RFP Workshop, Stockholm 9-11 /10/ 2008
Numerical studies of particle transport Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes mechanisms in RFX-mod low chaos regimes
M.Gobbin, L.Marrelli, L.Carraro, G.Spizzo
13rd RFP Workshop, 2008 October 9-11, Stockholm, Sweden
Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy
Princeton Plasma Physics Laboratory, Princeton, NJ, USAR.B. White
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.
Particle transport by the ORBIT[0] code in the helical geometry of QSH regimes: the method.
Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation.
Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.
Diffusion of impurities in MH and QSH states.
Summary and Conclusions.
Contents
[0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. 1
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.
Particle transport by the ORBIT code in the helical geometry of QSH Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. regimes: the method.
Ion and Electron diffusion coefficients in QSH regimes: discussion on Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. the ambipolar electric field implementation.
Diffusion of impurities in MH and QSH states.Diffusion of impurities in MH and QSH states.
Summary and Conclusions.Summary and Conclusions.
Contents
Different trapped and passing particles contribution to the diffusion Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.coefficents in high temperature helical structures.
RFP Workshop, Stockholm 9-11 /10/ 2008
Large helical structures appear in high current RFX-mod plasmas:
1.5MA
QSH
b1,7b1,8b1,9
I p(M
A)
b(
mT
)F
(ms)
Helical structure in RFX-mod plasmas
Ip 1.21.5 MA
ne 1 4·1019m-3
F - 0.02
Ns 1.05
Main parameters range
2
Ns1
2,1
2,1 /
n nnn bb
RFP Workshop, Stockholm 9-11 /10/ 2008
Helical structure in RFX-mod plasmas
Large helical structures appear in high current RFX-mod plasmas:
1.5MA
QSH
b1,7b1,8b1,9
I p(M
A)
b(
mT
)F
(ms)
Ip 1.21.5 MA
ne 1 4·1019m-3
F - 0.02
Ns 1.05
Significant electron temperature radial profile in the plasma core:
25-50% of plasma volume
1keV
Main parameters range
2
Ns1
2,1
2,1 /
n nnn bb
RFP Workshop, Stockholm 9-11 /10/ 2008
Poloidal PoincarèPoloidal Poincarè
p
Ip=1.5MA=20-30 cm
Plasma magnetic topology:
Magnetic topology related to QSH states
3
RFP Workshop, Stockholm 9-11 /10/ 2008
Small thermal structures:
Peaked Te profiles
Smaller helical structures:
-reduced stickyness
-localized magnetic island
-common at low Ip
Poloidal PoincarèPoloidal Poincarè
p
Ip=1.5MA=20-30 cm
Plasma magnetic topology:
Magnetic topology related to QSH states
3
RFP Workshop, Stockholm 9-11 /10/ 2008
Poloidal PoincarèPoloidal Poincarè
p
Ip=1.5MA=20-30 cm
Plasma magnetic topology:
SHAx states for high values of the dominant
mode [1].
helical field
SH (1,-7)
Small thermal structures:
Peaked Te profiles
m=1 spectrumm=1 spectrum SH PoincarèSH Poincarè
Need to perform particle and energy transport simulations in a helical
shaped geometry:
-helical equilibrium magnetic field
- superimposition of the residual chaos
Magnetic topology related to QSH states
[1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)
Smaller helical structures:
-reduced stickyness
-localized magnetic island
-common at low Ip
3
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.and magnetic topology.
Ion and Electron diffusion coefficients in QSH regimes: discussion on Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. the ambipolar electric field implementation.
Diffusion of impurities in MH and QSH states.Diffusion of impurities in MH and QSH states.
Summary and Conclusions.Summary and Conclusions.
Contents
Particle transport by the ORBIT[0] code in the helical geometry of QSH regimes: the method.
Different trapped and passing particles contribution to the diffusion Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.coefficents in high temperature helical structures.
[0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984.
RFP Workshop, Stockholm 9-11 /10/ 2008
nD
Loss SurfaceLoss Surface
n
SourceSource
helical magnetic flux M(x,z) associated to each point inside
the helix (1,-7) [2]
1.Helical geometry reconstruction:
M
2.Transport inside the helical structure
test particles deposited in the o-point
stationary regime achieved
particle distribution on helical domain
inclusion of collisions with the background
3.D estimation
ions and electrons
in SH and QSH
different energy
impurities transport
Particle transport simulation: the method
[2]Gobbin et al., Phys. Plasmas 14, (072305), 2007
4
RFP Workshop, Stockholm 9-11 /10/ 2008
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
5
RFP Workshop, Stockholm 9-11 /10/ 2008
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
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.and magnetic topology.
Particle transport by the ORBIT code in the helical geometry of QSH Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. regimes: the method.
Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation.
Diffusion of impurities in MH and QSH states.Diffusion of impurities in MH and QSH states.
Summary and Conclusions.Summary and Conclusions.
Contents
Different trapped and passing particles contribution to the diffusion Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.coefficents in high temperature helical structures.
RFP Workshop, Stockholm 9-11 /10/ 2008
Transport simulations for ions at different temperatures in QSH:
Particles distribution inside the helical core
tS
lost
out
#
Flux of ions and electrons at
different energy
D=const assumes a linear trend for density as function of MnD
6
RFP Workshop, Stockholm 9-11 /10/ 2008
Transport simulations for ions at different temperatures in QSH:
no linear distribution in helical flux above 500 eV
reduction of collisionality
reduced secondary modes
Particles distribution inside the helical core
tS
lost
out
#
Flux of ions and electrons at
different energy
D=const assumes a linear trend for density as function of MnD
6
RFP Workshop, Stockholm 9-11 /10/ 2008
Transport simulations for ions at different temperatures in QSH:
no linear distribution in helical flux above 500 eV
reduction of collisionality
reduced secondary modes
tS
lost
out
#
Flux of ions and electrons at
different energy
Estimate of a range values for DEstimate of a range values for D
minmin )( n
D
maxmax )( n
D
Particles distribution inside the helical core
nD
6
RFP Workshop, Stockholm 9-11 /10/ 2008
Ion Di in SH and QSH
The effect of residual chaos in QSH does not affect dramatically Di
A decrease of Di is expected at higher temperatures inside the
helical core both in SH and QSH
<500eV dominance of drift effects T
>500eV strong collisionality reduction 1/T3/2
Ion and electron diffusion coefficients in SH and QSH
7
RFP Workshop, Stockholm 9-11 /10/ 2008
Ion Di in SH and QSH
The effect of residual chaos in QSH does not affect dramatically Di
A decrease of Di is expected at higher temperatures inside the
helical core both in SH and QSH
<500eV dominance of drift effects T
>500eV strong collisionality reduction 1/T3/2
Electron diffusion coefficient 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 (800eV):
Di,QSH1-1.5 De,QSH
Ion and electron diffusion coefficients in SH and QSH
7
RFP Workshop, Stockholm 9-11 /10/ 2008
Is the ambipolar electric field important in QSH?
Transport simulation performed for different level of secondary modes:
n=8-24 x k
De(
m²/
s)
k
SH
MH
Typical RFX-mod
QSH
8
RFP Workshop, Stockholm 9-11 /10/ 2008
Transport simulation performed for different level of secondary modes:
n=8-24 x k
De(
m²/
s)
k
SH
MH
Typical RFX-mod
QSH
Ratio of Di and De at several level of secondary modes and more temperatures:
De/
Di (
m²/
s)
1keV0.7keV0.4keV
Ambipolar transport would take to: De/Di=1
For typical QSH in RFX-mod (k1) De and Di are about the same even without the
implementantion of an ambipolar electric field in the code
At lower k electron diffusion is strongly reduced while at higher k strongly enhanced
Dependence on temperature
k
Ambipolar transport in high temperature QSH plasma
8
RFP Workshop, Stockholm 9-11 /10/ 2008
Transport simulation performed for different level of secondary modes:
n=8-24 x k
De(
m²/
s)
k
SH
MH
Typical RFX-mod
QSH
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
Ambipolar transport in high temperature QSH plasma
8
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.and magnetic topology.
Particle transport by the ORBIT code in the helical geometry of QSH Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. regimes: the method.
Ion and Electron diffusion coefficients in QSH regimes: discussion on Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. the ambipolar electric field implementation.
Diffusion of impurities in MH and QSH states.Diffusion of impurities in MH and QSH states.
Summary and Conclusions.Summary and Conclusions.
Contents
Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.
RFP Workshop, Stockholm 9-11 /10/ 2008
Dynamic of trapped and passing ions in helical structures
PITCH ANGLE PITCH ANGLE DISTRIBUTION DISTRIBUTION Only trapped ions in
the tail of the density distribution [5]
Dpas/Dtrap~0.01
[5] M.Gobbin et al., poster ICPP Conf. 2008 9
Banana width:
Poloidal Trapping
Banana width: (800 eV)
0.2 cm
(from Predebon et al., PRL 93 145001, 2004)
Helical Trapping
0.5 - 5cm(300 – 1200eV)
Passing Ion
~1
Ion orbits in Ion orbits in helical helical
structuresstructures
RFP Workshop, Stockholm 9-11 /10/ 2008
PITCH ANGLE PITCH ANGLE DISTRIBUTION DISTRIBUTION
Simulations at 800 eV using
only passing or only trapped
ions.
Dpas/Dtrap~0.01Only trapped ions in the tail of the density
distribution
PASSINGPASSING particles withwell confined
SMALL THERMAL DRIFT
Few Losses because of (few) collisions
TRAPPEDTRAPPED particles diffuse across the helical structure
Dynamic of trapped and passing ions in helical structures
follow helical field lines Helical trapping
Poloidal trapping
Main contribution to D
9
Banana width:
Poloidal Trapping
Banana width: (800 eV)
0.2 cm
(from Predebon et al., PRL 93 145001, 2004)
Helical Trapping
0.5 - 5cm(300 – 1200eV)
Passing Ion
~1
Ion orbits in Ion orbits in helical helical
structuresstructures
RFP Workshop, Stockholm 9-11 /10/ 2008
Effect of the particles pitch angle on density distribution
: :
TRAPPEDTRAPPED
almost linear ions distribution for low pitch angle values
PASSINGPASSING
No significant
dependence on
as approaches to 1, ions are gradually less moved from their initial
helical flux location
Simulations with selected values of pitch angle range have been recently performed, with the following plasma parameters:
Ti~800eV ne~3·1019m-3~0.7kHz
10
RFP Workshop, Stockholm 9-11 /10/ 2008
Effect of the particles pitch angle on density distribution
Simulations with selected values of pitch angle range have been recently performed, with the following plasma parameters:
: :
TRAPPEDTRAPPED
almost linear ions distribution for low pitch angle values
PASSINGPASSING Note that:Note that:
Ti~800eV ne~3·1019m-3~0.7kHz
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
No significant
dependence on
as approaches to 1, ions are gradually less moved from their initial
helical flux location
10
RFP Workshop, Stockholm 9-11 /10/ 2008
High-current RFX-mod plasmas: main parameters, thermal structures High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.and magnetic topology.
Particle transport by the ORBIT code in the helical geometry of QSH Particle transport by the ORBIT code in the helical geometry of QSH regimes: the method. regimes: the method.
Ion and Electron diffusion coefficients in QSH regimes: discussion on Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation. the ambipolar electric field implementation.
Diffusion of impurities in MH and QSH states.
Summary and Conclusions.Summary and Conclusions.
Contents
Different trapped and passing particles contribution to the diffusion Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.coefficents in high temperature helical structures.
RFP Workshop, Stockholm 9-11 /10/ 2008
Impurities transport in QSH and MH
Experiments of laser blow off in QSH plasmas have been performed recently.
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.[5]
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:
[5] L.Carraro, submitted for IAEA Conf. 2008 11
20
0
RFP Workshop, Stockholm 9-11 /10/ 2008
DNi~ 0.5-2m²/s
DH+~ 20m²/s
MH
DNi~ 0.5-2m²/s
DH+~ 0.4-1.5m²/s
QSH
Qualitative agreement between experiment and simulation.
Differences on the order of DNi to be further investigated.
Impurities transport : a test particle approach
Collisions:Collisions:
25/toroidal transitNi:Ni:
0.1/toroidal transitHH++::
TNi=600eV=Ti
Te=800eV
TOVI=600eV=TCVnOVI=nCVI=1% ne
ne=nH+=3·1019m-3
nNi=0.1% ne
D (
m²/
s)
Collisions for toroidal transit
RFX-MOD @ 600eV
Investigation by ORBIT both in MH and QSH regimes:
Fully Collisional
Banana regimes
Plateau
12
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
Future Work-Full radial profiles of temperature and density to be implemented
- Collisionality depending on particle position
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05).
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
To higher NS values and for NS=1 the ambipolar field should be implemented. (In the range ~ 400-1000eV)
Future Work
The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05).
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05).
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.
The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05).
In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario.
13
RFP Workshop, Stockholm 9-11 /10/ 2008
Conclusions and future work
Strong reduction of the diffusion coefficients for the main gas in the large helical structure of high current RFX-mod plasmas.
Future Work Further investigation to understand the difference on the absolute values found.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.
Transport simulations are performed in a helical geometry defined by the dominant tearing mode m=1,n=-7 by using mono-energetic test particles.
The residual magnetic chaos and collisions are enough to ensure an ambipolar transport in QSH at high current between 400 and 1000 eV (Ns~1.05).
In high temperature low magnetic chaos QSH: passing ions well confined, trapped ions mostly contribute to transport. An opposite behavior respect to a MH scenario.
13
RFP Workshop, Stockholm 9-11 /10/ 2008
MORE....
RFP Workshop, Stockholm 9-11 /10/ 2008
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
RFP Workshop, Stockholm 9-11 /10/ 2008
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
RFP Workshop, Stockholm 9-11 /10/ 2008
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
RFP Workshop, Stockholm 9-11 /10/ 2008
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