Transport in the Helical Core of the RFP

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


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.


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’


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


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



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


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


..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…


..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


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


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


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


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


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)


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)


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)


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 ,,



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.



DNi,QSH DNi,MH

Qualitative agreement between theory and experiments. More investigation is required to understand the quantitative discrepancy.








DNi,QSH DNi,MH


Energy transport and heat balance in helical geometry is still under study: a complete description of the helical equilibrium is first required.








DNi,QSH DNi,MH


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.


Thanks for your attentionThanks for your attention



MORE....


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


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


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


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


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


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


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


~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 !!


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


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


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


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



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


with:


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

Documents

Transport in the Helical Core of the RFP