Heat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UW-Madison
|
|
- Loraine Tyler
- 6 years ago
- Views:
Transcription
1 Heat Transport in a Stochastic Magnetic Field John Sarff Physics Dept, UW-Madison CMPD & CMSO Winter School UCLA Jan 5-10, 2009
2 Magnetic perturbations can destroy the nested-surface topology desired for magnetic confinement. Stochastic instability occurs when magnetic islands overlap, causing the field lines to wander randomly throughout the plasma volume. Parallel streaming along the stochastic field leads to radial transport. Astrophysical plasmas have weak ordered field (naturally tangled ) nested magnetic surfaces (ideal) magnetic island formation if islands overlap, stochastic field (B perturbations from instability or error components)
3 Projection of radial field yields intuitive estimate of stochastic transport. Recall parallel heat transport T t = χ ( ˆ b ) 2 T where ˆ b = B/ B If B = B 0 + B r r ˆ where B 0 = well-ordered field, forming nested magnetic surfaces T t = χ ( b ˆ ) 2 B T = χ r 2 T B 0 r 2 2 effective perpendicular transport (not quite rigorous, ok for fluid limit)
4 Small fluctuation amplitudes can yield large transport. Recall for classical electron transport χ 2 ν c ~ λ mfp χ ρ ν c Small magnetic fluctuation amplitude yields substantial transport χ B r B 0 2 ~ χ for B r B 0 ~ 10 3
5 Outline. Model for stochastic transport Comparisons with experimental measurements (mostly from the RFP)
6 Fluctuation-induced transport fluxes. Linearizing the drift kinetic equation f t + v f = 0 f = f 0 + f f 0 t = v E f = B 0 2 B 0 B + v B 0 f drift associated with electrostatic fluctuations streaming associated with magnetic fluctuations
7 Fluctuation-induced transport fluxes. Moments of the d.k.e. lead to the fluctuation-induced transport fluxes particle Γ r = dv f E B 0 2 B 0 B + v B 0 r ˆ = n E / B 0 + J B r /eb 0 electrostatic magnetic energy Q r = dv v 2 f E B 0 2 B 0 B + v B 0 r ˆ = p E / B 0 + Q B r / B 0 where... denotes an appropriate average, e.g., over an unperturbed magnetic flux surface
8 Model for stochastic magnetic transport. Very few self-consistent models for magnetic fluctuation induced transport have been developed. Most analysis has been for a static, imposed set of magnetic fluctuations Error fields from misaligned magnets and other stray fields Low frequency turbulence Stochastic magnetic transport is described by a double diffusion process 1. Random walk of the magnetic field lines 2. Collisional or other cross-field transport process is required for particles to lose memory of which field line they follow
9 Magnetic diffusion. Divergence of neighboring field lines: flux tube r 0 distance, s, along unperturbed field B 0 r(s) = r 0 e s/lk δ δ(s) = r 0 e s/l K L K = Kolmogorov-Lyaponov length
10 Magnetic diffusion. Magnetic diffusion coefficient: D m = (Δr)2 Δs = 0 B r (0) B r (s)ds B 0 2 (units of length) = L ac B r 2 / B 0 2 L ac = auto-correlation length for B L ac is related to the width of the k spectrum, L ac π /Δk ( L K ) in general
11 Stochastic transport in the collisionless limit. Consider a test particle streaming along the magnetic field flux tube distance, s, along unperturbed field B 0 (Δr) 2 = D m Δs average radial displacement associated with field line diffusion For λ mfp >> L ac χ st = (Δr)2 Δt = D mλ mfp τ c = D m v T v T = T / m (thermal velocity) τ c = λ mfp /v T (collision time)
12 Stochastic transport in the collisional limit. For λ mfp << L ac Δs ~ L ac, test particle must first diffuse along the field The parallel diffusion is given by: χ = (Δs)2 Δt = λ 2 mfp τ c χ st = (Δr)2 Δt = D m Δs Δt = D m L ac L 2 ac / χ = D m v λ mfp T L ac B 2 = χ r B 0 2
13 Stochastic transport in the collisional limit. For λ mfp << L ac Δs ~ L ac, test particle must first diffuse along the field The parallel diffusion is given by: χ = (Δs)2 Δt = λ 2 mfp τ c χ st = (Δr)2 Δt = D m Δs Δt = D m L ac L 2 ac / χ = D m v λ mfp T L ac B 2 = χ r B 0 2 Smooth transitional form: χ st = v T L eff B r 2 B 0 2 with L 1 eff = L 1 1 ac + λ mfp Krommes et al. provided a unifying discussion of various collisional limits with respect to characteristic scale lengths.
14 How well does the static field model work? Few direct measurements of stochastic transport. Inferences via energetic particles in tokamak plasmas, exploiting expected velocity dependence. Self-organizing plasmas like the RFP and spheromak provide good opportunity to test expectations, because they exhibit a broad spectrum of low frequency magnetic fluctuations.
15 The Reversed Field Pinch plasma configuration. RFP Magnetic Geometry MST parameters: n ~ cm 3 T e < 2 kev T ion ~ T e B < 0.5 T ρ ion ~ 1 cm
16 The MST at UW-Madison. R = 1.5 m a = 0.5 m Ip < 0.6 MA
17 Main source of symmetry breaking magnetic field in the RFP is MHD tearing instability. Linear stability analysis using force balance J B = p B k = m θ ˆ n r R ˆ r F + φ F + k 2 B r 0 F = k B 0 F F ~ B 0 J ~ r B 0 B yields Growth rate depends on r J and the plasmaʼs resistivity Mode resonance appears at the minor radius where k B 0 0 k B 0 = 0 m n = rb φ RB θ = q(r) B r B 0 (see 2008 Winter School lectures) rdl θ Rdl φ
18 Tearing permits the creation of magnetic islands. resonant layer k B 0 0 r = r s r = r s Tearing reconnection magnetic island forms to B 0 island width w m,n = 4 B r,m,n (r s )L s B 0 (r s )k
19 Chirikov threshold condition for stochastic instability. If neighboring magnetic islands overlap, the field lines are allowed to wander from island-to-island randomly. s = 1 2 w n+1 + w n r s,n+1 r s,n stochasticity parameter (crudely the number of islands overlapping a given radial location) s < 1 : islands do not overlap, no stochastic transport (but transport across the island is typically enhanced by its topology) s ~ 1 : weakly stochastic, magnetic diffusion and transport are transitional (e.g., as discussed by Boozer and White) s >> 1 : magnetic field line wandering is well approximated as a random-walk diffusion process
20 Many possible tearing resonances occur across the radius of the RFP configuration. q(r) = rb φ RB θ B n B 0 1% Observed Spectrum Toroidal Mode, n
21 Chirikov threshold is exceeded, particularly in the mid-radius region where the density of rational magnetic surfaces is large q(r) s
22 Magnetic puncture plot indicates widespread magnetic stochasticity. B r,m,n (r) Eigenfunctions from nonlinear resistive MHD computation, normalized to measured B m,n (r = a). Field is modeled using B m,n (r) eigenfunctions, combined with equilibrium reconstruction that provides B 0 (r).
23 Direct measurement of magnetic fluctuation-induced stochastic transport. Measurements were made in MST (RFP), CCT (tokamak), and TJ-II (stellarator)
24 Measured electron heat flux in the edge of MST plasmas.
25 Measured island-induced heat flux in CCT (tokamak at UCLA). Heat flux in the magnetic island scales as if stochastic
26 The amplitude of the tearing fluctuations in the RFP can be reduced using current profile control (PPCD). ~5X reduction of most modes B n B 0 allows tests of χ st ~ B 2 r scaling and dependence on spectral features
27 Region of stochastic field shrinks with current profile control. Standard PPCD Toroidal, φ Toroidal, φ r / a r / a
28 Power balance measurements provide the experimental electron heat conductivity profile. Electron heat flux Q e = χ e n r T e Te 0.6 (KeV) PPCD-Improved PPCD Standard r/a χe (m2/s) Standard PPCD-Improved PPCD PPCD r/a
29 Measured heat diffusivity consistent with collisionless stochastic transport model (where the field is stochastic). Standard PPCD 1000 Magnetic diffusivity is evaluated directly from an ensemble of magnetic field lines. 100 L ac << λ mfp χ e 10 χ st ~1 m ~10ʼs m χ st χ st = D m v T r/a r/a 1
30 Magnetic diffusivity as expressed by Rechester-Rosenbluth, PRL ʼ78. D m = πr m,n B r,m,n (r) 2 B z 2 δ[ m /n q(r) ] auto-correlation length, L ac RMS fluctuation amplitude^2 but only k = 0 modes resonant nearby r
31 Estimate of the auto-correlation length from the spectral width. For a tokamak B φ >> B θ k = k B B 1 m B φ r B θ + n R B φ = 1 m R q + n Δk ~ Δr k = n r rs R Δr 1 dq q dr rs ~ 1 mode radial width ~ 1 R (n=1 typically dominant)
32 Rechester-Rosenbluth magnetic diffusivity overestimates χ st for regions with low s.
33 Electron temperature gradient correlates with amplitude of tearing modes resonant at mid-radius T e (0) 0.8 (kev) 0.6 PPCD 0.4 Standard B rms = 15 n=8 B 2 n (a) mid-radius modes m =1, n 8
34 Electron temperature gradient does not correlate with largest mode, resonant in the core T e (0) 0.8 (kev) 0.6 PPCD T e (0) 0.8 (kev) Standard B rms = 15 n=8 B 2 n (a) m = 1, n = Dominant Mode B 1,6
35 Though parallel streaming transport is nonlocal, the tearing reconnection process is local B r B 2 1,6 linear eigenmodes D m ~ m,n B r,m,n (r) 2 B z 2 δ[ m /n q(r) ] RMS m =1, n =8-15 illustrates importance of k = r/a 1,6
36 Stochastic particle transport is affected by its inherent non-ambipolar character. Since the thermal velocity is mass-dependent, electron and ion stochastic diffusion are not automatically ambipolar (unlike E B 0 motion). Harvey derived from the drift kinetic equation (collisionless limit) 1 Γ r ~ D m v T n 1 Q r ~ D m v T n n r + 1 2T n r + 3 2T T r + ee A T T r + ee A T n nt Setting and Γ r,e 0 Q r,e ~ D m v T n T r yields the ambipolar electric field E A = T e e r ln(nt 1/2 e )
37 Non-ambipolar transport predicts a radially outward directed electrostatic field due to the high mobility of electrons. Heavy ion beam probe observes the positive potential in the core. Lei et al. MST plasma
38 In astrophysical plasmas, stochastic field can reduce heat transport. Reflects large transport anisotropy in a magnetized plasma. Consider collisionless limit L ac << λ mfp : D χ st = D m v T = χ m L = χ ac B r λ mfp λ mfp B 0 2 < 1, even for B ~ B 0 Has been applied to cooling flows in galactic clusters to argue small heat conduction.
39 References 1. Rosenbluth, Sagdeev, Taylor, Nucl. Fusion 6, 297 (1966) 2. Jokipii and Parker, Ap. J. 155, 777 (1969) 3. Rechester and Rosenbluth, Phys. Rev. Lett. 40, 38 (1978) 4. Harvey, McCoy, Hsu, Mirin, Phys. Rev. Lett. 47, 102 (1981) 5. Boozer and White, Phys. Rev. Lett. 49, 786 (1982) 6. Krommes, Oberman, Kleva, J. Plasma Physics 30, 11 (1983) 7. Liewer, Nucl. Fusion 25, 543 (1985) 8. Prager, Plasma Phys. Control. Fusion 32, 903 (1990) 9. Stoneking et al., Phys. Rev. Lett. 73, 549 (1994) 10. Fiksel et al., Plasma Phys. Control. Fusion 38, A213 ( 1996) 11. Chandran and Cowley, Phys. Rev. Lett 80, 3077 (1998) 12. Biewer et al., Phys. Rev. Lett 91, (2003) 13. Fiksel et al, Phys. Rev. Lett 95, (2005)
40 Homework problem a) Consider the RFP magnetic equilibrium. Using the Chirikov stochasticity parameter, derive from the threshold condition, s=1, the recursion relation below for the width of the magnetic island associated with toroidal mode, n, so that it just touches its nearest neighbors (assume m=1 for all modes): w n = 1 1 q n n(n +1) where q n = dq and r n is the minor radius of the dr r=rn resonant surface b) Estimate the stochastic heat diffusivity, χ st, for a fluctuation spectrum described by the recursion relation above. c) For fusion parameters, discuss the magnitude of χ st relative to other transport mechanisms, such as classical (or neoclassical) transport and anomalous transport as observed in tokamak plasmas. For what n is χ e,st < 1 m 2 /s?
41 Homework problem (illustration and partial answer) n=6 w n = 4 B r,n (r n )r n B θ (r n )n q n (a=plasma minor radius)
The 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 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 informationMeasurement of magnetic fluctuation-induced heat transport in tokamaks and RFP
Plasma Phys. Control. Fusion 38 (1996) A213 A225. Printed in the UK Measurement of magnetic fluctuation-induced heat transport in tokamaks and RFP G Fiksel, Roger D Bengtson, M Cekic, D Den Hartog, S C
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 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 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 informationTokamak-like confinement at a high beta and low toroidal field in the MST reversed field pinch*
INSTITUTE OF PHYSICS PUBLISHING and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION Nucl. Fusion 43 (23) 1684 1692 PII: S29-5515(3)7949-1 Tokamak-like confinement at a high beta and low toroidal field
More informationMicrotearing Simulations in the Madison Symmetric Torus
Microtearing Simulations in the Madison Symmetric Torus D. Carmody, P.W. Terry, M.J. Pueschel - University of Wisconsin - Madison dcarmody@wisc.edu APS DPP 22 Overview PPCD discharges in MST have lower
More informationNeoclassical transport
Neoclassical transport Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 28 th January 2013 Dr Ben Dudson Magnetic Confinement Fusion (1 of 19) Last time Toroidal devices
More informationThe Role of Dynamo Fluctuations in Anomalous Ion Heating, Mode Locking, and Flow Generation
The Role of Dynamo Fluctuations in Anomalous Ion Heating, Mode Locking, and Flow Generation P. W. Terry 1), R. Gatto 1), R. Fitzpatrick 2), C.C. Hegna 3), and G. Fiksel 1) 1) Department of Physics, University
More informationCurrent Profile Control by ac Helicity Injection
Current Profile Control by ac Helicity Injection Fatima Ebrahimi and S. C. Prager University of Wisconsin- Madison APS 2003 Motivations Helicity injection is a method to drive current in plasmas in which
More informationElectron Thermal Transport Within Magnetic Islands in the RFP
Electron Thermal Transport Within Magnetic Islands in the RFP Hillary Stephens University of Wisconsin Madison APS-DPP Meeting November 3, 2009 J.R. Amubel, M.T. Borchardt, D.J. Den Hartog, C.C. Hegna,
More informationMeasured Energy Transport in the MST Reversed-Field Pinch. G.Fiksel University of Wisconsin-Madison. adison ymmetric orus
Measured Energy Transport in the MST Reversed-Field Pinch T.M. Biewer,, J.K. Anderson, B.E. Chapman, S.D. Terry 1, J.C. Reardon,, N.E. Lanier, G.Fiksel Fiksel,, D.J. Den Hartog,, S.C. Prager,, and C.B.
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 informationPlasma Flow in MST: Effects of Edge Biasing and Momentum Transport from Nonlinear Magnetic Torques
Plasma Flow in MST: Effects of Edge Biasing and Momentum Transport from Nonlinear Magnetic Torques J.S. Sarff, A.F. Almagri, J.K. Anderson, B.E. Chapman, D. Craig, C-S. Chiang, N.A. Crocker, D.J. Den Hartog,
More informationObservation of Neo-Classical Ion Pinch in the Electric Tokamak*
1 EX/P6-29 Observation of Neo-Classical Ion Pinch in the Electric Tokamak* R. J. Taylor, T. A. Carter, J.-L. Gauvreau, P.-A. Gourdain, A. Grossman, D. J. LaFonteese, D. C. Pace, L. W. Schmitz, A. E. White,
More informationAC loop voltages and MHD stability in RFP plasmas
AC loop voltages and MHD stability in RFP plasmas K. J. McCollam, D. J. Holly, V. V. Mirnov, J. S. Sar, D. R. Stone UW-Madison 54rd Annual Meeting of the APS-DPP October 29th - November 2nd, 2012 Providence,
More informationTheory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus. K. C. Shaing
Theory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus K. C. Shaing Plasma and Space Science Center, and ISAPS, National Cheng Kung University, Tainan, Taiwan 70101, Republic
More informationGTC Simulation of Turbulence and Transport in Tokamak Plasmas
GTC Simulation of Turbulence and Transport in Tokamak Plasmas Z. Lin University it of California, i Irvine, CA 92697, USA and GPS-TTBP Team Supported by SciDAC GPS-TTBP, GSEP & CPES Motivation First-principles
More informationCONFINEMENT IN THE RFP: LUNDQUIST NUMBER SCALING, PLASMA FLOW, AND REDUCED TRANSPORT
CONFINEMENT IN THE RFP: LUNDQUIST NUMBER SCALING, PLASMA FLOW, AND REDUCED TRANSPORT G. Fiksel, 1 A.F. Almagri, 1 J.K. Anderson, 1 T.M. Biewer, 1 D.L. Brower, 2 C-S. Chiang, 1 B.E. Chapman, 1 J.T. Chapman,
More informationA mechanism for magnetic field stochastization and energy release during an edge pedestal collapse
A mechanism for magnetic field stochastization and energy release during an edge pedestal collapse S. S. Kim, Hogun Jhang, T. Rhee, G. Y. Park, R. Singh National Fusion Research Institute, Korea Acknowledgements:
More informationTURBULENT TRANSPORT THEORY
ASDEX Upgrade Max-Planck-Institut für Plasmaphysik TURBULENT TRANSPORT THEORY C. Angioni GYRO, J. Candy and R.E. Waltz, GA The problem of Transport Transport is the physics subject which studies the physical
More informationIntroduction to Fusion Physics
Introduction to Fusion Physics Hartmut Zohm Max-Planck-Institut für Plasmaphysik 85748 Garching DPG Advanced Physics School The Physics of ITER Bad Honnef, 22.09.2014 Energy from nuclear fusion Reduction
More informationMST and the Reversed Field Pinch. John Sarff
MST and the Reversed Field Pinch John Sarff APAM Columbia University Sep 19, 2014 Outline Tutorial-level review of tearing stability, magnetic relaxation, and transport in the RFP Ion-related physics topics
More informationProgress and Plans on Physics and Validation
Progress and Plans on Physics and Validation T.S. Hahm Princeton Plasma Physics Laboratory Princeton, New Jersey Momentum Transport Studies: Turbulence and Neoclassical Physics Role of Trapped Electrons
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 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 information- Effect of Stochastic Field and Resonant Magnetic Perturbation on Global MHD Fluctuation -
15TH WORKSHOP ON MHD STABILITY CONTROL: "US-Japan Workshop on 3D Magnetic Field Effects in MHD Control" U. Wisconsin, Madison, Nov 15-17, 17, 2010 LHD experiments relevant to Tokamak MHD control - Effect
More informationElectron temperature barriers in the RFX-mod experiment
Electron temperature barriers in the RFX-mod experiment A. Scaggion Consorzio RFX, Padova, Italy Tuesday 5 th October 2010 ADVANCED PHYSICS LESSONS 27/09/2010 07/10/2010 IPP GARCHING JOINT EUROPEAN RESEARCH
More informationDensity Fluctuation Induced Kinetic Dynamo and Nonlinear Tearing Mode Saturation in the MST Reversed Field Pinch
Density Fluctuation Induced Kinetic Dynamo and Nonlinear Tearing Mode Saturation in the MST Reversed Field Pinch W.X.Ding, L. Lin, D.L. Brower, A. Almagri, B. Chapman, G. Fiksel, D.J. Den Hartog, J. Reusch,
More informationProgressing Performance Tokamak Core Physics. Marco Wischmeier Max-Planck-Institut für Plasmaphysik Garching marco.wischmeier at ipp.mpg.
Progressing Performance Tokamak Core Physics Marco Wischmeier Max-Planck-Institut für Plasmaphysik 85748 Garching marco.wischmeier at ipp.mpg.de Joint ICTP-IAEA College on Advanced Plasma Physics, Triest,
More informationNumerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations
PHYSICS OF PLASMAS 12, 072513 2005 Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations J. N. Talmadge and S. P. Gerhardt a HSX Plasma Laboratory, University
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 informationInnovative Concepts Workshop Austin, Texas February 13-15, 2006
Don Spong Oak Ridge National Laboratory Acknowledgements: Jeff Harris, Hideo Sugama, Shin Nishimura, Andrew Ware, Steve Hirshman, Wayne Houlberg, Jim Lyon Innovative Concepts Workshop Austin, Texas February
More informationGyrokinetic Simulations of Tearing Instability
Gyrokinetic Simulations of Tearing Instability July 6, 2009 R. NUMATA A,, W. Dorland A, N. F. Loureiro B, B. N. Rogers C, A. A. Schekochihin D, T. Tatsuno A rnumata@umd.edu A) Center for Multiscale Plasma
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 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 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 informationOscillating-Field Current-Drive Experiment on MST
Oscillating-Field Current-Drive Experiment on MST K. J. McCollam, J. K. Anderson, D. J. Den Hartog, F. Ebrahimi, J. A. Reusch, J. S. Sarff, H. D. Stephens, D. R. Stone University of Wisconsin-Madison D.
More informationTransition From Single Fluid To Pure Electron MHD Regime Of Tearing Instability
Transition From Single Fluid To Pure Electron MHD Regime Of Tearing Instability V.V.Mirnov, C.C.Hegna, S.C.Prager APS DPP Meeting, October 27-31, 2003, Albuquerque NM Abstract In the most general case,
More informationIssues of Perpendicular Conductivity and Electric Fields in Fusion Devices
Issues of Perpendicular Conductivity and Electric Fields in Fusion Devices Michael Tendler, Alfven Laboratory, Royal Institute of Technology, Stockholm, Sweden Plasma Turbulence Turbulence can be regarded
More informationGyrokinetic Transport Driven by Energetic Particle Modes
Gyrokinetic Transport Driven by Energetic Particle Modes by Eric Bass (General Atomics) Collaborators: Ron Waltz, Ming Chu GSEP Workshop General Atomics August 10, 2009 Outline I. Background Alfvén (TAE/EPM)
More informationImpurity expulsion in an RFP plasma and the role of temperature screening
Impurity expulsion in an RFP plasma and the role of temperature screening S. T. A. Kumar, D. J. Den Hartog, R. M. Magee, G. Fiksel, D. Craig Department of Physics, University of Wisconsin-Madison, Madison,Wisconsin,
More informationToroidal confinement devices
Toroidal confinement devices Dr Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 24 th January 2014 Dr Ben Dudson Magnetic Confinement Fusion (1 of 20) Last time... Power
More informationProgress Towards Confinement Improvement Using Current Profile Modification In The MST Reversed Field Pinch
Progress Towards Confinement Improvement Using Current Profile Modification In The MST Reversed Field Pinch C.B. Forest 1), J.K. Anderson 1), T.M. Biewer 1), D. Brower 2), B.E. Chapman 1), P.K. Chattopadhyay
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 informationThe role of stochastization in fast MHD phenomena on ASDEX Upgrade
1 EX/P9-10 The role of stochastization in fast MHD phenomena on ASDEX Upgrade V. Igochine 1), O.Dumbrajs 2,3), H. Zohm 1), G. Papp 4), G. Por 4), G. Pokol 4), ASDEX Upgrade team 1) 1) MPI für Plasmaphysik,
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 informationInter-linkage of transports and its bridging mechanism
Interlinkage of transports and its bridging mechanism Katsumi Ida National Institute for Fusion Science 17 th International Toki Conference 1519 October 27, Toki OUTLINE 1 Introduction 2 particle pinch
More informationOperational Phase Space of the Edge Plasma in Alcator C-Mod
Operational Phase Space of the Edge Plasma in B. LaBombard, T. Biewer, M. Greenwald, J.W. Hughes B. Lipschultz, N. Smick, J.L. Terry, Team Contributed talk RO.00008 Presented at the 47th Annual Meeting
More informationSimulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD
1 Simulation Study of Interaction between Energetic Ions and Alfvén Eigenmodes in LHD Y. Todo 1), N. Nakajima 1), M. Osakabe 1), S. Yamamoto 2), D. A. Spong 3) 1) National Institute for Fusion Science,
More informationNonlinear Consequences of Weakly Driven Energetic Particle Instabilities
2008 International Sherwood Fusion Theory Conference March 30 - April 2, 2008, Boulder, Colorado Nonlinear Consequences of Weakly Driven Energetic Particle Instabilities Boris Breizman Institute for Fusion
More informationMagnetic Self-Organization in the RFP
Magnetic Self-Organization in the RFP Prof. John Sarff University of Wisconsin-Madison Joint ICTP-IAEA College on Plasma Physics ICTP, Trieste, Italy Nov 7-18, 2016 The RFP plasma exhibits a fascinating
More informationParticle Transport and Edge Dynamo in the MST RFP
Particle Transport and Edge Dynamo in the ST RFP International RFP Workshop 28 February 2000, adison, WI D. J. Den Hartog Department of Physics University of Wisconsin adison In collaboration with J. K.
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 informationStability of a plasma confined in a dipole field
PHYSICS OF PLASMAS VOLUME 5, NUMBER 10 OCTOBER 1998 Stability of a plasma confined in a dipole field Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received
More informationAdvances in stellarator gyrokinetics
Advances in stellarator gyrokinetics Per Helander and T. Bird, F. Jenko, R. Kleiber, G.G. Plunk, J.H.E. Proll, J. Riemann, P. Xanthopoulos 1 Background Wendelstein 7-X will start experiments in 2015 optimised
More informationShear Flow Generation in Stellarators - Configurational Variations
Shear Flow Generation in Stellarators - Configurational Variations D. A. Spong 1), A. S. Ware 2), S. P. Hirshman 1), J. H. Harris 1), L. A. Berry 1) 1) Oak Ridge National Laboratory, Oak Ridge, Tennessee
More informationBounce-averaged gyrokinetic simulations of trapped electron turbulence in elongated tokamak plasmas
Bounce-averaged gyrokinetic simulations of trapped electron turbulence in elongated tokamak plasmas Lei Qi a, Jaemin Kwon a, T. S. Hahm a,b and Sumin Yi a a National Fusion Research Institute (NFRI), Daejeon,
More informationINTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS
INTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS A. Ishizawa and N. Nakajima National Institute for Fusion Science F. L. Waelbroeck, R. Fitzpatrick, W. Horton Institute for Fusion Studies, University
More informationSize Scaling and Nondiffusive Features of Electron Heat Transport in Multi-Scale Turbulence
Size Scaling and Nondiffusive Features of Electron Heat Transport in Multi-Scale Turbulence Z. Lin 1, Y. Xiao 1, W. J. Deng 1, I. Holod 1, C. Kamath, S. Klasky 3, Z. X. Wang 1, and H. S. Zhang 4,1 1 University
More informationOn the physics of shear flows in 3D geometry
On the physics of shear flows in 3D geometry C. Hidalgo and M.A. Pedrosa Laboratorio Nacional de Fusión, EURATOM-CIEMAT, Madrid, Spain Recent experiments have shown the importance of multi-scale (long-range)
More informationDIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH
DIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH by K.H. Burrell Presented at High Temperature Plasma Diagnostics 2 Conference Tucson, Arizona June 19 22, 2 134 /KHB/wj ROLE OF DIAGNOSTICS IN ADVANCED TOKAMAK
More informationDirect drive by cyclotron heating can explain spontaneous rotation in tokamaks
Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks J. W. Van Dam and L.-J. Zheng Institute for Fusion Studies University of Texas at Austin 12th US-EU Transport Task Force Annual
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 informationHigh-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows
TH/P3-3 High-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows A. Bierwage 1), S. Benkadda 2), M. Wakatani 1), S. Hamaguchi 3), Q. Yu
More informationIon orbits and ion confinement studies on ECRH plasmas in TJ-II stellarator
Ion orbits and ion confinement studies on ECRH plasmas in TJ-II stellarator F. Castejón 1,4, J. M. Reynolds 3,4, J. M. Fontdecaba 1, D. López-Bruna 1, R. Balbín 1, J. Guasp 1, D. Fernández-Fraile 2, L.
More informationPhysics of fusion power. Lecture 13 : Diffusion equation / transport
Physics of fusion power Lecture 13 : Diffusion equation / transport Many body problem The plasma has some 10 22 particles. No description is possible that allows for the determination of position and velocity
More informationGyrokinetic simulations including the centrifugal force in a strongly rotating tokamak plasma
Gyrokinetic simulations including the centrifugal force in a strongly rotating tokamak plasma F.J. Casson, A.G. Peeters, Y. Camenen, W.A. Hornsby, A.P. Snodin, D. Strintzi, G.Szepesi CCFE Turbsim, July
More informationMagnetic Fluctuations and Transport X. Garbet CEA Cadarache
Magnetic Fluctuations and Transport X. Garbet CEA Cadarache Thanks to: M. Bécoulet, C. Bourdelle, P. Beyer, L.Colas, P. Diamond, P. Ghendrih, F. Jenko, B.Labit, M.Ottaviani, Y.Peysson, S. Prager, P. Terry,
More informationMulti-scale turbulence, electron transport, and Zonal Flows in DIII-D
Multi-scale turbulence, electron transport, and Zonal Flows in DIII-D L. Schmitz1 with C. Holland2, T.L. Rhodes1, G. Wang1, J.C. Hillesheim1, A.E. White3, W. A. Peebles1, J. DeBoo4, G.R. McKee5, J. DeGrassie4,
More informationCoarse-graining the electron distribution in turbulence simulations of tokamak plasmas
Coarse-graining the electron distribution in turbulence simulations of tokamak plasmas Yang Chen and Scott E. Parker University of Colorado at Boulder Gregory Rewoldt Princeton Plasma Physics Laboratory
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 informationTheory and Simulation of Neoclassical Transport Processes, with Local Trapping
Theory and Simulation of Neoclassical Transport Processes, with Local Trapping Daniel H. E. Dubin Department of Physics, University of California at San Diego, La Jolla, CA USA 92093-0319 Abstract. Neoclassical
More informationTurbulence and Transport The Secrets of Magnetic Confinement
Turbulence and Transport The Secrets of Magnetic Confinement Presented by Martin Greenwald MIT Plasma Science & Fusion Center IAP January 2005 FUSION REACTIONS POWER THE STARS AND PRODUCE THE ELEMENTS
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 informationMHD Linear Stability Analysis Using a Full Wave Code
US-Japan JIFT Workshop on Progress of Extended MHD Models NIFS, Toki,Japan 2007/03/27 MHD Linear Stability Analysis Using a Full Wave Code T. Akutsu and A. Fukuyama Department of Nuclear Engineering, Kyoto
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 informationMeasurement of core velocity fluctuations and the
Measurement of core velocity fluctuations and the dynamo in a reversed-field pinch D. J. Den Hartog 1, J. T. Chapman 2, D. Craig, G. Fiksel, P. W. Fontana, S. C. Prager, and J. S. Sarff Department of Physics,
More informationA Hybrid Inductive Scenario for a Pulsed- Burn RFP Reactor with Quasi-Steady Current. John Sarff
A Hybrid Inductive Scenario for a Pulsed- Burn RFP Reactor with Quasi-Steady Current John Sarff 12th IEA RFP Workshop Kyoto Institute of Technology, Kyoto, Japan Mar 26-28, 2007 The RFP fusion development
More informationFriday Morning. 9! 5 Nonlinear Periodic Waves in Plasma E. R. TRACY, College of William and Mary.
not Friday Morning 9! 3 2F: A Generalized Energy Principle for Determining Linear and Nonlinear Stability.* P. L MORRISON,* * Institutefor Fusion Studies, The University of Texas at Austin. A generalization
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 informationTurbulence and transport reduction with innovative plasma shapes in TCV - correlation ECE measurements and gyrokinetic simulations
Turbulence and transport reduction with innovative plasma shapes in TCV - correlation ECE measurements and gyrokinetic simulations A. Pochelon, and the TCV team 1 Ecole Polytechnique de Lausanne (EPFL)
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 informationFinite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena
1 TH/P2-18 Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena S. Satake 1), M. Okamoto 1), N. Nakajima 1), H. Sugama 1), M. Yokoyama 1), and C. D. Beidler 2) 1)
More informationMeasurement of core velocity fluctuations and the dynamo in a reversed-field pinch*
PHYSICS OF PLASMAS VOLUME 6, NUMBER 5 MAY 1999 Measurement of core velocity fluctuations and the dynamo in a reversed-field pinch* D. J. Den Hartog,,a) J. T. Chapman, b) D. Craig, G. Fiksel, P. W. Fontana,
More informationDifferential Interferometry for Measurement of Density Fluctuations and Fluctuation Induced Transport
Differential Interferometry for Measurement of Density Fluctuations and Fluctuation Induced Transport Liang Lin University of California, Los Angeles, California, USA in collaboration with W. X. Ding,
More informationEvaluation of CT injection to RFP for performance improvement and reconnection studies
Evaluation of CT injection to RFP for performance improvement and reconnection studies S. Masamune A. Sanpei, T. Nagano, S. Nakanobo, R. Tsuboi, S. Kunita, M. Emori, H. Makizawa, H. Himura, N. Mizuguchi
More informationOscillating Field Current Drive on MST
Oscillating Field Current Drive on MST John Sarff A. Blair, K. McCollam, P. Nonn, J. Anderson, D. Brower 1, D. Craig, B. Deng 1, D. Den Hartog, W. Ding 1, F. Ebrahimi, D. Ennis, G. Fiksel, S. Gangadhara,
More information22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 15: Alternate Concepts (with Darren Sarmer)
22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 15: Alternate Concepts (with Darren Sarmer) 1. In todays lecture we discuss the basic ideas behind the main alternate concepts to the tokamak.
More informationb c. d a e Λ h α
MHD Phenomena and Transport of Energetic Ions in Spherical Tori Ya.I. Kolesnichenko ), V.V. Lutsenko ), V.S. Marchenko ), R.B. White ), Yu.V. Yakovenko ) ) Institute for Nuclear Research, National Academy
More informationIon plateau transport near the tokamak magnetic axis. Abstract
Ion plateau transport near the tokamak magnetic axis K.C. Shaing and R.D. Hazeltine Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (December 2, 1997) Abstract Conventional
More informationModelling of the penetration process of externally applied helical magnetic perturbation of the DED on the TEXTOR tokamak
INSTITUTE OF PHYSICS PUBLISHING Plasma Phys. Control. Fusion 8 (6) 69 8 PLASMA PHYSICS AND CONTROLLED FUSION doi:.88/7-/8// Modelling of the penetration process of externally applied helical magnetic perturbation
More informationFine-Scale Zonal Flow Suppression of Electron Temperature Gradient Turbulence
Fine-Scale Zonal Flow Suppression of Electron Temperature Gradient Turbulence S.E. Parker, J.J. Kohut, Y. Chen, Z. Lin, F.L. Hinton and W.W. Lee Center for Integrated Plasma Studies, University of Colorado,
More informationReduction of Neoclassical Transport and Observation of a Fast Electron Driven Instability with Quasisymmetry in HSX
Reduction of Neoclassical Transport and Observation of a Fast Electron Driven Instability with Quasisymmetry in HSX J.M. Canik 1, D.L. Brower 2, C. Deng 2, D.T.Anderson 1, F.S.B. Anderson 1, A.F. Almagri
More informationHelicity fluctuation, generation of linking number and effect on resistivity
Helicity fluctuation, generation of linking number and effect on resistivity F. Spineanu 1), M. Vlad 1) 1) Association EURATOM-MEC Romania NILPRP MG-36, Magurele, Bucharest, Romania spineanu@ifin.nipne.ro
More informationTowards Multiscale Gyrokinetic Simulations of ITER-like Plasmas
Frank Jenko Max-Planck-Institut für Plasmaphysik, Garching Universität Ulm Towards Multiscale Gyrokinetic Simulations of ITER-like Plasmas 23 rd IAEA Fusion Energy Conference 11-16 October 2010, Daejeon,
More informationSeptember Plasma Fusion Center Massachusetts Institute of Technology Cambridge, Massachusetts USA
PFC/JA-95-19 RF WAVE EFFECTS ON THE NEOCLASSICAL ELECTRON DISTRIBUTION FUNCTION IN TOKAMAKS S. D. Schultz, A. Bers, and A. K. Ram September 1995 Plasma Fusion Center Massachusetts Institute of Technology
More informationResearch of Basic Plasma Physics Toward Nuclear Fusion in LHD
Research of Basic Plasma Physics Toward Nuclear Fusion in LHD Akio KOMORI and LHD experiment group National Institute for Fusion Science, Toki, Gifu 509-5292, Japan (Received 4 January 2010 / Accepted
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 information