Download (a) Fig.3 (b)

Measurement and Analysis of Zeff
via Bremsstrahlung on EAST
Chen Yingjie
Directed by Prof. Wu Zhenwei
•
•
•
•
Some correction on Zeff caculation
System calibration
Experimental results
Summary and Some problems in Zeff
measurement
• The future plan
Principles of the measurement for Zeff
1/2
16e6   
 2  3
d
3c  6me 
dPff
ne ni Z i2 g ff
Te1/2  2
Z eff   ni Z i2 /  ni Z i 
i
i
1/2
16e6   
  
 2  3
d
3c  6me 
dPff
1
ne
 hc 
exp  


T
e 

n Z
i
2
i
i
ne2 Z eff g ff
Te1/2  2
 hc 
exp  


T
e 

Since  /   1, we can obtain：
1/2
16e6   
  2  3
3c  6me 
 Z eff
3c 2   



16e6  6me3 
ne2 Z eff g ff
Te1/2  2
1/2
 hc 
exp  
 
 Te 
 Te1/2 2
 ne2 g ff exp  hc / Te 
Fig.1 The bremsstrahlung
in a plasma predominantly
originates from free-free
transitions of an electron
in the electric field of an ion.
Gaunt factor
Several approximations of Gaunt factor：
2
3    Te  Te
Griem : g ff 
ln  

2    hc /   Z i2 Ry
 
   
 
 4Te 
ln 
   hc /  
 hc / 
3  3  Te 
Griem : g ff 
 ln  2   ln  2
  2  Z i Ry 
 4Z i Ry
Elwert : g ff 
Ramsey : g ff
3
 0.001Te 
 3.77
 5 
   
 2 
0.147
Z i0.0579
Fig 2
Since Te is in the range of 100eV and 2000eV，
The Gaunt factor can be well approximated by：g ff  1.35Te0.15
Moreover, the Te  g ff curve is flat and g ff changes slowly with Te
around 1keV, so gff can be seen as a const and is set equal to 3.8.
The line averaged ion effective charge
The line averaged Zeff is defined as：
a
Z eff 
3c   


16e6  6me3 
2
1/2

 r )dr
（
2
a
g ff 
a
2
1/2
n
(
r
)
T
(r ) exp  hc / Te  dr
e
e

a
 Te  r  
Define：   n (r ) 

T
 e0 
a
a
1/2
2
e


dr /   ne (r )dr 
a

a
2
We can rewrite the line averaged Zeff as follows：
a
Z eff
3c 2   



16e6  6me3 
1/2
2
Te1/2
 r )dr
0  （
 g ff   a
a

  ne (r )dr 
a

2
Fig.3 (a)
Fig.3 (b)
Fig.3(a) shows the relationship between  and  ，
And Fig.3(b) shows the relationship between  and 
with assumed Te and ne profiles
2
2 



r
r 
Te  Te 0 exp  
 , n  ne 0 1  2 
   a 2  e
 a 


The form factor curve changes slowly with  and  and in the
opposite tendency，so it is appropriate to treat  as a constant.
Line emission and bremstrahlung
In addition to bremstrahlung, line emission and recombination
also contribute to the emission from plasma. The spectral region used
for bremstrahlung measurement is fixed at 5780±10 Å on EAST and
is free of line emission, as shown in Fig.
Fig 4(a)
Fig 4(b)
Recombination radiation and Bremstrahlung
fb
ff
The spectral emission coefficients of recombination radiation j ( ) and bremstrahlung j ( ) are
jfb ( )   j fb (n, )  1.8 1032 T 3/2 Ne N Z Z 4 exp(
n  n0
 128
j ( )  
3 3
ff

Z 2IH
1
X   3 exp(
)
2
n
kTn
n  n0
h
) X
kT
2
h

2e  2  c 
N
N
Z
r
c
g

,
T
exp(

)


 e Z  c  0  v  ff
kT

   th 
 6.8 1038 Z 2 N e N Z T 1/2 g ff  , T  exp(
The ratio of the two emission coefficients is
(erg  s 1  cm3  Hz 1 )
(erg  s 1  cm3  Hz 1 )
h
)
kT
jfb ( )
101 X / T6
ff
j ( )
The ratio is far less than 1 in tokamak plasma at the wavelength of 5780 Å.
As a result, the bremstrahlung is dominant while recombination radiation is negligible.
The multi-channel visible bremsstrahlung measurement system
The measurement system consists of
an 8-channel photomultiplier tubes array,
and is arranged on the horizontal port C.
The 8 viewing chords are shown in Fig.4.
The line integrated bremsstrahlung intensity is
determined by the multi-channel visible bremsstrahlung
measurement system, the electron temperature profile
is measured by an array of 25 sight-lines from the
horizontal Thomson-scattering system (TS), a 10-channel
soft X-ray array and a 16-channel heterodyne ECE
system, and the line averaged electron density is measured
by a vertical three-channel FIR hydrogen cyanide (HCN)
laser interferometer on EAST tokamak as shown in Fig.4.
Fig 5
Calibration
The multi-channel visible bremsstrahlung system was absolutely
calibrated with an integrating sphere under different conditions.
The calibration has
been carried out several
times, and is in good
coincidence，as shown
in Fig 5.
The blue line is
the final data used for
Zeff caculation.
Fig 6
Experimental results
Comparison with Zeff from plasma resistivity
Fig 7
Fig 8
Limiter and Divertor
The divertor can reduce the impurity level apparently in tokamak plasma.
Compared with from 3 to 5 in a limiter configuration, typical values of Zeff
range from 2 to 4 in a divertor configuration.
Fig 9
Fig 12
Fig 11
Wall Conditioning
Fig 13
Fig 14
Reheating
Line averaged ion effective charge increases by 20~30% during the reheating discharge.
Typical shots for ICRF and LHW heating are shown in Fig(a) and Fig(b) respectively.
Fig 15
Fig 16
Summary
The Zeff derived from bremsstrahlung is valid and reliable.
Comparison with other methods
a) Plasma resistivity
b) Visible bremsstrahlung
c) Charge Exchange Spectroscopy(CXS)
Problems existing in the syestem
Error caused by recombination in some condition
Coupling of light into optical fibers
Reflections of the outer wall, metal or glass
Difficulty in inversion of line integrated bremsstrahlung signal
Outlook
Measuring bremsstrahlung at another wavelength
An extension of the multi-channel visible bremsstrahlung system
A horizontal array to acquire accurate Zeff profle
Thanks