Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes

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


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


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.


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


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


Poloidal PoincarèPoloidal Poincarè

p

Ip=1.5MA=20-30 cm

Plasma magnetic topology:

Magnetic topology related to QSH states

3


Small thermal structures:

Peaked Te profiles

Smaller helical structures:

-reduced stickyness

-localized magnetic island

-common at low Ip


p

Ip=1.5MA=20-30 cm



3



p

Ip=1.5MA=20-30 cm


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


[1]Lorenzini et al., Phys. Rev. Lett. 101, 025005 (2008)

Smaller helical structures:

-reduced stickyness

-localized magnetic island

-common at low Ip

3


High-current RFX-mod plasmas: main parameters, thermal structures High-current RFX-mod plasmas: main parameters, thermal structures and magnetic topology.and magnetic topology.




Contents

Particle transport by the ORBIT[0] code in the helical geometry of QSH regimes: the method.


[0] R. B. White and M. S. Chance, Phys. Fluids 27, 2455 1984.


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


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


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




Ion and Electron diffusion coefficients in QSH regimes: discussion on the ambipolar electric field implementation.



Contents



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



no linear distribution in helical flux above 500 eV

reduction of collisionality

reduced secondary modes


tS

lost

out

#


different energy

D=const assumes a linear trend for density as function of MnD

6



no linear distribution in helical flux above 500 eV

reduction of collisionality

reduced secondary modes

tS

lost

out

#


different energy

Estimate of a range values for DEstimate of a range values for D

minmin )( n

D

maxmax )( n

D


nD

6


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


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


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



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



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







Contents

Different trapped and passing particles contribution to the diffusion coefficents in high temperature helical structures.


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


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


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


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





Diffusion of impurities in MH and QSH states.


Contents



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


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


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





Future Work-Full radial profiles of temperature and density to be implemented

- Collisionality depending on particle position

13



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





To higher NS values and for NS=1 the ambipolar field should be implemented. (In the range ~ 400-1000eV)

Future Work


13




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





Nichel diffusion coefficients in QSH and MH are about the same. Dominance of collision mechanisms on magnetic perturbations effect.



13




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.




13


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


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

Numerical studies of particle transport mechanisms in RFX-mod low chaos regimes

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