Transcript Document

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
RFX-mod Workshop, Padova 20-22/01/ 2009
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
RFX-mod Workshop, Padova 20-22/01/ 2009
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
d=20-30 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.
[1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)
RFX-mod Workshop, Padova 20-22/01/ 2009
Transport in the helical core
Particle transport (main gas and impurities):
EXPERIMENT
THEORY
TEST PARTICLE APPROACH by
NUMERICAL SIMULATIONS
(ORBIT)
D values prediction for main gas
and impurities in helical states
PELLET INJECTION IN THE
HELICAL STRUCTURES
Laser Blow Off (LBO) –
IMPURITIES
TRANSPORT
Energy transport:
THEORY
EXPERIMENT
Development of new numerical
tools to solve the heat balance
equations in helical RFP plasmas.
Data from THOMSON
SCATTERING, BOLOMETRY
and other diagnostics
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.
HELICAL EQUILIBRIUM FROM
MAGNETIC TOPOLOGY
mode (1,-7) + B0
[2]Gobbin et al., Phys. Plasmas 14, (072305),
RFX-mod Workshop, Padova 20-22/01/ 2009
secondary modes
collisions with plasma
background
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.
HELICAL EQUILIBRIUM FROM
MAGNETIC TOPOLOGY
mode (1,-7) + B0
IONS
Di in SH and QSH
secondary modes
collisions with plasma
background
@Ti = 500-1000 eV
ELECTRONS
Di,QSH2Di,SH
De in SH and QSH
Di,QSH1.5-4 m2/s
x10
De in the helical core show a
very different behavior in SH
and QSH regimes:
De,QSH10·De,S
H
but:
De,QSH 2-3 m²/s Di,QSH
[2]Gobbin et al., Phys. Plasmas 14, (072305),
RFX-mod Workshop, Padova 20-22/01/ 2009
Diffusion coefficients depend on…
..the level of secondary modes:
De fast increases as Ns becomes
greater than 1 while Di is nearly
constant.
De> 10m2/s
m²/s
De
Di
De< 0.1m2/s
Ns 
1


n  b12,n / n b12,n 
(SH: Ns=1)
Ns
RFX-mod Workshop, Padova 20-22/01/ 2009
2
We expect from experimental data
a dependence of the global D on
the secondary modes amplitude.
Diffusion coefficients depend on…
..the level of secondary modes:
De fast increases as Ns becomes
greater than 1 while Di is nearly
constant.
De> 10m2/s
m²/s
De
Di
Ns 
De< 0.1m2/s
1


n  b12,n / n b12,n 
2
We expect from experimental data
a dependence of the global D on
the secondary modes amplitude.
(SH: Ns=1)
Ns
…the particles pitch angle!
~1
v
pitch:
vB

 cos( )
| v || B |

B
PASSING ions well
confined in the high T
helical structure
Dpas~0.02-0.1 m²/s
RFX-mod Workshop, Padova 20-22/01/ 2009
 ~ 0.1
TRAPPED particles
diffuse rapidly across
the helical structure
Dtrap~2-6 m²/s
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:
tQSH/tMH~2-3
ORBIT:
Di,QSH~ 2.5 – 4 m2/s
Di,MH~ 20m2/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.
- density refuelling in the hot helical structure
- estimate of the particle confinement time in MH
and QSH/SHAx regimes
PELLET:
tQSH/tMH~2-3
ORBIT:
Di,QSH~ 2.5 – 4 m2/s
Di,MH~ 20m2/s
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.
Fast CCD camera can provide informations on: - 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.
D(m²/s)
20
0
1D collisional-radiative impurity transport code
reproduces the emission pattern.
D and v radial profiles
v(m/s)
r/a
DQSH~20m²/s very close to the
one typical of MH regimes.
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
RFX-mod Workshop, Padova 20-22/01/ 2009
Ni ions diffusion in the helical core by ORBIT
Investigation by ORBIT both in MH and QSH regimes:
Collisions:
D (m²/s)
Test particles: Ni ions
RFX-MOD @ 600eV
Banana
regimes
Fully
Collisional
Ni:
25/toroidal transit
H+:
0.1/toroidal transit
Dominance of collisional effects on
magnetic topology in determining the
diffusion properties of Ni impurities.
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.
RFX-mod Workshop, Padova 20-22/01/ 2009
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) < 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 @ 1200eV
other impurities could allow
to test different regions of
collisionality;
Ne:
2 colls / tor. transit
Ar:
1.5 colls / tor. transit
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
RFX-mod Workshop, Padova 20-22/01/ 2009
Ne, Ar, Al
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 Te=Te(r);
helical flux
[5] Guo S.C., submitted to Phys. Rev. Lett. (2008)
RFX-mod Workshop, Padova 20-22/01/ 2009
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 Te=Te(r);
helical flux
The heat diffusion equation must be solved in a helical
geometry in order to evaluate the energy diffusion coefficients.
r
HELICAL
EQUILIBRIUM
DESCRIPTION
Metric tensor gij
h
Q  ncT
  Q  Pin  Pout
Semi-analytical and numerical approaches;
Adaption of stellarator codes (VMEC…)
(r, h, f)
[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 fluxsurface-averaged by an adaptation of existing
codes for stellarators, but a good description of
the helical equilibrium is first required.
Dij integration over energy (Maxwellian
distribution) allows to obtain informations on
flux-surface-averaged flows:
MONO-ENERGETIC Di,j
(by Monte-Carlo, full-f or df
schemes, variational
approach DKES)
particles flux density
energy flux density
current density
 T ,n, Er
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.
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
Nichel diffusion coefficients in QSH and MH are about the same.
Dominance of collision mechanisms on magnetic perturbations effect.
Qualitative
agreement
between
theory
and
experiments.
More investigation is required to understand the quantitative discrepancy.
RFX-mod Workshop, Padova 20-22/01/ 2009
DNi,QSH DNi,MH
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
Nichel diffusion coefficients in QSH and MH are about the same.
Dominance of collision mechanisms on magnetic perturbations effect.
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.
RFX-mod Workshop, Padova 20-22/01/ 2009
DNi,QSH DNi,MH
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
Nichel diffusion coefficients in QSH and MH are about the same.
Dominance of collision mechanisms on magnetic perturbations effect.
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.
RFX-mod Workshop, Padova 20-22/01/ 2009
DNi,QSH DNi,MH
Thanks for your attention
RFX-mod Workshop, Padova 20-22/01/ 2009
RFX-mod Workshop, Padova 20-22/01/ 2009
MORE....
RFX-mod Workshop, Padova 20-22/01/ 2009
Helical magnetic flux definition
Magnetic flux from Poincaré:
Helical flux contour on a
poloidal section :
M/Mloss
A    p   1,7 g  1,7 I
 M   B  dS   A  d l
S
C
A
dl
S C
test particles deposited
in the o-point

M
  (  I )dl  θ
C
RFX-mod Workshop, Padova 20-22/01/ 2009
Mo-point= 0
loss surface
Mloss
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.
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 :
RFX-mod Workshop, Padova 20-22/01/ 2009
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
 M 
 M
r
particles
deposition
r

M

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.
M
t(ms)
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:
M
Z
R
(R,Z,f)
h
mode (1,-7)
+
B0
(M, 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 Marrelli’s talk)
RFX-mod Workshop, Padova 20-22/01/ 2009
Effect of secondary modes on De
The level of secondary modes significantly affects the
diffusion of electrons in high temperature QSH.
Input to ORBIT
m²/s
De> 10m2/s
De
Di
De< 0.1m2/s
n=8-24 x k
Ns
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 
1


n  b12,n / n b12,n 
2
k
We expect from experimental data a
dependence of the global D on the
secondary modes.
(SH: Ns=1, k=0)
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.
Di,QSH (m²/s)
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)
RFX-mod Workshop, Padova 20-22/01/ 2009
bdom / bsec
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
RFX-mod Workshop, Padova 20-22/01/ 2009
E(eV)
5
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:
v


vB
 cos( )
| v || B |
B
PASSING ions with  1
are well confined in the
high T helical structure
TRAPPED particles
diffuse rapidly across the
helical structure
low collisionality and
residual chaos
poloidal and helical
trapping
follow helical field lines
banana orbits
small thermal drift  T
width:
0.5 - 5cm @ (300 – 1200eV)
 ~ 0.1
~1
RFX-mod Workshop, Padova 20-22/01/ 2009
Dpas~0.02-0.1 m²/s
Dtrap~2-6 m²/s
Dtrap/Dpas ~ 100 !!
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:
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.
[3] L.Carraro, submitted to Nucl. Fusion
RFX-mod Workshop, Padova 20-22/01/ 2009
While hydrogen injection by pellet shows
an improvement of confinement inside the
island, this is not observed for impurities.
De/Di (m²/s)
Ratio of Di and De at several level of
secondary modes and more temperatures:
1keV
0.7keV
0.4keV
Ns
p
Ns~1 (pure SH case):
1.03<Ns <1.1:
Ns >1.1:
RFX-mod Workshop, Padova 20-22/01/ 2009
Electrons are confined
in the magnetic island
De and Di are of the
same order (at 700eV)
De rapidly increase with the
level of secondary modes
De<<Di
De~Di
De>>Di
Effect of secondary modes on De
The level of secondary modes significantly affects
the diffusion of electrons in high temperature QSH:
De(m²/s)
MH
n=8-24 x k
De< 0.1m2/s
Typical RFX-mod
De> 12m2/s
QSH
De~ 3m2/s
SH
k
m²/s
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:
De
Di
Ns
Ns
RFX-mod Workshop, Padova 20-22/01/ 2009
1


n  b12,n / n b12,n 
2
k
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
M
with:
secondary modes
collisions with plasma
background
Source
n

helical magnetic flux M(X,Z,f)
associated to each point inside
the helix (1,-7) [2]
[2]Gobbin et al., Phys. Plasmas 14, (072305),
particles distribution
over the helical domain
is recorded
RFX-mod Workshop, Padova 20-22/01/ 2009
3.Evaluation of a
diffusion coefficient D
   D  n
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
Electron diffusion coefficients inside
the helical core show a very different
behavior in SH and QSH regimes:
@Ti = 500-1000 eV
De,QSH10·De,S
Di,QSH2Di,SH
Di,QSH2.5-4
H
Note that in QSH (@Te>800eV):
m2/s
RFX-mod Workshop, Padova 20-22/01/ 2009
De,QSH 2-3 m²/s Di,QSH