Extended Lumped Parameter Model of Resistive Wall Mode and The Effective SelfInductance


 Philippa Rogers
 1 years ago
 Views:
Transcription
1 Extended Lumped Parameter Model of Resistive Wall Mode and The Effective SelfInductance M.Okabayashi, M. Chance, M. Chu* and R. Hatcher A. Garofalo**, R. La Haye*, H. Remeirdes**, T. Scoville*, and T. Strait* Princeton Plasma Physics Laboratory * General Atomics ** Columbia Univeristy "Active Control of MHD Stability: Extension of Performance" Workshop under the auspices of the US/Japan Collaboration at Columbia University, 180 November 00
2 OUTLINE  Extended Lumped Parameter Model and RWM Effective SelfInductance MOTIVATION APPROACH AND ASSUMPTIONS OF EXTENDED LUMPED PARAMETER MODEL  Relation to recent other approaches (models) "RWM EFFECTIVE SELFINDUCTANCE"  Plasma response is conveniently characterized by one parameter APPLICATIONS  Dispersion relation / Initial value time dependent solution  Resonant magnetic braking,  Nonresonant braking,  Resonant Field Amplification
3 MOTIVATION  Develop simple description of RWM stabilization process, useful for qualitative and semiquantitative discussion.  M. Okabayashi, N. Pomphrey and R. Hatcher, N. Fusion. 38(1998) M. Okabayashi et al, EPS 00 (Plasma Phy. and Controlled Fusion in press)  The model to be consistent with MHD analysis models developed by various groups  A. Bondeson and D. Ward, Phys. Rev. Lett. 7 (1994)709  J. Bialek, etal., Phys. of Plasmas, 8 (001) M. Chu et al., (IAEA 00)  R. Fitzpatrick, Phy. Plasmas 9 (00) A. Garofalo, Sherwood meeting (00)
4 RWM AND ITS FEEDBACK CONTROL CAN BE CONSIDERED AS THE n=1 HELICAL INSTABILITY ANALOG TO THE n = 0 VERTICAL INSTABILITY Marginal Stability Parameter Vertical Drift RWM Feedback B r External Equi. Mag. Field Negative Curv. FIXED M t w g t 0 w 1 1 n c Eddy Flux Decay Induced Image Current Displacement Ideal kink Feedback Helical flux Vertical Helical "Mode Rigidity" is the fundamental assumption
5 RWM AND ITS FEEDBACK CONTROL CAN BE CONSIDERED AS THE n=1 HELICAL INSTABILITY ANALOG TO THE n = 0 VERTICAL INSTABILITY Feedback B r Vertical Drift External Equi. Mag. Field Negative Curv. FIXED M t w g t 0 w Marginal Stability Parameter 1 1 n c Eddy Flux Decay Induced Image Current Displacement RWM Ideal kink Feedback Helical flux no wall Limit 100 g Growth Rate without Feedback t 0 w Vertical Position Control g n=0 t w RWM Control = 710 RW M t w Ideal wall Limit g = 4 Vertical Helical Mode Strength Higher elongation "Mode Rigidity" is the fundamental assumption Higher b
6 Approach and Assumptions of Extended Lumped Parameter Model Include essential RWM physics  Pressure balance and Bnormal continuity on plasma surface  Rotation dissipation in adhoc manner, however, consistent with existing theories  Assumptions  Rigid displacement: justifiable based on experiments [M. Okabayashi et al., Phys. Plasmas 8,071(001)]  Cylindrical geometry  One mode excitation  No coupling to other [stable] modes
7 EXTENDED LUMPED PARAMETER RWM MODEL Explicit Usage of Boundary Conditions  on the Plasma Surface, Wall and Coil ( I p, I w, I c )  Independent parameters: plasma skin current, wall current, feedback coil current PLASMA x r M pw M pc M wc I I I p w c plasma passive shell Y active coil
8 EXTENDED LUMPED PARAMETER RWM MODEL Explicit Usage of Boundary Conditions  on the Plasma Surface, Wall and Coil ( I p, I w, I c )  Independent parameters: plasma skin current, wall current, feedback coil current PLASMA x r M pw M pc M wc I I I p w c plasma displacement fixed displacement h 0 approximation (available from experiment) rotational dissipation plasma plasma rotation (1/x r) d(rx r )/dr a (g + i W ) r=a + N f passive shell Pressure Balance and Bnormal Continuity on Plasma Surface toroidal number m  nq Y active coil external Y = S M Y i,j displacement A + + = (mf / g t +f ))(a y '(a )/ m y(a ) + /f) standard mutual inductance j
9 EXTENDED LUMPED PARAMETER RWM MODEL Explicit Usage of Boundary Conditions  on the Plasma Surface, Wall and Coil ( I p, I w, I c )  Independent parameters: plasma skin current, wall current, feedback coil current PLASMA x r M pw M pc M wc I I I p w c plasma displacement rotational dissipation plasma plasma rotation (1/x r) d(rx r )/dr a (g + i W ) r=a + N f passive shell Pressure Balance and Bnormal Continuity on Plasma Surface fixed displacement approximation m  nq Conveniently formulated "RWM effective selfinductance" V =d/dt h 0 L M M eff pw cp M L M wp w wc M M L pc cw c I p I w I c toroidal number active coil external Y = S M Y i,j displacement A + + = (mf / g t +f ))(a y '(a )/ m y(a ) + /f) b = /f 1 n L effi p + M pwi w+ M pci c =0 L eff = (h  b + a(g + inwf)) L 0 n / (h b  + a(g + inwf)) standard mutual inductance 0 Y n standard mutual inductance (f=1 <> no wall limit, b n =1) L eff represents all RWM characteristics currently considered j
10 EXTENDED LUMPED PARAMETER RWM MODEL Explicit Usage of Boundary Conditions  on the Plasma Surface, Wall and Coil ( I p, I w, I c )  Independent parameters: plasma skin current, wall current, feedback coil current PLASMA x r M pw M pc M wc I I I p w c plasma displacement rotational dissipation plasma plasma rotation (1/x r) d(rx r )/dr a (g + i W ) r=a + N f passive shell Pressure Balance and Bnormal Continuity on Plasma Surface fixed displacement approximation m  nq Conveniently formulated "RWM effective selfinductance" V =d/dt h 0 L M M eff pw cp M L M wp w wc M M L pc cw c I p I w I c toroidal number active coil external Y = S M Y i,j displacement A + + = (mf / g t +f ))(a y '(a )/ m y(a ) + /f) b = /f 1 n L effi p + M pwi w+ M pci c =0 L eff = (h  b + a(g + inwf)) L 0 n / (h b  + a(g + inwf)) standard mutual inductance 0 Y n standard mutual inductance magnetic decay index N''z + Br_ext =0 : vertical instability (f=1 <> no wall limit, b n =1) L eff represents all RWM characteristics currently considered j
11 Extended Lumped Parameter Model kinetic dissipation RWM Dispersion Relation Dispersion Relation with Extended Lumped Parameter Model Expresses Explicitly Geomertical Elements plasma beta wall time constant geometrical term [ c ( g + iw) + a(g +iw) +h  b ) ](g + t 1 k n )  g [c ( g + iw) + a( g + iw) + h  b  ] (M / L L ) =0 w k n pw w p 0 0 M = (r /r ) m ij i j
12 Extended Lumped Parameter Model kinetic dissipation RWM Dispersion Relation Dispersion Relation with Extended Lumped Parameter Model Expresses Explicitly Geomertical Elements plasma beta wall time constant [ c ( g + iw) + a(g +iw) +h  b ) ](g + t 1 k n )  g [c ( g + iw) + a( g + iw) + h  b  ] (M / L L ) =0 w k n pw w p 0 0 Fitzpatrick's " Simple Model of RWM... in Phys. Plasmas 9(00)3459 geometrical term M = (r /r ) m ij i j kinetic plasma beta dissipation* wall time constant* geometrical term
13 ñ Modeling of Feedback and Rotation Stabilization of the Resistive Wall Mode in tokamaks ñ IAEA Meeting, Lyon, France, October 14 to 19, 00 GENERAL FORMULATION INCLUDING PLASMA ROTATION AND DISSIPATION (M. CHU IAEA 00) The ìresistive wall modeî can be described in terms of circuits on the resisitive wall driven by the plasma or the external coils (7) The plasma responds to the magnetic field B lw on the resistive wall through the relationship The response of the RWM to the coil currents is therefore (8) (9)
14 Schematics of RWM Feedback Analysis with Toroidal Geometry Resistive Wall Thin Shell Approximation Plasma Surface Resistive Shell (eigen modes) Active Coil ï Introducing "skin current stream fluction" I w : j = Z x I w d(zz w ) ï normal magnetic field continuity dy /dn () = dy /dn (+) = Bn Helical Displacement Ip (t) C wp, C pw, y p y w B p  B w I w + y w + B w C wc I c ï Ampere's Law: Y(+)  Y() = I w ï Faraday's Law [h I w ] = (d /dt (B n ), assuming z = 1 s s B n I w z B n I w (q,f) can be expanded in eigenmodes PEST / VACUUM ds Green's theorem  + Green's theorem Resistive Shell
15 Modeling of Feedback and Rotation Stabilization of the Resistive Wall Mode in tokamaks IAEA Meeting, Lyon, France, October 14 19, 00 THE LUMPED PARAMETER MODEL AND RFA (M.CHU, IAEA00) For the least stable resistive wall mode and assuming the matrix elements of the energy and dissipation factors are constants, we arrive at a lumped parameter equation the total RWM field at wall external helical current (10) where A is the 'complex amplification factor'. Note that A = 1 in the absence of plasma potential energy with ideal wall d W IW (W) + aiw A = (11) d W (W) + aiw nw potential energy without wall In this equation we see that the dissipation on the wall and the dissipation is the plasma are separated 1. 'No External Coil': homogeneous equation, dissipation in plasma and the resistive wal (1). 'Steady State with External Coil': inhomogeneous equation. dissipation in plasma (13)
16 dw FORMULATION AND LUMPED PARAMETER MODEL M. Chu Formulation (IAEA 00) Extended Lumped Parameter Model growth rate total Bfield on wall 1/A = d W (W) + aiw nw d W (W) + aiw iw resonant field amplification
17 dw FORMULATION AND LUMPED PARAMETER MODEL M. Chu Formulation (IAEA 00) Extended Lumped Parameter Model growth rate total Bfield on wall tw I p + [L / ( L  M pw / L w )] t I p = 0 eff eff L = (h  b + iw) L / (h  b  + iw) eff 0 n p 0 n 1/A = d W (W) + aiw nw d W (W) + aiw iw resonant field amplification
18 dw FORMULATION AND LUMPED PARAMETER MODEL M. Chu Formulation (IAEA 00) Extended Lumped Parameter Model growth rate total Bfield on wall t I p w + [L / ( L  M pw / L w )] t I p = 0 eff eff gt w L = (h  b + iw) L / (h  b  + iw) eff 0 n p 0 n 1/A = d W (W) + aiw nw d W (W) + aiw iw  marginal stability b ( no wall limit) gt = 0 <> L =0 : h = b w eff n.w  Ideal wall limit gt = infinity > ( L ( b )  M L ) = 0 w eff I.w pw w 0 (b gt = n.w  b n + iaw) (b  b )/ () w (b  b + iaw) n.w I.w I.w n resonant field amplification
19 dw FORMULATION AND LUMPED PARAMETER MODEL M. Chu Formulation (IAEA 00) Extended Lumped Parameter Model growth rate total Bfield on wall t I p w + [L / ( L  M pw / L w )] t I p = 0 eff eff gt w L = (h  b + iw) L / (h  b  + iw) eff 0 n p 0 n 1/A = d W (W) + aiw nw d W (W) + aiw iw  marginal stability b ( no wall limit) gt = 0 <> L =0 : h = b w eff n.w  Ideal wall limit gt = infinity > ( L ( b )  M L ) = 0 w eff I.w pw w 0 resonant field amplification (b gt = n.w  b n + iaw) (b  b )/ () w (b  b + iaw) n.w I.w I.w n normalization constant
20 dw FORMULATION AND LUMPED PARAMETER MODEL M. Chu Formulation (IAEA 00) Extended Lumped Parameter Model growth rate total Bfield on wall t I p w + [L / ( L  M pw / L w )] t I p = 0 eff eff gt w L = (h  b + iw) L / (h  b  + iw) eff 0 n p 0 n 1/A = d W (W) + aiw nw d W (W) + aiw iw  marginal stability b ( no wall limit) gt = 0 <> L =0 : h = b w eff n.w  Ideal wall limit gt = infinity > ( L ( b )  M L ) = 0 w eff I.w pw w 0 resonant field amplification (b gt = n.w  b + iaw) (b  b )/ () w (b  b + iaw) n.w I.w I.w L I + M I + M I =0 eff p pw w pc c normalization constant I = p M pc L eff I c
21 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example(1): Magnetic Braking (Rotation slowing down with increasing mode amplitude) Steady target RWM amplitude coil current or error field W / t = (W  W) /t  C Im[dI p (t) di (t) )] 0 m vis c. momentum conf. time ~1/ a ( g + iw) > 1/(iaW) known as rotation dissipation "induction motor model"
22 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example(1): Magnetic Braking (Rotation slowing down with increasing mode amplitude) Steady target RWM amplitude coil current or error field W / t = (W  W) /t  C Im[dI p (t) di (t) )] 0 m vis c. momentum conf. time ~1/ a ( g + iw) > 1/(iaW) known as rotation dissipation "induction motor model" Experiment with Various External Fields C Coil79 (A) (khz) Reduced static n=1 error field Critical Rotation for onset of RWM n=1b r (gauss) Time (ms)
23 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example(1): Magnetic Braking (Rotation slowing down with increasing mode amplitude) Steady target RWM amplitude coil current or error field W / t = (W  W) /t  C Im[dI p (t) di (t) )] 0 m vis c. momentum conf. time ~1/ a ( g + iw) > 1/(iaW) known as rotation dissipation "induction motor model" C Coil79 (A) Critical Rotation for onset of RWM n=1b r (gauss) Experiment with Various External Fields (khz) Reduced static n=1 error field Time (ms) 0. (khz) 0.0 Ip (arb) Extended Lumped Parameter Model Simulation 1.6 Magnitude of External Field: 0.8,1.0,1., 1.4,1.8 (arb.) ROTATION Time (ms) AMPLITUDE
24 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example() : Active Magnetic Braking (Regulated rotation slowing down using mode amplitude controlled by feedback) Steady target RWM amplitude coil current momentum conf. time W / t = (W  W) /t  C Im[dI(t) p (di(t) + di(t) )] 0 m vis c.fb c.pre.pro di(t) = G / ( 1  G )di(t) p fb fb c.pre.pro feedback gain
25 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example() : Active Magnetic Braking (Regulated rotation slowing down using mode amplitude controlled by feedback) Steady target RWM amplitude coil current momentum conf. time W / t = (W  W) /t  C Im[dI(t) p (di(t) + di(t) )] 0 m vis c.fb c.pre.pro di(t) = G / ( 1  G )di(t) p fb fb c.pre.pro preprogrammed coil current Simulation Actual coil current feedback gain Plasma rotation Mode amplitude time [t w ]
26 RWM Time Evolution with Extended Lumped Parameter Model Plus Angular Momentum Balance  Example() : Active Magnetic Braking (Regulated rotation slowing down using mode amplitude controlled by feedback) Steady target RWM amplitude coil current momentum conf. time W / t = (W  W) /t  C Im[dI(t) p (di(t) + di(t) )] 0 m vis c.fb c.pre.pro di(t) = G / ( 1  G )di(t) p fb fb c.pre.pro preprogrammed coil current Simulation Actual coil current n1tc1curr Preprogrammed coil current feedback gain Experiment c79f Actual coil current Plasma rotation Plasma rotation cernrott6 I D Mode amplitude L > amplitude from MPID (Larry s matrix) Mode amplitude time [t w ] time (ms)
27 STABLE REGIME PREDICTED BY EXTENDED LUMPED PARAMETER MODEL IS CONSISTENT WITH EXPERIMENTALLY ACHIEVED PARAMETERS ideal wall limit bn / (.4 li) no wall limit Unstable Expected with Extended Lumped Parameter Model /106530/10653/ High bn shots in FY 00 * Steady State High bn Equilibrium used for RFA study time Toroidal Rotation (km/s) 008/MHDWKSP/00
28 RFA AMPLITUDE AND PHASE SHIFT INCREASE WITH INCREASE OF b n TO MARGINAL STABILITY b n db r at wall (G) Field component on /1 surface (G) n = 1 (plasma response only) No wall beta limit stable Time (ms) gt w Damping rate Unstable Marginal stability nowall b n /b n Amplitude 0.0 Toroidal phase shift Mode amplitude (degrees) DIII D NATIONAL FUSION FACILITY SAN DIEGO noise level nowall nowall b n /b n b n /b n 1760/jy
29 1.0 s /S Fitting deviation COMPARISON OF MODEL AND OBSERVATIONS SHOWS THAT DAMPING OF RFA ARISES FROM ROTATIONAL DISSIPATION Fit of Dissipation Coeff. Best Fit A h o =1.3 =1.4 = Dissipation coeff a/t Mode amplitude noise level Observed Plasma Response to Amplitude (degrees) Toroidal phase shift 0.0 Damping Rate gt w Best fit to the model with the dissipation parameter a /t =5. Mode amplitude (arb.) Amplitude 0.0 A EXP MODEL Toroidal phase shift g t W nowall b n / b n nowall b / n bn dissipation / damping rate : a W f/ g t ª exp w nowall b n / bn DIII D NATIONAL FUSION FACILITY SAN DIEGO
30 Modeling of Feedback and Rotation Stabilization of the Resistive Wall Mode in tokamaks IAEA Meeting, Lyon, France, October 14 19, 00 COMPARISON OF LUMPED PARAMETER MODEL WITH EXPERIMENT amplitude (model) phase (model) amplitude (model) amplitude (observed) phase (model) phase (observed) N N (arb) amplitude (observed) A = phase (observed) [d W (W=0) + ew ] + aiw IW [d W (W=0)+ ew ] + aiw nw Qualitative agreement is also obtained by using the present lumped parameter model with different forms for A. This indicates more details should be included in future comparisons (14) 700/JY
31 SUMMARY Extended Lumped Parameter Model includes the essence of RWM physics The present approach is consistent with other approaches Comparison with experimental results provides semiquantitative discussion of the present RWM understandings.
Modeling of active control of external magnetohydrodynamic instabilities*
PHYSICS OF PLASMAS VOLUME 8, NUMBER 5 MAY 2001 Modeling of active control of external magnetohydrodynamic instabilities* James Bialek, Allen H. Boozer, M. E. Mauel, and G. A. Navratil Department of Applied
More informationPlasma 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 informationAnalysis and modelling of MHD instabilities in DIIID plasmas for the ITER mission
Analysis and modelling of MHD instabilities in DIIID plasmas for the ITER mission by F. Turco 1 with J.M. Hanson 1, A.D. Turnbull 2, G.A. Navratil 1, C. PazSoldan 2, F. Carpanese 3, C.C. Petty 2, T.C.
More informationControl 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.plasmph] 2 Jun 214 D. P. Brennan and J. M. Finn June 23, 214 Department of Astrophysical
More informationAnalytical Study of RWM Feedback Stabilisation with Application to ITER
CT/P Analytical Study of RWM Feedback Stabilisation with Application to ITER Y Gribov ), VD Pustovitov ) ) ITER International Team, ITER Naka Joint Work Site, Japan ) Nuclear Fusion Institute, Russian
More informationSupported by. Role of plasma edge in global stability and control*
NSTX Supported by College W&M Colorado Sch Mines Columbia U CompX General Atomics INL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U Purdue U
More informationDynamic Resonant Error Field Correction with CCOIL and ICOIL in the DIIID device
Dynamic Resnant Errr Field Crrectin with CCOIL and ICOIL in the DIIID device M. Okabayashi, M.S. Chance, R, Hatcher, J. Manickam P P P L, J. Bialek, A.M. Garfal, G.A. Navratil, H. Reimerdes, C lumbia
More informationEffects of stellarator transform on sawtooth oscillations in CTH. Jeffrey Herfindal
Effects of stellarator transform on sawtooth oscillations in CTH Jeffrey Herfindal D.A. Ennis, J.D. Hanson, G.J. Hartwell, E.C. Howell, C.A. Johnson, S.F. Knowlton, X. Ma, D.A. Maurer, M.D. Pandya, N.A.
More informationDIII D Research in Support of ITER
Research in Support of ITER by E.J. Strait and the Team Presented at 22nd IAEA Fusion Energy Conference Geneva, Switzerland October 1318, 28 DIIID Research Has Made Significant Contributions in the Design
More informationLinjin Zheng, Infernal Modes at Tokamak H mode Pedestal A Physics Interpreta;on for Edge Harmonic Oscilla;on (EHO)
International Sherwood Fusion Theory Conference, Austin, May 24, 2011 Infernal Modes at Tokamak H mode Pedestal A Physics Interpreta;on for Edge Harmonic Oscilla;on (EHO) Linjin Zheng, M. T. Kotschenreuther,
More informationarxiv: v1 [physics.plasmph] 11 Mar 2016
1 Effect of magnetic perturbations on the 3D MHD selforganization of shaped tokamak plasmas arxiv:1603.03572v1 [physics.plasmph] 11 Mar 2016 D. Bonfiglio 1, S. Cappello 1, M. Veranda 1, L. Chacón 2 and
More informationGA A26887 ADVANCES TOWARD QHMODE VIABILITY FOR ELMFREE OPERATION IN ITER
GA A26887 ADVANCES TOWARD QHMODE VIABILITY FOR ELMFREE OPERATION IN ITER by A.M. GAROFALO, K.H. BURRELL, M.J. LANCTOT, H. REIMERDES, W.M. SOLOMON and L. SCHMITZ OCTOBER 2010 DISCLAIMER This report was
More informationActive and Fast Particle Driven Alfvén Eigenmodes in Alcator CMod
Active and Fast Particle Driven Alfvén Eigenmodes in Alcator CMod JUST DID IT. J A Snipes, N Basse, C Boswell, E Edlund, A Fasoli #, N N Gorelenkov, R S Granetz, L Lin, Y Lin, R Parker, M Porkolab, J
More informationELM Suppression in DIIID Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations
1 EXC/P502 ELM Suppression in DIIID Hybrid Plasmas Using n=3 Resonant Magnetic Perturbations B. Hudson 1, T.E. Evans 2, T.H. Osborne 2, C.C. Petty 2, and P.B. Snyder 2 1 Oak Ridge Institute for Science
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 informationThe FieldReversed Configuration (FRC) is a highbeta compact toroidal in which the external field is reversed on axis by azimuthal plasma The FRC is
and Stability of FieldReversed Equilibrium with Toroidal Field Configurations Atomics General Box 85608, San Diego, California 921865608 P.O. APS Annual APS Meeting of the Division of Plasma Physics
More informationMHD instability driven by suprathermal electrons in TJII stellarator
MHD instability driven by suprathermal electrons in TJII stellarator K. Nagaoka 1, S. Yamamoto 2, S. Ohshima 2, E. Ascasíbar 3, R. JiménezGómez 3, C. Hidalgo 3, M.A. Pedrosa 3, M. Ochando 3, A.V. Melnikov
More informationGA A23713 RECENT ECCD EXPERIMENTAL STUDIES ON DIII D
GA A271 RECENT ECCD EXPERIMENTAL STUDIES ON DIII D by C.C. PETTY, J.S. degrassie, R.W. HARVEY, Y.R. LINLIU, J.M. LOHR, T.C. LUCE, M.A. MAKOWSKI, Y.A. OMELCHENKO, and R. PRATER AUGUST 2001 DISCLAIMER This
More informationBifurcated states of a rotating tokamak plasma in the presence of a static errorfield
Bifurcated states of a rotating tokamak plasma in the presence of a static errorfield Citation: Physics of Plasmas (1994present) 5, 3325 (1998); doi: 10.1063/1.873000 View online: http://dx.doi.org/10.1063/1.873000
More informationTokamak/Helical Configurations Related to LHD and CHSqa
9TH WORKSHOP ON MHD STABILITY CONTROL: "CONTROL OF MHD STABILITY: BACK TO THE BASICS" NOVEMBER 2123, 2004, PRINCETON PLASMA PHYSICS LABORATORY Tokamak/Helical Configurations Related to LHD and CHSqa
More informationPlasma models for the design of the ITER PCS
Plasma models for the design of the ITER PCS G. De Tommasi 1,2 on behalf of the CREATE team 1 Consorzio CREATE, Naples, Italy 2 Department of Electrical Engineering and Information Technology, University
More informationSTABILIZATION OF m=2/n=1 TEARING MODES BY ELECTRON CYCLOTRON CURRENT DRIVE IN THE DIII D TOKAMAK
GA A24738 STABILIZATION OF m=2/n=1 TEARING MODES BY ELECTRON CYCLOTRON CURRENT DRIVE IN THE DIII D TOKAMAK by T.C. LUCE, C.C. PETTY, D.A. HUMPHREYS, R.J. LA HAYE, and R. PRATER JULY 24 DISCLAIMER This
More informationMacroscopic Stability of High β N MAST Plasmas
1 EXS/P54 Macroscopic Stability of High β N MAST Plasmas I.T. Chapman 1), R.J. Akers 1), L.C. Appel 1), N.C. Barratt 2), M.F. de Bock 1,7), A.R. Field 1), K.J. Gibson 2), M.P. Gryaznevich 1), R.J. Hastie
More informationW.M. Solomon 1. Presented at the 54th Annual Meeting of the APS Division of Plasma Physics Providence, RI October 29November 2, 2012
Impact of Torque and Rotation in High Fusion Performance Plasmas by W.M. Solomon 1 K.H. Burrell 2, R.J. Buttery 2, J.S.deGrassie 2, E.J. Doyle 3, A.M. Garofalo 2, G.L. Jackson 2, T.C. Luce 2, C.C. Petty
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 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 informationAmplification of magnetic fields in core collapse
Amplification of magnetic fields in core collapse Miguel Àngel Aloy Torás, Pablo CerdáDurán, Thomas Janka, Ewald Müller, Martin Obergaulinger, Tomasz Rembiasz Universitat de València; MaxPlanckInstitut
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 informationSMR/ Summer College on Plasma Physics. 30 July  24 August, Introduction to Magnetic Island Theory.
SMR/18561 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 informationDYNAMO THEORY: THE PROBLEM OF THE GEODYNAMO PRESENTED BY: RAMANDEEP GILL
DYNAMO THEORY: THE PROBLEM OF THE GEODYNAMO PRESENTED BY: RAMANDEEP GILL MAGNETIC FIELD OF THE EARTH DIPOLE Field Structure Permanent magnetization of Core? 80% of field is dipole 20 % is non dipole 2)
More informationStability Properties of Toroidal Alfvén Modes Driven. N. N. Gorelenkov, S. Bernabei, C. Z. Cheng, K. Hill, R. Nazikian, S. Kaye
Stability Properties of Toroidal Alfvén Modes Driven by Fast Particles Λ N. N. Gorelenkov, S. Bernabei, C. Z. Cheng, K. Hill, R. Nazikian, S. Kaye Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton,
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 informationGA A23736 EFFECTS OF CROSSSECTION SHAPE ON L MODE AND H MODE ENERGY TRANSPORT
GA A3736 EFFECTS OF CROSSSECTION SHAPE ON L MODE AND H MODE ENERGY TRANSPORT by T.C. LUCE, C.C. PETTY, and J.E. KINSEY AUGUST DISCLAIMER This report was prepared as an account of work sponsored by an
More informationReport submitted to Prof. P. Shipman for Math 540, Fall 2009
Dynamics at the Horsetooth Volume 1, 009. ThreeWave Interactions of Spin Waves Aaron Hagerstrom Department of Physics Colorado State University aaronhag@rams.colostate.edu Report submitted to Prof. P.
More informationIntroduction to Fusion Physics
Introduction to Fusion Physics Hartmut Zohm MaxPlanckInstitut für Plasmaphysik 85748 Garching DPG Advanced Physics School The Physics of ITER Bad Honnef, 22.09.2014 Energy from nuclear fusion Reduction
More informationNonlinear modeling of the Edge Localized Mode control by Resonant Magnetic Perturbations in ASDEX Upgrade
1 TH/P126 Nonlinear modeling of the Edge Localized Mode control by Resonant Magnetic Perturbations in ASDEX Upgrade F.Orain 1, M.Hölzl 1, E.Viezzer 1, M.Dunne 1, M.Bécoulet 2, P.Cahyna 3, G.T.A.Huijsmans
More informationEXAMINATION QUESTION PAPER
Faculty of Science and Technology EXAMINATION QUESTION PAPER Exam in: Fys2009 Introduction to Plasma Physics Date: 20161202 Time: 09.0013.00 Place: Åsgårdvegen 9 Approved aids: Karl Rottmann: Matematisk
More informationImpact of Localized ECRH on NBI and ICRH Driven Alfven Eigenmodes in the ASDEX Upgrade Tokamak
Impact of Localized ECRH on NBI and ICRH Driven Alfven Eigenmodes in the ASDEX Upgrade Tokamak M. GarciaMunoz M. A. Van Zeeland, S. Sharapov, Ph. Lauber, J. Ayllon, I. Classen, G. Conway, J. Ferreira,
More informationRotation and Neoclassical Ripple Transport in ITER
Rotation and Neoclassical Ripple Transport in ITER Elizabeth J. Paul 1 Matt Landreman 1 Francesca Poli 2 Don Spong 3 Håkan Smith 4 William Dorland 1 1 University of Maryland 2 Princeton Plasma Physics
More informationDIII D INTEGRATED PLASMA CONTROL SOLUTIONS FOR ITER AND NEXT GENERATION TOKAMAKS
GA A25808 DIII D INTEGRATED PLASMA CONTROL SOLUTIONS FOR ITER AND NEXT GENERATION TOKAMAKS by D.A. HUMPHREYS, J.R. FERRON, A.W. HYATT, R.J. La HAYE, J.A. LEUER, B.G. PENAFLOR, M.L. WALKER, A.S. WELANDER,
More informationYell if you have any questions
Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored
More informationObservation 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 informationRLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is
RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge
More informationELM control with RMP: plasma response models and the role of edge peeling response
ELM control with RMP: plasma response models and the role of edge peeling response Yueqiang Liu 1,2,3,*, C.J. Ham 1, A. Kirk 1, Li Li 4,5,6, A. Loarte 7, D.A. Ryan 8,1, Youwen Sun 9, W. Suttrop 10, Xu
More informationStellarators. Dr Ben Dudson. 6 th February Department of Physics, University of York Heslington, York YO10 5DD, UK
Stellarators Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 6 th February 2014 Dr Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously... Toroidal devices
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 MagnetoHydro Dynamics, MHD Plasmas without magnetic fields Cold plasmas Transverse waves
More informationBasics of rotordynamics 2
Basics of rotordynamics Jeffcott rotor 3 M A O a rigid rotor disk rotates at angular frequency W massless shaft acts as a spring restoring displacements disk can move only in the plane defined by axes
More informationq(0) pressure after crash 1.0 Single tearing on q=2 Double tearing on q=2 0.5
EX/P1 MHD issues in Tore Supra steadystate fully noninductive scenario P Maget 1), F Imbeaux 1), G Giruzzi 1), V S Udintsev ), G T A Huysmans 1), H Lütjens 3), JL Ségui 1), M Goniche 1), Ph Moreau
More informationGA A25853 FAST ION REDISTRIBUTION AND IMPLICATIONS FOR THE HYBRID REGIME
GA A25853 FAST ION REDISTRIBUTION AND IMPLICATIONS FOR THE HYBRID REGIME by R. NAZIKIAN, M.E. AUSTIN, R.V. BUDNY, M.S. CHU, W.W. HEIDBRINK, M.A. MAKOWSKI, C.C. PETTY, P.A. POLITZER, W.M. SOLOMON, M.A.
More informationA Study of Directly Launched Ion Bernstein Waves in a Tokamak
PFC/JA866 A Study of Directly Launched Ion Bernstein Waves in a Tokamak Y. Takase, J. D. Moody, C. L. Fiore, F. S. McDermott, M. Porkolab, and J. Squire Plasma Fusion Center Massachusetts Institute
More informationRecent Development of LHD Experiment. O.Motojima for the LHD team National Institute for Fusion Science
Recent Development of LHD Experiment O.Motojima for the LHD team National Institute for Fusion Science 4521 1 Primary goal of LHD project 1. Transport studies in sufficiently high n E T regime relevant
More informationModel based optimization and estimation of the field map during the breakdown phase in the ITER tokamak
Model based optimization and estimation of the field map during the breakdown phase in the ITER tokamak Roberto Ambrosino 1 Gianmaria De Tommasi 2 Massimiliano Mattei 3 Alfredo Pironti 2 1 CREATE, Università
More informationExam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field
Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P361 Before Starting All of your grades should now be posted
More informationFast Secondary Reconnection and the Sawtooth Crash
Fast Secondary Reconnection and the Sawtooth Crash Maurizio Ottaviani 1, Daniele Del Sarto 2 1 CEAIRFM, SaintPaullezDurance (France) 2 Université de Lorraine, Institut Jean Lamour UMRCNRS 7198, Nancy
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 USEU Transport Task Force Annual
More informationNonlinear MHD Modelling of Rotating Plasma Response to Resonant Magnetic Perturbations.
Nonlinear MHD Modelling of Rotating Plasma Response to Resonant Magnetic Perturbations. M. Becoulet 1, F. Orain 1, G.T.A. Huijsmans 2, P. Maget 1, N. Mellet 1, G. DifPradalier 1, G. Latu 1, C. Passeron
More informationChapter 15 Magnetic Circuits and Transformers
Chapter 15 Magnetic Circuits and Transformers Chapter 15 Magnetic Circuits and Transformers 1. Understand magnetic fields and their interactio with moving charges. 2. Use the righthand rule to determine
More informationarxiv:physics/ v1 [physics.plasmph] 5 Nov 2004
Ion Resonance Instability in the ELTRAP electron plasma G. Bettega, 1 F. Cavaliere, 2 M. Cavenago, 3 A. Illiberi, 1 R. Pozzoli, 1 and M. Romé 1 1 INFM Milano Università, INFN Sezione di Milano, Dipartimento
More informationImpact of EnergeticIonDriven Global Modes on Toroidal Plasma Confinements
Impact of EnergeticIonDriven Global Modes on Toroidal Plasma Confinements Kazuo TOI CHS & LHD Experimental Group National Institute for Fusion Science Toki 595292, Japan Special contributions from:
More informationPrinceton Plasma Physics Laboratory
Princeton Plasma Physics Laboratory PPPL4239 PPPL4239 Computation of Three Dimensional Tokamak and Spherical Torus Equilibria Jongkyu Park, Allen H. Boozer, and Alan H. Glasser (Preprint) May 27 Prepared
More informationCurrent density modelling in JET and JT60U identity plasma experiments. Paula Sirén
Current density modelling in JET and JT60U identity plasma experiments Paula Sirén 1/12 1/16 EuratomTEKES EuratomTekes Annual Seminar 2013 28 24 May 2013 Paula Sirén Current density modelling in JET
More informationThe RFP: Plasma Confinement with a Reversed Twist
The RFP: Plasma Confinement with a Reversed Twist JOHN SARFF Department of Physics University of WisconsinMadison Invited Tutorial 1997 Meeting APS DPP Pittsburgh Nov. 19, 1997 A tutorial on the Reversed
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 informationTurbulence Analysis of a Flux Rope Plasma on the Swarthmore Spheromak Experiment
Research supported by US DOE and NSF Turbulence Analysis of a Flux Rope Plasma on the Swarthmore Spheromak Experiment David Schaffner Swarthmore College, NSF Center for Magnetic SelfOrganization with
More informationTokamak Edge Turbulence background theory and computation
ASDEX Upgrade Tokamak Edge Turbulence background theory and computation B. Scott Max Planck Institut für Plasmaphysik Euratom Association D85748 Garching, Germany Krakow, Sep 2006 Outline Basic Concepts
More informationCharacterization of neoclassical tearing modes in highperformance I mode plasmas with ICRF mode conversion flow drive on Alcator CMod
1 EX/P422 Characterization of neoclassical tearing modes in highperformance I mode plasmas with ICRF mode conversion flow drive on Alcator CMod Y. Lin, R.S. Granetz, A.E. Hubbard, M.L. Reinke, J.E.
More informationTH/P614 Integrated particle simulation of neoclassical and turbulence physics in the tokamak pedestal/edge region using XGC a)
1 TH/P614 Integrated particle simulation of neoclassical and turbulence physics in the tokamak pedestal/edge region using XGC a) 1 Chang, C.S., 1 Ku, S., 2 Adams M., 3 D Azevedo, G., 4 Chen, Y., 5 Cummings,
More informationTokamak operation at low q and scaling toward a fusion machine. R. Paccagnella^
Tokamak operation at low q and scaling toward a fusion machine R. Paccagnella^ Consorzio RFX, Associazione EuratomENEA sulla Fusione, Padova, Italy ^ and Istituto Gas Ionizzati del Consiglio Nazionale
More informationHeat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UWMadison
Heat Transport in a Stochastic Magnetic Field John Sarff Physics Dept, UWMadison CMPD & CMSO Winter School UCLA Jan 510, 2009 Magnetic perturbations can destroy the nestedsurface topology desired for
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, Ibarakiken, 3110193 Japan
More informationNonsolenoidal Startup and Plasma Stability at NearUnity Aspect Ratio in the Pegasus Toroidal Experiment
1 EXS/P207 Nonsolenoidal Startup and Plasma Stability at NearUnity Aspect Ratio in the Pegasus Toroidal Experiment R.J. Fonck 1), D.J. Battaglia 2), M.W. Bongard 1), E.T. Hinson 1), A.J. Redd 1), D.J.
More informationPlasma and Fusion Research: Regular Articles Volume 10, (2015)
Possibility of QuasiSteadyState Operation of LowTemperature LHDType DeuteriumDeuterium (DD) Reactor Using Impurity Hole Phenomena DD Reactor Controlled by Solid Boron Pellets ) Tsuguhiro WATANABE
More informationAdvancing Toward Reactor Relevant Startup via Localized Helicity Injection at the Pegasus Toroidal Experiment
Advancing Toward Reactor Relevant Startup via Localized Helicity Injection at the Pegasus Toroidal Experiment E. T. Hinson J. L. Barr, M. W. Bongard, M. G. Burke, R. J. Fonck, J. M. Perry, A. J. Redd,
More informationFaraday's Law ds B B G G ΦB B ds Φ ε = d B dt
Faraday's Law ds ds ε= d Φ dt Φ Global Review Electrostatics» motion of q in external Efield» Efield generated by Σq i Magnetostatics» motion of q and i in external field» field generated by I Electrodynamics»
More informationMODELING PLASMA PROCESSING DISCHARGES
MODELING PROCESSING DISCHARGES M.A. Lieberman Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 Collaborators: E. Kawamura, D.B. Graves, and A.J. Lichtenberg,
More informationPHYSICS Course Structure Units Topics Marks Electrostatics Current Electricity III Magnetic Effect of Current & Magnetism
PHYSICS Course Structure Units Topics Marks I Chapter 1 Chapter 2 II Chapter 3 III Chapter 4 Chapter 5 IV Chapter 6 Chapter 7 V Chapter 8 VI Chapter 9 Electrostatics Electric Charges and Fields Electrostatic
More informationSmallScale Dynamo and the Magnetic Prandtl Number
MRI Turbulence Workshop, IAS, Princeton, 17.06.08 SmallScale Dynamo and the Magnetic Prandtl Number Alexander Schekochihin (Imperial College) with Steve Cowley (Culham & Imperial) Greg Hammett (Princeton)
More informationRole of Flow Shear in Enhanced Core Confinement
PPPL3156, Preprint: March 1996, UC420, 427 Role of Flow Shear in Enhanced Core Confinement Regimes TS Hahm and KH Burrell The importance of the ExB fla shear in arioi s enhanced confinement regimes is
More informationThe Virial Theorem, MHD Equilibria, and ForceFree Fields
The Virial Theorem, MHD Equilibria, and ForceFree Fields Nick Murphy HarvardSmithsonian Center for Astrophysics Astronomy 253: Plasma Astrophysics February 10 12, 2014 These lecture notes are largely
More informationThe Madison Dynamo Experiment: magnetic instabilities driven by sheared flow in a sphere. Cary Forest Department of Physics University of Wisconsin
The Madison Dynamo Experiment: magnetic instabilities driven by sheared flow in a sphere Cary Forest Department of Physics University of Wisconsin February 28, 2001 Planets, stars and perhaps the galaxy
More informationPROGRESS IN STEADYSTATE SCENARIO DEVELOPMENT IN THE DIIID TOKAMAK
PROGRESS IN STEADYSTATE SCENARIO DEVELOPMENT IN THE DIIID TOKAMAK by T.C. LUCE, J.R. FERRON, C.T. HOLCOMB, F. TURCO, P.A. POLITZER, and T.W. PETRIE GA A26981 JANUARY 2011 DISCLAIMER This report was prepared
More informationPhysics 2220 Fall 2010 George Williams THIRD MIDTERM  REVIEW PROBLEMS
Physics 2220 Fall 2010 George Williams THIRD MIDTERM  REVIEW PROBLEMS Solution sets are available on the course web site. A data sheet is provided. Problems marked by "*" do not have solutions. 1. An
More informationTokamak Fusion Basics and the MHD Equations
MHD Simulations for Fusion Applications Lecture 1 Tokamak Fusion Basics and the MHD Equations Stephen C. Jardin Princeton Plasma Physics Laboratory CEMRACS 1 Marseille, France July 19, 21 1 Fusion Powers
More informationWhat place for mathematicians in plasma physics
What place for mathematicians in plasma physics Eric Sonnendrücker IRMA Université Louis Pasteur, Strasbourg projet CALVI INRIA Nancy Grand Est 1519 September 2008 Eric Sonnendrücker (U. Strasbourg) Math
More informationImpact of neutral atoms on plasma turbulence in the tokamak edge region
Impact of neutral atoms on plasma turbulence in the tokamak edge region C. Wersal P. Ricci, F.D. Halpern, R. Jorge, J. Morales, P. Paruta, F. Riva Theory of Fusion Plasmas Joint VarennaLausanne International
More informationNeoclassical Tearing Modes
Neoclassical Tearing Modes O. Sauter 1, H. Zohm 2 1 CRPPEPFL, Lausanne, Switzerland 2 MaxPlanckInstitut für Plasmaphysik, Garching, Germany Physics of ITER DPG Advanced Physics School 2226 Sept, 2014,
More informationEFFECT OF EDGE NEUTRAL SOUCE PROFILE ON HMODE PEDESTAL HEIGHT AND ELM SIZE
EFFECT OF EDGE NEUTRAL SOUCE PROFILE ON HMODE PEDESTAL HEIGHT AND ELM SIZE T.H. Osborne 1, P.B. Snyder 1, R.J. Groebner 1, A.W. Leonard 1, M.E. Fenstermacher 2, and the DIIID Group 47 th Annual Meeting
More informationINITIAL EVALUATION OF COMPUTATIONAL TOOLS FOR STABILITY OF COMPACT STELLARATOR REACTOR DESIGNS
INITIAL EVALUATION OF COMPUTATIONAL TOOLS FOR STABILITY OF COMPACT STELLARATOR REACTOR DESIGNS A.D. Turnbull and L.L. Lao General Atomics (with contributions from W.A. Cooper and R.G. Storer) Presentation
More informationFINITE ELEMENT CENTER
FINITE ELEMENT CENTER PREPRINT 25 7 Modeling of resistive wall mode and its control in experiments and ITER Yueqiang Liu, M.S. Chu, A.M. Garofalo, Y. Gribov, M. Gryaznevich, T.C. Hender, D.F. Howell, R.J.
More informationQ, Breakeven and the nτ E Diagram for Transient Fusion Plasmas
Q, Breakeven and the nτ E Diagram for Transient Plasmas Dale M. Meade Princeton University P.O. Box 451, Princeton, N. J. 08543 Abstract  Q, breakeven and the nτe diagram are well defined and understood
More informationAP Physics C. Magnetism  Term 4
AP Physics C Magnetism  Term 4 Interest Packet Term Introduction: AP Physics has been specifically designed to build on physics knowledge previously acquired for a more in depth understanding of the world
More informationHybrid Simulations: Numerical Details and Current Applications
Hybrid Simulations: Numerical Details and Current Applications Dietmar KraussVarban and numerous collaborators Space Sciences Laboratory, UC Berkeley, USA Boulder, 07/25/2008 Content 1. Heliospheric/Space
More informationCHAPTER 2. COULOMB S LAW AND ELECTRONIC FIELD INTENSITY. 2.3 Field Due to a Continuous Volume Charge Distribution
CONTENTS CHAPTER 1. VECTOR ANALYSIS 1. Scalars and Vectors 2. Vector Algebra 3. The Cartesian Coordinate System 4. Vector Cartesian Coordinate System 5. The Vector Field 6. The Dot Product 7. The Cross
More informationHeat and Mass Transfer Effects on MHD Flow. of Viscous Fluid through NonHomogeneous Porous. Medium in Presence of Temperature. Dependent Heat Source
Int. J. Contemp. Math. Sciences, Vol. 7,, no. 3, 59764 Heat and Mass Transfer Effects on MHD Flow of Viscous Fluid through NonHomogeneous Porous Medium in Presence of Temperature Dependent Heat Source
More informationGA A25351 PHYSICS ADVANCES IN THE ITER HYBRID SCENARIO IN DIIID
GA A25351 PHYSICS ADVANCES IN THE ITER HYBRID SCENARIO IN DIIID by C.C. PETTY, P.A. POLITZER, R.J. JAYAKUMAR, T.C. LUCE, M.R. WADE, M.E. AUSTIN, D.P. BRENNAN, T.A. CASPER, M.S. CHU, J.C. DeBOO, E.J. DOYLE,
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 Quasineutrality
More informationMODELING AND SIMULATION OF LOW TEMPERATURE PLASMA DISCHARGES
MODELING AND SIMULATION OF LOW TEMPERATURE PLASMA DISCHARGES Michael A. Lieberman University of California, Berkeley lieber@eecs.berkeley.edu DOE Center on Annual Meeting May 2015 Download this talk: http://www.eecs.berkeley.edu/~lieber
More informationInductance and Magnetic Energy
Mutual Inductance Inductance and Magnetic Energy Consider two wire loops or coils. Their geometries can be completely general, and there might be some magnetic materials inside the coils or around them
More informationEffect 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 (1994present) 16, 052502 (2009); doi: 10.1063/1.3126964
More information