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MHD Stability and Confinement of Plasmas in a Single Mirror Cell

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MHD Stability and Confinement of Plasmas in a Single Mirror Cell Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 155 MHD Stability and Confinement of Plasmas in a Single Mirror Cell NATALIA SAVENKO ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 UPPSALA ISBN 91-554-6497-1 2006 urn:nbn:se:uu:diva-6637 !" "##$ !#%!& ' ' ' ( ) * + ( , - .( "##$( /0 , 1 ' ' , / 1( ( !&&( 2 !## ( ( 3,4. 5!6&&76$7586!( ) ' ' ' ( 3' '' * ' * ( ) ' * 4 ' ' ' * /0 ' ' ' ' 9 ' ( , ' ( 1 ' :;!# ' <( 1 * ' ( ' ' = '>( ) 1 ' * ' ' '( ) 1 ' ? @ ' ( ) * @ ' ' 9 ( 1 ' ' ' ' ' ( 1 * '' ' 9 A#(" ( ' ( ' ' ' @ ( /0 ' ! " # " # $ %" & ' ()*" " #+,(-.- " B . , - "##$ 3,,. !$&!6$"!7 3,4. 5!6&&76$7586! % %%% 6$$C8 D %EE (-(E F G % %%% 6$$C8H To my parents Nina & Alex iv List of Papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I O. Ågren, and N. Savenko, ‘Magnetic mirror minimum B field with optimal ellipticity’, Physics of Plasmas, 11, 5041, (2004). II O. Ågren and N. Savenko, ‘Theoretical study of increased elec- tron temperature in mirror machines by tuned ion cyclotron reso- nance heating cycles’, Physics of Plasmas, 12, ID 022506, (2005). III O. Ågren and N. Savenko, ‘Minimum B field and idea for im- proved axial confinement by tuned ICRH cycles’, Transaction of Plasma Science and Technology, Vol. 47, No 1T, 285, (2005), ISSN: 1536-1055. IV O. Ågren and N. Savenko, ‘Rigid rotation symmetry of a mar- ginally stable minimum B field and analytical expressions of the flux coordinates’, Physics of Plasmas, 12, ID 042505, (2005). V O. Ågren and N. Savenko, ‘Sloshing ion distribution function in a minimum B mirror field’, Physics of Plasmas, Vol. 12, ID 022504, (2005). VI O. Ågren, V. Moiseenko, N. Savenko ‘Constants of motion in a minimum B mirror magnetic field’, Physical Review E, 72, ID 026408, (2005). VII O.Ågren and N. Savenko, ‘Theory of the straight field line mir- ror’, Conference Proceedings of the 32nd EPS Plasma Physics Conference in Tarragona, Spain 27 June-1 July 2005, ECA Vol. 29C, P.-4.069, (2005). (The paper has been also presented at the Poster Session of the 42nd Culham Plasma Physics Summer School 18th-29th July 2005) VIII N.Savenko and O. Agren, ‘Finite beta correction to the ellipticity of the magnetic flux tube of the straight field line mirror’, sub- mitted to Physics of Plasmas in March (2006). IX O.Ågren, V. Moiseenko, C. Johansson, and N. Savenko, ’ Gyro center invariant and associated diamagnetic current’, Physics of Plasmas, 12, ID 122503, (2005). Reprints were made with permission from the publishers. v Author’s Contributions and Comments In Paper I the thesis author has contributed with the literature survey, derivation of some of the formulae, geometrical interpretation of the stability conditions, figure plots, participated in planning and writing the article. In Paper II comments on resent research on the subject of the paper and the figure plots are made by the thesis author. The thesis author has also participated in the preparation of the article. Paper III is a non-refereed Conference article, which presents the results of Paper I and Paper II. The thesis author has participated in planning, writ- ing the article, preparing the poster and presentation of the results. In Paper IV the thesis author has participated in the analytical part of the work, discussions and preparing of the paper. The thesis author contributions to Paper V are the figure plots, some dis- cussions and the asymptotic formulae. Paper VI has been primarily written by Dr. O. Ågren. The thesis author has taken part in the discussions and preparing the article. Paper VII is a Conference article, based on results of Papers I, II, IV, V, and VI. The thesis author has contributed with planning, writing, preparing the article and the Conference poster and participated in the presentation. Paper VIII has been mainly written by the thesis author with helpful dis- cussions and improvements, made by Dr. O. Ågren. Paper IX has been initiated and written by Dr. O. Ågren. The thesis au- thor has contributed with some discussions and preparation of some of the figure plots, used in the article. vi LIST OF SYMBOLS Symbol Units Quantity B T Magnetic field Im Tm Magnetic scalar potential E V/m Electric field I V Scalar electric potential j Am/ 2 Current density B()z T Magnetic field strength at the z-axis a m Magnetic flux tube radius at the mid plane c m Characteristic length of the device 2 \ ,,TIm (Tm , rad, Tm) Flux coordinates x00,,ys m Flux coordinates rs00,,T m, rad, m Flux coordinates P kg m22/( T s ) Magnetic moment H eV Total energy 2 J& ms/ Longitudinal invariant eCElectron charge vd ,A m/s Cross field drift velocity Hmax Maximum ellipticity of the magnetic flux tube Rm Mirror ratio s m Magnetic field arc length kB eV/K Bolzmann constant TTei, eV Temperature of electrons and ions 3 nnie, m Density T p rad Pitch angle vii 2 PP,,A P& Nm/ Pressure tensor components 2 E Plasma beta, i.e. 2/P0 PBA 1 :0 s Ion gyro frequency, qB0 / mi Q Energy gain factor viii Abbrevations MHD Magnetohydrodynamics ICRH Ion cyclotron resonant heating ECRH Electron cyclotron resonance heating RF Radio frequency Earlier magnetic mirror facilities 2XIIB Single mirror cell mirror facility at Livermore, USA TM Tandem mirror PHAEDRUS Tandem mirror facility at Wisconsin, USA TARA Medium sized tandem mirror at MIT, USA TMX Small tandem mirror at Livermore, USA TMX-U Tandem mirror with thermal barrier, upgraded TMX facility MFTF Largest experimental tandem mirror built at Livermore Operating mirror traps GAMMA 10 Large advanced tandem mirror at Tsukuba, Japan HIEI Small tandem mirror at Kyoto, Japan HANBIT Mirror facility with one plug and one anchor cells at Korea AMBAL-M Large tandem mirror at Novosibirsk, Russia GDT Gas dynamic trap at Novosibirsk GOL-3 Multimirror trap at Novosibirsk Some alternative magnetic confinement schemes FRC Field reversed concept FRM Field reversed mirror RFP Reversed field pinch Microinstabilities which can occur in a high density plasma DGH Dary-Guest-Harris ix DH Double-Hump HFCLC High frequency convective loss cone DCLC Drift cyclotron loss cone AIC Alfven ion cyclotron Toroidal devices ITER International Thermonuclear Experimental Reactor JET Joint European Torus, located at Culham in the UK MAST Mega-Ampere Spherical Tokamak at Culham Science Centre, UK TFTR Tokamak Fusion Test Reactor, at Princeton in the USA EXTRAP An RFP experiment at KTH, Sweden. x Contents 1. Introduction.................................................................................................1 2. Literature review: Theory and experiments in fusion research...................6 2.1 Thermonuclear reaction........................................................................6 2.2 Technical requirements for a fusion reaction .......................................8 2.3 Plasma. Definition and conditions......................................................10 2.4 Plasma confinement ...........................................................................12 2.5 Magnetic bottle. Adiabatic invariants ................................................13 2.6 MHD equilibrium. Plasma beta..........................................................16 2.7 MHD stability. Magnetic well stabilization. ......................................19 2.8 Linear collider ....................................................................................25 2.9 Kinetic Stabilizer................................................................................25 2.10 Microinstabilities in mirrors.............................................................26 2.11 Plasma heating..................................................................................28 2.12 Earlier mirror experimental facilities ...............................................31 2.12.1 Phaedrus....................................................................................31 2.12.2 TARA .......................................................................................31 2.12.4 2XIIB........................................................................................32 2.12.3 TMX .........................................................................................32 2.12.5 MFTF........................................................................................33 2.13 Present mirror facilities; their parameters and obtained experimental data ...........................................................................................................34 2.13.1 GAMMA 10 .............................................................................34 2.13.2 AMBAL-M...............................................................................36 2.13.3 GDT (Gas Dynamic Trap) ........................................................37 2.13.4 GOL-3.......................................................................................39 2.13.5 HANBIT ...................................................................................40
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