Shear flows generated by plasma turbulence and their influence on transport

1
Shear flows generated by plasma turbulence and
their influence on transport
V.Antoni, E. Spada, N. Vianello, M. Spolaore, R.
Cavazzana, G. Serianni, E.Martines Presented by
V. Antoni Consorzio RFX, Associazione
Euratom-ENEA sulla Fusione, Padova, Italy
2
Foreword

• Flow generation by turbulence and effect of flow
  on transport are important subjects of
  investigation in astrophysics and laboratory
  plasmas and play a key role in performance of
  present and future fusion experiments.
• Theory and numerical simulations predict they are
  non linearly coupled
• Experimental measurements supporting theory are
  challenging tasks in fusion plasmas
• This talk would illustrate these subjects
  presenting the status of the art of the
  experimental investigation for a specific field
  flows and turbulence due to electric drift in the
  edge region of fusion experiments

3
Outline

• Introduction
• Magnetic configurations, plasma turbulence and
  transport
• Influence of plasma flow on turbulent transport
• Flow generation by turbulence
• Momentum balance
• Turbulence driving term
• Viscous damping
• Energy transfer from turbulence to mean flow
• Turbulence self-regulation

4
Magnetic configurations (i)
Introduction

• Toroidal magnetic configuration

S.O.L.
edge
core
Magnetic field lines
Nested flux surfaces
The edge region is the relatively cold plasma
right inside the separatrix or Last Closed Flux
Surface (LCFS) which separates plasma from Scrape
Off Layer (SOL)
5
Magnetic configurations (ii)
Introduction
Tokamak
Reversed Field Pinch (RFP)
Stellarator
6
ExB flow
Introduction

• The ExB drift is
• perpendicular to the magnetic field
• independent of charge and mass and therefore
  identical for all species.

7
Plasma turbulence
Introduction

• Fluctuations leading to plasma turbulence can be
  grouped in
• Electrostatic
• Magnetic
• Electric field fluctuations produce fluctuating
  ExB drift velocities perpendicular to the
  magnetic field

8
Turbulence transport Turbulent transport
Introduction
Fluctuation coupling results in turbulent
transport
Energy flux
Particle flux

• In all experiments electrostatic turbulence
  drives most ( or an important fraction ) of the
  particle and energy transport at the edge
  (anomalous transport)

Particle confinement time
Energy confinement time
With temperature and density tp and tE
characterizing fusion experiment performance
in RFPs still controversial
9
Edge turbulence measurements Electric probes
Introduction
Arrays of Langmuir probes can provide the
required local, simultaneous measurements of
different parameters with high resolution in
space and time
HT-7
JET
1 cm
1 cm
EXTRAP- T2R
2 cm
10
Improved confinement regimes and transport barrier
FlowTransport

• In ASDEX (1982) first observation of improved
  confinement (H-mode) triggered by the application
  of additional heating power.
• H-mode is characterized by steeper temperature
  and density profiles at the edge

ASDEX
improved
standard
Wagner, F., et al., 1982, Phys. Rev. Lett. 49,
1408.

• Since then, barrier formation has been reported
  from a large number of devices

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ExB Flow Transport Barriers
FlowTransport

• Highly sheared ExB flow at the edge are
  associated to steeper profiles of plasma density
  and temperature and to the drop of turbulent
  transport and turbulence amplitude.

DIIID
edge
SOL
SOL
K H Burrell PFCF 34, 1859 (I992)
edge
Causality between ExB flow shear and turbulent
transport reduction demonstrated by edge biasing
experiments
G Van Oost PPCF 45 (2003) 621643
Theory predicts reduction of turbulent transport
by ExB flow shear Itoh S-I, PRL 1994 72 1200,
Ware A S, 1998 Phys. Plasmas 5 173, Biglari H
1989 Phys. Fluids B 2 1
12
Spontaneous ExB flows in tokamaks
FlowTransport

• HT-7

• JET

C. Hidalgo, New Journal of Physics 4 (2002) 51.1
G.S Xu et al., PRL 91, 125001 (2003)
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Spontaneous ExB flows in stellarators
FlowTransport
Wendelstein 7-AS
C. Hidalgo et al New J.Phys. 4 (2002) 51.1 J
Bleuel et al, New J.Phys. 4 38.1 (2002)
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Spontaneous ExB flows in RFPs
FlowTransport
RFX
EXTRAP T2R
The ExB velocity is higher as the (mainly
poloidal) magnetic field at the edge is lower
than in Tokamaks and Stellarators
V. Antoni et al., Phys. Rev. Lett. 80, 4185
(1998).
N.Vianello et al, PPCF 44 2513 (2002)
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Flow and flow shear
FlowTransport
Substituting turbulence characteristic space and
time scales
Turbulence characteristic time (autocorrelation
time)
Turbulence mean perpendicular wave-length
(perpendicular correlation length)
Turbulence radial correlation length
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FlowTransport
Flow shear and turbulence scales
Small scales of turbulence and large scales of
ExB flow are coupled
When the equality holds the shear is marginal
for turbulence suppression
Stellarator C.Hidalgo et al, New. J.Phys. 4 51.1
(2002) J Bleuel et al, New J.Phys. 4 38.1 (2002)
RFP N.Vianello et al, PPCF 44 2513 (2002) V.
Antoni et al., PRL 80 4185 (1998) B.E.Chapman et
al, PRL 80 2137 (1998)
Tokamak S.Coda et al., Phys.Lett. A, 273, 125
(2000) E.J.Doyle et al., Phys.Fluids B 3 2300
(1991) G.S.Xu et al, Phys.Rev.Lett. 91 125001
(2003) Ch.P.Ritz et al, PRL 65 2543 (1990) B.
Gonçalves et al, Czech. J.Phys. 51 995 (2001)
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Momentum Balance Equation (i)
Flow Generation

• The MHD momentum equation for an incompressible
  plasma reads

• Substituting Ampere law the
  equation in tensorial notation becomes

Total pressure
Maxwell stress
Reynolds stress
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Momentum Balance Equation (ii)
Flow Generation
In stationary equilibrium with
Experimentally radial gradients larger than
gradients along f and q
where
Reynolds stress here represents the radial flux
of momentum perpendicular to the magnetic field.
In general it is related to the degree of
anisotropy in the structure of the turbulence
A Yoshizawa, et al PFCF 46 (2004) R25
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Reynolds Stress Measurements
Flow Generation

• In HT-7 Tokamak the complete Reynolds stress has
  been measured

Magnetic RS MRS

• ltgt is a time average

Electrostatic RS ERS
High Reynolds stress gradient associated to high
EXB flow shear MRS opposite and lower than ERS
ERS gradient accounts for most of RS gradient
G.S. Xu et al. IAEA conf. 2004, EX/8-4Rb
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Reynolds Stress Measurements
Flow Generation
EXTRAP-T2R
In RFPs

• Also in RFPs, where magnetic fluctuations are
  larger, Reynolds stress gradient is mostly due to
  electrostatic component

N. Vianello et al., PRL 94 (2005) 135001
Coincidence between gradients of electrostatic
Reynolds stress and ExB flow shear observed also
in ISTTOK and TJ-IU
Hidalgo C, et al, 1999 Phys. Rev. Lett. 83 2203
C. Hidalgo et al.,PFCF 42 (2000) A153
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Edge Viscosity in RFP
Flow Generation
Kinematic viscosity
Kinematic viscosity is anomalous and consistent
with anomalous diffusivity due to turbulent
transport RS drives the ExB shear opposing the
flattening action of the viscous damping
N. Vianello et al., IAEA Conf (2004)
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Energy Transfer between Turbulence and Mean Flow
Flow Generation
To study the evolution of the energy of the mean
flow the momentum equation is multiplied by the
mean velocity
By assuming larger radial gradients and
stationary equilibrium the equation for the
energy of the flow becomes
Energy inflow and outflow rate across the surface
(mean energy) production term
Viscous damping
Rate of strain tensor
Kinematic viscosity
Reynolds stress
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Radial profile of Production Term in JET
Flow Generation
With negligible magnetic fluctuations
edge
sol
Limiter configuration
The production term changes sign when crossing
the separatrix and turbulence transfers energy to
the mean flow in the SOL On assuming stationary
conditions the viscosity has been estimated
Viscosity results anomalous and consistent with
turbulence diffusivity in the SOL
E. Sanchez JNM 337-339 (2005) 296
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Radial profile of Production Term in EXTRAP-T2R
Flow Generation
EXTRAP-T2R
edge
SOL
P
Electrostatic contribution is dominant. The
production term is positive in the edge region
where a high ExB shear takes place
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Time behaviour of Production term in EXTRAP-T2R
Flow Generation
Numerical simulations of interchange turbulence
in SOL predict self-regulation mechanism by which
energy is transferred from fluctuating to mean
velocity
O. E. Garcia, PoP 12(2005), 62309
Recent modelling with toroidal geometry and
magnetic field curvature predicts turbulence as a
source of shear flow and oscillating time
behaviour
V. Naulin, PoP 12(2005), 52515-1
Preliminary results from EXTRAP-T2R confirm that
energy transfer from turbulence to mean flow
exhibits oscillations
Effective viscosity is anomalous and consistent
with that from momentum balance
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Edge viscosity in stellarators and tokamaks
Flow Generation
Parallel and perpendicular viscosity estimates
are still controversial. Further experiments
supporting anomalous viscosity Edge biasing
experiments in Tokamaks ISSTOK (Silva Nucl.
Fusion 44 (2004) 799810) and CASTOR (Hron, ICPP
2004). Experiments supporting neoclassical
viscosity Edge biasing in TEXTOR (Jachmich S,
2002 29th EPS Conf O-1.01) Momentum balance in
HT-7 (G.S. Xu et al. IAEA conf. 2004, EX/8-4Rb)
Quasi-Helical-Symmetry configuration in HSX
stellarator (S. Gerhardt PoP 2005) Transient
edge biasing in TJ-II suggests two time scales
for flow damping and leave open the issue of
possible co-existence of neoclassical and
anomalous viscosity (C. Hidalgo, et al. PFCF 46
(2004) 287)
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Viscosity modelling
Flow Generation

• In Tokamaks (Staebler et al., NF (1993)) and RFPs
  (Guo S C, et al. PoP (1994)) quasi-linear models
  predict anomalous viscosity
• from Ion Temperature Gradient (ITG) turbulence .

Model predicts viscosity

• Higher than classical or neo-classical
• ExB shear dependent
• With a maximum

• The existence of a maximum in the turbulent
  viscosity could explain the transition to
  improved confinement regimes

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Hints on driving and damping due to turbulence
Flow Generation
Frequency resolved Reynolds Stress and turbulent
particle flux reveal different time scales an
indication of different instabilities
EXTRAP-T2R
N. Vianello et al. to be published in Nuclear
Fusion
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Self-regulation
Towards a self-regulation model for edge
turbulence
Electrostatic fluctuations
Electrostatic turbulence provides an important
fraction of the particle and energy losses in all
experiments
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Self-regulation
Towards a self-regulation model for edge
turbulence
Electrostatic fluctuations
Turbulence Driving term
Electrostatic turbulence drives most of mean flow
through velocity coupling
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Self-regulation
Towards a self-regulation model for edge
turbulence
Electrostatic fluctuations
Turbulence Driving term
Momentum Damping
ExB Sheared flow
ExB sheared flow is the result of the
counteracting action of turbulence driving and
viscous damping
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Self-regulation
Towards a self-regulation model for edge
turbulence
Electrostatic fluctuations
Turbulence Driving term
Turbulence Damping term
ExB Sheared flow
Edge viscosity might be anomalous and in some
experiments results consistent with anomalous
diffusivity.
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Self-regulation
Towards a self-regulation model for edge
turbulence
Electrostatic fluctuations
Turbulence Driving term
Turbulence Damping term
ExB Sheared flow
Theory predicts and some experiments confirm
that ExB flow shear is effective in reducing the
coupling between density and velocity
fluctuations
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Self-regulation
Towards a self-regulation model for edge
turbulence
Models suggest that ExB flow shear might modify
turbulence anisotropy and then the Reynolds
stress
Garcia L, et al. 2001 Phys. Plasmas 8 4111
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Conclusions

• Progress in edge turbulence physics understanding
• In all devices, despite the different magnetic
  configurations and instabilities, the ExB flow
  shear is found marginal for turbulence
  suppression
• Reynolds stress is always a driving term (this
  implies non-isotropic turbulence)
• Reynolds stress is mainly driven by electrostatic
  turbulence (even in RFPs where magnetic
  fluctuations are large). This implies that the
  edge turbulence contributing to the driving term
  is not purely alfvenic
• In several experiments viscosity is anomalous and
  in some case consistent with anomalous
  diffusivity due to turbulence
• Some experimental results support a turbulence
  self-regulation process at the edge by which
  turbulence drives the ExB flow shear marginal
• The results can contribute to advances in other
  areas as
• Parallel flow generation in the core
• Interplay between flows and coherent structures
• Generation of large structures like zonal flows
  and streamers
• Edge Turbulence investigation represents a good
  example of how fusion plasma physics can take
  advantage of studies performed in different
  magnetic configurations