HEAT TRANSPORTHEAT TRANSPORTandand

CONFINEMENTCONFINEMENTin in

EXTRAP T2R EXTRAP T2R

L. Frassinetti, P.R. Brunsell, M. Cecconello, S. Menmuir and J.R. Drake

OUTLINE

• Device and diagnostics

• Heat transport model

• Heat diffusivity and confinement estimations

• Scaling with plasma current

• Conclusions

EXTRAP T2R – the device

• R=1.24m• a=0.18m

• Ip 80kA (standard current plasma)• Ip 150kA (High current plasma)

• ne≈1019m-3

•Te ≈200-400eV

• pulse≈20ms (no feedback)• pulse≈up to 90ms (IS)

EXTRAP T2R – the diagnostics

• PLASMA CURRENT-F-OHMIC POWER standard magnetic diagnostics

•RADIATED POWER Eight chord bolometric system

• ELECTRON TEMPERATURE Ruby laser Thomson Scattering diagnostic at a single point, single time.

• ELECTRON DENSITY line averaged density two color interferometer core density Thomson scattering

• MAGNETIC FLUCTUATIONS 256 coils (4 poloidal x 64 toroidal) m=1 connected toroidal resolution |n|=32

• Soft X Ray 10-chord camera with a 9m Be filter

• ION TEMPERATURE AND VELOCITY 1m Czerny-Turner grating (2400lines/mm) spectrometer for 278.1nm OV spectral line measurement

THE HEAT TRANSPORT MODEL/1

How to determine the heat diffusivity?

The usual power balance is not a good choice.

We use a heat transport model and the corresponding numerical code developed for RFX-mod [Frassinetti L. et al., Nucl. Fusion 48, 045007 (2008)]

e is estimated using the model (and free parameters)

Te(r,t)

Using the heat equation

Comparison between simulated Te(r,t) and the experimental Te.

Determination of the free parametersand

validation of the model

The code must be adapted to take into consideration the T2R experimental data

RFX-mod data

core≈1.5 [D’Angelo F. and Paccagnella R. Phys. Plasmas 3, 2353 (1996)]

[Terranova D. et al., Plasma Phys. Control. Fusion 42, 843 (2000)]

( )( )

( )

core

coree

b tt

B t

m=1 magnetic fluctuationsB equilibrium magnetic field

A- Core 1- RFP plasma core is stochastic 2- In stochastic fields the heat diffusivity can be modeled using the RR formula:

B- Reversal 1- the reversal region is probably less stochastic 2- We assume

sec

21,n

n

b b

1( )

( )

rev

reve t

B t

rev=1

THE HEAT TRANSPORT MODEL/2

1

( )( )

( )

core

coree

b tt k

B t

0

1( )

( )

rev

reve t k

B t

The model has four free parameters

k1 determine absolute value of ecore

k0 determine absolute value of erev

r1 separation between core and reversal regionr0 separation between reversal and edge region

Constant radial profile is assumed

We need to:

(1) verify that the model is valid also in EXTRAP T2R(2) determine the free parameters

THE HEAT TRANSPORT MODEL/3

Te(r,t)Using the heat equation

2( , ) ( )SXR eff e er t Z n f T

(a) Zeff profile experimentally determined [Corre Y. et al., Phys Scripta 71, 523 (2005)]

(b) Assumption: Zeff has no time evolution

(c) Assumption: SXR emissivity is due only to Bremsstrahlung

f(Te) is numerically determined using

the transmission function of the Be filter

To have a direct comparison with experimental data.

sxrSXR dl

THE HEAT TRANSPORT MODEL/4

APPLICATION OF THE MODEL

Free parameters of the model

determined in order to minimize

the difference between experimental

and simulated data

21000coree m s

2150reve m s

During the flat-top

Discharge with Ip≈80kA and NO feedback

UNCERTAINTIES

Uncertainties can be determined by considering experimental errors on the input data

1- The simulation is repeated by varying the input the data within their error

2- The range of variation of e and Te can be determined

• ne profile and ne

• Experimental Te

• Zeff profile• Pin

• SXR

( )sim

Ein sim

W

P dW dt

3

2sim

sim e eW n T dV

STANDARD and IS PLASMAS

ISstd

<TeIS >=28040eV

<Testd >=22030eV

Std and IS plasmasjust before a crash

Simulation suggests that the higher Te in IS plasmais due mainly to a lower e in the core region

<ecore >IS = 300150m2/s

<ecore >std=1000300m2/s Average over

10 shots<e

rev >IS = 11040m2/s<e

rev >std= 15050m2/s

ISstd

1 rev

reve B

rev=2

Example of high Ip plasma

HIGH CURRENT PLASMAS

SCALING WITH PLASMA CURRENTExperimental results - particles

ee

nD n cH

t

Density increases with current

1. Reduction of particle diffusivity?2. Increase of the source term?

The source increases with Ip

Data suggests that the particle diffusivitydoes not change significantly with current

Experimental data

SCALING WITH PLASMA CURRENTExperimental results – heat

e ee e e in

n Tn T P

t

Temperature increases with current

1. Reduction of heat diffusivity?2. Increase of the input power?

The input power increases with IpBut also the density increases with Ip.

Data suggests that the increase of the temperaturecan be due to a reduction of the heat transport

Experimental data

SCALING WITH PLASMA CURRENTSimulation results – heat

Low Ip High Ip

<ecore > 300150m2/

s200100m2/

s

<erev > 11040m2/s 8530m2/s

<e> 0.150.04ms

0.190.05ms

Improvement of the confinement at high current

SCALING WITH PLASMA CURRENT

What happens to ions?

Ion (OV) temperature steadily increases with Ip

Ion (OV) velocity increases with Ipbut then saturates.

TM velocity (m=1,n=-12) has a trendvery similar to ion velocity

Good agreement between TM and ion velocity

CONCLUSIONS

• Heat transport and confinement estimated with a model

• Core heat transport dominated by magnetic fluctuations

• Heat transport reduced in the core of IS plasma

• Heat transport reduced in high current plasmas

<Te > <ecore > <e

rev > <e>

No FB Low IpNo FB Low Ip 22022030eV30eV 10001000300m300m22

/s/s15015050m50m22/s/s 0.090.090.03ms0.03ms

IS Low IpIS Low Ip 27027050eV50eV 300300150m150m22/s/s 11011040m40m22/s/s 0.150.150.04ms0.04ms

IS High IpIS High Ip 38038060eV60eV 200200100m100m22/s/s 858530m30m22/s/s 0.190.190.05ms0.05ms