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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.

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slide1

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

slide2

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.

1

[0]

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

RFP Workshop, Stockholm 9-11 /10/ 2008

slide3

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

slide4

Ns

Helical structure in RFX-mod plasmas

Main parameters range

Large helical structures appear in high current RFX-mod plasmas:

Ip 1.21.5 MA

F  - 0.02

1.5MA

Ns 1.05

ne 1 4·1019m-3

Ip(MA)

QSH

b1,7

bf(mT)

b1,8

b1,9

F

(ms)

2

RFP Workshop, Stockholm 9-11 /10/ 2008

slide5

Ns

Helical structure in RFX-mod plasmas

Main parameters range

Large helical structures appear in high current RFX-mod plasmas:

Ip 1.21.5 MA

F  - 0.02

1.5MA

Ns 1.05

ne 1 4·1019m-3

Ip(MA)

1keV

QSH

b1,7

bf(mT)

b1,8

b1,9

F

Significant electron temperature radial profile in the plasma core:

25-50% of plasma volume

(ms)

2

RFP Workshop, Stockholm 9-11 /10/ 2008

slide6

Magnetic topology related to QSH states

Plasma magnetic topology:

Poloidal Poincarè

d

p

d=20-30 cm

Ip=1.5MA

3

RFP Workshop, Stockholm 9-11 /10/ 2008

slide7

Magnetic topology related to QSH states

Plasma magnetic topology:

Small thermal structures:

Poloidal Poincarè

Peaked Te profiles

d

Smaller helical structures:

-reduced stickyness

-localized magnetic island

-common at low Ip

p

d=20-30 cm

Ip=1.5MA

3

RFP Workshop, Stockholm 9-11 /10/ 2008

slide8

Magnetic topology related to QSH states

Plasma magnetic topology:

Small thermal structures:

Poloidal Poincarè

Peaked Te profiles

d

Smaller helical structures:

-reduced stickyness

-localized magnetic island

-common at low Ip

p

d=20-30 cm

Ip=1.5MA

m=1 spectrum

SH Poincarè

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
  • - superimposition of the residual chaos

helical field

3

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

RFP Workshop, Stockholm 9-11 /10/ 2008

slide9

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

slide10

Particle transport simulation: the method

1.Helical geometryreconstruction:

2.Transport inside the helical structure

3.D estimation

y M

Source

n

ions and electrons

G

in SH and QSH

Loss Surface

different energy

test particles deposited in the o-point

stationary regime achieved

impurities transport

inclusion of collisions with the background

helical magnetic flux yM(x,z,f) associated to each point inside the helix (1,-7) [2]

particle distribution on helical domain

4

[2]Gobbin et al., Phys. Plasmas 14, (072305), 2007

RFP Workshop, Stockholm 9-11 /10/ 2008

slide11

rL

B

b

va

va

q

b

B

Interaction of test particles with the plasma background

test particlea backgroundb:

aare mono-energetic and energy is conserved during collision mechanisms

aparticles change their guiding center position randomly by a gyroradius

aparticles change randomly also their velocity direction with respect to B

pitch

angle:

5

RFP Workshop, Stockholm 9-11 /10/ 2008

slide12

a

main gas ions

electrons

CVI

OVII

impurities

rL

B

b

nttor

H+

RFX-mod

>1.2MA

e-

va

va

q

b

B

E(eV)

Interaction of test particles with the plasma background

test particlea backgroundb:

aare mono-energetic and energy is conserved during collision mechanisms

aparticles change their guiding center position randomly by a gyroradius

[3]

aparticles change randomly also their velocity direction with respect to B

pitch

angle:

5

[3] B.A.Trubnikov, Rev. Plasma Phys. 1, (105), 1965

RFP Workshop, Stockholm 9-11 /10/ 2008

slide13

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

slide14

Particles distribution inside the helical core

Transport simulations for ions at different temperatures in QSH:

Flux of ions and electrons at different energy

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

6

RFP Workshop, Stockholm 9-11 /10/ 2008

slide15

Particles distribution inside the helical core

Transport simulations for ions at different temperatures in QSH:

Flux of ions and electrons at different energy

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

no linear distribution in helical flux above 500 eV

reduction of collisionality

reduced secondary modes

6

RFP Workshop, Stockholm 9-11 /10/ 2008

slide16

Particles distribution inside the helical core

Transport simulations for ions at different temperatures in QSH:

Flux of ions and electrons at different energy

Estimate of a range values for D

no linear distribution in helical flux above 500 eV

reduction of collisionality

reduced secondary modes

6

RFP Workshop, Stockholm 9-11 /10/ 2008

slide17

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

Ion and electron diffusion coefficients in SH and QSH

Ion Di in SH and QSH

<500eV dominance of drift effects  T

>500eV strong collisionality reduction  1/T3/2

7

RFP Workshop, Stockholm 9-11 /10/ 2008

slide18

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

Ion and electron diffusion coefficients in SH and QSH

Ion Di in SH and QSH

Electron De in SH and QSH

x10

Electron diffusion coefficient inside the helical core show a very different behavior in SH and QSH regimes:

De,QSH10·De,SH

Note that in QSH (800eV):

<500eV dominance of drift effects  T

Di,QSH1-1.5 De,QSH

>500eV strong collisionality reduction  1/T3/2

7

RFP Workshop, Stockholm 9-11 /10/ 2008

slide19

Is the ambipolar electric field important in QSH?

Transport simulation performed for different level of secondary modes:

n=8-24 x k

MH

Typical RFX-mod QSH

De(m²/s)

SH

k

8

RFP Workshop, Stockholm 9-11 /10/ 2008

slide20

Ambipolar transport in high temperature QSH plasma

Transport simulation performed for different level of secondary modes:

Ratio of Di and De at several level of secondary modes and more temperatures:

De/Di (m²/s)

1keV

0.7keV

n=8-24 x k

0.4keV

MH

k

Ambipolar transport would take to: De/Di=1

Typical RFX-mod QSH

De(m²/s)

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

SH

At lower k electron diffusion is strongly reduced while at higher k strongly enhanced

k

Dependence on temperature

8

RFP Workshop, Stockholm 9-11 /10/ 2008

slide21

Electrons are confined in the magnetic island

Ns~1 (pure SH case):

De<<Di

De and Di are of the same order (at 700eV)

1.03<Ns<1.1:

De~Di

De rapidly increase with the level of secondary modes

De>>Di

Ns>1.1:

Ambipolar transport in high temperature QSH plasma

Transport simulation performed for different level of secondary modes:

Ratio of Di and De at several level of secondary modes and more temperatures:

De/Di (m²/s)

1keV

0.7keV

n=8-24 x k

0.4keV

MH

Ns

Typical RFX-mod QSH

De(m²/s)

SH

k

8

RFP Workshop, Stockholm 9-11 /10/ 2008

slide22

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

slide23

Ion orbits in helical structures

Passing Ion

l~1

Poloidal Trapping

l0.4

Banana width:

0.2 cm

(800 eV)

Helical Trapping

l0.4

0.5 - 5cm

(300 – 1200eV)

(from Predebon et al., PRL 93 145001, 2004)

Dynamic of trapped and passing ions in helical structures

PITCH ANGLE DISTRIBUTION

Dpas/Dtrap~0.01

Only trapped ions in the tail of the density distribution [5]

Banana width:

9

[5] M.Gobbin et al., poster ICPP Conf. 2008

RFP Workshop, Stockholm 9-11 /10/ 2008

slide24

Ion orbits in helical structures

Passing Ion

l~1

Poloidal Trapping

l0.4

Banana width:

0.2 cm

(800 eV)

Helical Trapping

l0.4

0.5 - 5cm

(300 – 1200eV)

(from Predebon et al., PRL 93 145001, 2004)

Dynamic of trapped and passing ions in helical structures

PITCH ANGLE DISTRIBUTION

Dpas/Dtrap~0.01

Only trapped ions in the tail of the density distribution

Simulations at 800 eV using only passing or only trapped ions.

PASSINGparticles with l 1well confined

TRAPPED particles diffuse across the helical structure

Helical trapping

follow helical field lines

Poloidal trapping

SMALL THERMAL DRIFT

Main contribution to D

Few Losses because of (few) collisions

Banana width:

9

RFP Workshop, Stockholm 9-11 /10/ 2008

slide25

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:

Ti~800eV

n~0.7kHz

ne~3·1019m-3

TRAPPED

PASSING

No significant dependence on l

+l

almost linear ions distribution for low pitch angle values

as lapproaches to 1, ions are gradually less moved from their initial helical flux location

10

RFP Workshop, Stockholm 9-11 /10/ 2008

slide26

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:

Ti~800eV

n~0.7kHz

ne~3·1019m-3

TRAPPED

PASSING

Note that:

Electrons experience very small neoclassical effects : their banana orbits are less than few mm still at 800 eV.

No significant dependence on l

For a given energy E the banana size of an impurity with atomic mass A is proportional to :

+l

v (E/A)1/2

almost linear ions distribution for low pitch angle values

as lapproaches to 1, ions are gradually less moved from their initial helical flux location

10

RFP Workshop, Stockholm 9-11 /10/ 2008

slide27

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

slide28

D(m²/s)

simulated

v(m/s)

experiment

r/a

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:

20

0

with DQSH~20m²/s very close to the one typical of MH case.

t(s)

While hydrogen injection by pellet shows an improvementof confinement inside the island, this is not observed for impurities.

1D collisional-radiative impurity transport code reproduces the emission pattern.

11

[5] L.Carraro, submitted for IAEA Conf. 2008

RFP Workshop, Stockholm 9-11 /10/ 2008

slide29

ne=nH+=3·1019m-3

Te=800eV

TNi=600eV=Ti

nNi=0.1% ne

nOVI=nCVI=1% ne

TOVI=600eV=TCV

QSH

MH

DNi~ 0.5-2m²/s

DNi~ 0.5-2m²/s

DH+~ 0.4-1.5m²/s

DH+~ 20m²/s

Impurities transport : a test particle approach

Investigation by ORBIT both in MH and QSH regimes:

RFX-MOD @ 600eV

D (m²/s)

Banana regimes

Fully Collisional

Collisions:

Plateau

Ni:

25/toroidal transit

0.1/toroidal transit

H+:

Collisions for toroidal transit

Qualitative agreement between experiment and simulation.

Differences on the order of DNi to be further investigated.

12

RFP Workshop, Stockholm 9-11 /10/ 2008

slide30

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

slide31

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.

  • Full radial profiles of temperature and density to be implemented
  • Collisionality depending on particle position

Future Work

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide32

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).

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide33

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

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

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide34

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.

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide35

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.

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide36

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

Further investigation to understand the difference on the absolute values found.

13

RFP Workshop, Stockholm 9-11 /10/ 2008

slide37

MORE....

RFP Workshop, Stockholm 9-11 /10/ 2008

slide38

Magnetic flux from Poincaré:

yM/yMloss

A

dl

C

S

Helical magnetic flux definition

Helical flux contour on a poloidal section :

test particles deposited in the o-point

yMo-point= 0

loss surface

yMloss

RFP Workshop, Stockholm 9-11 /10/ 2008

slide39

Banana orbits size increases with their energy

Passing ion orbit in a QSH (1,-7)

Trapped ion orbit

0.2 cm(800 eV)

Poloidal banana width:

Colors of the trajectories are relative to different helical flux values.

0.5 - 5cm

300 – 1200eV

Helical banana size:

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

RFP Workshop, Stockholm 9-11 /10/ 2008

slide40

particles deposition

Almost constant inside the helical structure: 1-5m²/s

Dloc (m²/s)

(Dr)² (cm²)

yM

t(ms)

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

Trapped, passing, uniform pitch particles show different slopes for the relation Dr² versus time t.

RFP Workshop, Stockholm 9-11 /10/ 2008

slide41

Correlation of D with experimental magnetic perturbations

Di,QSH (m²/s)

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.

(mT)

Di,QSH (m²/s)

Di,SH/Di,QSH

Best QSH are very close to the corresponding SH case for ions

(mT)

RFP Workshop, Stockholm 9-11 /10/ 2008