial failure. Towards that publically acceptable, and as simple as possible from a end, a number of technological considerations are descri- regulatory standpoint. In a preceding paper [1] the ITER- bed, believed important to successful fusion research. -
Fusion: the Way Ahead
Fusion: the way ahead Feature: Physics World March 2006 pages 20 - 26 The recent decision to build the world's largest fusion experiment - ITER - in France has thrown down the gauntlet to fusion researchers worldwide. Richard Pitts, Richard Buttery and Simon Pinches describe how the Joint European Torus in the UK is playing a key role in ensuring ITER will demonstrate the reality of fusion power At a Glance: Fusion power • Fusion is the process whereby two light nuclei bind to form a heavier nucleus with the release of energy • Harnessing fusion on Earth via deuterium and tritium reactions would lead to an environmentally friendly and almost limitless energy source • One promising route to fusion power is to magnetically confine a hot, dense plasma inside a doughnut-shaped device called a tokamak • The JET tokamak provides a vital testing ground for understanding the physics and technologies necessary for an eventual fusion reactor • ITER is due to power up in 2016 and will be the next step towards a demonstration fusion power plant, which could be operational by 2035 By 2025 the Earth's population is predicted to reach eight billion. By the turn of the next century it could be as many as 12 billion. Even if the industrialized nations find a way to reduce their energy consumption, this unprecedented increase in population - coupled with rising prosperity in the developing world - will place huge demands on global energy supplies. As our primary sources of energy - fossil fuels - begin to run out, and burning them causes increasing environmental concerns, the human race faces the challenge of finding new energy sources. -
DISTRIBUTION of THIS DOCUMENT IS UNLIMITED Temperatures in the Range 5-10 Kev Are Still Needed, but the Lawson Number Can Be Reduced to the Low 10 Cm Sec Range
TFTR and Other Large Tokamaks Plasma Physics Laboratory, Princeton University Princeton, New Jersey 08544 H.P. Furth CONF-8604223—1 DE86 012761 Introduction The near-term goal of fusion research is to produce deuterium-tritium plasmas with temperatures above 10 keV and Lawson numbers nTE above 10 cm sec. As indicated in Fig. 1, experiments entering this parameter range will be able to satisfy Lawson's break-even criterion, where the fusion power output equals the required plasma-heating-power input (Q = 1 ). The ultimate reactor goal is to reach equilibrium-burn conditions, where the energetic alpha particles generated by the D-T reaction are sufficient to maintain the plasma temperature against all heat losses (Q = °°). At the outset of the international controlled-fusion research effort in the 19 50's, Lawson's goal seemed intimidatingly remote from experimental capabilities. During the following ten years, substantial scientific progress was made, but the rate of advance in the Lawson diagram was not such as to inspire confidence that the fusion program would reach fruition within the lifetime of its pioneers. The notable success of the Kurchatov Institute's T-3 tokamak during 1968-69 brightened the outlook considerably. The tokamak configuration was recognized as a cost-effective experimental tool and has permitted steady progress during subsequent decades. World-wide recognition of the favorable experimental opportunity for entry into the reactor plasma regime led to the initiation, in the mid-1970's, of four large new tokamak projects (Table I). Plans for the Joint European Torus (JET) were defined in 1971-73: th_ very large plasma size and high current of the JET plasma offered a potential for exceeding the Lawson break- even criterion and possibly evan reaching ignition in D-T plasmas.