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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
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