Transport in the Helical Core of the RFP

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RFX-mod Programme Workshop 2009, January 20-22,
Padova, Italy
Transport in the Helical Core of the RFP
M.Gobbin, G.Spizzo, L.Marrelli, L.Carraro,
R.Lorenzini, D.Terranova and the RFX-mod team
Consorzio RFX, Associazione Euratom-Enea sulla
Fusione, Padova, Italy
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Contents
Introduction helical states in RFX-mod high
current plasmas.
Diagnostics and numerical tools to investigate
the energy/particle transport in helical-shaped
plasmas.
Particle transport for the main gas
diffusion coefficients from numerical simulations
pellet experiments
Diffusion of impurities in MH and QSH plasmas.
Comparison between LBO experiments and numerical
simulations.
Energy transport in helical plasmas.
Summary and conclusions
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Helical structures in RFX-mod plasmas
In high current RFX-mod plasmas, the magnetic
topology is not anymore axisymmetric but
helically deformed1.
Evidences from

• Thomson scattering (TS)

-radiation distribution from bolometry

• SXR diagnostics

• magnetic signals ? topology reconstructions
  (ORBIT and FLiT codes)

SXR
TS
POINCARE
d
d20-30 cm
The (1,-7) mode is not anymore just a small
perturbation.
A helical geometry in the core must be considered
while studying the particle and energy transport
in RFX-mod.
1Lorenzini et al., Phys. Rev. Lett. 101, 025005
(2008)
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Transport in the helical core
Particle transport (main gas and impurities)
D values prediction for main gas and impurities
in helical states
Energy transport
5
Test particle approach in helical RFX-mod plasmas
Up to now a test particle approach has been used
by the code ORBIT to obtain an estimation of the
particle diffusion coefficients in many
experimental RFX-mod plasmas2.
secondary modes
HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY
collisions with plasma background
mode (1,-7) B0
2Gobbin et al., Phys. Plasmas 14, (072305), 2007
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Test particle approach in helical RFX-mod plasmas
Up to now a test particle approach has been used
by the code ORBIT to obtain an estimation of the
particle diffusion coefficients in many
experimental RFX-mod plasmas2.
secondary modes
HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY
collisions with plasma background
mode (1,-7) B0
_at_Ti 500-1000 eV
Di,QSH?2Di,SH
Di,QSH?1.5-4 m2/s
De in the helical core show a very different
behavior in SH and QSH regimes
De,QSH?10De,SH
but
De,QSH? 2-3 m²/s? Di,QSH
2Gobbin et al., Phys. Plasmas 14, (072305), 2007
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Diffusion coefficients depend on
..the level of secondary modes
De fast increases as Ns becomes greater than 1
while Di is nearly constant.
We expect from experimental data a dependence of
the global D on the secondary modes amplitude.
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Diffusion coefficients depend on
..the level of secondary modes
De fast increases as Ns becomes greater than 1
while Di is nearly constant.
We expect from experimental data a dependence of
the global D on the secondary modes amplitude.
the particles pitch angle!
pitch
PASSING ions well confined in the high T helical
structure
TRAPPED particles diffuse rapidly across the
helical structure
Dpas0.02-0.1 m²/s
Dtrap2-6 m²/s
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Experimental data pellet injection in helical
structures
Injection of pellet in the helical structures can
give informations on particles transport for the
main gas to be compared with the predictions from
ORBIT numerical simulations.
- density refuelling in the hot helical structure
- estimate of the particle confinement time in MH
and QSH/SHAx regimes
PELLET
ORBIT
tQSH/tMH2-3
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Experimental data pellet injection in helical
structures
Injection of pellet in the helical structures can
give informations on particles transport for the
main gas to be compared with the predictions from
ORBIT numerical simulations.
- density refuelling in the hot helical structure
- estimate of the particle confinement time in MH
and QSH/SHAx regimes
PELLET
ORBIT
tQSH/tMH2-3
More experiments in QSH/SHAx plasmas are required
to obtain D values considering an helical
geometry while analyzing the pellet ablation and
diffusion mechanisms.
Experimental estimates of D with different plasma
temperature, density and level of perturbations
to test the theoretical results on particle
transport.
- pellet trajectory and ablation - magnetic field
structure
Fast CCD camera can provide informations on
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Impurities diffusion laser blow- off with Ni
Experiments of laser blow-off have been recently
performed to study impurities diffusion in the
helical core of RFX-mod high current plasmas.
Emission lines Ni XVII 249 Å and Ni XVIII 292 Å
have been observed, indicating that the impurity
reached the high temperature regions inside the
helical structure3.
1D collisional-radiative impurity transport code
reproduces the emission pattern.
D and v radial profiles
While hydrogen injection by pellet shows an
improvement of confinement inside the island,
this is not observed for Ni impurities.
3 Carraro et al., submitted to Nucl. Fusion
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Ni ions diffusion in the helical core by ORBIT
Investigation by ORBIT both in MH and QSH regimes
Collisions
Test particles Ni ions
RFX-MOD _at_ 600eV
Ni
25/toroidal transit
0.1/toroidal transit
H
Dominance of collisional effects on magnetic
topology in determining the diffusion properties
of Ni impurities.
D (m²/s)
Fully Collisional
Banana regimes
Plateau
MH
DNi 0.4-2m²/s
QSH
DNi 0.1-1.5m²/s
Collisions per toroidal transit
Ni diffusion coefficients from numerical
simulations are nearly the same in QSH and MH
plasmas.
Qualitative agreement between experiment and
simulations.
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Other analysis on impurities diffusion
More LBO tests are required to investigate on the
quantitative discrepancy between ORBIT results
and the experimental data.
DNi (ORBIT) lt DNi (EXP)
Use of different impurities at more plasma
temperatures
D increases with ion temperature but the general
behavior is still the same
Ni-H simulations _at_ 1200eV
other impurities could allow to test different
regions of collisionality
Ne
2 colls / tor. transit
Ar
1.5 colls / tor. transit
Ne, Ar, Al
Al
2.3 colls / tor. transit
The propagation of cold pulses after the LBO
could be analyzed to evaluate the perturbed
electron energy diffusion coefficient ce4.
4 M.W.Kissick et al., Nucl.Fusion 34,1994
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Energy transport in progress...
Plasmas with large helical structures are
characterized by
- a reduction of the energy transport and an
increase of the confinement time (about a factor
2-4)
- low residual magnetic chaos ?drift modes of
electrostatic nature in helical structure may
become important for transport5
- isothermal helical flux surfaces TeTe(r)
5 Guo S.C., submitted to Phys. Rev. Lett. (2008)
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Energy transport in progress...
Plasmas with large helical structures are
characterized by
- a reduction of the energy transport and an
increase of the confinement time (about a factor
2-4)
- low residual magnetic chaos ?drift modes of
electrostatic nature in helical structure may
become important for transport5
- isothermal helical flux surfaces TeTe(r)
HELICAL EQUILIBRIUM DESCRIPTION
Metric tensor gij
Semi-analytical and numerical approaches
Adaption of stellarator codes (VMEC)
5 Guo S.C., submitted to Phys. Rev. Lett. (2008)
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A more complete description of transport
Numerical methods to study the neoclassical
transport in realistic 3-D magnetic topologies,
by solving a linearized drift kinetic equation.
Transport coefficients can be obtained as
flux-surface-averaged by an adaptation of
existing codes for stellarators, but a good
description of the helical equilibrium is first
required.
(by Monte-Carlo, full-f or df schemes,
variational approach DKES)
Dij integration over energy (Maxwellian
distribution) allows to obtain informations on
flux-surface-averaged flows
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Summary and conclusions
The presence of an helical core in high current
RFX-mod plasmas requires to perform
energy/particles transport analysis in a
helically-shaped geometry.
18
Summary and conclusions
The presence of an helical core in high current
RFX-mod plasmas requires to perform
energy/particles transport analysis in a
helically-shaped geometry.
Particle transport simulations in helical states
by ORBIT
Di,QSH? De,QSH ? 2.5-4m2/s ? 1/5 DMH (_at_ T600eV
1keV)
Strong dependence of De on NS and a better
confinement for passing particles
Qualitative agreement with pellet experiments
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Summary and conclusions
The presence of an helical core in high current
RFX-mod plasmas requires to perform
energy/particles transport analysis in a
helically-shaped geometry.
Particle transport simulations in helical states
by ORBIT
Di,QSH? De,QSH ? 2.5-4m2/s ? 1/5 DMH (_at_ T600eV
1keV)
Strong dependence of De on NS and a better
confinement for passing particles
Qualitative agreement with pellet experiments
Nichel diffusion coefficients in QSH and MH are
about the same. Dominance of collision mechanisms
on magnetic perturbations effect.
DNi,QSH? DNi,MH
Qualitative agreement between theory and
experiments.
More investigation is required to understand
the quantitative discrepancy.
20
Summary and conclusions
The presence of an helical core in high current
RFX-mod plasmas requires to perform
energy/particles transport analysis in a
helically-shaped geometry.
Particle transport simulations in helical states
by ORBIT
Di,QSH? De,QSH ? 2.5-4m2/s ? 1/5 DMH (_at_ T600eV
1keV)
Strong dependence of De on NS and a better
confinement for passing particles
Qualitative agreement with pellet experiments
Nichel diffusion coefficients in QSH and MH are
about the same. Dominance of collision mechanisms
on magnetic perturbations effect.
DNi,QSH? DNi,MH
Qualitative agreement between theory and
experiments.
More investigation is required to understand
the quantitative discrepancy.
Energy transport and heat balance in helical
geometry is still under study a complete
description of the helical equilibrium is first
required.
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Summary and conclusions
The presence of an helical core in high current
RFX-mod plasmas requires to perform
energy/particles transport analysis in a
helically-shaped geometry.
Particle transport simulations in helical states
by ORBIT
Di,QSH? De,QSH ? 2.5-4m2/s ? 1/5 DMH (_at_ T600eV
1keV)
Strong dependence of De on NS and a better
confinement for passing particles
Qualitative agreement with pellet experiments
Nichel diffusion coefficients in QSH and MH are
about the same. Dominance of collision mechanisms
on magnetic perturbations effect.
DNi,QSH? DNi,MH
Qualitative agreement between theory and
experiments.
More investigation is required to understand
the quantitative discrepancy.
Energy transport and heat balance in helical
geometry is still under study a complete
description of the helical equilibrium is first
required.
Numerical methods adopted in the stellarator
community to study global neoclassical transport
could be applied also to helical RFP plasmas.
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Thanks for your attention
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MORE....
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Helical magnetic flux definition
Helical flux contour on a poloidal section
test particles deposited in the o-point
loss surface
yMo-point 0
yMloss
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Banana orbits size increases with their energy
Passing ion orbit in a QSH (1,-7)
Trapped ion orbit
0.2 cm (800 eV)
Poloidal banana width
Colors of the trajectories are relative to
different helical flux values.
0.5 - 5cm
300 1200eV
Helical banana size
Electrons experience very small neoclassical
effects their banana orbits are less than few
mm still at 800 eV.
For a given energy E the banana size of an
impurity with atomic mass A is proportional to
?v ?(E/A)1/2
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Local diffusion coefficient evaluation
Di is evaluated locally too because -it may vary
inside the helical domain -the approximations due
to the non linear density distribution are avoided
particles deposition
Almost constant inside the helical structure
1-5m²/s
Dloc (m²/s)
Trapped, passing, uniform pitch particles show
different slopes for the relation Dr² versus time
t.
yM
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Energy transport is still under study ...
A first step required to write the heat balance
equations in the RFX-mod QSH plasmas is the
complete description of the helical equilibrium
yM
Z
mode (1,-7) B0
h
R
(R,Z,f)
(yM, h, f)
Once defined the change of coordinates, the
metric tensor can be computed and so energy
transport equations can be written for quantities
as function of the helical flux.
Semi-analytical from the knowledge of the (1,-7)
eigenfunction and of the equilibrium poloidal and
toroidal fluxes (E.Martines)
Numerical reconstruction of the helical flux and
helical angle (from magnetic topology)
Adaptation of codes such as VMEC and TRANSP (see
Marrellis talk)
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Effect of secondary modes on De
The level of secondary modes significantly
affects the diffusion of electrons in high
temperature QSH.
Degt 10m2/s
De
Input to ORBIT
m²/s
Di
Delt 0.1m2/s
Ns
n8-24 x k
Secondary modes spectrum is multiplied by a
constant k this changes the Ns parameter
De increases rapidily as Ns becomes greater than
1 while Di is nearly constant.
Ns ?
We expect from experimental data a dependence of
the global D on the secondary modes.
(SH Ns1, k0)
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Correlation of D with experimental magnetic
perturbations
Di,QSH (m²/s)
Di,QSH (m²/s)
Correlations between the magnetic energy of the
dominant (1,-7) mode and of the secondary modes
with the ion transport properties in the analyzed
experimental shots.
(mT)
Di,QSH (m²/s)
Di,SH/Di,QSH
Best QSH are very close to the corresponding SH
case for ions
(mT)
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Interaction of test particles with the plasma
background
test particle a ? background b
a are mono-energetic and energy is conserved
during collision mechanisms
a particles change their guiding center position
randomly by a gyroradius
3
a particles change randomly also their velocity
direction with respect to B
pitch angle
5
3 B.A.Trubnikov, Rev. Plasma Phys. 1, (105),
1965
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Trapped and passing ions in helical structures
The pitch angle of the particle is an other key
parameter in the determination of particles
diffusion coefficients.
pitch
PASSING ions with l ?1 are well confined in the
high T helical structure
TRAPPED particles diffuse rapidly across the
helical structure
Dpas0.02-0.1 m²/s
Dtrap2-6 m²/s
poloidal and helical trapping
low collisionality and residual chaos
banana orbits
Dtrap/Dpas 100 !!
width
0.5 - 5cm
_at_ (300 1200eV)
l 0.1
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Impurities diffusion LBO in QSH and MH plasmas
Experiments of laser blow-off have been performed
recently to study impurities diffusion in the
helical core of RFX-mod high current plasmas.
Emission lines Ni XVII 249 Å and Ni XVIII 292 Å
have been observed, indicating that the impurity
reached the high temperature regions inside the
helical structure.3
D and v radial profiles to be implemented in the
code for a good matching with experimental data
20
0
with DQSH20m²/s very close to the one typical of
MH case.
t(s)
While hydrogen injection by pellet shows an
improvement of confinement inside the island,
this is not observed for impurities.
1D collisional-radiative impurity transport code
reproduces the emission pattern.
3 L.Carraro, submitted to Nucl. Fusion
34
Ratio of Di and De at several level of secondary
modes and more temperatures
De/Di (m²/s)
1keV
0.7keV
0.4keV
Ns
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Effect of secondary modes on De
The level of secondary modes significantly
affects the diffusion of electrons in high
temperature QSH
MH
Degt 12m2/s
Typical RFX-mod QSH
De(m²/s)
n8-24 x k
De 3m2/s
Delt 0.1m2/s
SH
k
The ion diffusion coefficient depends slightly on
the level of secondary modes
but experimentally the global ambipolar D will
be a function of the Ns parameter
Ns?
36
Test particle approach in helical RFX-mod plasmas
Up to now a test particle approach has been used
by the code ORBIT to obtain an estimation of the
particle diffusion coefficients in many
experimental RFX-mod plasmas, considering the
real helical geometry.
1.Helical flux used as new radial flux coordinate
2.Transport inside the helical structure
with
secondary modes
y M
collisions with plasma background
Source
n
G
3.Evaluation of a diffusion coefficient D
particles distribution over the helical domain is
recorded
helical magnetic flux yM(X,Z,f) associated to
each point inside the helix (1,-7) 2
2Gobbin et al., Phys. Plasmas 14, (072305), 2007
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Ion and electron diffusion coefficients in SH and
QSH
Ion Di in SH and QSH
Electron De in SH and QSH
x10
Electron diffusion coefficients inside the
helical core show a very different behavior in SH
and QSH regimes
The effect of residual chaos in QSH does not
affect dramatically Di
_at_Ti 500-1000 eV
De,QSH?10De,SH
Di,QSH?2Di,SH
Note that in QSH (_at_Tegt800eV)
Di,QSH?2.5-4 m2/s
De,QSH? 2-3 m²/s? Di,QSH