Neoclassical transport
|
|
- Maryann Richards
- 5 years ago
- Views:
Transcription
1 Neoclassical transport Dr Ben Dudson Department of Physics, University of York Heslington, York YO10 5DD, UK 28 th January 2013 Dr Ben Dudson Magnetic Confinement Fusion (1 of 19)
2 Last time Toroidal devices such as the Stellarator and Tokamak Need for a rotational transform to short out the vertical electric field caused by the B drift This can either be created using shaped coils (Stellarators) or by running a current in the plasma (Tokamaks) Dr Ben Dudson Magnetic Confinement Fusion (2 of 19)
3 Last time Toroidal devices such as the Stellarator and Tokamak Need for a rotational transform to short out the vertical electric field caused by the B drift This can either be created using shaped coils (Stellarators) or by running a current in the plasma (Tokamaks) Calculated the classical transport of particles and energy out of a tokamak. This gave a wildly unrealistic confinement This lecture we ll look at one reason why... Dr Ben Dudson Magnetic Confinement Fusion (2 of 19)
4 Particle trapping In a tokamak, the magnetic field varies with the major radius Z B φ R B φ 1/R r R Dr Ben Dudson Magnetic Confinement Fusion (3 of 19)
5 Particle trapping In a tokamak, the magnetic field varies with the major radius Z B φ R B φ 1/R There is now a minimum in the B field at the outboard (large R) side of the tokamak Trapped particles. The study of these particles and their effect is called Neoclassical theory. R Dr Ben Dudson Magnetic Confinement Fusion (3 of 19)
6 Large aspect-ratio approximation A useful approximation is that the variation in major radius R is small, and that the toroidal field is much bigger than the poloidal field. For a circular cross-section of radius r, the major radius varies Z like r Hence For small ɛ 1 θ R B R = R 0 +r cos θ = R 0 (1 + ɛ cos θ) ɛ = r/r 0 ratio B ɛ cos θ B B 0 (1 ɛ cos θ) is inverse aspect Dr Ben Dudson Magnetic Confinement Fusion (4 of 19)
7 Particle trapping (redux) If there is no electrostatic potential φ, Kinetic energy 1 2 mv 2 is conserved (i.e. speed is conserved) Magnetic magnetic moment also conserved µ = mv 2 /2B Dr Ben Dudson Magnetic Confinement Fusion (5 of 19)
8 Particle trapping (redux) If there is no electrostatic potential φ, Kinetic energy 1 2 mv 2 is conserved (i.e. speed is conserved) Magnetic magnetic moment also conserved µ = mv 2 /2B Define velocity at the outboard side (θ = 0): v 0 and v 0. K.E. conserved ( v 2 = v 2 + v 2 = v v 0 2 v 2 = v 2 1 v 2 ) v 2 Conservation of µ v 2 ( v 2 = v 2 1 v ɛ cos θ v 2 1 ɛ v 2 0 B 0 (1 ɛ cos θ) = B 0 (1 ɛ) ) ( = v 2 1 v 0 2 v 2 [1 + ɛ (1 cos θ)] ) Dr Ben Dudson Magnetic Confinement Fusion (5 of 19)
9 Particle trapping (redux) If there is no electrostatic potential φ, Kinetic energy 1 2 mv 2 is conserved (i.e. speed is conserved) Magnetic magnetic moment also conserved µ = mv 2 /2B Define velocity at the outboard side (θ = 0): v 0 and v 0. K.E. conserved ( v 2 = v 2 + v 2 = v v 0 2 v 2 = v 2 1 v 2 ) v 2 Conservation of µ v 2 ( v 2 = v 2 1 v ɛ cos θ v 2 1 ɛ v 2 0 B 0 (1 ɛ cos θ) = B 0 (1 ɛ) ) ( = v 2 1 v 0 2 v 2 [1 + ɛ (1 cos θ)] ) v 2 = v 2 ( 1 v 2 0 v 2 [ 1 + 2ɛ sin 2 (θ/2) ] ) Dr Ben Dudson Magnetic Confinement Fusion (5 of 19)
10 Particle trapping (redux) ( v 2 = v 2 1 v 0 2 [ 1 + 2ɛ sin 2 v 2 (θ/2) ] ) If v 2 < 0 for any θ then a particle is trapped. Therefore, if v 2 (θ = π) 0 Particle is trapped v 0 2 v 2 [1 + 2ɛ] 1 v 0 v 1 ɛ For trapped particles v 0 Slope 1 2ɛ v 0 v 2 v ɛ v v 2 0 v ɛ Untrapped v 0 v 0 2ɛ Dr Ben Dudson Magnetic Confinement Fusion (6 of 19)
11 Particle drifts As particles move around the torus, their orbits drift. We have already come across the B drift: v B = v 2 B B 2Ω B 2 but there is also the curvature drift R C Dr Ben Dudson Magnetic Confinement Fusion (7 of 19)
12 Particle drifts As particles move around the torus, their orbits drift. We have already come across the B drift: but there is also the curvature drift v B = v 2 B B 2Ω B 2 In the frame of the particle, there is a centrifugal force F R = mv 2 R C R 2 C R C This therefore causes a drift ( ) v R = 1 mv 2R C /RC 2 B q B 2 = m qb v 2R C B RC 2 B = v 2 Ω Dr Ben Dudson Magnetic Confinement Fusion (7 of 19) R C B R 2 C B
13 Particle drifts So how big are these drifts, and what direction are they in? v B = v 2 B B 2Ω B 2 B B 0 e φ B 0 1 R B B 0 R R B B B 2 e φ R R v B = v 2 2ΩR e Z = e Z R Dr Ben Dudson Magnetic Confinement Fusion (8 of 19)
14 Particle drifts So how big are these drifts, and what direction are they in? v B = v 2 B B v R = v 2 R C B 2Ω B 2 Ω RC 2 B B B 0 e φ B 0 1 R B B 0 R R B B B 2 e φ R R v B = v 2 2ΩR e Z = e Z R R C = R R v R = v 2 R e φ Ω R = v 2 e Z Ω R Dr Ben Dudson Magnetic Confinement Fusion (8 of 19)
15 Particle drifts So how big are these drifts, and what direction are they in? v B = v 2 B B v R = v 2 R C B 2Ω B 2 Ω RC 2 B B B 0 e φ B 0 1 R B B 0 R R B B B 2 e φ R R v B = v 2 2ΩR e Z Total drift is therefore = e Z R v B + v R = ( v 2 + v 2 /2 ) RΩ R C = R R v R = v 2 R e φ Ω R = v 2 e Z Ω R Note that the drift is in the vertical direction and opposite for electrons and ions e Z Dr Ben Dudson Magnetic Confinement Fusion (8 of 19)
16 Banana orbits Z Without drifts Z With drifts R R δr b Characteristic shape of the orbits in the poloidal plane gives this the name banana orbit. The width of this orbit is the banana width, often denoted δr bj or ρ bj with j indicating electrons or ions. Dr Ben Dudson Magnetic Confinement Fusion (9 of 19)
17 Banana orbit characteristics Let us calculate the banana width for a barely trapped particle i.e. one with a bounce point at θ = π, on the inboard side Time for half an orbit: Velocity along the field-line v 2ɛv is small. Total speed is therefore approximately v v. This will be approximately the thermal speed v v th. v 2ɛv th For trapped particles π θ 0 π Bounce point Bounce point 2πR φ Distance travelled = 2πRq so time for a trapped particle to execute half an orbit t b = 2πRq v th 2ɛ Dr Ben Dudson Magnetic Confinement Fusion (10 of 19)
18 Banana orbit characteristics ) During this time t b = 2πRq/ (v th 2ɛ, the particle drifts to a new flux surface, a distance δr b from the original one. δr b = (V B + V R ) 2πRq v th 2ɛ Dr Ben Dudson Magnetic Confinement Fusion (11 of 19)
19 Banana orbit characteristics ) During this time t b = 2πRq/ (v th 2ɛ, the particle drifts to a new flux surface, a distance δr b from the original one. δr b = (V B + V R ) 2πRq v th 2ɛ 1 RΩ [ 2ɛv th 2 }{{} v 2 + v th 2 ] }{{} 2 v 2 /2 2πRq v th 2ɛ Dr Ben Dudson Magnetic Confinement Fusion (11 of 19)
20 Banana orbit characteristics ) During this time t b = 2πRq/ (v th 2ɛ, the particle drifts to a new flux surface, a distance δr b from the original one. δr b = (V B + V R ) 2πRq v th 2ɛ 1 RΩ [ 2ɛv th 2 }{{} = π v th (4ɛ + 1) q π r L q 2 }{{} Ω ɛ 2 ɛ r L v 2 + v th 2 ] }{{} 2 v 2 /2 Note that this is much larger than the Larmor radius r L does this provide another transport mechanism? 2πRq v th 2ɛ Dr Ben Dudson Magnetic Confinement Fusion (11 of 19)
21 Collisions We ve already seen collisions, and come across the collision times mi 1 τ ei < τ ii m e Z 2 < τ ie m i τ ei m e τ jk average times it takes to change the velocity of particles of species j by 90 o, through scattering with species k. To take a step of size δr b, a particle doesn t need to be deflected by 90 o. It just needs to be scattered from a trapped into a passing particle. To do this, the parallel velocity needs to be changed by v ɛv th The effective collision time is therefore τ eff τɛ We can also define a collision frequency, which is just ν 1 τ, and so an effective collision frequency for trapped particles ν eff ν ɛ = 1 τɛ Dr Ben Dudson Magnetic Confinement Fusion (12 of 19)
22 Collisionality A useful quantity used in MCF is the collisionality ν. This is the average number of times a particle is scattered into a passing particle before completing a banana orbit. ν t b τ eff Dr Ben Dudson Magnetic Confinement Fusion (13 of 19)
23 Collisionality A useful quantity used in MCF is the collisionality ν. This is the average number of times a particle is scattered into a passing particle before completing a banana orbit. ν t b τ eff = ν ɛ Rq ɛvth Dr Ben Dudson Magnetic Confinement Fusion (13 of 19)
24 Collisionality A useful quantity used in MCF is the collisionality ν. This is the average number of times a particle is scattered into a passing particle before completing a banana orbit. ν t b τ eff = ν ɛ Rq ɛvth ν = νrq ɛ 3/2 v th Note that if ν > 1 then trapped particles do not complete a full banana orbit before being scattered. Thus trapped particles only exist for ν < 1. Dr Ben Dudson Magnetic Confinement Fusion (13 of 19)
25 Collisionality For electrons colliding with ions or electrons, τ e m1/2 e Te 3/2 n ν e nrq ɛ 3/2 T 2 e For ions colliding with ions (ion-electron negligible) τ i m1/2 i Te 3/2 n ν i nrq ɛ 3/2 T 2 i Dr Ben Dudson Magnetic Confinement Fusion (14 of 19)
26 Collisionality For electrons colliding with ions or electrons, τ e m1/2 e Te 3/2 n ν e nrq ɛ 3/2 T 2 e For ions colliding with ions (ion-electron negligible) Note that τ i m1/2 i Te 3/2 n ν i The ratio ν i /ν e m e /m i 1 nrq ɛ 3/2 T 2 i Collisionality is independent of mass ( equal for ions and electrons) ν n/t 2 very low for hot tokamaks so trapped particles become more important Dr Ben Dudson Magnetic Confinement Fusion (14 of 19)
27 Neoclassical transport At low collisionality When ν 1, trapped particles exist for many banana orbits. This is called the banana regime. After N steps in a random direction, particles or energy will diffuse an average of N steps N t 2ɛ τ eff Note that N is multiplied by the fraction of trapped particles. Dr Ben Dudson Magnetic Confinement Fusion (15 of 19)
28 Neoclassical transport At low collisionality When ν 1, trapped particles exist for many banana orbits. This is called the banana regime. After N steps in a random direction, particles or energy will diffuse an average of N steps N t 2ɛ τ eff Note that N is multiplied by the fraction of trapped particles. The typical distance energy diffuses in a time t is t 2ɛ t 2 d neo δr b = τ eff τ ɛ δr b π q } 2 1/4 {{ ɛ 3/4 } t τ ii r Li }{{} Classical result Classical transport needed minor radius r 14cm Neoclassical transport increases this by 10. ITER (expected Q = 10) has a minor radius of 2m. Most transport in tokamaks is anomalous, due to turbulence Dr Ben Dudson Magnetic Confinement Fusion (15 of 19)
29 Diffusion equations Consider a volume of plasma containing a particle density n and energy density nt Flux of particles is Γ Flux of energy is Q Dr Ben Dudson Magnetic Confinement Fusion (16 of 19)
30 Diffusion equations Consider a volume of plasma containing a particle density n and energy density nt Flux of particles is Γ n t = Γ Continuity gives Flux of energy is Q (nt ) = Q t Dr Ben Dudson Magnetic Confinement Fusion (16 of 19)
31 Diffusion equations Consider a volume of plasma containing a particle density n and energy density nt Flux of particles is Γ Continuity gives Flux of energy is Q n t = Γ (nt ) = Q t Diffusive process: flux gradient (Fick s law) Γ = D n Q = nχ T n t = (D n) so if D is approximately constant: (nt ) = (nχ T ) t Assuming n constant: n t = D 2 n T t = (χ T ) Dr Ben Dudson Magnetic Confinement Fusion (16 of 19)
32 Diffusion equations From the units of D and χ (L 2 /T ), they must be the step size squared over the step time. For classical transport, D i = D e r 2 Le /τ ei m 2 /s χ i r 2 Li /τ ii m 2 /s χ e r 2 Le /τ ei m 2 /s Dr Ben Dudson Magnetic Confinement Fusion (17 of 19)
33 Diffusion equations From the units of D and χ (L 2 /T ), they must be the step size squared over the step time. For classical transport, D i = D e r 2 Le /τ ei m 2 /s χ i r 2 Li /τ ii m 2 /s χ e r 2 Le /τ ei m 2 /s For neoclassical transport, χ e χ i δr 2 be δr 2 bi }{{} m e/m i χ i 2ɛδr 2 bi /τ eff 0.4m 2 /s τ ii τ ei }{{} m i /m e = χ i me m i χ i / m 2 /s What about neoclassical particle transport D i,e? Dr Ben Dudson Magnetic Confinement Fusion (17 of 19)
34 Neoclassical particle transport For classical transport, collisions between particles of the same species didn t contribute to particle transport In this case most of the particles a trapped particle is colliding with are passing particles so this is no longer true χ i 60χ e so does this mean that D i 60D e? Dr Ben Dudson Magnetic Confinement Fusion (18 of 19)
35 Neoclassical particle transport For classical transport, collisions between particles of the same species didn t contribute to particle transport In this case most of the particles a trapped particle is colliding with are passing particles so this is no longer true χ i 60χ e so does this mean that D i 60D e? If this happened (and it does in some situations), the plasma would start to charge up, creating an electric field which held the ions back: this is called non-ambipolar transport It turns out that due to momentum conservation, ions and electrons actually diffuse at the same rate without an electric field (intrinsically ambipolar) Neoclassical particle diffusivity is comparable to χ e χ e D e D i q2 ɛ 3/2 r 2 Le /τ ei χ i mi m e χ e Dr Ben Dudson Magnetic Confinement Fusion (18 of 19)
36 Summary In toroidal machines, the variation in magnetic field strength leads to particle trapping The Grad-B and curvature drifts cause trapped particles to follow banana orbits Collisions scatter trapped particles into passing particles, and collisionality ν is the average number effective collision times τ eff τɛ per banana orbit This leads to a diffusion with a step size of the banana width δr b and time scale τ eff : χ δr 2 b /τ eff This neoclassical transport is the minimum possible in a toroidal device Measured diffusivities in tokamaks are typically times larger than neoclassical: they are anomalous This is due to turbulence, which we ll study later in the course Dr Ben Dudson Magnetic Confinement Fusion (19 of 19)
Toroidal confinement devices
Toroidal confinement devices Dr Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 24 th January 2014 Dr Ben Dudson Magnetic Confinement Fusion (1 of 20) Last time... Power
More 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 informationPhysics of fusion power. Lecture 13 : Diffusion equation / transport
Physics of fusion power Lecture 13 : Diffusion equation / transport Many body problem The plasma has some 10 22 particles. No description is possible that allows for the determination of position and velocity
More informationMagnetically Confined Fusion: Transport in the core and in the Scrape- off Layer Bogdan Hnat
Magnetically Confined Fusion: Transport in the core and in the Scrape- off Layer ogdan Hnat Joe Dewhurst, David Higgins, Steve Gallagher, James Robinson and Paula Copil Fusion Reaction H + 3 H 4 He + n
More information0 Magnetically Confined Plasma
0 Magnetically Confined Plasma 0.1 Particle Motion in Prescribed Fields The equation of motion for species s (= e, i) is written as d v ( s m s dt = q s E + vs B). The motion in a constant magnetic field
More 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 informationPerformance 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 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 informationIon plateau transport near the tokamak magnetic axis. Abstract
Ion plateau transport near the tokamak magnetic axis K.C. Shaing and R.D. Hazeltine Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (December 2, 1997) Abstract Conventional
More informationHeating 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 informationCurrent-driven instabilities
Current-driven instabilities Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 21 st February 2014 Ben Dudson Magnetic Confinement Fusion (1 of 23) Previously In the last
More informationPlasma instabilities. Dr Ben Dudson, University of York 1 / 37
Plasma instabilities Dr Ben Dudson, University of York 1 / 37 Previously... Plasma configurations and equilibrium Linear machines, and Stellarators Ideal MHD and the Grad-Shafranov equation Collisional
More informationA.G. PEETERS UNIVERSITY OF BAYREUTH
IN MEMORIAM GRIGORY PEREVERZEV A.G. PEETERS UNIVERSITY OF BAYREUTH ESF Workshop (Garching 2013) Research areas Grigory Pereverzev. Current drive in magnetized plasmas Transport (ASTRA transport code) Wave
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 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 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 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 informationTheory and Simulation of Neoclassical Transport Processes, with Local Trapping
Theory and Simulation of Neoclassical Transport Processes, with Local Trapping Daniel H. E. Dubin Department of Physics, University of California at San Diego, La Jolla, CA USA 92093-0319 Abstract. Neoclassical
More informationHeat Transport in a Stochastic Magnetic Field. John Sarff Physics Dept, UW-Madison
Heat Transport in a Stochastic Magnetic Field John Sarff Physics Dept, UW-Madison CMPD & CMSO Winter School UCLA Jan 5-10, 2009 Magnetic perturbations can destroy the nested-surface topology desired for
More informationMotion of Charged Particles in Fields
Chapter Motion of Charged Particles in Fields Plasmas are complicated because motions of electrons and ions are determined by the electric and magnetic fields but also change the fields by the currents
More informationLectures on basic plasma physics: Hamiltonian mechanics of charged particle motion
Lectures on basic plasma physics: Hamiltonian mechanics of charged particle motion Department of applied physics, Aalto University March 8, 2016 Hamiltonian versus Newtonian mechanics Newtonian mechanics:
More informationION THERMAL CONDUCTIVITY IN TORSATRONS. R. E. Potok, P. A. Politzer, and L. M. Lidsky. April 1980 PFC/JA-80-10
ION THERMAL CONDUCTIVITY IN TORSATRONS R. E. Potok, P. A. Politzer, and L. M. Lidsky April 1980 PFC/JA-80-10 ION THERMAL CONDUCTIVITY IN TORSATRONS R.E. Potok, P.A. Politzer, and L.M. Lidsky Plasma Fusion
More informationModelling of plasma edge turbulence with neutrals
Modelling of plasma edge turbulence with neutrals Ben Dudson 1 1 York Plasma Institute, Department of Physics, University of York, Heslington, York YO1 5DD, UK 7 th IAEA TM on Plasma Instabilities 4-6
More informationPer Helander. Contributions from: R. Kleiber, A. Mishchenko, J. Nührenberg, P. Xanthopoulos. Wendelsteinstraße 1, Greifswald
Rotation and zonal flows in stellarators Per Helander Wendelsteinstraße 1, 17491 Greifswald Contributions from: R. Kleiber, A. Mishchenko, J. Nührenberg, P. Xanthopoulos What is a stellarator? In a tokamak
More informationITER operation. Ben Dudson. 14 th March Department of Physics, University of York, Heslington, York YO10 5DD, UK
ITER operation Ben Dudson Department of Physics, University of York, Heslington, York YO10 5DD, UK 14 th March 2014 Ben Dudson Magnetic Confinement Fusion (1 of 18) ITER Some key statistics for ITER are:
More informationConfiguration Optimization of a Planar-Axis Stellarator with a Reduced Shafranov Shift )
Configuration Optimization of a Planar-Axis Stellarator with a Reduced Shafranov Shift ) Shoichi OKAMURA 1,2) 1) National Institute for Fusion Science, Toki 509-5292, Japan 2) Department of Fusion Science,
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 informationMotion of a charged particle in an EM field
Department of physics Seminar - 4 th year Motion of a charged particle in an EM field Author: Lojze Gačnik Mentor: Assoc. Prof. Tomaž Gyergyek Ljubljana, November 2011 Abstract In this paper I will present
More informationEUROFUSION WPJET1-PR(16) CG Albert et al.
EUROFUSION WPJET1-PR(16) 15331 CG Albert et al. Hamiltonian approach for evaluation of toroidal torque from finite amplitude non-axisymmetric perturbations of a tokamak magnetic field in resonant transport
More informationCharged particle motion in external fields
Chapter 2 Charged particle motion in external fields A (fully ionized) plasma contains a very large number of particles. In general, their motion can only be studied statistically, taking appropriate averages.
More informationFinite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena
1 TH/P2-18 Finite-Orbit-Width Effect and the Radial Electric Field in Neoclassical Transport Phenomena S. Satake 1), M. Okamoto 1), N. Nakajima 1), H. Sugama 1), M. Yokoyama 1), and C. D. Beidler 2) 1)
More informationObservation of Neo-Classical Ion Pinch in the Electric Tokamak*
1 EX/P6-29 Observation of Neo-Classical Ion Pinch in the Electric Tokamak* R. J. Taylor, T. A. Carter, J.-L. Gauvreau, P.-A. Gourdain, A. Grossman, D. J. LaFonteese, D. C. Pace, L. W. Schmitz, A. E. White,
More informationINTRODUCTION TO MAGNETIC NUCLEAR FUSION
INTRODUCTION TO MAGNETIC NUCLEAR FUSION S.E. Sharapov Euratom/CCFE Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, UK With acknowledgments to B.Alper for use of his transparencies
More informationDirect drive by cyclotron heating can explain spontaneous rotation in tokamaks
Direct drive by cyclotron heating can explain spontaneous rotation in tokamaks J. W. Van Dam and L.-J. Zheng Institute for Fusion Studies University of Texas at Austin 12th US-EU Transport Task Force Annual
More informationSingle Particle Motion
Single Particle Motion C ontents Uniform E and B E = - guiding centers Definition of guiding center E gravitation Non Uniform B 'grad B' drift, B B Curvature drift Grad -B drift, B B invariance of µ. Magnetic
More informationInter-linkage of transports and its bridging mechanism
Interlinkage of transports and its bridging mechanism Katsumi Ida National Institute for Fusion Science 17 th International Toki Conference 1519 October 27, Toki OUTLINE 1 Introduction 2 particle pinch
More informationG. Rewoldt, W.X. Wang, M. Bell, S. Kaye, W. Solomon, R. Nazikian, and W.M. Tang Princeton Plasma Physics Lab 1
Studies with GTC-Neo, including: Recent Applications of GTC-Neo for: (1)Studies of Toroidal Angular Momentum and Ion Heat Transport, and (2)Implications for CHERS Temperature Measurements G. Rewoldt, W.X.
More informationLecture 2: Plasma particles with E and B fields
Lecture 2: Plasma particles with E and B fields Today s Menu Magnetized plasma & Larmor radius Plasma s diamagnetism Charged particle in a multitude of EM fields: drift motion ExB drift, gradient drift,
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 informationParticle Pinch Model of Passing/Trapped High-Z Impurity with Centrifugal Force Effect )
Particle Pinch Model of Passing/Trapped High-Z Impurity with Centrifugal Force Effect ) Yusuke SHIMIZU, Takaaki FUJITA, Atsushi OKAMOTO, Hideki ARIMOTO, Nobuhiko HAYASHI 1), Kazuo HOSHINO 2), Tomohide
More informationEdge Momentum Transport by Neutrals
1 TH/P3-18 Edge Momentum Transport by Neutrals J.T. Omotani 1, S.L. Newton 1,2, I. Pusztai 1 and T. Fülöp 1 1 Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden 2 CCFE,
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 informationShear Flow Generation in Stellarators - Configurational Variations
Shear Flow Generation in Stellarators - Configurational Variations D. A. Spong 1), A. S. Ware 2), S. P. Hirshman 1), J. H. Harris 1), L. A. Berry 1) 1) Oak Ridge National Laboratory, Oak Ridge, Tennessee
More informationNumerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations
PHYSICS OF PLASMAS 12, 072513 2005 Numerical calculation of the Hamada basis vectors for three-dimensional toroidal magnetic configurations J. N. Talmadge and S. P. Gerhardt a HSX Plasma Laboratory, University
More informationChapter 5 MAGNETIZED PLASMAS. 5.1 Introduction. 5.2 Diamagnetic current
Chapter 5 MAGNETIZED PLASMAS 5.1 Introduction We are now in a position to study the behaviour of plasma in a magnetic field. In the first instance we will re-examine particle diffusion and mobility with
More informationEFFECT OF ION CYCLOTRON HEATING ON FAST ION TRANSPORT AND PLASMA ROTATION IN TOKAMAKS
EFFECT OF ION CYCLOTRON HEATING ON FAST ION TRANSPORT AND PLASMA ROTATION IN TOKAMAKS by V.S. Chan, S.C. Chiu, and Y.A. Omelchenko Presented at the American Physical Society Division of Plasma Physics
More informationInvestigation of Intrinsic Rotation Dependencies in Alcator C-Mod
Investigation of Intrinsic Rotation Dependencies in Alcator C-Mod D. Kwak, A. E. White, J. E. Rice, N. T. Howard, C. Gao, M. L. Reinke, M. Greenwald, C. Angioni, R. M. McDermott, and the C-Mod and ASDEX
More informationProgressing Performance Tokamak Core Physics. Marco Wischmeier Max-Planck-Institut für Plasmaphysik Garching marco.wischmeier at ipp.mpg.
Progressing Performance Tokamak Core Physics Marco Wischmeier Max-Planck-Institut für Plasmaphysik 85748 Garching marco.wischmeier at ipp.mpg.de Joint ICTP-IAEA College on Advanced Plasma Physics, Triest,
More informationSawtooth mixing of alphas, knock on D, T ions and its influence on NPA spectra in ITER plasma
Sawtooth mixing of alphas, knock on D, T ions and its influence on NPA spectra in ITER plasma F.S. Zaitsev 1, 4, N.N. Gorelenkov 2, M.P. Petrov 3, V.I. Afanasyev 3, M.I. Mironov 3 1 Scientific Research
More informationSimple examples of MHD equilibria
Department of Physics Seminar. grade: Nuclear engineering Simple examples of MHD equilibria Author: Ingrid Vavtar Mentor: prof. ddr. Tomaž Gyergyek Ljubljana, 017 Summary: In this seminar paper I will
More informationEffect of Ion Orbit Loss on Rotation and the Radial Electric Field in the DIII-D Tokamak
Effect of Ion Orbit Loss on Rotation and the Radial Electric Field in the DIII-D Tokamak by T.M. Wilks 1 with W.M. Stacey 1 and T.E. Evans 2 1 Georgia Institute of Technology 2 General Atomics Presented
More informationTH/P4-9. T. Takizuka 1), K. Shimizu 1), N. Hayashi 1), M. Hosokawa 2), M. Yagi 3)
1 Two-dimensional Full Particle Simulation of the Flow Patterns in the Scrape-off-layer Plasma for Upper- and Lower- Null Point Divertor Configurations in Tokamaks T. Takizuka 1), K. Shimizu 1), N. Hayashi
More informationª 10 KeV. In 2XIIB and the tandem mirrors built to date, in which the plug radius R p. ª r Li
Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies R. F. Post, T. K. Fowler*, R. Bulmer, J. Byers, D. Hua, L. Tung Lawrence Livermore National Laboratory *Consultant, Presenter This talk
More informationIntroduction to Nuclear Fusion. Prof. Dr. Yong-Su Na
Introduction to Nuclear Fusion Prof. Dr. Yong-Su Na What is a stellarator? M. Otthe, Stellarator: Experiments, IPP Summer School (2008) 2 Closed Magnetic System ion +++ ExB drift Electric field, E - -
More informationIon orbits and ion confinement studies on ECRH plasmas in TJ-II stellarator
Ion orbits and ion confinement studies on ECRH plasmas in TJ-II stellarator F. Castejón 1,4, J. M. Reynolds 3,4, J. M. Fontdecaba 1, D. López-Bruna 1, R. Balbín 1, J. Guasp 1, D. Fernández-Fraile 2, L.
More informationParallel transport and profile of boundary plasma with a low recycling wall
1 TH/P4-16 Parallel transport and profile of boundary plasma with a low recycling wall Xian-Zhu Tang 1 and Zehua Guo 1 1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.
More informationSeptember Plasma Fusion Center Massachusetts Institute of Technology Cambridge, Massachusetts USA
PFC/JA-95-19 RF WAVE EFFECTS ON THE NEOCLASSICAL ELECTRON DISTRIBUTION FUNCTION IN TOKAMAKS S. D. Schultz, A. Bers, and A. K. Ram September 1995 Plasma Fusion Center Massachusetts Institute of Technology
More 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 informationPartially Coherent Fluctuations in Novel High Confinement Regimes of a Tokamak
Partially Coherent Fluctuations in Novel High Confinement Regimes of a Tokamak István Cziegler UCSD, Center for Energy Research Center for Momentum Transport and Flow Organization Columbia Seminar Feb
More informationMHD-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 informationJ.C. Sprott. Plasma Studies. University of Wisconsin
BOOTSTRAP-CURRENT-DRIVEN STEADY-STATE TOKAMAK J.C. Sprott PLP 891 January 1983 Plasma Studies University of Wisconsin These PLP Reports are informal and preliminary and as such may contain errors not yet
More informationSimulation of alpha particle current drive and heating in spherical tokamaks
Simulation of alpha particle current drive and heating in spherical tokamaks R. Farengo 1, M. Zarco 1, H. E. Ferrari 1, 1 Centro Atómico Bariloche and Instituto Balseiro, Argentina. Consejo Nacional de
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 informationAMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code
AMSC 663 Project Proposal: Upgrade to the GSP Gyrokinetic Code George Wilkie (gwilkie@umd.edu) Supervisor: William Dorland (bdorland@umd.edu) October 11, 2011 Abstract Simulations of turbulent plasma in
More informationLectures on basic plasma physics: Introduction
Lectures on basic plasma physics: Introduction Department of applied physics, Aalto University Compiled: January 13, 2016 Definition of a plasma Layout 1 Definition of a plasma 2 Basic plasma parameters
More informationInitial Experimental Program Plan for HSX
Initial Experimental Program Plan for HSX D.T. Anderson, A F. Almagri, F.S.B. Anderson, J. Chen, S. Gerhardt, V. Sakaguchi, J. Shafii and J.N. Talmadge, UW-Madison HSX Plasma Laboratory Team The Helically
More informationFundamentals of Plasma Physics
Fundamentals of Plasma Physics Definition of Plasma: A gas with an ionized fraction (n i + + e ). Depending on density, E and B fields, there can be many regimes. Collisions and the Mean Free Path (mfp)
More informationGuiding Center Orbit Studies in a Tokamak Edge Geometry Employing Boozer and Cartesian Coordinates
Contrib. Plasma Phys. 48, No. -3, 4 8 (8) / DOI./ctpp.839 Guiding Center Orbit Studies in a Tokamak Edge Geometry Employing Boozer and Cartesian Coordinates Y. Nishimura,Y.Xiao,and Z. Lin Department of
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 Varenna-Lausanne International
More informationIntrinsic rotation due to non- Maxwellian equilibria in tokamak plasmas. Jungpyo (J.P.) Lee (Part 1) Michael Barnes (Part 2) Felix I.
Intrinsic rotation due to non- Maxwellian equilibria in tokamak plasmas Jungpyo (J.P.) Lee (Part 1) Michael Barnes (Part 2) Felix I. Parra MIT Plasma Science & Fusion Center. 1 Outlines Introduction to
More information14. Energy transport.
Phys780: Plasma Physics Lecture 14. Energy transport. 1 14. Energy transport. Chapman-Enskog theory. ([8], p.51-75) We derive macroscopic properties of plasma by calculating moments of the kinetic equation
More informationIntegration of Fokker Planck calculation in full wave FEM simulation of LH waves
Integration of Fokker Planck calculation in full wave FEM simulation of LH waves O. Meneghini S. Shiraiwa R. Parker 51 st DPP APS, Atlanta November 4, 29 L H E A F * Work supported by USDOE awards DE-FC2-99ER54512
More informationTriggering Mechanisms for Transport Barriers
Triggering Mechanisms for Transport Barriers O. Dumbrajs, J. Heikkinen 1, S. Karttunen 1, T. Kiviniemi, T. Kurki-Suonio, M. Mantsinen, K. Rantamäki 1, S. Saarelma, R. Salomaa, S. Sipilä, T. Tala 1 Euratom-TEKES
More informationTurbulent Transport of Toroidal Angular Momentum in Low Flow Gyrokinetics
PSFC/JA-09-27 Turbulent Transport of Toroidal Angular Momentum in Low Flow Gyrokinetics Felix I. Parra and P.J. Catto September 2009 Plasma Science and Fusion Center Massachusetts Institute of Technology
More informationUnderstanding physics issues of relevance to ITER
Understanding physics issues of relevance to ITER presented by P. Mantica IFP-CNR, Euratom/ENEA-CNR Association, Milano, Italy on behalf of contributors to the EFDA-JET Work Programme Brief summary of
More informationPlasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi
Plasma Physics Prof. V. K. Tripathi Department of Physics Indian Institute of Technology, Delhi Module No. # 01 Lecture No. # 22 Adiabatic Invariance of Magnetic Moment and Mirror Confinement Today, we
More informationNUMERICAL SIMULATION OF NEOCLASSICAL CURRENTS, PARALLEL VISCOSITY, AND RADIAL CURRENT BALANCE IN TOKAMAK PLASMAS
Department of Engineering Physics and Mathematics Helsinki University of Technology Espoo, Finland NUMERICAL SIMULATION OF NEOCLASSICAL CURRENTS, PARALLEL VISCOSITY, AND RADIAL CURRENT BALANCE IN TOKAMAK
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 informationComparison of Ion Internal Transport Barrier Formation between Hydrogen and Helium Dominated Plasmas )
Comparison of Ion Internal Transport Barrier Formation between Hydrogen and Helium Dominated Plasmas ) Kenichi NAGAOKA 1,2), Hiromi TAKAHASHI 1,2), Kenji TANAKA 1), Masaki OSAKABE 1,2), Sadayoshi MURAKAMI
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 informationDIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH
DIAGNOSTICS FOR ADVANCED TOKAMAK RESEARCH by K.H. Burrell Presented at High Temperature Plasma Diagnostics 2 Conference Tucson, Arizona June 19 22, 2 134 /KHB/wj ROLE OF DIAGNOSTICS IN ADVANCED TOKAMAK
More informationEffects 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 informationIntroduction to Fusion Physics
Introduction to Fusion Physics Hartmut Zohm Max-Planck-Institut für Plasmaphysik 85748 Garching DPG Advanced Physics School The Physics of ITER Bad Honnef, 22.09.2014 Energy from nuclear fusion Reduction
More informationThesis for the degree of Doctor of Philosophy. Turbulent and neoclassical transport in tokamak plasmas. István Pusztai
Thesis for the degree of Doctor of Philosophy Turbulent and neoclassical transport in tokamak plasmas István Pusztai Nuclear Engineering Department of Applied Physics Chalmers University of Technology
More informationDOPPLER 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 informationPhysics of fusion power. Lecture 14: Anomalous transport / ITER
Physics of fusion power Lecture 14: Anomalous transport / ITER Thursday.. Guest lecturer and international celebrity Dr. D. Gericke will give an overview of inertial confinement fusion.. Instabilities
More informationCorrelation Between Plasma Rotation and Electron Temperature Gradient Scale Length in LOC/SOC Transition at Alcator C-Mod
Correlation Between Plasma Rotation and Electron Temperature Gradient Scale Length in LOC/SOC Transition at Alcator C-Mod Saeid Houshmandyar 1 W. L. Rowan, 1 P. E. Phillips, 1 M. J. Greenwald, 2 J. W.
More informationReduction of Neoclassical Transport and Observation of a Fast Electron Driven Instability with Quasisymmetry in HSX
1 Reduction of Neoclassical Transport and Observation of a Fast Electron Driven Instability with Quasisymmetry in HSX J.M. Canik 1), D.L. Brower 2), C. Deng 2), D.T. Anderson 1), F.S.B. Anderson 1), A.F.
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 informationGyrokinetic theory for particle transport in fusion plasmas
Gyrokinetic theory for particle transport in fusion plasmas Matteo Valerio Falessi 1,2, Fulvio Zonca 3 1 INFN - Sezione di Roma Tre, Via della Vasca Navale, 84 (00146) Roma (Roma), Italy 2 Dipartimento
More informationSingle particle motion and trapped particles
Single particle motion and trapped particles Gyromotion of ions and electrons Drifts in electric fields Inhomogeneous magnetic fields Magnetic and general drift motions Trapped magnetospheric particles
More informationNew bootstrap current formula valid for steep edge pedestal, and its implication to pedestal stability
1 TH/P4-12 New bootstrap current formula valid for steep edge pedestal, and its implication to pedestal stability C.S. Chang 1,2, Sehoon Koh 2,*, T. Osborne 3, R. Maingi 4, J. Menard 1, S. Ku 1, Scott
More informationPoloidal Variation of High-Z Impurity Density in ICRF- Heated Alcator C-Mod Plasmas
Poloidal Variation of High-Z Impurity Density in ICRF- Heated Alcator C-Mod Plasmas M.L. Reinke, I.H. Hutchinson, J.E. Rice, N.T. Howard, A. Bader, S. Wukitch, Y. Lin, D.C. Pace, A. Hubbard, J.W. Hughes
More informationOverview 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 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 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 informationKinetic theory of ions in the magnetic presheath
Kinetic theory of ions in the magnetic presheath Alessandro Geraldini 1,2, Felix I. Parra 1,2, Fulvio Militello 2 1. Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, Oxford
More informationNon-perturbative statistical theory of intermittency in ITG drift wave turbulence with zonal flows
Non-perturbative statistical theory of intermittency in ITG drift wave turbulence with zonal flows Johan Anderson 1 and Eun-jin Kim University of Sheffield Department of Applied Mathematics Hicks Building,
More informationElectron temperature barriers in the RFX-mod experiment
Electron temperature barriers in the RFX-mod experiment A. Scaggion Consorzio RFX, Padova, Italy Tuesday 5 th October 2010 ADVANCED PHYSICS LESSONS 27/09/2010 07/10/2010 IPP GARCHING JOINT EUROPEAN RESEARCH
More informationA kinetic neutral atom model for tokamak scrape-off layer tubulence simulations. Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva
A kinetic neutral atom model for tokamak scrape-off layer tubulence simulations Christoph Wersal, Paolo Ricci, Federico Halpern, Fabio Riva CRPP - EPFL SPS Annual Meeting 2014 02.07.2014 CRPP The tokamak
More information