RFX-mod Workshop, Padova 20-22/01/ 2009
Transport in the Helical Core of the RFPTransport in the Helical Core of the RFPM.Gobbin, G.Spizzo, L.Marrelli,
L.Carraro, R.Lorenzini, D.Terranova and the RFX-mod team
RFX-mod Programme Workshop 2009, January 20-22, Padova, Italy
Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy
RFX-mod Workshop, Padova 20-22/01/ 2009
Particle transport for the main gas:
Diffusion of impurities in MH and QSH plasmas.
Comparison between LBO experiments and numerical simulations.
Summary and conclusions
Contents
Introduction: helical states in RFX-mod high current plasmas.
diffusion coefficients from numerical simulations
pellet experiments
Energy transport in helical plasmas.
Diagnostics and numerical tools to investigate the energy/particle transport in helical-shaped plasmas.
RFX-mod Workshop, Padova 20-22/01/ 2009
Helical structures in RFX-mod plasmas
=20-30 cm
The (1,-7) mode is not anymore just a small perturbation.
In high current RFX-mod plasmas, the magnetic topology is not anymore axisymmetric but helically deformed1.
-Thomson scattering (TS)
-SXR diagnostics -radiation distribution from bolometry
-magnetic signals topology reconstructions (ORBIT and FLiT codes)
Evidences from::
A helical geometry in the core must be considered while studying the particle and energy transport in RFX-mod.
[1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)
SXR TS POINCARE’
RFX-mod Workshop, Padova 20-22/01/ 2009
Transport in the helical core
Particle transport Particle transport (main gas and impurities):
Energy transport:Energy transport:
PELLET INJECTIONPELLET INJECTION IN THE HELICAL STRUCTURES
Laser Blow Off (LBOLBO) – IMPURITIES TRANSPORT
EXPERIMENT
TEST PARTICLE APPROACH by NUMERICAL SIMULATIONS
(ORBIT)
THEORY
Development of new numerical tools to solve the heat balance
equations in helical RFP plasmas.
THEORY
Data from THOMSON THOMSON SCATTERINGSCATTERING, BOLOMETRYBOLOMETRY
and other diagnostics
EXPERIMENT
D values prediction for main gas and impurities in helical states
RFX-mod Workshop, Padova 20-22/01/ 2009
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
collisions with plasma background
HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY
[2]Gobbin et al., Phys. Plasmas 14, (072305), 2007
mode (1,-7) + B0
RFX-mod Workshop, Padova 20-22/01/ 2009
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
collisions with plasma background
HELICAL EQUILIBRIUM FROM MAGNETIC TOPOLOGY
[2]Gobbin et al., Phys. Plasmas 14, (072305), 2007
mode (1,-7) + B0
Di,QSH1.5-4 m2/s
Di,QSH2Di,SH
De,QSH10·De,SH
De,QSH 2-3 m²/s Di,QSH
@Ti = 500-1000 eV
De in the helical core show a very different behavior in SH
and QSH regimes:
but:
Di in SH and QSH De in SH and QSH
x10
IONSIONS ELECTRONSELECTRONS
RFX-mod Workshop, Padova 20-22/01/ 2009
..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.
De
Di
Ns
m²/
s
De< 0.1m2/s
De> 10m2/s
Ns
n nnn bb
2
2,1
2,1 /
1
(SH: Ns=1)
Diffusion coefficients depend on…
RFX-mod Workshop, Padova 20-22/01/ 2009
..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.
De
Di
Ns
m²/
s
De< 0.1m2/s
De> 10m2/s
Ns
n nnn bb
2
2,1
2,1 /
1
(SH: Ns=1)
…the particles pitch angle!
Diffusion coefficients depend on…
pitch:
)cos(||||
Bv
Bv
B
v
~1 ~
PASSING ions well confined in the high T
helical structure
Dpas~0.02-0.1 m²/s
TRAPPED particles diffuse rapidly across the helical structure
Dtrap~2-6 m²/s
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
ORBIT: Di,QSH~ 2.5 – 4 m2/s
Di,MH~ 20m2/s
QSH/MH~2-3
- density refuelling in the hot helical structure
PELLET:
- estimate of the particle confinement time in MH and QSH/SHAx regimes
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
ORBIT:
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.
Di,QSH~ 2.5 – 4 m2/s
Di,MH~ 20m2/s
QSH/MH~2-3
- density refuelling in the hot helical structure
Fast CCD camera can provide informations on:
PELLET:
- estimate of the particle confinement time in MH and QSH/SHAx regimes
- pellet trajectory and ablation
- magnetic field structure
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
DQSH~20m²/s very close to the one typical of MH regimes.
r/a
D(m²/s)
v(m/s)
20
0
[3] Carraro et al., submitted to Nucl. Fusion
RFX-mod Workshop, Padova 20-22/01/ 2009
Qualitative agreement between experiment and simulations.
Ni ions diffusion in the helical core by ORBIT
Collisions:Collisions:
25/toroidal transitNi:Ni:
0.1/toroidal transitHH++::
D (
m²/
s)
RFX-MOD @ 600eV
Investigation by ORBIT both in MH and QSH regimes:
Fully Collisional
Banana regimes
Ni diffusion coefficients from numerical simulations are nearly the same in QSH and MH plasmas.
Test particles: Ni ions
Plateau
DNi~ 0.4-2m²/sMH:
DNi~ 0.1-1.5m²/sQSH:
Dominance of collisional effects on magnetic topology in determining the diffusion properties of Ni impurities.
Collisions per toroidal transit
RFX-mod Workshop, Padova 20-22/01/ 2009
More LBO tests are required to investigate on the quantitative discrepancy between ORBIT results and the experimental data.
Use of different impurities at more plasma temperatures:
The propagation of cold pulses after the LBO could be analyzed to evaluate the perturbed electron energy diffusion coefficient e
4.
D increases with ion temperature but the general behavior is still the same;
other impurities could allow to test different regions of collisionality;
Ne: 2 colls / tor. transit
Ni-H simulations @ 1200eV
Ne, Ar, Al
Ar: 1.5 colls / tor. transit
Al: 2.3 colls / tor. transit
Other analysis on impurities diffusion
[4] M.W.Kissick et al., Nucl.Fusion 34,1994
DNi (ORBIT) < DNi (EXP)
RFX-mod Workshop, Padova 20-22/01/ 2009
Energy transport: in progress...
- isothermal helical flux surfaces Te=Te();
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);
helical flux
- low residual magnetic chaos drift modes of electrostatic nature in helical structure may become important for transport5;
[5] Guo S.C., submitted to Phys. Rev. Lett. (2008)
RFX-mod Workshop, Padova 20-22/01/ 2009
Energy transport: in progress...
- isothermal helical flux surfaces Te=Te();
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);
Semi-analytical and numerical approaches;
Adaption of stellarator codes (VMEC…)
The heat diffusion equation must be solved in a helical geometry in order to evaluate the energy diffusion coefficients.
outin PPQ
TnQ HELICAL EQUILIBRIUM DESCRIPTION
Metric tensor gij
, ,
helical flux
- low residual magnetic chaos drift modes of electrostatic nature in helical structure may become important for transport5;
[5] Guo S.C., submitted to Phys. Rev. Lett. (2008)
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
MONO-ENERGETIC Di,j
Dij integration over energy (Maxwellian distribution) allows to obtain informations on flux-surface-averaged flows:
particles flux density
energy flux density
current density
(by Monte-Carlo, full-f or f schemes, variational
approach DKES)
rEnT ,,
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
RFX-mod Workshop, Padova 20-22/01/ 2009
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 (@ T=600eV –1keV)Strong dependence of De on NS and a better confinement for passing particles
Qualitative agreement with pellet experiments
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.
Particle transport simulations in helical states by ORBIT:
Di,QSH De,QSH 2.5-4m2/s 1/5 DMH (@ T=600eV –1keV)Strong dependence of De on NS and a better confinement for passing particles
DNi,QSH DNi,MH
Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy.
Qualitative agreement with pellet experiments
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.
Particle transport simulations in helical states by ORBIT:
Di,QSH De,QSH 2.5-4m2/s 1/5 DMH (@ T=600eV –1keV)Strong dependence of De on NS and a better confinement for passing particles
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.
Qualitative agreement with pellet experiments
RFX-mod Workshop, Padova 20-22/01/ 2009
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.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.
Particle transport simulations in helical states by ORBIT:
Di,QSH De,QSH 2.5-4m2/s 1/5 DMH (@ T=600eV –1keV)Strong dependence of De on NS and a better confinement for passing particles
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.
Qualitative agreement with pellet experiments
Numerical methods adopted in the stellarator community to study global neoclassical transport could be applied also to helical RFP plasmas.
RFX-mod Workshop, Padova 20-22/01/ 2009
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RFX-mod Workshop, Padova 20-22/01/ 2009
RFX-mod Workshop, Padova 20-22/01/ 2009
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RFX-mod Workshop, Padova 20-22/01/ 2009
C
S
M dd lASB
θdl )( IC
M
Igp 7,17,1A
dlA
S C
Magnetic flux from Poincaré: Helical flux contour on a poloidal section :
test particles deposited in the o-point
loss surfaceM
loss
Mloss
Mo-point= 0
Helical magnetic flux definition
RFX-mod Workshop, Padova 20-22/01/ 2009
Banana orbits size increases with their energy
Passing ion orbit in a QSH (1,-7)
Colors of the trajectories are relative to different helical flux values.
Trapped ion orbit
Helical banana size: 0.5 - 5cm 300 – 1200eV
Poloidal banana width: 0.2 cm (800 eV)
For a given energy E the banana size of an impurity with atomic mass A is proportional to :
Electrons experience very small neoclassical effects : their banana orbits are less than few mm still at 800 eV.
v (E/A)1/2
RFX-mod Workshop, Padova 20-22/01/ 2009
Local diffusion coefficient evaluation
DDii is evaluated locally too because: is evaluated locally too because:
-it may vary inside the helical domain
-the approximations due to the non linear density distribution are avoided
rr MM
MM
0
t
rD tloc
2
0
)(lim
(r)
² (c
m²)
t(ms)
Trapped, passing, uniform pitch
particles show different slopes for
the relation r² versus time t.
M
Dlo
c (m
² /s)
Almost constant inside the helical structure: 1-5m²/s
particles deposition
RFX-mod Workshop, Padova 20-22/01/ 2009
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:
(R,Z, M, ,
Z
Rmode (1,-7)
+ B0
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 Marrelli’s talk)
M
RFX-mod Workshop, Padova 20-22/01/ 2009
The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH.
Ns
n nnn bb
2
2,1
2,1 /
1k
n=8-24 x k
Secondary modes spectrum is multiplied by a constant k; this changes
the Ns parameter:
Effect of secondary modes on De
De
Di
Ns
m²/
s
De increases rapidily 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. (SH: Ns=1, k=0)
Input to ORBIT
De< 0.1m2/s
De> 10m2/s
RFX-mod Workshop, Padova 20-22/01/ 2009
Correlation of D with experimental magnetic perturbations
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.
nm
arn rdrbb
,1 0
2,1sec )(
a
rdom rdrbb
0
27,1 )(
Di,QSH (m²/s) Di,QSH (m²/s)
Di,SH/Di,QSH
Di,QSH (m²/s)
sec/ bbdom
secb (mT)sec/ bbdom
domb (mT)
Best QSH are very close to the corresponding SH case
for ions
RFX-mod Workshop, Padova 20-22/01/ 2009
v
v/
dt
dtest particle background :
are mono-energetic and energy is conserved during collision mechanisms
particles change their guiding center position randomly by a gyroradius
particles change randomly also their velocity direction with respect to B
pitch angle:
)cos(||||
Bv
Bv
B
v
v
BrL
Interaction of test particles with the plasma background
main gas ions
electrons
impurities CVI
OVII
H/
e/
X/
XeH ///
E(eV)
tor
RFX-mod>1.2MA e-
H+
[3]
[3] B.A.Trubnikov, Rev. Plasma Phys. 1, (105), 1965 5
RFX-mod Workshop, Padova 20-22/01/ 2009
~1 ~
PASSINGPASSING ions witharewell confined in the high T
helical structure
low collisionality and residual chaos
TRAPPEDTRAPPED particles diffuse rapidly across the
helical structure
poloidal and helical trapping
banana orbits
pitch:
)cos(||||
Bv
Bv
B
v
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.
Dpas~0.02-0.1 m²/s
small thermal drift
follow helical field lines
T0.5 - 5cm @ (300 – 1200eV)
width:
Dtrap~2-6 m²/s
Dtrap/Dpas ~ 100 !!
RFX-mod Workshop, Padova 20-22/01/ 2009
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]
1D collisional-radiative impurity transport code reproduces the emission pattern.
While hydrogen injection by pellet shows an improvement of confinement inside the island, this is not observed for impurities.
t(s)
with DQSH~20m²/s very close to the one typical of MH case.
experiment
simulated
r/a
D(m²/s)
v(m/s)
D and v radial profiles to be implemented in the code for a good matching with experimental data:
[3] L.Carraro, submitted to Nucl. Fusion
20
0
RFX-mod Workshop, Padova 20-22/01/ 2009
p
Ratio of Di and De at several level of secondary modes and more temperatures:
De/
Di (
m²/
s)
1keV0.7keV0.4keV
Ns~1 (pure SH case):
1.03<Ns <1.1:
Electrons are confined in the magnetic island
De and Di are of the same order (at 700eV)
Ns >1.1: De rapidly increase with the level of secondary modes
De<<Di
De~Di
De>>Di
Ns
RFX-mod Workshop, Padova 20-22/01/ 2009
The level of secondary modes significantly affects the diffusion of electrons in high temperature QSH:
n=8-24 x k
Effect of secondary modes on De
The ion diffusion coefficient depends slightly on the level of secondary modes…
De
Di
Ns
m²/
s
… but experimentally the global ambipolar Dglobal ambipolar D will be a function of the Ns parameter:D
e(m
²/s)
k
SH
MH
Typical RFX-mod
QSH
De~ 3m2/sDe< 0.1m2/s
De> 12m2/s
Ns
n nnn bb
2
2,1
2,1 /
1k
RFX-mod Workshop, Padova 20-22/01/ 2009
nD
n
SourceSource
helical magnetic flux M(X,Z) associated to each point inside
the helix (1,-7) [2]
1.Helical flux used as new radial flux coordinate
M
2.Transport inside the helical structure
particles distribution over the helical domain
is recorded
3.Evaluation of a diffusion coefficient D
Test particle approach in helical RFX-mod plasmas
[2]Gobbin et al., Phys. Plasmas 14, (072305), 2007
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.
secondary modes
collisions with plasma background
with:
RFX-mod Workshop, Padova 20-22/01/ 2009
Ion Di in SH and QSH
The effect of residual chaos in QSH does not affect dramatically Di
Electron diffusion coefficients inside the helical core show a very different behavior in SH and QSH regimes:
Electron De in SH and QSH
x10
De,QSH10·De,SH
Note that in QSH (@Te>800eV):
De,QSH 2-3 m²/s Di,QSH
Ion and electron diffusion coefficients in SH and QSH
Di,QSH2.5-4 m2/s
Di,QSH2Di,SH
@Ti = 500-1000 eV