Quasi-separatrix layers and 3D reconnection diagnostics for linetied
|
|
- Marilynn Little
- 5 years ago
- Views:
Transcription
1 Quasi-separatrix layers and 3D reconnection diagnostics for linetied tearing modes John M. Finn, LANL A. Steve Richardson, NRL CMSO, Oct 2011 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA U N C L A S S I F I E D
2 Outline Review of Magnetohydrodynamics (MHD) and Reconnection Reconnection Diagnostics Squashing degree Q and quasi-separatrix layer (QSL) Ideal MHD electrostatic potential (Δϕi) and resistive MHD potential (Δϕr) Examples of the Diagnostics Q: simple doublet field Δϕ's & Q: tearing mode in an infinite cylinder Line Tied Modes Two mode approximation for line tied modes Compare Q and Δϕ's for a line tied mode Short case (resistive diffusion) and long case (tearing mode) Summary and Conclusions U N C L A S S I F I E D Slide 2 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
3 Magnetohydrodynamics (MHD) Visco-resistive MHD Force free (zero β) plasma Mass Conservation: Momentum and Ohm's law: Maxwell: U N C L A S S I F I E D Slide 3 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
4 Ideal MHD If plasma resistivity is zero, (ideal Ohm s law) This approximation is good for hot (low resistivity), strongly magnetized plasmas Also good for long length scale, fast plasma dynamics E.g., outer layer for tearing modes; reconnection only occurs in the tearing layer. Outer layer: Ideal MHD is a good From Ideal Ohm s law, the perpendicular fluid velocity is The EXB drift of a particle. U N C L A S S I F I E D Slide 4 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
5 Frozen-in-flux Consider the flux through an arbitrary surface ΔS: U N C L A S S I F I E D Slide 5 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
6 Reconnection If the plasma has finite resistivity (or other non-ideal effects), then frozen flux no longer holds -- the plasma and field lines can slip past one another For large η, this happens globally -- resistive diffusion For very small η, this can only occur locally, associated with changing the magnetic topology -- reconnection Squashing of flux tubes At the origin U N C L A S S I F I E D Slide 6 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33 Outline Review of Magnetohydrodynamics (MHD) and Reconnection Reconnection Diagnostics Squashing degree Q and quasi-separatrix layer (QSL) Ideal MHD electrostatic potential (Δϕi) and resistive MHD potential (Δϕr) Examples of the Diagnostics Q: simple doublet field Δϕ's & Q: tearing mode in an infinite cylinder Line Tied Modes Two mode approximation for line tied modes Compare Q and Δϕ's for a line tied mode Short case (resistive diffusion) and long case (tearing mode) Summary and Conclusions U N C L A S S I F I E D Slide 7 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
34 Reconnection Diagnostics: the squashing degree Geometrically, reconnection is associated with the stretching and squashing of flux tubes Squashing degree is defined using a field line mapping Field lines define mapping: Jacobian J maps tangent vectors: Max and min eigenvalues of minor axis of ellipse from z=-l to z=+l (Singular values of J) 2 give lengths of major and Since we are interested in squashing and not flux tube expansion, take ratio of singular values to find aspect ratio of ellipse Aspect ratio is a function of squashing degree Q [Priest Démoulin 95, Titov 07] Large Q -- Quasi-separatrix layers (QSLs) U N C L A S S I F I E D Slide 8 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
35 Reconnection Diagnostics: potentials Δϕi and Δϕr Reconnection is due to a localized breakdown of the ideal Ohm s law (consider resistive MHD as a special case) Given magnetic fields B and vector potential A(x,t), we can compute two potentials: These equations can be integrated along field lines from one end of the system to the other to obtain Δϕi and Δϕr The ideal potential Δϕi was considered in Lau and Finn, ApJ, 350: , Feb The difference between these is the integrated parallel current, or quasi potential : Hesse, Forbes, and Birn, ApJ, 631(2):1227, Regions where these two quantities differ significantly are reconnection sites U N C L A S S I F I E D Slide 9 /25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
36 Outline Review of Magnetohydrodynamics (MHD) and Reconnection Reconnection Diagnostics Squashing degree Q and quasi-separatrix layer (QSL) Ideal MHD electrostatic potential (Δϕi) and resistive MHD potential (Δϕr) Examples of the Diagnostics Q: simple doublet field Δϕ's & Q: tearing mode in an infinite cylinder Line Tied Modes Two mode approximation for line tied modes Compare Q and Δϕ's for a line tied mode Short case (resistive diffusion) and long case (tearing mode) Summary and Conclusions U N C L A S S I F I E D Slide 10/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
37 Examples of Diagnostics: Q for Doublet Field Doublet-like field contains X-point, flux tube stretching, and real separatrix when L goes to infinity Magnetic field: x Integrating field lines gives mapping M Regions of large Q define the quasiseparatrix layer (QSL) on the stable manifold (a) 1 (b) 1 x L=1 L=2 x2 0 x x 1 U N C L A S S I F I E D x 1 Slide 11/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
38 Examples of Diagnostics: Q for Doublet Field Q is a function of field line, so can be plotted as a function of initial or final point (integrating backwards -- unstable manifold) (a) (b) x X L= x...or as an isosurface 1 in 3D space In 3D, the QSL looks like a hyperbolic flux tube, a structure studied in solar physics in models of reconnection in solar flares 0 x X U N C L A S S I F I E D 1 x z 2 Slide 12/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
39 Second Example: Bifurcation of an arcade QSLs could also indicate the onset of reconnection, just before a bifurcation causes the creation of closed flux surfaces Example: Magnetic Arcade to plasmoid bifurcation L/L L/L x ini x ini y y y x x x U N C L A S S I F I E D Slide 13/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
40 Examples of Diagnostics: m=1 Tearing Mode in a Periodic Cylinder Solve linearized force-free MHD equations -- tokamak-like, cylindrical Zero β Tearing mode is localized near the mode rational surface, where and goes like, growth rate γ B r B q B z v r v q v z 0 B 0 ṽ U N C L A S S I F I E D Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA Slide 14/25
41 Examples of Diagnostics: Periodic Tearing Mode For infinitesimal tearing mode, can estimate Δϕi Integrating z=-l to z=l gives The argument of the sinc function is approximately linear in r, centered at the mode rational surface The width of the sinc function is then approximately U N C L A S S I F I E D Slide 15/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
42 Examples of Diagnostics: Periodic Tearing Mode Mode amplitude = 1x10-3 (a) r Numerical results are in good agreement with the sinc function calculation Δϕideal Δϕresistive Difference (b) 1.4 (c) p/2 /p/ 3p/2/2p/ 0 p/2 /p/ 3p/2/2p/ 0 p/2 /p/ 3p/2/2p/ r r q q U N C L A S S I F I E D Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA Mode amplitude = 1x10-2 (b) 1.4 Δϕideal (c) 1.3 r p/2 /p/ 3p/2/2p/ q r q Difference p/2 /p/ 3p/2/2p/ q Slide 16/25
43 Examples of Diagnostics: Periodic Tearing Mode Calculation of Q shows peak near stable manifold, which indicates presence of a QSL (mode amplitude = 1x10-3 ) log(q) θ=π/2 As amplitude increases, Q becomes more peaked at the stable manifold. U N C L A S S I F I E D Slide 17/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
44 Outline Review of Magnetohydrodynamics (MHD) and Reconnection Reconnection Diagnostics Squashing degree Q and quasi-separatrix layer (QSL) Ideal MHD electrostatic potential (Δϕi) and resistive MHD potential (Δϕr) Examples of the Diagnostics Q: simple doublet field Δϕ's & Q: tearing mode in an infinite cylinder Line Tied Modes Two mode approximation for line tied modes Compare Q and Δϕ's for a line tied mode Short case (resistive diffusion) and long case (tearing mode) Summary and Conclusions U N C L A S S I F I E D Slide 18/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
45 Line Tied Modes: The Two-Mode Approximation Consider the same cylindrical system, but with line-tied boundary conditions Satisfy BCs by expanding in radial eigenfunctions of the infinite cylinder [Evstatiev et al. 2006] Expansion coefficients εk chosen so that the BCs are satisfied For large L, two modes with very similar k will have nearly the same radial form BCs then imply a matrix equation for εk, k1, k2, and L, which gives U N C L A S S I F I E D Slide 19/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
46 Line Tied Modes: Two-Mode Approximation Compute growth rate for a range of k s, and pick k1 and k2 with the same γ Modes have similar r dependance Distance between mode rational surfaces gives the geometric width wg of the LT mode: Delzanno & Finn, 2008 Huang & Zweibel, 2009 U N C L A S S I F I E D Slide 20/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
47 Line Tied Modes: Two Cases Examine two cases Case I: wt>wg (Large L), this mode should behave like a tearing mode (with reconnection). Case II: wt<wg, (Small L) this mode should just have global resistive diffusion (not reconnection) Apply reconnection diagnostics to these, to see if the two cases can be distinguished Previous work showed that Case I has reconnection, but Case II has only resistive diffusion... Delzanno & Finn, 2008; Huang & Zweibel, 2009 U N C L A S S I F I E D Slide 21/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
48 Case I (wt>wg, large L): Diagnostics for amplitude = 1x10-3 (a) (c) (b) r Δϕideal r Q p/2 /p/ 3p/2/2p/ p/2 /p/ 3p/2/2p/ 2.5 q q Dots: surface of section U N C L A S S I F I E D Slide 22/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
49 Larger amplitude -- nonlinear... r r (a) (b) p/2 /p/ 3p/2/2p/ q Δϕideal Δϕresistive r (c) p/2 /p/ 3p/2/2p/ q - Surface of section shows chaotic region Q p/2 /p/ 3p/2/2p/ q U N C L A S S I F I E D Slide 23/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
50 Case II (wt<wg, small L): Two-mode results Amplitude=1x10-3 for calculation of Δϕ's Range of amplitudes used for Q calculations Neither Q nor alone can distinguish between Case I and Case II U N C L A S S I F I E D Slide 24/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
51 Summary and Conclusions Reviewed two reconnection diagnostics Electrostatic potentials Δϕi (~ideal MHD) and Δϕr (resistive MHD). Better than just the difference -- Squashing degree Q Applied these to two simple examples Doublet-like field: Q becomes localized along the separatrix for long systems Q measures geometry and topology of field lines Single tearing mode: Δϕ becomes localized at the mode rational surface Δϕ measures mode dynamics through A/ t, as well as field line geometry Δϕ good even for infinitesimal modes Q measures equilibrium field rather than tearing mode for small amplitude modes Applied to two cases (L large; L small) for 'line tied' modes Q and Δϕ s both detect tearing mode By comparing (Δϕi - Δϕr)= to Δϕi the cases can be distinguished U N C L A S S I F I E D Slide 25/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
52 References Lau Finn, 1990 Priest Démoulin, 1995 Titov, 2007 Delzanno Finn, 2008 Huang Zweibel, 2009 U N C L A S S I F I E D Slide 26/25 Operated by Los Alamos National Security, LLC for the U.S. Department of Energy s NNSA
MAGNETOHYDRODYNAMICS
Chapter 6 MAGNETOHYDRODYNAMICS 6.1 Introduction Magnetohydrodynamics is a branch of plasma physics dealing with dc or low frequency effects in fully ionized magnetized plasma. In this chapter we will study
More informationOn the nature of three-dimensional magnetic reconnection
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A7, 1285, doi:10.1029/2002ja009812, 2003 On the nature of three-dimensional magnetic reconnection E. R. Priest School of Mathematics and Statistics, University
More informationTwo Fluid Dynamo and Edge-Resonant m=0 Tearing Instability in Reversed Field Pinch
1 Two Fluid Dynamo and Edge-Resonant m= Tearing Instability in Reversed Field Pinch V.V. Mirnov 1), C.C.Hegna 1), S.C. Prager 1), C.R.Sovinec 1), and H.Tian 1) 1) The University of Wisconsin-Madison, Madison,
More informationSMR/ Summer College on Plasma Physics. 30 July - 24 August, Introduction to Magnetic Island Theory.
SMR/1856-1 2007 Summer College on Plasma Physics 30 July - 24 August, 2007 Introduction to Magnetic Island Theory. R. Fitzpatrick Inst. for Fusion Studies University of Texas at Austin USA Introduction
More informationConservation Laws in Ideal MHD
Conservation Laws in Ideal MHD Nick Murphy Harvard-Smithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 3, 2016 These lecture notes are largely based on Plasma Physics for Astrophysics
More informationMagnetic Reconnection: Recent Developments and Future Challenges
Magnetic Reconnection: Recent Developments and Future Challenges A. Bhattacharjee Center for Integrated Computation and Analysis of Reconnection and Turbulence (CICART) Space Science Center, University
More informationFundamentals of Magnetic Island Theory in Tokamaks
Fundamentals of Magnetic Island Theory in Tokamaks Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX, USA Talk available at http://farside.ph.utexas.edu/talks/talks.html
More informationCurrent-driven instabilities
Current-driven instabilities Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 21 st February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously In the last
More informationMagnetic Reconnection: explosions in space and astrophysical plasma. J. F. Drake University of Maryland
Magnetic Reconnection: explosions in space and astrophysical plasma J. F. Drake University of Maryland Magnetic Energy Dissipation in the Universe The conversion of magnetic energy to heat and high speed
More informationSW103: Lecture 2. Magnetohydrodynamics and MHD models
SW103: Lecture 2 Magnetohydrodynamics and MHD models Scale sizes in the Solar Terrestrial System: or why we use MagnetoHydroDynamics Sun-Earth distance = 1 Astronomical Unit (AU) 200 R Sun 20,000 R E 1
More informationMomentum transport from magnetic reconnection in laboratory an. plasmas. Fatima Ebrahimi
Momentum transport from magnetic reconnection in laboratory and astrophysical plasmas Space Science Center - University of New Hampshire collaborators : V. Mirnov, S. Prager, D. Schnack, C. Sovinec Center
More informationReduced MHD. Nick Murphy. Harvard-Smithsonian Center for Astrophysics. Astronomy 253: Plasma Astrophysics. February 19, 2014
Reduced MHD Nick Murphy Harvard-Smithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 19, 2014 These lecture notes are largely based on Lectures in Magnetohydrodynamics by Dalton
More informationEvolution of Twisted Magnetic Flux Ropes Emerging into the Corona
Evolution of Twisted Magnetic Flux Ropes Emerging into the Corona Yuhong Fan High Altitude Observatory, National Center for Atmospheric Research Collaborators: Sarah Gibson (HAO/NCAR) Ward Manchester (Univ.
More informationExact solutions for magnetic annihilation in curvilinear geometry
Exact solutions for magnetic annihilation in curvilinear geometry E. Tassi b,, V.S. Titov and G. Hornig Theoretische Physik IV, Ruhr-Universität Bochum, 44780 Bochum, Germany b Theoretische Physik IV,
More informationIssues in Neoclassical Tearing Mode Theory
Issues in Neoclassical Tearing Mode Theory Richard Fitzpatrick Institute for Fusion Studies University of Texas at Austin Austin, TX Tearing Mode Stability in Tokamaks According to standard (single-fluid)
More information(a) (b) (c) (d) (e) (f) r (minor radius) time. time. Soft X-ray. T_e contours (ECE) r (minor radius) time time
Studies of Spherical Tori, Stellarators and Anisotropic Pressure with M3D 1 L.E. Sugiyama 1), W. Park 2), H.R. Strauss 3), S.R. Hudson 2), D. Stutman 4), X-Z. Tang 2) 1) Massachusetts Institute of Technology,
More informationRECURSIVE RECONNECTION AND MAGNETIC SKELETONS
The Astrophysical Journal, 675:1656 1665, 2008 March 10 # 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A. A RECURSIVE RECONNECTION AND MAGNETIC SKELETONS C. E. Parnell and
More informationMacroscopic plasma description
Macroscopic plasma description Macroscopic plasma theories are fluid theories at different levels single fluid (magnetohydrodynamics MHD) two-fluid (multifluid, separate equations for electron and ion
More informationFormation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas )
Formation and Long Term Evolution of an Externally Driven Magnetic Island in Rotating Plasmas ) Yasutomo ISHII and Andrei SMOLYAKOV 1) Japan Atomic Energy Agency, Ibaraki 311-0102, Japan 1) University
More information0 Magnetically Confined Plasma
0 Magnetically Confined Plasma 0.1 Particle Motion in Prescribed Fields The equation of motion for species s (= e, i) is written as d v ( s m s dt = q s E + vs B). The motion in a constant magnetic field
More informationWhy are flare ribbons associated with the spines of magnetic null points generically elongated?
Solar Physics DOI: 10.1007/ - - - - Why are flare ribbons associated with the spines of magnetic null points generically elongated? David Pontin 1 Klaus Galsgaard 2 Pascal Démoulin 3 c Springer Abstract
More informationSimple examples of MHD equilibria
Department of Physics Seminar. grade: Nuclear engineering Simple examples of MHD equilibria Author: Ingrid Vavtar Mentor: prof. ddr. Tomaž Gyergyek Ljubljana, 017 Summary: In this seminar paper I will
More informationHeat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UW-Madison
Heat Transport in a Stochastic Magnetic Field John Sarff Physics Dept, UW-Madison CMPD & CMSO Winter School UCLA Jan 5-10, 2009 Magnetic perturbations can destroy the nested-surface topology desired for
More informationSolar Flare. A solar flare is a sudden brightening of solar atmosphere (photosphere, chromosphere and corona)
Solar Flares Solar Flare A solar flare is a sudden brightening of solar atmosphere (photosphere, chromosphere and corona) Flares release 1027-1032 ergs energy in tens of minutes. (Note: one H-bomb: 10
More informationControl of linear modes in cylindrical resistive MHD with a resistive wall, plasma rotation, and complex gain
Control of linear modes in cylindrical resistive MHD with a resistive wall, plasma rotation, and complex gain Dylan Brennan 1 and John Finn 2 contributions from Andrew Cole 3 1 Princeton University / PPPL
More informationThe Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin
The Linear Theory of Tearing Modes in periodic, cyindrical plasmas Cary Forest University of Wisconsin 1 Resistive MHD E + v B = ηj (no energy principle) Role of resistivity No frozen flux, B can tear
More informationINTERACTION OF AN EXTERNAL ROTATING MAGNETIC FIELD WITH THE PLASMA TEARING MODE SURROUNDED BY A RESISTIVE WALL
INTERACTION OF AN EXTERNAL ROTATING MAGNETIC FIELD WITH THE PLASMA TEARING MODE SURROUNDED BY A RESISTIVE WALL S.C. GUO* and M.S. CHU GENERAL ATOMICS *Permanent Address: Consorzio RFX, Padova, Italy **The
More informationarxiv: v1 [physics.plasm-ph] 11 Mar 2016
1 Effect of magnetic perturbations on the 3D MHD self-organization of shaped tokamak plasmas arxiv:1603.03572v1 [physics.plasm-ph] 11 Mar 2016 D. Bonfiglio 1, S. Cappello 1, M. Veranda 1, L. Chacón 2 and
More informationNonlinear 3D MHD physics of the helical reversed-field pinch
Nonlinear 3D MHD physics of the helical reversed-field pinch Daniele Bonfiglio* Consorzio RFX, Euratom-ENEA Association, Padova, Italy *In collaboration with: S. Cappello, L. Chacón (Oak Ridge National
More informationFluid equations, magnetohydrodynamics
Fluid equations, magnetohydrodynamics Multi-fluid theory Equation of state Single-fluid theory Generalised Ohm s law Magnetic tension and plasma beta Stationarity and equilibria Validity of magnetohydrodynamics
More informationSpace Plasma Physics Thomas Wiegelmann, 2012
Space Plasma Physics Thomas Wiegelmann, 2012 1. Basic Plasma Physics concepts 2. Overview about solar system plasmas Plasma Models 3. Single particle motion, Test particle model 4. Statistic description
More information3D hybrid-kinetic turbulence and phase-space cascades
3D hybrid-kinetic turbulence and phase-space cascades ( in a β = 1 plasma ) Silvio Sergio Cerri Department of Astrophysical Sciences, Princeton University, USA 11th Plasma Kinetics Working Meeting WPI
More informationRecapitulation: Questions on Chaps. 1 and 2 #A
Recapitulation: Questions on Chaps. 1 and 2 #A Chapter 1. Introduction What is the importance of plasma physics? How are plasmas confined in the laboratory and in nature? Why are plasmas important in astrophysics?
More informationCurrent associated with a voltage increase over magnetic flux ropes in a helium plasma Sarah Smolenski 1, Walter Gekelman 2, Timothy DeHass 2
Current associated with a voltage increase over magnetic flux ropes in a helium plasma Sarah Smolenski 1, Walter Gekelman 2, Timothy DeHass 2 1 : Department of Physics and Astronomy, University of California
More informationAsymmetric Magnetic Reconnection and the Motion of Magnetic Null Points
Asymmetric Magnetic Reconnection and the Motion of Magnetic Null Points Nick Murphy Harvard-Smithsonian Center for Astrophysics 10th Cambridge Workshop on Magnetic Reconnection Santa Fe, New Mexico September
More informationResistive MHD, reconnection and resistive tearing modes
DRAFT 1 Resistive MHD, reconnection and resistive tearing modes Felix I. Parra Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK (This version is of 6 May 18 1. Introduction
More informationMHD RELATED TO 2-FLUID THEORY, KINETIC THEORY AND MAGANETIC RECONNECTION
MHD RELATED TO 2-FLUID THEORY, KINETIC THEORY AND MAGANETIC RECONNECTION Marty Goldman University of Colorado Spring 2017 Physics 5150 Issues 2 How is MHD related to 2-fluid theory Level of MHD depends
More informationIdeal Magnetohydrodynamics (MHD)
Ideal Magnetohydrodynamics (MHD) Nick Murphy Harvard-Smithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 1, 2016 These lecture notes are largely based on Lectures in Magnetohydrodynamics
More informationThe kink instability of a coronal magnetic loop as a trigger mechanism for solar eruptions
The kink instability of a coronal magnetic loop as a trigger mechanism for solar eruptions T. Török 1 and B. Kliem 2 1 School of Mathematics and Statistics, University of St. Andrews St. Andrews, Fife
More informationThe nature of separator current layers in MHS equilibria. I. Current parallel to the separator
A&A 573, A44 (2015) DOI: 10.1051/0004-6361/201424348 c ESO 2014 Astronomy & Astrophysics The nature of separator current layers in MHS equilibria I. Current parallel to the separator J. E. H. Stevenson,
More informationUniversity of Warwick institutional repository:
University of Warwick institutional repository: http://go.warwick.ac.uk/wrap This paper is made available online in accordance with publisher policies. Please scroll down to view the document itself. Please
More informationAsymmetric Magnetic Reconnection in the Solar Atmosphere
Asymmetric Magnetic Reconnection in the Solar Atmosphere Nick Murphy Harvard-Smithsonian Center for Astrophysics Pre-Hurricane NIMROD Team Meeting Providence, Rhode Island October 27, 2012 Collaborators:
More informationDispersive Media, Lecture 7 - Thomas Johnson 1. Waves in plasmas. T. Johnson
2017-02-14 Dispersive Media, Lecture 7 - Thomas Johnson 1 Waves in plasmas T. Johnson Introduction to plasmas as a coupled system Magneto-Hydro Dynamics, MHD Plasmas without magnetic fields Cold plasmas
More informationAsymmetric Magnetic Reconnection in the Solar Atmosphere
Asymmetric Magnetic Reconnection in the Solar Atmosphere Nick Murphy Harvard-Smithsonian Center for Astrophysics October 23, 2013 NASA Goddard Space Flight Center Collaborators and Co-Conspirators: John
More informationSawteeth in Tokamaks and their relation to other Two-Fluid Reconnection Phenomena
Sawteeth in Tokamaks and their relation to other Two-Fluid Reconnection Phenomena S. C. Jardin 1, N. Ferraro 2, J. Chen 1, et al 1 Princeton Plasma Physics Laboratory 2 General Atomics Supported by the
More informationAstronomy. Astrophysics. Numerical modelling of 3D reconnection. II. Comparison between rotational and spinning footpoint motions
A&A 459, 627 639 (2006) DOI: 10.1051/0004-6361:20065716 c ESO 2006 Astronomy & Astrophysics Numerical modelling of 3D reconnection II. Comparison between rotational and spinning footpoint motions I. De
More informationControl of Neo-classical tearing mode (NTM) in advanced scenarios
FIRST CHENGDU THEORY FESTIVAL Control of Neo-classical tearing mode (NTM) in advanced scenarios Zheng-Xiong Wang Dalian University of Technology (DLUT) Dalian, China Chengdu, China, 28 Aug, 2018 Outline
More informationWhere will efficient energy release occur in 3D magnetic configurations?
Where will efficient energy release occur in 3D magnetic configurations? P. Démoulin Observatoire de Paris, section de Meudon, LESIA, UMR 8109 (CNRS), F-9195 Meudon Cedex, France Abstract The energy needed
More informationSpace Physics. An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres. May-Britt Kallenrode. Springer
May-Britt Kallenrode Space Physics An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres With 170 Figures, 9 Tables, Numerous Exercises and Problems Springer Contents 1. Introduction
More informationPHYSICS. Chapter 24 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 24 Lecture RANDALL D. KNIGHT Chapter 24 Gauss s Law IN THIS CHAPTER, you will learn about and apply Gauss s law. Slide 24-2 Chapter
More informationExperimental Investigations of Magnetic Reconnection. J Egedal. MIT, PSFC, Cambridge, MA
Experimental Investigations of Magnetic Reconnection J Egedal MIT, PSFC, Cambridge, MA Coronal Mass Ejections Movie from NASA s Solar Dynamics Observatory (SDO) Space Weather The Solar Wind affects the
More informationPlasma spectroscopy when there is magnetic reconnection associated with Rayleigh-Taylor instability in the Caltech spheromak jet experiment
Plasma spectroscopy when there is magnetic reconnection associated with Rayleigh-Taylor instability in the Caltech spheromak jet experiment KB Chai Korea Atomic Energy Research Institute/Caltech Paul M.
More informationA Lagrangian approach to the kinematic dynamo
1 A Lagrangian approach to the kinematic dynamo Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc/ 5 March 2001 with Allen
More informationSpecial topic JPFR article Prospects of Research on Innovative Concepts in ITER Era contribution by M. Brown Section 5.2.2
Special topic JPFR article Prospects of Research on Innovative Concepts in ITER Era contribution by M. Brown Section 5.2.2 5.2.2 Dynamo and Reconnection Research: Overview: Spheromaks undergo a relaxation
More informationDerivation of dynamo current drive in a closed current volume and stable current sustainment in the HIT SI experiment
Derivation of dynamo current drive and stable current sustainment in the HIT SI experiment 1 Derivation of dynamo current drive in a closed current volume and stable current sustainment in the HIT SI experiment
More informationMAGNETIC NOZZLE PLASMA EXHAUST SIMULATION FOR THE VASIMR ADVANCED PROPULSION CONCEPT
MAGNETIC NOZZLE PLASMA EXHAUST SIMULATION FOR THE VASIMR ADVANCED PROPULSION CONCEPT ABSTRACT A. G. Tarditi and J. V. Shebalin Advanced Space Propulsion Laboratory NASA Johnson Space Center Houston, TX
More informationUniform Electric Fields
Uniform Electric Fields The figure shows an electric field that is the same in strength and direction at every point in a region of space. This is called a uniform electric field. The easiest way to produce
More informationHighlights from (3D) Modeling of Tokamak Disruptions
Highlights from (3D) Modeling of Tokamak Disruptions Presented by V.A. Izzo With major contributions from S.E. Kruger, H.R. Strauss, R. Paccagnella, MHD Control Workshop 2010 Madison, WI ..onset of rapidly
More informationCoronal Magnetic Field Extrapolations
3 rd SOLAIRE School Solar Observational Data Analysis (SODAS) Coronal Magnetic Field Extrapolations Stéphane RÉGNIER University of St Andrews What I will focus on Magnetic field extrapolation of active
More informationOn magnetic reconnection and flux rope topology in solar flux emergence
MNRAS 438, 1500 1506 (2014) Advance Access publication 2013 December 19 doi:10.1093/mnras/stt2285 On magnetic reconnection and flux rope topology in solar flux emergence D. MacTaggart 1 and A. L. Haynes
More informationPhysical modeling of coronal magnetic fields and currents
Physical modeling of coronal magnetic fields and currents Participants: E. Elkina,, B. Nikutowski,, A. Otto, J. Santos (Moscow,Lindau,, Fairbanks, São José dos Campos) Goal: Forward modeling to understand
More informationMHD SIMULATIONS IN PLASMA PHYSICS
MHD SIMULATIONS IN PLASMA PHYSICS P. Jelínek 1,2, M. Bárta 3 1 University of South Bohemia, Department of Physics, Jeronýmova 10, 371 15 České Budějovice 2 Charles University, Faculty of Mathematics and
More informationNIMROD FROM THE CUSTOMER S PERSPECTIVE MING CHU. General Atomics. Nimrod Project Review Meeting July 21 22, 1997
NIMROD FROM THE CUSTOMER S PERSPECTIVE MING CHU General Atomics Nimrod Project Review Meeting July 21 22, 1997 Work supported by the U.S. Department of Energy under Grant DE-FG03-95ER54309 and Contract
More information3/22/2016. Chapter 27 Gauss s Law. Chapter 27 Preview. Chapter 27 Preview. Chapter Goal: To understand and apply Gauss s law. Slide 27-2.
Chapter 27 Gauss s Law Chapter Goal: To understand and apply Gauss s law. Slide 27-2 Chapter 27 Preview Slide 27-3 Chapter 27 Preview Slide 27-4 1 Chapter 27 Preview Slide 27-5 Chapter 27 Preview Slide
More informationMagnetic Reconnection in Laboratory, Astrophysical, and Space Plasmas
Magnetic Reconnection in Laboratory, Astrophysical, and Space Plasmas Nick Murphy Harvard-Smithsonian Center for Astrophysics namurphy@cfa.harvard.edu http://www.cfa.harvard.edu/ namurphy/ November 18,
More informationJet Stability: A computational survey
Jet Stability Galway 2008-1 Jet Stability: A computational survey Rony Keppens Centre for Plasma-Astrophysics, K.U.Leuven (Belgium) & FOM-Institute for Plasma Physics Rijnhuizen & Astronomical Institute,
More informationIntegrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport
1 Integrated Simulation of ELM Energy Loss Determined by Pedestal MHD and SOL Transport N. Hayashi, T. Takizuka, T. Ozeki, N. Aiba, N. Oyama Japan Atomic Energy Agency, Naka, Ibaraki-ken, 311-0193 Japan
More informationNumerical Simulations on Flux Tube Tectonic Model for Solar Coronal Heating
Numerical Simulations on Flux Tube Tectonic Model for Solar Coronal Heating C. M. S. Negi Assistant Professor, Department of Applied Science, Nanhi Pari Seemant Engineering Institute, Pithoragarh (Uttarakhand)
More informationp = nkt p ~! " !" /!t + # "u = 0 Assumptions for MHD Fluid picture !du/dt = nq(e + uxb) " #p + other Newton s 2nd law Maxwell s equations
Intro to MHD Newton s 2nd law Maxwell s equations Plasmas as fluids Role of magnetic field and MHD Ideal MHD What do we need to know to understand the sun, solar wind&shocks, magnetospheres? Some material
More informationKINEMATIC MAGNETIC RECONNECTION AT 3D NULL POINTS
KINEMATIC MAGNETIC RECONNECTION AT 3D NULL POINTS D. I. Pontin, G. Hornig, and E. R. Priest Mathematical Institute, Universit of St Andrews, St Andrews, Fife, KY6 9SS, UK, Email: davidp@mcs.st-and.ac.uk
More informationMagnetically Confined Fusion: Transport in the core and in the Scrape- off Layer Bogdan Hnat
Magnetically Confined Fusion: Transport in the core and in the Scrape- off Layer ogdan Hnat Joe Dewhurst, David Higgins, Steve Gallagher, James Robinson and Paula Copil Fusion Reaction H + 3 H 4 He + n
More informationRandom Walk on the Surface of the Sun
Random Walk on the Surface of the Sun Chung-Sang Ng Geophysical Institute, University of Alaska Fairbanks UAF Physics Journal Club September 10, 2010 Collaborators/Acknowledgements Amitava Bhattacharjee,
More informationA Simulation Model for Drift Resistive Ballooning Turbulence Examining the Influence of Self-consistent Zonal Flows *
A Simulation Model for Drift Resistive Ballooning Turbulence Examining the Influence of Self-consistent Zonal Flows * Bruce I. Cohen, Maxim V. Umansky, Ilon Joseph Lawrence Livermore National Laboratory
More information2/8/16 Dispersive Media, Lecture 5 - Thomas Johnson 1. Waves in plasmas. T. Johnson
2/8/16 Dispersive Media, Lecture 5 - Thomas Johnson 1 Waves in plasmas T. Johnson Introduction to plasma physics Magneto-Hydro Dynamics, MHD Plasmas without magnetic fields Cold plasmas Transverse waves
More informationAsymmetric Magnetic Reconnection in Coronal Mass Ejection Current Sheets
Asymmetric Magnetic Reconnection in Coronal Mass Ejection Current Sheets Nicholas Murphy, 1 Mari Paz Miralles, 1 Crystal Pope, 1,2 John Raymond, 1 Kathy Reeves, 1 Dan Seaton, 3 & David Webb 4 1 Harvard-Smithsonian
More informationA Lagrangian approach to the study of the kinematic dynamo
1 A Lagrangian approach to the study of the kinematic dynamo Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc/ October
More informationIntroduction to Magnetohydrodynamics (MHD)
Introduction to Magnetohydrodynamics (MHD) Tony Arber University of Warwick 4th SOLARNET Summer School on Solar MHD and Reconnection Aim Derivation of MHD equations from conservation laws Quasi-neutrality
More informationPh.D. QUALIFYING EXAMINATION PART A. Tuesday, January 3, 2012, 1:00 5:00 P.M.
PhD QUALIFYING EXAMINATION PART A Tuesday, January 3, 212, 1: 5: PM Work each problem on a separate sheet(s) of paper and put your identifying number on each page Do not use your name Each problem has
More informationSimulations of Sawteeth in CTH. Nicholas Roberds August 15, 2015
Simulations of Sawteeth in CTH Nicholas Roberds August 15, 2015 Outline Problem Description Simulations of a small tokamak Simulations of CTH 2 Sawtoothing Sawtoothing is a phenomenon that is seen in all
More informationIntroduction to Plasma Physics
Introduction to Plasma Physics Hartmut Zohm Max-Planck-Institut für Plasmaphysik 85748 Garching DPG Advanced Physics School The Physics of ITER Bad Honnef, 22.09.2014 A simplistic view on a Fusion Power
More informationCHAPTER 8 CONSERVATION LAWS
CHAPTER 8 CONSERVATION LAWS Outlines 1. Charge and Energy 2. The Poynting s Theorem 3. Momentum 4. Angular Momentum 2 Conservation of charge and energy The net amount of charges in a volume V is given
More informationMeasuring from electron temperature fluctuations in the Tokamak Fusion Test Reactor
PHYSICS OF PLASMAS VOLUME 5, NUMBER FEBRUARY 1998 Measuring from electron temperature fluctuations in the Tokamak Fusion Test Reactor C. Ren, a) J. D. Callen, T. A. Gianakon, and C. C. Hegna University
More informationScaling of Magnetic Reconnection in Collisional and Kinetic Regimes
Scaling of Magnetic Reconnection in Collisional and Kinetic Regimes William Daughton Los Alamos National Laboratory Collaborators: Vadim Roytershteyn, Brian Albright H. Karimabadi, Lin Yin & Kevin Bowers
More informationStabilization of sawteeth in tokamaks with toroidal flows
PHYSICS OF PLASMAS VOLUME 9, NUMBER 7 JULY 2002 Stabilization of sawteeth in tokamaks with toroidal flows Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College
More informationApplying Asymptotic Approximations to the Full Two-Fluid Plasma System to Study Reduced Fluid Models
0-0 Applying Asymptotic Approximations to the Full Two-Fluid Plasma System to Study Reduced Fluid Models B. Srinivasan, U. Shumlak Aerospace and Energetics Research Program, University of Washington, Seattle,
More informationarxiv:astro-ph/ v1 27 May 2005
2D stationary resistive MHD flows: borderline to magnetic reconnection solutions D.H. Nickeler a,, H.-J. Fahr b arxiv:astro-ph/0505554v1 27 May 2005 a Astronomical Institute, Utrecht University, Princetonplein
More informationFast Magnetic Reconnection in Fluid Models of (Pair) Plasma
Fast Magnetic Reconnection in Fluid Models of (Pair) Plasma E. Alec Johnson Department of Mathematics, UW-Madison Presented on September 10, 2009, Postdoctoral Research Symposium, Argonne National Laboratories.
More informationGoing with the flow: A study of Lagrangian derivatives
1 Going with the flow: A study of Lagrangian derivatives Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc/ 12 February
More informationStructure of magnetic separators and separator reconnection
Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi:10.1029/2009ja014557, 2010 Structure of magnetic separators and separator reconnection C. E. Parnell, 1 A. L. Haynes, 1 and K.
More informationThe RFP: Plasma Confinement with a Reversed Twist
The RFP: Plasma Confinement with a Reversed Twist JOHN SARFF Department of Physics University of Wisconsin-Madison Invited Tutorial 1997 Meeting APS DPP Pittsburgh Nov. 19, 1997 A tutorial on the Reversed
More informationCLASSICAL ELECTRICITY
CLASSICAL ELECTRICITY AND MAGNETISM by WOLFGANG K. H. PANOFSKY Stanford University and MELBA PHILLIPS Washington University SECOND EDITION ADDISON-WESLEY PUBLISHING COMPANY Reading, Massachusetts Menlo
More informationNumerical experiments on wave propagation toward a 3D null point due to rotational motions
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A1, 1042, doi:10.1029/2002ja009393, 2003 Numerical experiments on wave propagation toward a 3D null point due to rotational motions K. Galsgaard and E. R.
More informationCHAPTER 7 ELECTRODYNAMICS
CHAPTER 7 ELECTRODYNAMICS Outlines 1. Electromotive Force 2. Electromagnetic Induction 3. Maxwell s Equations Michael Faraday James C. Maxwell 2 Summary of Electrostatics and Magnetostatics ρ/ε This semester,
More informationFast Ion Confinement in the MST Reversed Field Pinch
Fast Ion Connement in the MST Reversed Field Pinch Gennady Fiksel B. Hudson, D.J. Den Hartog, R.M. Magee, R. O'Connell, S.C. Prager MST Team - University of Wisconsin - Madison Center for Magnetic Self-Organization
More informationNovember 2, Monday. 17. Magnetic Energy Release
November, Monday 17. Magnetic Energy Release Magnetic Energy Release 1. Solar Energetic Phenomena. Energy Equation 3. Two Types of Magnetic Energy Release 4. Rapid Dissipation: Sweet s Mechanism 5. Petschek
More informationSolar Flares and Particle Acceleration
Solar Flares and Particle Acceleration Loukas Vlahos In this project many colleagues have been involved P. Cargill, H. Isliker, F. Lepreti, M. Onofri, R. Turkmani, G. Zimbardo,, M. Gkioulidou (TOSTISP
More informationOn existence of resistive magnetohydrodynamic equilibria
arxiv:physics/0503077v1 [physics.plasm-ph] 9 Mar 2005 On existence of resistive magnetohydrodynamic equilibria H. Tasso, G. N. Throumoulopoulos Max-Planck-Institut für Plasmaphysik Euratom Association
More informationAsymmetric Magnetic Reconnection in the Solar Atmosphere
Asymmetric Magnetic Reconnection in the Solar Atmosphere Nick Murphy Harvard-Smithsonian Center for Astrophysics November 1, 2013 MIT PSFC Seminar Collaborators and Co-Conspirators: John Raymond, Mari
More informationFundamentals of Magnetohydrodynamics (MHD)
Fundamentals of Magnetohydrodynamics (MHD) Thomas Neukirch School of Mathematics and Statistics University of St. Andrews STFC Advanced School U Dundee 2014 p.1/46 Motivation Solar Corona in EUV Want to
More information