Transcript Document

13rd RFP Workshop, 2008 October 9-11, Stockholm, Sweden
Numerical studies of particle transport
mechanisms in RFX-mod low chaos regimes
M.Gobbin, L.Marrelli, L.Carraro, G.Spizzo
Consorzio RFX, Associazione Euratom-Enea sulla Fusione, Padova, Italy
R.B. White
Princeton Plasma Physics Laboratory, Princeton, NJ, USA
RFP Workshop, Stockholm 9-11 /10/ 2008
Contents
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.
[0]R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. RFP Workshop, Stockholm 9-11 /10/ 2008
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Contents
High-current RFX-mod plasmas: main parameters, thermal structures
and magnetic topology.
Particle transport by the ORBIT 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.
RFP Workshop, Stockholm 9-11 /10/ 2008
Helical structure in RFX-mod plasmas
Large helical structures appear in
high current RFX-mod plasmas:
Ip(MA)
1.5MA
Main parameters range
Ip  1.21.5 MA
F  - 0.02
ne  1 4·1019m-3
Ns 1.05
Ns


n  b12,n / n b12,n 
1
bf(mT)
QSH
F
b1,7
b1,8
b1,9
(ms)
RFP Workshop, Stockholm 9-11 /10/ 2008
2
Helical structure in RFX-mod plasmas
Large helical structures appear in
high current RFX-mod plasmas:
Ip(MA)
1.5MA
Main parameters range
Ip  1.21.5 MA
F  - 0.02
ne  1 4·1019m-3
Ns 1.05
Ns


n  b12,n / n b12,n 
1
1keV
bf(mT)
QSH
F
b1,7
b1,8
b1,9
Significant electron temperature
radial profile in the plasma core:
25-50% of plasma volume
(ms)
RFP Workshop, Stockholm 9-11 /10/ 2008
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Magnetic topology related to QSH states
Plasma magnetic topology:
Poloidal Poincarè
d
p
d=20-30 cm
Ip=1.5MA
RFP Workshop, Stockholm 9-11 /10/ 2008
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Magnetic topology related to QSH states
Plasma magnetic topology:
Small thermal structures:
Poloidal Poincarè
Peaked Te profiles
d
p
d=20-30 cm
Ip=1.5MA
Smaller helical
structures:
-reduced stickyness
-localized magnetic
island
-common at low Ip
RFP Workshop, Stockholm 9-11 /10/ 2008
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Magnetic topology related to QSH states
Plasma magnetic topology:
Small thermal structures:
Poloidal Poincarè
Peaked Te profiles
d
p
d=20-30 cm
Ip=1.5MA
Smaller helical
structures:
-reduced stickyness
-localized magnetic
island
m=1 spectrum
SH Poincarè
-common at low Ip
SH (1,-7)
SHAx states for
high values of
the dominant
mode [1].
Need to perform particle and energy
transport simulations in a helical
shaped geometry:
-helical equilibrium magnetic field
helical field
[1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)
RFP Workshop, Stockholm 9-11 /10/ 2008
- superimposition of the residual chaos
3
Contents
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.
[0]R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984. RFP Workshop, Stockholm 9-11 /10/ 2008
Particle transport simulation: the method
1.Helical geometry
reconstruction:
2.Transport inside the
helical structure
yM
Source
3.D estimation
   D  n
n
ions and electrons

Loss Surface
test particles deposited
in the o-point
in SH and QSH
different energy
stationary regime achieved
helical magnetic flux yM(x,z,f)
associated to each point inside
the helix (1,-7) [2]
[2]Gobbin et al., Phys. Plasmas 14, (072305),
inclusion of collisions
with the background
impurities transport
particle distribution
on helical domain
RFP Workshop, Stockholm 9-11 /10/ 2008
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Interaction of test particles with the plasma background
dv
   /  v
dt
test particle   background  :
 are mono-energetic and energy is
conserved during collision mechanisms
 particles change their guiding center
position randomly by a gyroradius
rL
B

 particles change randomly also their
velocity direction with respect to B
v
v
pitch   v  B  cos( )
| v || B |
angle:


B
RFP Workshop, Stockholm 9-11 /10/ 2008
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Interaction of test particles with the plasma background
dv
   /  v
dt
test particle   background  :

 / H
main gas ions

electrons   / e 
 are mono-energetic and energy is
conserved during collision mechanisms
 particles change their guiding center
rL
 / X
OVII
     / H   / e   / X

 particles change randomly also their
velocity direction with respect to B
ttor
RFX-mod
>1.2MA

[3]
H+
e-
v
v
[3] B.A.Trubnikov, Rev. Plasma Phys. 1, (105), 1965

B

pitch   v  B  cos( )
| v || B |
angle:
CVI
impurities
position randomly by a gyroradius


B
RFP Workshop, Stockholm 9-11 /10/ 2008
E(eV)
5
Contents
High-current RFX-mod plasmas: main parameters, thermal structures
and magnetic topology.
Particle transport by the ORBIT 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.
RFP Workshop, Stockholm 9-11 /10/ 2008
Particles distribution inside the helical core
Transport simulations for ions at
different temperatures in QSH:
Flux of ions and
electrons at
different energy

# lost
S out t
D=const assumes a linear trend
   D n for density as function of yM

RFP Workshop, Stockholm 9-11 /10/ 2008
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Particles distribution inside the helical core
Transport simulations for ions at
different temperatures in QSH:
Flux of ions and
electrons at
different energy

# lost
S out t
D=const assumes a linear trend
   D n for density as function of yM

no linear distribution in helical
flux above 500 eV
reduction of
collisionality
reduced
secondary modes
RFP Workshop, Stockholm 9-11 /10/ 2008
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Particles distribution inside the helical core
Transport simulations for ions at
different temperatures in QSH:
Flux of ions and
electrons at
different energy

# lost
S out t
   D  n Estimate of a range values for D
no linear distribution in helical
flux above 500 eV
reduction of
collisionality
Dmin 

(n) min
Dmax 

(n) max
reduced
secondary modes
RFP Workshop, Stockholm 9-11 /10/ 2008
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Ion and electron diffusion coefficients in SH and QSH
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
RFP Workshop, Stockholm 9-11 /10/ 2008
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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
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
RFP Workshop, Stockholm 9-11 /10/ 2008
Electron diffusion coefficient inside the
helical core show a very different
behavior in SH and QSH regimes:
De,QSH10·De,S
H
Note that in QSH (800eV):
Di,QSH1-1.5 De,QSH
7
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)
MH
Typical RFX-mod
QSH
SH
k
RFP Workshop, Stockholm 9-11 /10/ 2008
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Ambipolar transport in high temperature QSH plasma
n=8-24 x k
MH
De(m²/s)
Ratio of Di and De at several level of
secondary modes and more temperatures:
De/Di (m²/s)
Transport simulation performed for
different level of secondary modes:
1keV
0.7keV
0.4keV
k
Ambipolar transport would take to: De/Di=1
Typical RFX-mod
For typical QSH in RFX-mod (k 1) De and Di are
about the same even without the implementantion
of an ambipolar electric field in the code
QSH
SH
At lower k electron diffusion is strongly
reduced while at higher k strongly enhanced
k
Dependence on temperature
RFP Workshop, Stockholm 9-11 /10/ 2008
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Ambipolar transport in high temperature QSH plasma
Ratio of Di and De at several level of
secondary modes and more temperatures:
De/Di (m²/s)
Transport simulation performed for
different level of secondary modes:
n=8-24 x k
De(m²/s)
MH
1keV
0.7keV
0.4keV
Ns
Ns~1 (pure SH case):
Typical RFX-mod
Electrons are confined
in the magnetic island
De<<Di
QSH
1.03<Ns <1.1:
De and Di are of the
same order (at 700eV)
De~Di
SH
k
Ns >1.1:
RFP Workshop, Stockholm 9-11 /10/ 2008
De rapidly increase with the
level of secondary modes
De>>Di
8
Contents
High-current RFX-mod plasmas: main parameters, thermal structures
and magnetic topology.
Particle transport by the ORBIT 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.
RFP Workshop, Stockholm 9-11 /10/ 2008
Dynamic of trapped and passing ions in helical structures
Only trapped ions in
the tail of the density
distribution [5]
PITCH ANGLE
DISTRIBUTION
Dpas/Dtrap~0.01
Ion orbits in
helical structures
Passing Ion
~1
Poloidal Trapping
0.4
Banana width:
(800 eV)
0.2 cm
Helical Trapping
0.4
Banana width: 0.5 - 5cm
(300 – 1200eV)
(from Predebon et al., PRL 93 145001, 2004)
[5] M.Gobbin et al., poster ICPP Conf. 2008
RFP Workshop, Stockholm 9-11 /10/ 2008
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Dynamic of trapped and passing ions in helical
structures
Only trapped ions in
the tail of the density
distribution
PITCH ANGLE
DISTRIBUTION
Dpas/Dtrap~0.01
Simulations at
800 eV using
only passing or
only trapped
ions.
Ion orbits in
helical structures
Passing Ion
~1
Poloidal Trapping
0.4
PASSING particles with
 1 well confined
TRAPPED particles diffuse
Banana width:
(800 eV)
0.2 cm
across the helical structure
follow helical field lines
Helical trapping
SMALL THERMAL DRIFT
Poloidal trapping
Few Losses because
of (few) collisions
Main contribution to D
Helical Trapping
0.4
Banana width: 0.5 - 5cm
(300 – 1200eV)
(from Predebon et al., PRL 93 145001, 2004)
RFP Workshop, Stockholm 9-11 /10/ 2008
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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:
~0.7kHz
Ti~800eV
ne~3·1019m-3
TRAPPED
PASSING
:
:
No
significant
dependence
on 
almost linear ions distribution
for low pitch angle values

as  approaches to 1,
ions are gradually less
moved from their initial
helical flux location
RFP Workshop, Stockholm 9-11 /10/ 2008
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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:
~0.7kHz
Ti~800eV
ne~3·1019m-3
TRAPPED
PASSING
:
:
No
significant
dependence
on 

Note that:
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
almost linear ions distribution
for low pitch angle values
as  approaches to 1,
ions are gradually less
moved from their initial
helical flux location
RFP Workshop, Stockholm 9-11 /10/ 2008
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Contents
High-current RFX-mod plasmas: main parameters, thermal structures
and magnetic topology.
Particle transport by the ORBIT 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.
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]
D and v radial profiles to be implemented in the
code for a good matching with experimental data:
D(m²/s)
20
simulated
experiment
0
v(m/s)
r/a
with DQSH~20m²/s very close to
the one typical of MH case.
t(s)
1D
collisional-radiative
impurity
transport
code
reproduces
the
emission pattern.
[5] L.Carraro, submitted for IAEA Conf. 2008
RFP Workshop, Stockholm 9-11 /10/ 2008
While hydrogen injection by pellet shows
an improvement of confinement inside the
island, this is not observed for impurities.
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Impurities transport : a test particle approach
Investigation by ORBIT both in MH and QSH regimes:
D (m²/s)
RFX-MOD @ 600eV
Banana
regimes
ne=nH+=3·1019m-3
Te=800eV
TNi=600eV=Ti
nNi=0.1% ne
TOVI=600eV=TCV
nOVI=nCVI=1% ne
Fully
Collisional
Collisions:
Plateau
Collisions for toroidal transit
Ni:
25/toroidal transit
H+:
0.1/toroidal transit
MH
QSH
DNi~ 0.5-2m²/s
DH+~ 20m²/s
DNi~ 0.5-2m²/s
DH+~ 0.4-1.5m²/s
Qualitative agreement between experiment and simulation.
Differences on the order of DNi to be further investigated.
RFP Workshop, Stockholm 9-11 /10/ 2008
12
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.
RFP Workshop, Stockholm 9-11 /10/ 2008
13
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
RFP Workshop, Stockholm 9-11 /10/ 2008
13
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.
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).
RFP Workshop, Stockholm 9-11 /10/ 2008
13
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.
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).
Future Work
RFP Workshop, Stockholm 9-11 /10/ 2008
To higher NS values and for NS=1 the
ambipolar field should be implemented.
(In the range ~ 400-1000eV)
13
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.
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.
RFP Workshop, Stockholm 9-11 /10/ 2008
13
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.
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.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of
collision mechanisms on magnetic perturbations effect.
RFP Workshop, Stockholm 9-11 /10/ 2008
13
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.
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.
Nichel diffusion coefficients in QSH and MH are about the same. Dominance of
collision mechanisms on magnetic perturbations effect.
Future Work
RFP Workshop, Stockholm 9-11 /10/ 2008
Further investigation to understand
the difference on the absolute
values found.
13
MORE....
RFP Workshop, Stockholm 9-11 /10/ 2008
Helical magnetic flux definition
Magnetic flux from Poincaré:
Helical flux contour on a
poloidal section :
yM/yMloss
A  y y p   1,7 g  1,7 I
y M   B  dS   A  d l
S
C
A
dl
S C
test particles deposited
in the o-point
y
M
  (y  I )dl  θ
C
RFP Workshop, Stockholm 9-11 /10/ 2008
yMo-point= 0
loss surface
yMloss
Banana orbits size increases with their energy
Passing ion orbit in a QSH (1,-7)
Trapped ion orbit
Poloidal banana width: 0.2 cm (800 eV)
Colors of the trajectories are relative
to different helical flux values.
Electrons
experience
very
small neoclassical effects :
their banana orbits are less
than few mm still at 800 eV.
RFP Workshop, Stockholm 9-11 /10/ 2008
Helical banana size: 0.5 - 5cm 300 – 1200eV
For a given energy E the banana
size of an impurity with atomic
mass A is proportional to :
v (E/A)1/2
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
y M 
y M
r
particles
deposition
r
y
M
y
M0
Dloc  limt 0
(r ) 2
t
(r)² (cm²)
Almost constant
inside the helical
structure: 1-5m²/s
Trapped, passing,
uniform pitch
particles show
different slopes for
the relation r²
versus time t.
yM
t(ms)
RFP Workshop, Stockholm 9-11 /10/ 2008
Correlation of D with experimental magnetic perturbations
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.
Di,QSH (m²/s)
a
bsec 
  (b
m 1, n 0
r
2
1, n
) rdr
bdom / bsec
Di,QSH (m²/s)
a
bdom 
bdom (mT)
r
2
(
b
)
rdr
1
,
7

0
Di,SH/Di,QSH
Best QSH are very close to
the corresponding SH case
for ions
bsec (mT)
RFP Workshop, Stockholm 9-11 /10/ 2008
bdom / bsec