THEORY AND SIMULATION OF ROTATIONAL SHEAR STABILIZATION OF TURBULENCE
|
|
- Rosemary Little
- 5 years ago
- Views:
Transcription
1 THEORY AND SIMULATION OF ROTATIONAL SHEAR STABILIZATION OF TURBULENCE R.E. WALTZ, R.L.DEWAR*, and X. GARBET** *The Australian National University, **Association Euratom-CEA Cadarache GENERAL ATOMICS San Diego, California Division of Plasma Physics APS Meeting, Pittsburgh, PA, November 17-21, 1997
2 WHAT THIS TALK IS ABOUT This talk is about the quench rule for rotational shear stabilization of turbulence in tokamaks: when the ExB shear rate γ E =(r/q) (qv ExB /r)/ r exceeds the maximum local ballooning mode growth rate γ max turbulent diffusion is quenched. This rule is the basis for transport models χ=(1 -γ E/ γ max )χ describing core transport barriers (Waltz, Staebler, Dorland, Hammett, Kotschenreuther & Konings 1997) This talk is not about the experimental fidelity of the rule. For this see Burrell (APS review talk 1996 ); Synakowski et al & Greenfield et al (APS invited papers 1996 ) Lao et al (APS invited paper 1995) This talk is about the numerical and theoretical evidence and limitations for the rule.
3 BACKGROUND TO ANALYTIC THEORIES ExB shear rate : γ E =(r/q) (qv ExB /r)/ r complex ballooning mode growth rate: γ nonlinear 2 point renormalization linear eigenmode stability ρ Connor,Taylor,&Wilson 1993 V ExB >> V EXB shear only x-variation only Im (dγ /dx) = ky γ E Biglari, Diamond, &Terry 199 Shaing, Crume,& Houlberg 199 Zhang & Mahajan 1992 turbulence suppression γ E _norm ω( kx/ ky) ω D kx 2 no distinction slab / torus toroidal process at smallest γ E reduces eigenmode rate to small ballooning mode angle average rate transport follows eigenmode rate resulting in slab-like levels ρ finite V ExB =O ( V ) x-variation (dγ /dx) = γ ' profile shear x2-variation (d2γ dx2) =γ '' profile curvature Rominelli & Zonca 1993 Dewar 1996 profile curvature Re(γ '') works against profile shear stabilizationim(γ ')
4 PREVIOUS NONLINEAR SIMULATIONS ExB shear rate : γ E =(r/q) (qv ExB /r)/ r complex ballooning mode growth rate: γ gyrofluid ITG ballooning mode or "flux tube" code ρ V ExB >> V EXB shear only x-variation only Im (dγ /dx) = ky γ E Waltz, Kerbel, & Milovich 1994 turbulence quenched γ E _crit γ max = max {Re (γ )} χ /[cs ρ s 2 /a γ P =18γ E γ 3 3 P =12γ 3 E.5 3 γ P = γ E /[c s /a] γ E γ max χ=(1 -γ E/ γ max )χ basis of models for core transport barriers Get quench for fixed γ P but for pure toroidal rotation, parallel shear rate γ P =(Rq/r)γ E can increase γ max (γ P ) faster than γ E avoiding quench. Superficial resemblance to Biglari, Diamond,&Terry rule since ω ( kx/ ky) tracks γ max for isotropic turbulence Appears not to follow eigenmode stability byconnor, Taylor,& Wilson rule since eigenmodes are stable at very small γ E here.
5 OUTLINE TO NEW WORK Review of the ExB shear in ballooning mode representations Coupling in ballooning angle θ versus convection in ballooning angle θ How a new mode centered Floquet ballooning representation avoids numerical "box mode" instabilities. Gyrofluid ITG ballooning mode or ρ "flux tube" numerical illustrations showing how the γ E _crit γ max quench rule results from a nonlinear convective amplification process unique to toroidal geometry. Likely modifications and limitations on the γ E _crit γ max quench rule for finite ρ and general profile shear and profile curvature: lessons from the ballooning- Schrodinger eigenmode equation.
6 BALLOONING MODE AND REPRESENTATIONS df/dt = F/ t + v~ ExB F ExB nonlinear coupling x'-space radial direction V ExB = γ E x' γ E =(r/q) (qv ExB /r)/ r df/dt = -(γ E x') i ky F + L F L linear operations transform kx'-space or ballooning mode -space F(θ,θ) x'f = -i F/ kx' kx' kys^θ ky nq / r s^ ( r/q ) ( d q/dr ) df(θ,θ)/dt = -(γ E /s^) F(θ,θ)/ θ + L[θ -θ, cos(θ), / θ] F(θ,θ) _each F(θ,θ) centered at θ θ _For finite γ E, θ is no longer a "good quantum number" _ExB shear γ E linearly "couples"θ 's _θ discrete: F/ θ F/ θ
7 BALLOONING MODE AND REPRESENTATIONS continued Cooper transformation θ θ+(γ E /s^)t "Floquet ballooning mode" F'(θ,θ) df'(θ,θ)/dt = L [θ - (θ+(γ E /s^)t), cos(θ), / θ ] F'(θ,θ) _ExB shear γ E linearly convects each θ _Easy to see Connor,Taylor, & Wilson rule for eigenmode or time average growth rate at small γ E /s^ when modes not distorted or broken up: γ = γ ( θ ) d θ / π 2 << γ ()
8 BALLOONING MODE AND REPRESENTATIONS continued Rotating frame transformation θ θ+(γ E /s^)t "centered Floquet ballooning mode" F''(θ,θ) df''(θ,θ)/dt=(γ E /s^) F"(θ,θ)/ θ+l[θ-θ,cos(θ+(γ E /s^)t), / θ] F''(θ,θ) _Explicitly displays "poloidal breakup term " which stabilizes modes in the slab when cos( ) dependence is dropped or stabilizes toroidal modes at large γ E /s^ even when γ = γ ( θ ) d θ / π 2 >. _Leaves nonlinear terms invariant, modes stay centered at θ θ and do not rotate out of the finite θ numerical box
9 Why the centered Floquet ballooning mode representation is best for numerical simulations _All represenations are equivalent if θ is a continuous variable! _But to do ( ky, kx') nonlinear coupling we must treat [kx'=kys^θ] θ as a discreet variable. Discreteness in θ means we have a "cyclic box" in x-space Two "visions" of "homogeneous" ExB shear. "box modes" live in corners of shear θ continuum _Miller and Waltz (1994) showed that discrete θ could lead to "box modes" which require a finite γ E to stabilize, even when "true" continuum eigenmodes were stable v E γ = γ ( θ ) d θ / π 2 < cyclic boxes x θ grid _The quench rule γ E_crit γ max in the discrete θ nonlinear ballooning mode code was later found to be associated with linear stabilization of "box modes".
10 Numerical illustrations with new centered Floquet ballooning mode representation which avoids numerical "box modes" but still recovers approximate quench rule γ E_crit γ max ITG with adiabatic electrons R / a = 3, a/ln=1, a/lt=3, q=2, s^=1, α=, γ P = At γ E =.3, least stable mode kyρs=.3 time average growth rate or eigenmode rate same as ballooning mode angle average rate γ = γ ( θ ) d θ / π 2 = -.33 which is negative. Convective amplification of 316x
11 At small γ E turbulence persists from convective amplification and nonlinear coupling even with stable eigenmodes. ITG with adiabatic electrons At γ E =.3 diffusion is only slightly suppressed. After multiplying all amplitudes by.1x, the turbulence is able recover but it does not recover after.1x. Implies that Floquet modes passing bad curvature region are convectively amplified and nonlinearly couple energy to convectively decaying modes passing good curvature region preventing eigenmode decay.
12 At higher shear rates turbulence quenched at near γ E _crit γ max R / a = 3, a/ln=1, s^=1, α=, γ P = χ i / [c s ρ s2 /a] =4 =3 γ max s^=1. q=2 γ max χ i / [c s ρ s2 /a] q=3 q=2 q=4 γ max γ max s^=1. =3 γ max γ E γ E
13 kyρs-spectrum as a function of γe R / a = 3, a/ln=1, a/lt=3, q=2, s^=1, α=, γ P = Depletion at low-ky suggests local rule γ E _crit γ (ky) may be justified. (n~/n ) rms = ( Σ kx [(n~/n ) rms ]2 )1/ γ E = ρ s k y s^=1. =3 q=3
14 Quench rule γ E _crit γ max persists at low s^ = (r/q ) (d q/ dr) Even though the Floquet θ rotation rate is γ E/ s^, there is no evidence that the critical γ E s^ γ max. Hence no evidence here that s^= is the "seat" of core reversed shear transport barrier. χ i /χ i () C G K O s^=.25 s^=.5 s^=1. s^=1.5 =3 χ i /χ i () C G K O S s^=.25 s^=.5 s^=1. s^=1.5 s^=2. = γ E / γ max γ E / γ max (γ E /s^)/γ max scaling does not give a good invariance with s^.
15 At low s^ convection speed γe/s^ goes up, but most unstable mode at θ = must convect 1/s^ times farther in θ to reach stability. θ π/2 θ 4π Heuristic argument: Balancing growth time with convection time implies γ E _crit s^ θ γ max Ο(1) γ max
16 γ E_crit does not follow eigenmode stability in toroidal geometry R / a = 3, a/ln=1, q=2, α=, γ P = γ E_ <γ> is the ExB shear rate for eigenmode stability <γ> =. Due to the poloidal breakup effect, actual rate <γ> <γ> Connor,Taylor,& Wilson rate.2.4 γ E_crit.15 γ max =3.3 γ max.1 γ E_crit.2.5 γ E_<γ>=.1 γ E_<γ>= = s^ s^
17 γ E_crit does follow eigenmode stability in slab geometry γ E _crit >> γ max R / a = 3, a/ln=1, a/lt=3, q=2, s^=1, α=, γ P = toroidal curvature terms "turned off".8.7 slab no curvature γ max =3 s^=1. poloidal breakup rate χ i / [c s ρ s2 /a] =3 s^=1. γ max = γ E γ E
18 Summary of ITG simulation cases for quench rule R / a = 3, a/ln=1, α=, γ P = γ max B D F a/l =4 T s^ =2.->.25 =3 s^ =1.5->.25 a/l =3 T q =2->4 In summary, for the vanishing ρ limit, it appears that γ E_crit 4/3 γ max is the best approximate description of the critical ExB shear rate for quenching transport in toroidal geometry..1 slab γ E_crit
19 Quantitative test of 2-point nonlinear renormalization theories _Theory: nonvanishing suppression factor χ/χ = 1/[1 + (γ E /γ E_norm )2 ] γ E_norm ω t ( k x / k y ) ω t = D k x 2 used interchangeably ω t ( k x / k y ) B E H =4 s^ =2.->.25 =3 s^ =1.->.5 =3 q =2->4 slab 2 ω t =D k x γ max χ i /χ i () =4 s^=1.5 1 / [1+(γ E /γ norm ) 2 ] γ max 2-pt. renorm. theory toroidal ITG simulation γ E ω t ( k x / k y ) does tracks γ max using D = χ But supression formula gives less than 1% reduction at the actual quench point. _Most importantly, this (ρ ->) theory does not account for the difference between simulations in slab and toroidal geometry.
20 Likely modifications and limitations on the γ E _crit γ max quench rule : lessons from the ballooning-schrodinger eigenmode equation. complex ballooning mode growth rate: γ (x,θ) expand in x=r-r ρ finite V ExB = O ( V ) x-variation (dγ /dx) = γ ' profile shear Im(dγ /dx)=ky γ mode x2-variation (d2γ dx2) =γ '' profile curvature γ = γ + γ' x + γ''/2 x2 + [Re(γ ) -<γ> ][cos(θ)-1] x i ss / θ θ i ss / x generalize γ E γ mode =(r/q) (qv mode /r)/ r to include shear in intrinsic mode phase velocity not just ExB Doppler shift γ mode _crit γ max
21 Likely modifications and limitations on the γ E _crit γ max quench rule : lessons from the ballooning-schrodinger eigenmode equation...continued eigenmode growth rate o ballooning mode at γ mode = x with 1/n radial stabilization "bound" harmonic oscillator solution <γ> "passing" CTW solution jump < γ > with poloidal breakup Im(γ ) / k y = γ mode γ bound =γ -1/2 (-γ '' ss 2γ )1/2-1/2(γ '2/ γ '' ) γ pass = γ = γ ( θ ) dθ / π 2 Re (γ) = max {Re ( γ bound ), Re ( γ pass ) } 1/n "radial correction" is small Ballooning-Schrodinger equation does not contain poloidal breakup Jump point likely criterion for minimum profile shear γ ' or γ mode to ignore profile curvature γ '' which prevents mode circulation and convective amplifcation: Re [1/2 (γ'2/ γ'' )] > Re [ γ -<γ>] otherwise quench rule may not hold
22 CONCLUSIONS From ITG adiabatic electron simulations the quench rule for rotational shear stabilization γ E =(r/q) (qvexb/r)/ r γ max results from a nonlinear convective amplification process unique to toroidal geometry. The rule holds over a wide parameter range including low s^= (r/q ) (d q/dr) at vanishing ρ ExB shear stabilization does not follow eigenmode stability in toroidal geometry but does follow eigenmode stability in slab geometry. From the ballooning-schrodinger eigenmode equation at finite ρ we speculate: The rule should be modified to include the total mode velocity not just the EXB Dopper shift. The quench rule is likely to hold only if the profile shear γ '= dγ /dx is large enough to overcome profile curvature γ '' = d2γ /dx2 which prevents full circulation in ballooning mode angle and convective amplifcation. Studies with 3D full radius nonlinear simulations are needed at finite but small ρ
Fine-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 informationBursty Transport in Tokamaks with Internal Transport Barriers
Bursty Transport in Tokamaks with Internal Transport Barriers S. Benkadda 1), O. Agullo 1), P. Beyer 1), N. Bian 1), P. H. Diamond 3), C. Figarella 1), X. Garbet 2), P. Ghendrih 2), V. Grandgirard 1),
More information1 THC/P4-01. Shear flow suppression of turbulent transport and self-consistent profile evolution within a multi-scale gyrokinetic framework
THC/P4- Shear flow suppression of turbulent transport and self-consistent profile evolution within a multi-scale gyrokinetic framework M. Barnes,2), F. I. Parra ), E. G. Highcock,2), A. A. Schekochihin
More informationI. INTRODUCTION PHYSICS OF PLASMAS VOLUME 5, NUMBER 5 MAY 1998
PHYSICS OF PLASMAS VOLUME 5, NUMBER 5 MAY 1998 Sheared rotation effects on kinetic stability in enhanced confinement tokamak plasmas, and nonlinear dynamics of fluctuations and flows in axisymmetric plasmas*
More informationUCIrvine. Gyrokinetic Studies of Turbulence Spreading IAEA-CN-116/TH1-4
AEA-CN-116/TH1-4 Gyrokinetic Studies of Turbulence Spreading T.S. Hahm, Z. Lin, a P.H. Diamond, b G. Rewoldt, W.X. Wang, S. Ethier, O. Gurcan, b W. Lee, and W.M. Tang Princeton University, Plasma Physics
More informationGyrokinetic Simulations of Tokamak Microturbulence
Gyrokinetic Simulations of Tokamak Microturbulence W Dorland, Imperial College, London With key contributions from: S C Cowley F Jenko G W Hammett D Mikkelsen B N Rogers C Bourdelle W M Nevins D W Ross
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 informationReduced Electron Thermal Transport in Low Collisionality H-mode Plasmas in DIII-D and the Importance of Small-scale Turbulence
1 Reduced Electron Thermal Transport in Low Collisionality H-mode Plasmas in DIII-D and the Importance of Small-scale Turbulence L. Schmitz, 1 C. Holland, 2 T.L. Rhodes, 1 G. Wang, 1 L. Zeng, 1 A.E. White,
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 informationCharacteristics of the H-mode H and Extrapolation to ITER
Characteristics of the H-mode H Pedestal and Extrapolation to ITER The H-mode Pedestal Study Group of the International Tokamak Physics Activity presented by T.Osborne 19th IAEA Fusion Energy Conference
More informationL 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 informationW.A. HOULBERG Oak Ridge National Lab., Oak Ridge, TN USA. M.C. ZARNSTORFF Princeton Plasma Plasma Physics Lab., Princeton, NJ USA
INTRINSICALLY STEADY STATE TOKAMAKS K.C. SHAING, A.Y. AYDEMIR, R.D. HAZELTINE Institute for Fusion Studies, The University of Texas at Austin, Austin TX 78712 USA W.A. HOULBERG Oak Ridge National Lab.,
More informationA Dimensionless Criterion for Characterising Internal Transport Barriers in JET
EFDA JET PR(00)09 G Tresset et al A Dimensionless Criterion for Characterising Internal Transport Barriers in JET This document is intended for publication in the open literature. It is made available
More informationElectron Transport Stiffness and Heat Pulse Propagation on DIII-D
Electron Transport Stiffness and Heat Pulse Propagation on DIII-D by C.C. Petty, J.C. DeBoo, C.H. Holland, 1 S.P. Smith, A.E. White, 2 K.H. Burrell, J.C. Hillesheim 3 and T.C. Luce 1 University of California
More informationOn the Nature of ETG Turbulence and Cross-Scale Coupling
J. Plasma Fusion Res. SERIES, Vol. Vol. 6 6 (2004) (2004) 11 16 000 000 On the Nature of ETG Turbulence and Cross-Scale Coupling JENKO Frank Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-85748
More informationCORE TURBULENCE AND TRANSPORT REDUCTION IN DIII-D DISCHARGES WITH WEAK OR NEGATIVE MAGNETIC SHEAR
I JUL 2 5 m 7 GA-A22617 CORE TURBULENCE AND TRANSPORT REDUCTION IN DIII-D DISCHARGES WITH WEAK OR NEGATIVE MAGNETIC SHEAR by G.M. STAEBLER, C.M. GREENFIELD, D.P. SCHISSEL, K.H. BURRELL, T.A. CASPER, J.C.
More informationGA A26866 REDUCED ELECTRON THERMAL TRANSPORT IN LOW COLLISIONALITY H-MODE PLASMAS IN DIII-D AND THE IMPORTANCE OF SMALL-SCALE TURBULENCE
GA A26866 REDUCED ELECTRON THERMAL TRANSPORT IN LOW COLLISIONALITY H-MODE PLASMAS IN DIII-D AND THE IMPORTANCE OF SMALL-SCALE TURBULENCE by L. SCHMITZ, C. HOLLAND, T.L. RHODES, G. WANG, L. ZENG, A.E. WHITE,
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 informationGyrokinetic Theory and Dynamics of the Tokamak Edge
ASDEX Upgrade Gyrokinetic Theory and Dynamics of the Tokamak Edge B. Scott Max Planck Institut für Plasmaphysik D-85748 Garching, Germany PET-15, Sep 2015 these slides: basic processes in the dynamics
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 informationImpact of diverted geometry on turbulence and transport barrier formation in 3D global simulations of tokamak edge plasma
1 Impact of diverted geometry on turbulence and transport barrier formation in 3D global simulations of tokamak edge plasma D. Galassi, P. Tamain, H. Bufferand, C. Baudoin, G. Ciraolo, N. Fedorczak, Ph.
More informationThe RFP: Plasma Confinement with a Reversed Twist
The RFP: Plasma Confinement with a Reversed Twist JOHN SARFF Department of Physics University of Wisconsin-Madison Invited Tutorial 1997 Meeting APS DPP Pittsburgh Nov. 19, 1997 A tutorial on the Reversed
More 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 informationGYRO gyrokinetic simulations and TGLF gyrofluid transport models: from core to the edge. R.E. Waltz* General Atomics
GYRO gyrokinetic simulations and TGLF gyrofluid transport models: from core to the edge R.E. Waltz* PERSISTENT SURVEILLANCE FOR PIPELINE PROTECTION AND THREAT INTERDICTION General Atomics * Work with J.
More informationLong Time Simulations of Microturbulence in Fusion Plasmas
Long Time Simulations of Microturbulence in Fusion Plasmas W. W. Lee, S. Ethier, T. G. Jenkins, W. X. Wang, J. L. V. Lewandowski, G. Rewoldt, and W. M. Tang Princeton Plasma Physics Laboratory, Princeton,
More informationMHD Pedestal Paradigm (Conventional Wisdom)
Pedestal Transport D. R. Hatch M. Kotschenreuther, X. Liu, S. M. Mahajan, (Institute for Fusion Studies, University of Texas at Austin) S. Saarelma, C. Maggi, C. Giroud, J. Hillesheim (CCFE) J. Hughes
More informationInteraction between EGAMs and turbulence in full-f gyrokinetic simulations
Interaction between EGAMs and turbulence in full-f gyrokinetic simulations David Zarzoso 1 X Garbet 1, Y Sarazin 1, V Grandgirard 1, J Abiteboul 1, A Strugarek 1,2, G Dif-Pradalier 1, R Dumont 1, G Latu
More informationTransport Improvement Near Low Order Rational q Surfaces in DIII D
Transport Improvement Near Low Order Rational q Surfaces in DIII D M.E. Austin 1 With K.H. Burrell 2, R.E. Waltz 2, K.W. Gentle 1, E.J. Doyle 8, P. Gohil 2, C.M. Greenfield 2, R.J. Groebner 2, W.W. Heidbrink
More informationGA A23428 IMPROVEMENT OF CORE BARRIERS WITH ECH AND COUNTER-NBI IN DIII D
GA A348 IMPROVEMENT OF CORE BARRIERS WITH ECH by C.M. GREENFIELD, K.H. BURRELL, T.A. CASPER, J.C. DeBOO, E.J. DOYLE, P. GOHIL, R.J. GROEBNER, J.E. KINSEY, J. LOHR, M. MAKOWSKI, G.R. McKEE, M. MURAKAMI,
More informationUCLA POSTECH UCSD ASIPP U
Supported by College W&M Colorado Sch Mines Columbia U CompX General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U Purdue U SNL
More informationStudies of Turbulence-driven FLOWs:
Studies of Turbulence-driven FLOWs: a) V ", V Competition in a Tube b) Revisiting Zonal Flow Saturation J.C. Li, P.H. Diamond, R. Hong, G. Tynan University of California San Diego, USA This material is
More informationHow Shear Increments Affect the Flow Production Branching Ratio in CSDX. Abstract
How Shear Increments Affect the Flow Production Branching Ratio in CSDX J. C. Li 1 and P. H. Diamond 1 1 CASS, University of California, San Diego, California 92093, USA Abstract The coupling of turbulence-driven
More informationComparing simulation of plasma turbulence with experiment. II. Gyrokinetic simulations
PHYSICS OF PLASMAS VOLUME 9, NUMBER 12 DECEMBER 2002 Comparing simulation of plasma turbulence with experiment. II. Gyrokinetic simulations David W. Ross a) Fusion Research Center, The University of Texas,
More informationIntermediate Nonlinear Development of a Line-tied g-mode
Intermediate Nonlinear Development of a Line-tied g-mode Ping Zhu University of Wisconsin-Madison In collaboration with C. C. Hegna and C. R. Sovinec (UW-Madison) A. Bhattacharjee and K. Germaschewski
More informationGyrokinetic Turbulence in Tokamaks and Stellarators
Gyrokinetic Turbulence in Tokamaks and Stellarators Frank Jenko IPP, Germany Acknowledgements: P. Xanthopoulos, F. Merz, T. Görler, M. Pueschel, D. Told; A. Boozer, G. Hammett, D. Mikkelsen, M. Zarnstorff,
More informationNumKin, Strasbourg, October 17 th, 2016
F. Palermo 1 A.Biancalani 1, C.Angioni 1, F.Zonca 2, A.Bottino 1, B.Scott 1, G.D.Conway 1, E.Poli 1 1 Max Planck Institut für Plasmaphysik, Garching, Germany 2 ENEA C. R. Frascati - Via E. Fermi 45, CP
More informationTurbulence spreading into the linearly stable zone and transport scaling
INSTITUTE OF PHYSICS PUBLISHING Plasma Phys. Control. Fusion 46 (2004) A323 A333 PLASMA PHYSICS AND CONTROLLED FUSION PII: S0741-3335(04)70280-8 Turbulence spreading into the linearly stable zone and transport
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 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 informationMeasurements of Core Electron Temperature Fluctuations in DIII-D with Comparisons to Density Fluctuations and Nonlinear GYRO Simulations
Measurements of Core Electron Temperature Fluctuations in DIII-D with Comparisons to Density Fluctuations and Nonlinear GYRO Simulations A.E. White,a) L. Schmitz,a) G.R. McKee,b) C. Holland,c) W.A. Peebles,a)
More informationTheory Work in Support of C-Mod
Theory Work in Support of C-Mod 2/23/04 C-Mod PAC Presentation Peter J. Catto for the PSFC theory group MC & LH studies ITB investigations Neutrals & rotation BOUT improvements TORIC ICRF Mode Conversion
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 informationParticle-in-cell simulations of electron transport from plasma turbulence: recent progress in gyrokinetic particle simulations of turbulent plasmas
Institute of Physics Publishing Journal of Physics: Conference Series 16 (25 16 24 doi:1.188/1742-6596/16/1/2 SciDAC 25 Particle-in-cell simulations of electron transport from plasma turbulence: recent
More informationQTYUIOP LOCAL ANALYSIS OF CONFINEMENT AND TRANSPORT IN NEUTRAL BEAM HEATED DIII D DISCHARGES WITH NEGATIVE MAGNETIC SHEAR D.P. SCHISSEL.
LOCAL ANALYSIS OF CONFINEMENT AND TRANSPORT IN NEUTRAL BEAM HEATED DIII D DISCHARGES WITH NEGATIVE MAGNETIC SHEAR Presented by D.P. SCHISSEL for the DIII D Team* Presented to 16th IAEA Fusion Conference
More informationToroidal 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 informationEdge Rotational Shear Requirements for the Edge Harmonic Oscillation in DIII D Quiescent H mode Plasmas
Edge Rotational Shear Requirements for the Edge Harmonic Oscillation in DIII D Quiescent H mode Plasmas by T.M. Wilks 1 with A. Garofalo 2, K.H. Burrell 2, Xi. Chen 2, P.H. Diamond 3, Z.B. Guo 3, X. Xu
More informationImproved Plasma Confinement by Ion Bernstein Waves (IBWs) Interacting with Ions in JET (Joint European Torus)
Improved Plasma Confinement by Ion Bernstein Waves (IBWs) Interacting with Ions in JET (Joint European Torus) PD/P-01 C. Castaldo 1), R. Cesario 1), Y, Andrew 2), A. Cardinali 1), V. Kiptly 2), M. Mantsinen
More informationDynamics of Zonal Shear Collapse in Hydrodynamic Electron Limit. Transport Physics of the Density Limit
Dynamics of Zonal Shear Collapse in Hydrodynamic Electron Limit Transport Physics of the Density Limit R. Hajjar, P. H. Diamond, M. Malkov This research was supported by the U.S. Department of Energy,
More informationNSTX. Investigation of electron gyro-scale fluctuations in the National Spherical Torus Experiment. David Smith. Advisor: Ernesto Mazzucato
NSTX Supported by Investigation of electron gyro-scale fluctuations in the National Spherical Torus Experiment David Smith Advisor: Ernesto Mazzucato Final public oral exam February 26, 2009 Investigation
More informationUnderstanding and Controlling Turbulent Mixing in a Laboratory Magnetosphere
Understanding and Controlling Turbulent Mixing in a Laboratory Magnetosphere Mike Mauel Department of Applied Physics and Applied Math, Columbia University, New York, NY USA (Acknowledging the work from
More informationGlobal particle-in-cell simulations of Alfvénic modes
Global particle-in-cell simulations of Alfvénic modes A. Mishchenko, R. Hatzky and A. Könies Max-Planck-Institut für Plasmaphysik, EURATOM-Association, D-749 Greifswald, Germany Rechenzentrum der Max-Planck-Gesellschaft
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 informationFormation and Back Transition of Internal Transport Barrier in Reversed Shear Plasmas
Formation and Back Transition of Internal Transport Barrier in Reversed Shear Plasmas S. S. Kim [1], Hogun Jhang [1], P. H. Diamond [1,2], [1] WCI Center for Fusion Theory, NFRI [2] CMTFO and CASS, UCSD,
More informationModeling of ELM Dynamics for ITER
Modeling of ELM Dynamics for ITER A.Y. PANKIN 1, G. BATEMAN 1, D.P. BRENNAN 2, A.H. KRITZ 1, S. KRUGER 3, P.B. SNYDER 4 and the NIMROD team 1 Lehigh University, 16 Memorial Drive East, Bethlehem, PA 18015
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 informationCritical gradient formula for toroidal electron temperature gradient modes
PHYSICS OF PLASMAS VOLUME 8, NUMBER 9 SEPTEMBER 2001 Critical gradient formula for toroidal electron temperature gradient modes F. Jenko, W. Dorland, a) and G. W. Hammett b) Max-Planck-Institut für Plasmaphysik,
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 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 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 informationarxiv: v1 [physics.plasm-ph] 20 Dec 2018
arxiv:181.08566v1 [physics.plasm-ph] 0 Dec 018 The effect of background flow shear on gyrokinetic turbulence in the cold ion limit 1. Introduction Justin Ball 1, Stephan Brunner 1, and Ben F. McMillan
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 informationExponential Growth and Filamentary Structure of Nonlinear Ballooning Instability 1
Exponential Growth and Filamentary Structure of Nonlinear Ballooning Instability 1 Ping Zhu in collaboration with C. C. Hegna and C. R. Sovinec University of Wisconsin-Madison Sherwood Conference Denver,
More informationEFFECT OF EDGE NEUTRAL SOUCE PROFILE ON H-MODE PEDESTAL HEIGHT AND ELM SIZE
EFFECT OF EDGE NEUTRAL SOUCE PROFILE ON H-MODE 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 DIII-D Group 47 th Annual Meeting
More informationQTYUIOP ENERGY TRANSPORT IN NEUTRAL BEAM HEATED DIII D DISCHARGES WITH NEGATIVE MAGNETIC SHEAR D.P. SCHISSEL. Presented by. for the DIII D Team*
ENERGY TRANSPORT IN NEUTRAL BEAM HEATED DIII D DISCHARGES WITH NEGATIVE MAGNETIC SHEAR Presented by D.P. SCHISSEL for the DIII D Team* Presented to 38th APS/DPP Meeting NOVEMBER 11 15, 1996 Denver, Colorado
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 informationStudies of Turbulence and Transport in Alcator C- Mod H-Mode Plasmas with Phase Contrast Imaging and Comparisons with GYRO*
Studies of Turbulence and Transport in C- Mod H-Mode Plasmas with Phase Contrast Imaging and Comparisons with GYRO* M. Porkolab 1, L. Lin 1, E.M. Edlund 1, J.C. Rost 1, C.L. Fiore 1, M. Greenwald 1, Y.
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 informationELMs and Constraints on the H-Mode Pedestal:
ELMs and Constraints on the H-Mode Pedestal: A Model Based on Peeling-Ballooning Modes P.B. Snyder, 1 H.R. Wilson, 2 J.R. Ferron, 1 L.L. Lao, 1 A.W. Leonard, 1 D. Mossessian, 3 M. Murakami, 4 T.H. Osborne,
More informationEnergetics of the interaction between electromagnetic ExB turbulence and zonal flows
Energetics of the interaction between electromagnetic ExB turbulence and zonal flows Bruce D Scott Max-Planck-Institut für Plasmaphysik, Euratom Association, D-85748 Garching, Germany E-mail: bds@ipp.mpg.de
More informationRole of Flow Shear in Enhanced Core Confinement
PPPL-3156, Preprint: March 1996, UC-420, 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 informationActive and Fast Particle Driven Alfvén Eigenmodes in Alcator C-Mod
Active and Fast Particle Driven Alfvén Eigenmodes in Alcator C-Mod 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 informationTurbulence in Tokamak Plasmas
ASDEX Upgrade Turbulence in Tokamak Plasmas basic properties and typical results B. Scott Max Planck Institut für Plasmaphysik Euratom Association D-85748 Garching, Germany Uni Innsbruck, Nov 2011 Basics
More informationFlow, turbulence and transport in laboratory plasmas (at least in LAPD and DIII-D)
Flow, turbulence and transport in laboratory plasmas (at least in LAPD and DIII-D) T.A. Carter, D. Schaffner, B. Friedman, J. Hillesheim, W.A. Peebles, G. Rossi, M.V. Umansky 2, D. Guice, S. Vincena, J.E.
More informationDevelopment and Validation of a Predictive Model for the Pedestal Height (EPED1)
Development and Validation of a Predictive Model for the Pedestal Height (EPED1) P.B. Snyder 1 with R.J. Groebner 1, A.W. Leonard 1, T.H. Osborne 1, M. Beurskens 3, L.D. Horton 4, A.E. Hubbard 5, J.W.
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 informationEFFECT OF PLASMA FLOWS ON TURBULENT TRANSPORT AND MHD STABILITY*
EFFECT OF PLASMA FLOWS ON TURBULENT TRANSPORT AND MHD STABILITY* by K.H. BURRELL Presented at the Transport Task Force Meeting Annapolis, Maryland April 3 6, 22 *Work supported by U.S. Department of Energy
More informationComparative studies of nonlinear ITG and ETG dynamics
1 I1-S1 Comparative studies of nonlinear ITG and ETG dynamics F. Zonca 1), L. Chen ), Z. Lin ), and R. B. White 3) 1) ENEA C. R. Frascati, C.P. 65, 00044 Frascati, Rome, Italy ) Dept. of Physics and Astronomy,
More informationLarge scale flows and coherent structure phenomena in flute turbulence
Large scale flows and coherent structure phenomena in flute turbulence I. Sandberg 1, Zh. N. Andrushcheno, V. P. Pavleno 1 National Technical University of Athens, Association Euratom Hellenic Republic,
More informationOverview of Gyrokinetic Theory & Properties of ITG/TEM Instabilities
Overview of Gyrokinetic Theory & Properties of ITG/TEM Instabilities G. W. Hammett Princeton Plasma Physics Lab (PPPL) http://w3.pppl.gov/~hammett AST559: Plasma & Fluid Turbulence Dec. 5, 2011 (based
More informationMicro-stability and Transport Modelling of Internal Transport Barriers on JET.
1 Micro-stability and Transport Modelling of Internal Transport Barriers on JET. X. Garbet 1, Y. Baranov, G. Bateman 3, S. Benkadda 4, P. Beyer 4, R. Budny, F. Crisanti 6, B. Esposito 6, C. Figarella 4,
More informationKinetic damping in gyro-kinetic simulation and the role in multi-scale turbulence
2013 US-Japan JIFT workshop on New Aspects of Plasmas Kinetic Simulation NIFS, November 22-23, 2013 Kinetic damping in gyro-kinetic simulation and the role in multi-scale turbulence cf. Revisit for Landau
More informationControlling H-Mode Particle Transport with Modulated Electron Heating in DIII-D and Alcator C-Mod via TEM Turbulence
Controlling H-Mode Particle Transport with Modulated Electron Heating in DIII-D and Alcator C-Mod via TEM Turbulence D.R. Ernst 1, K.H. Burrell 2, W. Guttenfelder 3, T.L. Rhodes 4, L. Schmitz 4, A.M. Dimits
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 informationObservation of Reduced Core Electron Temperature Fluctuations and Intermediate Wavenumber Density Fluctuations in H- and QH-mode Plasmas
Observation of Reduced Core Electron Temperature Fluctuations and Intermediate Wavenumber Density Fluctuations in H- and QH-mode Plasmas EX/P5-35 L. Schmitz 1), A.E. White 1), G. Wang 1), J.C. DeBoo 2),
More informationMHD Analysis of the Tokamak Edge Pedestal in the Low Collisionality Regime Thoughts on the Physics of ELM-free QH and RMP Discharges
MHD Analysis of the Tokamak Edge Pedestal in the Low Collisionality Regime Thoughts on the Physics of ELM-free QH and RMP Discharges P.B. Snyder 1 Contributions from: H.R. Wilson 2, D.P. Brennan 1, K.H.
More informationGA A23114 DEPENDENCE OF HEAT AND PARTICLE TRANSPORT ON THE RATIO OF THE ION AND ELECTRON TEMPERATURES
GA A311 DEPENDENCE OF HEAT AND PARTICLE TRANSPORT ON THE RATIO OF THE ION AND ELECTRON TEMPERATURES by C.C. PETTY, M.R. WADE, J.E. KINSEY, R.J. GROEBNER, T.C. LUCE, and G.M. STAEBLER AUGUST 1999 This report
More informationA THEORETICAL AND EXPERIMENTAL INVESTIGATION INTO ENERGY TRANSPORT IN HIGH TEMPERATURE TOKAMAK PLASMAS
A THEORETICAL AND EXPERIMENTAL INVESTIGATION INTO ENERGY TRANSPORT IN HIGH TEMPERATURE TOKAMAK PLASMAS Presented by D.P. SCHISSEL Presented to APS Centennial Meeting March 20 26, 1999 Atlanta, Georgia
More informationNonlinear Gyrokinetic Simulations of Ion Turbulence in Impurity Seeded and High Density Toroidal Plasmas
Nonlinear Gyrokinetic Simulations of Ion Turbulence in Impurity Seeded and High Density Toroidal Plasmas R.D. Sydora, J.-N. Leboeuf, J. M. Dawson, V.K. Decyk, M.W. Kissick, C. L. Rettig, T. L. Rhodes,
More informationCharacterizing electron temperature gradient turbulence via numerical simulation
Characterizing electron temperature gradient turbulence via numerical simulation W. M. Nevins Lawrence Livermore National Laboratory, Livermore, California 94551 J. Candy General Atomics, San Diego, California
More informationL-H Transition Dynamics and Power Threshold Minimum
L-H Transition Dynamics and Power Threshold Minimum M.A. Malkov 1, P.H. Diamond 1,2, K. Miki 2,3 and G.R. Tynan 1 1 University of California, San Diego, USA; e-mail: mmalkov@ucsd.edu 2 WCI, NFRI Daejeon,
More informationGyrokinetic simulations of magnetic fusion plasmas
Gyrokinetic simulations of magnetic fusion plasmas Tutorial 2 Virginie Grandgirard CEA/DSM/IRFM, Association Euratom-CEA, Cadarache, 13108 St Paul-lez-Durance, France. email: virginie.grandgirard@cea.fr
More informationOn the Physics of the L/H Transition
ASDEX Upgrade On the Physics of the L/H Transition B. Scott Max Planck Institut für Plasmaphysik Euratom Association D-85748 Garching, Germany EFDA-TTG Workshop, Sep 2010, updated Apr 2012 Outline Physical
More informationGlobal Magnetorotational Instability with Inflow
Global Magnetorotational Instability with Inflow Evy Kersalé PPARC Postdoctoral Research Associate Dept. of Appl. Maths University of Leeds Collaboration: D. Hughes & S. Tobias (Appl. Maths, Leeds) N.
More informationInternational Workshop on the Frontiers of Modern Plasma Physics July On the Nature of Plasma Core Turbulence.
1953-43 International Workshop on the Frontiers of Modern Plasma Physics 14-25 July 2008 On the Nature of Plasma Core Turbulence. F. Jenko Max-Planck Institute fuer Plasmaphysik Garching bei Munchen Germany
More informationInternal Transport Barrier Triggering by Rational Magnetic Flux Surfaces in Tokamaks
EFDA JET CP(0)07/09 E. Joffrin, C.D. Challis, G.D. Conway, X. Garbet, A. Gude, S. Guenther, N. C. Hawkes, T.C. Hender, D. Howell, G.T.A. Huysmans, E. Lazarro, P. Maget, M. Marachek, A.G. Peeters, S.D.
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 informationComputational Issues in the Continuum Gyrokinetic Code GYRO
Computational Issues in the Continuum Gyrokinetic Code GYRO presented by: Eric Bass GSEP SciDAC project at General Atomics CScADS Workshop Snowbird, UT July 19, 2010 About GYRO Purpose: To predict transport
More informationGA A27418 THE ROLE OF ZONAL FLOWS AND PREDATOR- PREY OSCILLATIONS IN THE FORMATION OF CORE AND EDGE TRANSPORT BARRIERS
GA A27418 THE ROLE OF ZONAL FLOWS AND PREDATOR- PREY OSCILLATIONS IN THE FORMATION OF CORE AND EDGE TRANSPORT BARRIERS by L. SCHMITZ, L. ZENG, T.L. RHODES, J.C. HILLESHEIM, W.A. PEEBLES, R.J. GROEBNER,
More informationTurbulence spreading and transport scaling in global gyrokinetic particle simulations
PHYSICS OF PLASMAS VOLUME 11, NUMBER 3 MARCH 2004 Turbulence spreading and transport scaling in global gyrokinetic particle simulations Z. Lin Department of Physics and Astronomy, University of California,
More informationInfluence of Beta, Shape and Rotation on the H-mode Pedestal Height
Influence of Beta, Shape and Rotation on the H-mode Pedestal Height by A.W. Leonard with R.J. Groebner, T.H. Osborne, and P.B. Snyder Presented at Forty-Ninth APS Meeting of the Division of Plasma Physics
More information