The Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin

Size: px
Start display at page:

Download "The Linear Theory of Tearing Modes in periodic, cyindrical plasmas. Cary Forest University of Wisconsin"

Transcription

1 The Linear Theory of Tearing Modes in periodic, cyindrical plasmas Cary Forest University of Wisconsin 1

2 Resistive MHD E + v B = ηj (no energy principle) Role of resistivity No frozen flux, B can tear If fluid moves relative to B then ηj = v B J = v B η F = J B = = B2 η v (v B) B η Restoring force B v Vanishingly small eta can allow tearing when B->0! 2

3 Resistive MHD B t Same energy source as in ideal MHD, but more states are accessible Dimensionless measure of resistivity ( B) = E = v B η µ 0 LHS resistive term B/τ A ηb/a 2 µ 0 = µ 0a 2 /η τ A = τ R τa S τ R = B θ,teslat 7 τ A n 1/2 20 3/2 e,kev a m, and τ R µ 0a 2 η 50 T 3/2 e,kev Z eff sec S= ; although S>>1, its finiteness permits topological changes and new instabilities 3

4 Experimental Importance Disruptions beta limits Stochastic magnetic fields Realization of reconnection phenomena 4

5 Consider torus with helical field B = B φ ˆφ + Bθ ˆθ { { toroidal poloidal B Field lines lie on circles 5

6 Magnetic Surfaces B Ideally, concentric tori In general, there is shear 6

7 Add a small perturbation in radial magnetic field: b r with b rb 1 Possible sources of perturbations:! -instability! -magnetic field error! -deliberate additional field How can a small perturbation have a large effect on the field structure? 7

8 If k = 0 then small magnetic fluctuation gives large field line excursion b r B 8

9 add a perturbation (e.g., an instability) B = B(r) + b r (r) sin(mθ nφ)ˆr Thus, wavenumber consider region near k = m r ˆθ n R ˆφ k = 0 where k B = m r B θ n R B φ = 0 or where q(r) = m n where q(r) = rb φ RB θ 9

10 Define a coordinate χ, perpendicular to B,ˆr: χ = mθ nφ so that B r = b r (r) sin χ Perturbation is constant along B at one radius χ B φ θ r 10

11 Field line equation dr = h χdχ B r B dr = h χdχ b r (r) sin χ B r rdr b r = h χ dχ B sin χ r = ± h χ b r cos χ + C 4 B 11

12 Field lines without perturbations r = constant radius χ 12

13 Field lines with perturbation r = ± h χ b r 4 B cos χ + C Reconnection has occurred: w = 2 hχ b r B 13

14 Field lines respond to resonant perturbation in torus q=3 surface n=1, m=3 perturbation: b r = b cos(3θ φ) 14

15 SXR imaging of m=3 islands in tokamak 15

16 SXR imaging of flux surfaces With one dominant tearing instability From a reversed field pinch experiment (similar to a tokamak) 16

17 SXR tomography with 2 tearing modes 17

18 Disruptions can be due to overlapping islands Asdex-U tokamak 18

19 References Furth, Killeen and Rosenbluth, Finite Resistivity instabilities of a sheet pinch, Phys. Fluids 6, 459 (1963). Furth, Rutherford and Selberg, Tearing mode in the cylindrical tokamak, Phys. Fluids 16, 1054 (1973). Coppi, Greene and Johnson, Nucl. Fusion 6, 101 (1966). Tokamaks, 3rd ed. Wesson Theory of Tokamak Plasmas, White. 19

20 Cylindrical Tearing Mode: Linear Theory 1. Solve for magnetic perturbation in outer region: use force balance, ignoring inertia Use ideal MHD, ignoring resistivity 2.Outer solution determines stability, drives reconnection 3.Inner solution solves resistive MHD equations for narrow current sheet Inertia, resistivity both important 4.Matching inner solution to step in B r determines growth rate 20

21 Outer region! Ion Equation of motion ρ dv dt = J B P in the outer region, inertia is negligible, and plasma is in force equilibrium P = J B and since the curl of a gradient is zero J B = 0 Using B = 0 and J = 0 B J J B = 0 21

22 Reduced MHD Ordering The large aspect-ratio, reduced MHD ordering will be used. Taking ɛ = a/r 1, the equililibrium quantities are ordered as B θ 1 r db φ dr ɛb φ, and J θ ɛj φ while the perturbed quantities are ordered as b φ ɛb r ɛb θ, and j θ ɛj φ Use the toroidal component. Since J B B J, the equation governing the outer region is B j φ + b J φ = 0 22

23 Representation of perturbed field Use a vector potential (flux function) to represent the perturbed flux b = a with a = ψ ˆφ : so that b r = 1 r ψ θ, b θ = ψ r which can be related (by Ampere s law) to the perturbed toroidal current density: µ 0 j φ = 2 ψ = 1 r r r ψ r ψ r 2 θ 2 Assuming that the perturbations are double periodic and have the form e i(mθ nφ) b r = i m r ψ 23

24 Equation governing outer solution Inserting j φ into the governing equation, and noting that J φ only varies in the radial direction so that b J φ = i m dj φ r dr ψ gives F µ 0 2 ψ m r where F (r) = k B = m r B θ(r) nb φ R Equivalently, dj φ dr ψ = 0, = m r B θ(r) ( ) 1 nq(r). m 1 r d dr r dψ dr = m2 r 2 ψ + mµ 0 rf dj φ dr ψ This equation is well-behaved and solvable, except where F = 0 (resonance). 24

25 Independently solve ψ in two regions: I) 0 < r < r s and II) r s < r < a where r s is the resonant surface where F (r s ) = 0. One way to do this is by by integrating the coupled first order equations from boundaries into resonant surface: d dr ψ = m2 r 2 ψ ψ d dr ψ = ψ r + mµ 0 rf dj φ dr ψ Matching conditions: b r (ψ) continuous, but db r dr (ψ ) is discontinuous. Matching to inner solution will determine growth rate. This discontinuity is quantified by = lim ɛ 0 [ ψ ψ rs +ɛ ψ ψ ] rs ɛ. 25

26 HOMEWORK: Numerically calculate for tokamak-like profiles of q rb φ RB θ (using Excel, IDL or your favorite programming language). Begin by assuming a current profile of the form ( ) ν j φ = j 0 1 r2 a 2 where ν can be related to the safety factor at the axis q 0 and at the boundary q a : ν = q a q0 1. Typically, q 0 1 and q a 3 5. For this current profile, B θ (r) = µ 0j 0 a 2 2r (ν + 1) ( ) ν 1 ) 1 (1 r2. For these profiles, begin by computing defining a radial grid array r i = i r that covers the range 0 r a with several hundred discrete radii. Then compute the profiles of F (r) = k B for an m = 2, n = 1 tearing mode. Plot it, and then determine the resonant surface r s where F (r s ) = 0. Next, solve for the perturbed flux in the two regions I) 0 < r < r s and II) r s < r < a. Do this is by by integrating the coupled first order equations ψ i+1 = ψ i + r ψ i+1 = ψ i + r ψ i ( m 2 r 2 i a 2 ψ i ψ i r i + mµ 0 r i F (r i ) dj φ dr ) ψ i i from boundaries into the resonant surface. For the inside solution, carry out this integration by starting the couple equations with the boundary conditions ψ(r = 0) = 0 (regularity), ψ (r = 0) = C and integrate outward to r = r s ɛ. Use a similar scheme to integrate the equations backwards from the outer wall at r = a to r = r s +ɛ (assuming that ψ(r = a) = 0 due to a conducting wall). Finally, take your two solutions for the inside and outside regions and scale them to match amplitudes on each side of the resonant surface. Finally, from the scaled solutions, find the derivatives on either side of the resonance to compute. = lim ɛ 0 [ ψ ψ rs +ɛ ψ ψ rs ɛ ] 26

27 Solution q j [Amps/cm 2 ] djdr B=1 T R=1.5 m a=0.5 m btheta [T] k. B psi m=2,n=1 q a =3.5 q 0 =1.0 r s =

28 Perturbed flux function 28

29 Resistive Layer In the resistive layer, ideal MHD breaks down and two key assumptions fail: the neglect of resistivity in Ohm s law and and the neglect of inertia in the force balance equation. Combining Ohm s law, E + v B = µ 0 J with Faraday s law and Ampere s law gives the magnetic diffusion equation: B t = v B η 2 B µ 0 29

30 Take the radial component of this equation to give b r t = B v r + η 2 b r µ 0 Assuming that the instability time dependence e γt and that the growth rate γ is real, b r = imψ/r and that r is constant in the layer, gives γψ + B θ (1 nq m )v r = η 2 ψ µ 0 The resistive layer is so narrow that radial derivatives in 2 will dominate, so that d 2 ψ dr 2 = µ 0γ η ψ + µ 0B θ η (1 nq m )v r 30

31 Assuming b r does not vary much (constant ψ), integrating across layer gives jump in : [ 1 dψ inner = ψ(r s ) dr dψ ] rs +ɛ dr rs ɛ = µ ( 0γ 1 + B ) θ nq(r) (1 η γ m ) v r dr ψ(r s ) Furthermore, we can make a linear expansion of F about the resonance surface so that 1 q(r)n m = q q (r r s ) rs so that = µ 0γ η (1 + B θq γq (r r s) ) v r ψ(r s ) dr 31

32 Equation of motion In the vicinity of the island, inertia must be taken into account to find v r. The φ component of the inertial term is ˆφ ρ dv dt = γρ v θ r = γρ ir m 2 v r r 2 where incompressibility has been used to relate v r and v θ. Including this inertial term in the force balance equation yields γρr 2 m 2 d 2 v r dr 2 = B θ µ 0 ( 1 nq(r) m ) d 2 ψ dr 2 dj φ dr ψ 32

33 Using the result from Ohm s law that relates d2 ψ dr to v 2 r, d 2 ( v r B 2 dr 2 θ m 2 q 2 ) ργηr 2 q 2 (r r s ) 2 v r = B θm 2 q ρηr 2 q (r r s) ψ m2 dj φ ργr 2 dr ψ Dimensional analysis gives a characteristic scale length δ = ( ρηγr 2 s q 2 B 2 θ m2 q 2 ) 1/4, = (γτ R) 1/4 S 1/2 ( r 2 s L 2 q a 4 ) 1/4 a (γτ R) 1/4 a S 1/2 33

34 The equation of motion for v r /ψ can be recast as d 2 y dy 2 x2 y = x C, where x = (r r s )/δ, y = ργr2 s q v r m 2 B θ q δ 3 ψ and a inner = γτ R δ a + (1 xy)dx Notes: Only odd part of y contributes to integral; y = x(1 xy) can be solved numerically to find y. Solution for y can be integrated to find a inner = 2.12γτ R δ a 34

35 Expressing δ in terms of γτ R results in or equivalently a inner = 2.12 (γτ R) 5/4 S 1/2 ( r 2 s L 2 q a 4 ) 1/4, γτ R = 0.55S 2/5 ( a 4 r 2 sl 2 q ) 1/5 (a outer) 4/5 Express δ as δ a = outer) 1/5 0.86(a S 2/5 ( a 4 r 2 sl 2 q ) 1/20 35

36 Summary Finite resistivity allows topology to change, and islands to form Outer solution determines stability > 0 Unstable Growth rate is a hybrid between resistive and Alfven growth rates: γ (a outer) 4/5 τ 3/5 R τ 2/5 A 36

Current-driven instabilities

Current-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 information

Formation 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 ) 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 information

Fundamentals of Magnetic Island Theory in Tokamaks

Fundamentals 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 information

SMR/ Summer College on Plasma Physics. 30 July - 24 August, Introduction to Magnetic Island Theory.

SMR/ 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 information

The RFP: Plasma Confinement with a Reversed Twist

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 information

Two Fluid Dynamo and Edge-Resonant m=0 Tearing Instability in Reversed Field Pinch

Two 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 information

Stabilization of sawteeth in tokamaks with toroidal flows

Stabilization 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 information

Resistive MHD, reconnection and resistive tearing modes

Resistive 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 information

Issues in Neoclassical Tearing Mode Theory

Issues 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

Momentum transport from magnetic reconnection in laboratory an. plasmas. Fatima Ebrahimi

Momentum 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 information

2D theory and simulations of Neoclassical Tearing Modes

2D theory and simulations of Neoclassical Tearing Modes 2D theory and simulations of Neoclassical Tearing Modes Jacco Heres 3118231 FOM-institute DIFFER - Dutch Institute for Fundamental Energy Research; Institute for Theoretical Physics, Utrecht University

More information

MHD Linear Stability Analysis Using a Full Wave Code

MHD 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 information

Measuring from electron temperature fluctuations in the Tokamak Fusion Test Reactor

Measuring 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 information

Heat 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 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 information

arxiv: v1 [physics.plasm-ph] 11 Mar 2016

arxiv: 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 information

Performance limits. Ben Dudson. 24 th February Department of Physics, University of York, Heslington, York YO10 5DD, UK

Performance limits. Ben Dudson. 24 th February Department of Physics, University of York, Heslington, York YO10 5DD, UK Performance limits Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 24 th February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 24) Previously... In the last few

More information

MAGNETOHYDRODYNAMICS

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 information

Lecture # 3. Introduction to Kink Modes the Kruskal- Shafranov Limit.

Lecture # 3. Introduction to Kink Modes the Kruskal- Shafranov Limit. Lecture # 3. Introduction to Kink Modes the Kruskal- Shafranov Limit. Steve Cowley UCLA. This lecture is meant to introduce the simplest ideas about kink modes. It would take many lectures to develop the

More information

High-m Multiple Tearing Modes in Tokamaks: MHD Turbulence Generation, Interaction with the Internal Kink and Sheared Flows

High-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 information

Fast Ion Confinement in the MST Reversed Field Pinch

Fast 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 information

35. RESISTIVE INSTABILITIES: CLOSING REMARKS

35. RESISTIVE INSTABILITIES: CLOSING REMARKS 35. RESISTIVE INSTABILITIES: CLOSING REMARKS In Section 34 we presented a heuristic discussion of the tearing mode. The tearing mode is centered about x = 0, where F x that B 0 ( ) = k! B = 0. Note that

More information

Effect of magnetic reconnection on CT penetration into magnetized plasmas

Effect of magnetic reconnection on CT penetration into magnetized plasmas Earth Planets Space, 53, 547 55, 200 Effect of magnetic reconnection on CT penetration into magnetized plasmas Yoshio Suzuki, Takaya Hayashi 2, and Yasuaki Kishimoto Naka Fusion esearch Establishment,

More information

Modelling of the penetration process of externally applied helical magnetic perturbation of the DED on the TEXTOR tokamak

Modelling 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 information

INTERACTION 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 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 information

Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks

Direct 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 information

Transition From Single Fluid To Pure Electron MHD Regime Of Tearing Instability

Transition 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 information

Simple examples of MHD equilibria

Simple 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 information

Surface currents associated with external kink modes in tokamak

Surface currents associated with external kink modes in tokamak Surface currents associated with external kink modes in tokamak plasmas during a major disruption C. S. Ng 1,2,a), and A. Bhattacharjee 1 1 Princeton Plasma Physics Laboratory, Princeton University, Princeton,

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

(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 information

Gyrokinetic Simulations of Tearing Instability

Gyrokinetic 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 information

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is

The Field-Reversed Configuration (FRC) is a high-beta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is and Stability of Field-Reversed Equilibrium with Toroidal Field Configurations Atomics General Box 85608, San Diego, California 92186-5608 P.O. APS Annual APS Meeting of the Division of Plasma Physics

More information

arxiv:physics/ v1 [physics.plasm-ph] 14 Nov 2005

arxiv:physics/ v1 [physics.plasm-ph] 14 Nov 2005 arxiv:physics/0511124v1 [physics.plasm-ph] 14 Nov 2005 Early nonlinear regime of MHD internal modes: the resistive case M.C. Firpo Laboratoire de Physique et Technologie des Plasmas (C.N.R.S. UMR 7648),

More information

Control 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 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 information

Control of Neo-classical tearing mode (NTM) in advanced scenarios

Control 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 information

Observation of Neo-Classical Ion Pinch in the Electric Tokamak*

Observation 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 information

Magnetohydrodynamic stability of negative central magnetic shear, high pressure ( pol 1) toroidal equilibria

Magnetohydrodynamic stability of negative central magnetic shear, high pressure ( pol 1) toroidal equilibria Magnetohydrodynamic stability of negative central magnetic shear, high pressure ( pol 1) toroidal equilibria Robert G. Kleva Institute for Plasma Research, University of Maryland, College Park, Maryland

More information

Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas

Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas Effect of local E B flow shear on the stability of magnetic islands in tokamak plasmas R. Fitzpatrick and F. L. Waelbroeck Citation: Physics of Plasmas (1994-present) 16, 052502 (2009); doi: 10.1063/1.3126964

More information

Heating and current drive: Radio Frequency

Heating and current drive: Radio Frequency Heating and current drive: Radio Frequency Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 13 th February 2012 Dr Ben Dudson Magnetic Confinement Fusion (1 of 26)

More information

Plasma 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 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 information

NIMROD 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 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 information

Electron Thermal Transport Within Magnetic Islands in the RFP

Electron 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 information

Theory 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 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 information

Exact solutions for magnetic annihilation in curvilinear geometry

Exact 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 information

Current Profile Control by ac Helicity Injection

Current 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 information

A Study of 3-Dimensional Plasma Configurations using the Two-Fluid Plasma Model

A Study of 3-Dimensional Plasma Configurations using the Two-Fluid Plasma Model A Study of 3-Dimensional Plasma Configurations using the Two-Fluid Plasma Model B. Srinivasan, U. Shumlak Aerospace and Energetics Research Program University of Washington IEEE International Conference

More information

Toroidal flow stablization of disruptive high tokamaks

Toroidal flow stablization of disruptive high tokamaks PHYSICS OF PLASMAS VOLUME 9, NUMBER 6 JUNE 2002 Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College Park, Maryland 20742-3511 Received 4 February 2002; accepted

More information

Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations

Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations Overview of Tokamak Rotation and Momentum Transport Phenomenology and Motivations Lecture by: P.H. Diamond Notes by: C.J. Lee March 19, 2014 Abstract Toroidal rotation is a key part of the design of ITER

More information

Waves in plasma. Denis Gialis

Waves in plasma. Denis Gialis Waves in plasma Denis Gialis This is a short introduction on waves in a non-relativistic plasma. We will consider a plasma of electrons and protons which is fully ionized, nonrelativistic and homogeneous.

More information

Supersonic drift-tearing magnetic islands in tokamak plasmas

Supersonic drift-tearing magnetic islands in tokamak plasmas Supersonic drift-tearing magnetic islands in tokamak plasmas R. Fitzpatrick, and F.L. Waelbroeck Institute for Fusion Studies Department of Physics University of Texas at Austin Austin, TX 78712 A two-fluid

More information

Ideal MHD Equilibria

Ideal MHD Equilibria CapSel Equil - 01 Ideal MHD Equilibria keppens@rijnh.nl steady state ( t = 0) smoothly varying solutions to MHD equations solutions without discontinuities conservative or non-conservative formulation

More information

Introduction to Fusion Physics

Introduction 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 information

AC loop voltages and MHD stability in RFP plasmas

AC 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 information

Particle transport results from collisionality scans and perturbative experiments on DIII-D

Particle transport results from collisionality scans and perturbative experiments on DIII-D 1 EX/P3-26 Particle transport results from collisionality scans and perturbative experiments on DIII-D E.J. Doyle 1), L. Zeng 1), G.M. Staebler 2), T.E. Evans 2), T.C. Luce 2), G.R. McKee 3), S. Mordijck

More information

MHD Simulation of High Wavenumber Ballooning-like Modes in LHD

MHD Simulation of High Wavenumber Ballooning-like Modes in LHD 1 TH/P9-16 MHD Simulation of High Wavenumber Ballooning-like Modes in LHD H. Miura and N. Nakajima National Institute for Fusion Science, 322-6 Oroshi, Toki, Gifu 509-5292, JAPAN e-mail contact of main

More information

Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow

Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow Home Search Collections Journals About Contact us My IOPscience Nonlinear magnetohydrodynamic effects on Alfvén eigenmode evolution and zonal flow generation This article has been downloaded from IOPscience.

More information

Oscillating-Field Current-Drive Experiment on MST

Oscillating-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 information

Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER

Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER G. Vlad, S. Briguglio, G. Fogaccia, F. Zonca Associazione Euratom-ENEA sulla Fusione, C.R.

More information

3-D Random Reconnection Model of the Sawtooth Crash

3-D Random Reconnection Model of the Sawtooth Crash 3-D Random Reconnection Model of the Sawtooth Crash Hyeon K. Park Princeton Plasma PhysicsN Laboratory Princeton University at IPELS, 2007 Cairns, Australia August 5-9, 2007 Collaboration with N.C. Luhmann,

More information

Bifurcated states of a rotating tokamak plasma in the presence of a static error-field

Bifurcated states of a rotating tokamak plasma in the presence of a static error-field Bifurcated states of a rotating tokamak plasma in the presence of a static error-field Citation: Physics of Plasmas (1994-present) 5, 3325 (1998); doi: 10.1063/1.873000 View online: http://dx.doi.org/10.1063/1.873000

More information

Fast Secondary Reconnection and the Sawtooth Crash

Fast Secondary Reconnection and the Sawtooth Crash Fast Secondary Reconnection and the Sawtooth Crash Maurizio Ottaviani 1, Daniele Del Sarto 2 1 CEA-IRFM, Saint-Paul-lez-Durance (France) 2 Université de Lorraine, Institut Jean Lamour UMR-CNRS 7198, Nancy

More information

Control of resistive wall modes in a cylindrical tokamak with plasma rotation and complex gain

Control of resistive wall modes in a cylindrical tokamak with plasma rotation and complex gain Control of resistive wall modes in a cylindrical tokamak with plasma rotation and complex gain arxiv:146.5245v1 [physics.plasm-ph] 2 Jun 214 D. P. Brennan and J. M. Finn June 23, 214 Department of Astrophysical

More information

CONFINEMENT IN THE RFP: LUNDQUIST NUMBER SCALING, PLASMA FLOW, AND REDUCED TRANSPORT

CONFINEMENT 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 information

Microtearing Simulations in the Madison Symmetric Torus

Microtearing 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 information

INTERACTION OF DRIFT WAVE TURBULENCE AND MAGNETIC ISLANDS

INTERACTION 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 information

PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH

PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH .- " Reprint from PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH 1984 PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH HELD BYTHE INTERNATIONAL

More information

Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations

Numerical 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 information

Neoclassical Tearing Modes

Neoclassical Tearing Modes Neoclassical Tearing Modes O. Sauter 1, H. Zohm 2 1 CRPP-EPFL, Lausanne, Switzerland 2 Max-Planck-Institut für Plasmaphysik, Garching, Germany Physics of ITER DPG Advanced Physics School 22-26 Sept, 2014,

More information

Collisionless nonideal ballooning modes

Collisionless nonideal ballooning modes PHYSICS OF PLASMAS VOLUME 6, NUMBER 1 JANUARY 1999 Collisionless nonideal ballooning modes Robert G. Kleva and Parvez N. Guzdar Institute for Plasma Research, University of Maryland, College Park, Maryland

More information

0 Magnetically Confined Plasma

0 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 information

MHD. Jeff Freidberg MIT

MHD. Jeff Freidberg MIT MHD Jeff Freidberg MIT 1 What is MHD MHD stands for magnetohydrodynamics MHD is a simple, self-consistent fluid description of a fusion plasma Its main application involves the macroscopic equilibrium

More information

Real Plasma with n, T ~ p Equilibrium: p = j B

Real Plasma with n, T ~ p Equilibrium: p = j B Real Plasma with n, T ~ p Equilibrium: p = j B B lines must lie in isobaric surfaces. Since B = 0, only possible if isobaric surfaces are topological tori. Magnetic field lines must form nested tori. Equilibrium

More information

L Aquila, Maggio 2002

L Aquila, Maggio 2002 Nonlinear saturation of Shear Alfvén Modes and energetic ion transports in Tokamak equilibria with hollow-q profiles G. Vlad, S. Briguglio, F. Zonca, G. Fogaccia Associazione Euratom-ENEA sulla Fusione,

More information

Evaluation of CT injection to RFP for performance improvement and reconnection studies

Evaluation 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 information

The Virial Theorem, MHD Equilibria, and Force-Free Fields

The Virial Theorem, MHD Equilibria, and Force-Free Fields The Virial Theorem, MHD Equilibria, and Force-Free Fields Nick Murphy Harvard-Smithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 10 12, 2014 These lecture notes are largely

More information

DIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH

DIAGNOSTICS 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 information

DOPPLER RESONANCE EFFECT ON ROTATIONAL DRIVE BY ION CYCLOTRON MINORITY HEATING

DOPPLER RESONANCE EFFECT ON ROTATIONAL DRIVE BY ION CYCLOTRON MINORITY HEATING DOPPLER RESONANCE EFFECT ON ROTATIONAL DRIVE BY ION CYCLOTRON MINORITY HEATING V.S. Chan, S.C. Chiu, Y.A. Omelchenko General Atomics, San Diego, CA, U.S.A. 43rd Annual APS Division of Plasma Physics Meeting

More information

Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena

Finite-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 information

- Effect of Stochastic Field and Resonant Magnetic Perturbation on Global MHD Fluctuation -

- 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 information

Macroscopic plasma description

Macroscopic 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 information

MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF PLASMA

MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF PLASMA University of Ljubljana Faculty of Mathematics and Physics Seminar 1 b -1st year, II. cycle MAGNETOHYDRODYNAMIC EQUILIBRIUM AND STABILITY OF PLASMA Author: Lino alamon Advisor: prof. dr. Tomaº Gyergyek

More information

Plasmoid Motion in Helical Plasmas

Plasmoid Motion in Helical Plasmas Plasmoid Motion in Helical Plasmas Ryuichi ISHIZAKI and Noriyoshi NAKAJIMA National Institute for Fusion Science, Toki 509-5292, Japan (Received 12 December 2009 / Accepted 18 May 2010) In order to explain

More information

Resistive Wall Mode Control in DIII-D

Resistive Wall Mode Control in DIII-D Resistive Wall Mode Control in DIII-D by Andrea M. Garofalo 1 for G.L. Jackson 2, R.J. La Haye 2, M. Okabayashi 3, H. Reimerdes 1, E.J. Strait 2, R.J. Groebner 2, Y. In 4, M.J. Lanctot 1, G.A. Navratil

More information

Equilibrium and transport in Tokamaks

Equilibrium and transport in Tokamaks Equilibrium and transport in Tokamaks Jacques Blum Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis Parc Valrose 06108 Nice Cedex 02, France jblum@unice.fr 08 septembre 2008 Jacques Blum

More information

2/8/16 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 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 information

Determination of q Profiles in JET by Consistency of Motional Stark Effect and MHD Mode Localization

Determination of q Profiles in JET by Consistency of Motional Stark Effect and MHD Mode Localization Determination of q Profiles in JET by Consistency of Motional Stark Effect and MHD Mode Localization R. De Angelis 1), F. Orsitto1), M. Baruzzo 2), P. Buratti 1), B. Alper 3), L. Barrera 4), A. Botrugno

More information

MHD-particle simulations and collective alpha-particle transport: analysis of ITER scenarios and perspectives for integrated modelling

MHD-particle simulations and collective alpha-particle transport: analysis of ITER scenarios and perspectives for integrated modelling MHD-particle simulations and collective alpha-particle transport: analysis of ITER scenarios and perspectives for integrated modelling G. Vlad, S. Briguglio, G. Fogaccia, F. Zonca Associazione Euratom-ENEA

More information

A 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 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 information

Two-fluid magnetic island dynamics in slab geometry

Two-fluid magnetic island dynamics in slab geometry Two-fluid magnetic island dynamics in slab geometry Richard Fitzpatrick and François L. Waelbroeck Institute for Fusion Studies Department of Physics University of Texas at Austin Austin, TX 78712 A novel

More information

Collisionless magnetic reconnection with arbitrary guide-field

Collisionless magnetic reconnection with arbitrary guide-field Collisionless magnetic reconnection with arbitrary guide-field Richard Fitzpatrick Center for Magnetic Reconnection Studies Institute for Fusion Studies Department of Physics University of Texas at Austin

More information

Sawteeth in Tokamaks and their relation to other Two-Fluid Reconnection Phenomena

Sawteeth 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 information

Plasma Stability in Tokamaks and Stellarators

Plasma Stability in Tokamaks and Stellarators Plasma Stability in Tokamaks and Stellarators Gerald A. Navratil GCEP Fusion Energy Workshop Princeton, NJ 1- May 006 ACKNOWLEDGEMENTS Borrowed VGs from many colleagues: J. Bialek, A. Garofalo,R. Goldston,

More information

Dispersive Media, Lecture 7 - Thomas Johnson 1. Waves in plasmas. T. Johnson

Dispersive 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 information

Plasma turbulence measured by fast sweep reflectometry on TORE SUPRA

Plasma turbulence measured by fast sweep reflectometry on TORE SUPRA Plasma turbulence measured by fast sweep reflectometry on TORE SUPRA F. Clairet &, L. Vermare &, S. Heuraux, G. Leclert # & Association Euratom-CEA sur la fusion, DSM/DRFC/SCCP C.E. Cadarache, 8 Saint-Paul-lès-Durance,

More information

Density 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 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 information

A numerical study of forced magnetic reconnection in the viscous Taylor problem

A numerical study of forced magnetic reconnection in the viscous Taylor problem A numerical study of forced magnetic reconnection in the viscous Taylor problem Richard Fitzpatrick Citation: Physics of Plasmas (1994-present) 10, 2304 (2003); doi: 10.1063/1.1574516 View online: http://dx.doi.org/10.1063/1.1574516

More information

SW103: Lecture 2. Magnetohydrodynamics and MHD models

SW103: 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 information

Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell

Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell PHYSICS OF PLASMAS VOLUME 11, NUMBER 5 MAY 2004 Observation of tearing mode deceleration and locking due to eddy currents induced in a conducting shell B. E. Chapman Department of Physics, University of

More information

Peeling mode relaxation ELM model

Peeling mode relaxation ELM model Peeling mode relaxation ELM model C. G. Gimblett EURATOM/UKAEA Fusion Association, Culham Science Centre Abingdon, Oxon, OX14 3DB, United Kingdom Abstract. This paper discusses an approach to modelling

More information

POWER DENSITY ABSORPTION PROFILE IN TOKAMAK PLASMA WITH ICRH

POWER DENSITY ABSORPTION PROFILE IN TOKAMAK PLASMA WITH ICRH Dedicated to Professor Oliviu Gherman s 80 th Anniversary POWER DENSITY ABSORPTION PROFILE IN TOKAMAK PLASMA WITH ICRH N. POMETESCU Association EURATOM-MECTS Romania, University of Craiova, Faculty of

More information

A Comparison between the Two-fluid Plasma Model and Hall-MHD for Captured Physics and Computational Effort 1

A Comparison between the Two-fluid Plasma Model and Hall-MHD for Captured Physics and Computational Effort 1 A Comparison between the Two-fluid Plasma Model and Hall-MHD for Captured Physics and Computational Effort 1 B. Srinivasan 2, U. Shumlak Aerospace and Energetics Research Program University of Washington,

More information