22P172-B
Probe measurement under the influence of secondary electron emission
プラズマの二次電子放出を考慮したプローブ測定
Takehito Tawaraya, Akira Tsushima and Yoshimura Shinji
俵谷 岳人, 津島 晴，吉村信次
Yokohama National Univ.
79-5, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
横浜国立大学 〒240-8501 横浜市保土ヶ谷区常盤台79-5
For a plasma with an electron tempertature, being high enough with influence of secondary electronemission by electron impact to an electrode, the electron temperaure can be estimated from a slope of thelogarithmic plot of the probe V-I characteristics. However, an electon density needs to be estimated using acorrection factor depending on the electron temperature.

1. Introduction
To improve probe measurements of tokamak
boundary plasmas with energetic electrons, weneed to consider secondary electron emission byelectron impact. Then, the effective coefficient ofsecondary electron emission depending on anelectron temperature has been derived from anempirical formula of secondary electron emission
for a plasma with a Maxwellian electron velocity
distribution. The validity of the effective
coefficient was experimentally investigated usingprobes with electrodes made of tungsten andmolybdenum electrodes.
2. Coefficient of secondary electron emission
The coefficient of secondary electron emission isa function of the energy of primary electron, Ep ,and might be given by an empirical formula of thecoefficient as follows: [1]E   2.72  mexp   2 p  .
EmEm 2Ep(1)

Fig.1 Dependence of with Te . Solid curve
indicates for tungsten (W) and broken curve
indicates for molybdenum (Mo).
For a Maxwellian electron velocity distribution
with an temperature, Te , the effective value of

secondary electron emission coefficient,  , can be
defined by
Here,  m is the maximum yield and Em is theprimary energy with the maximum yield;  m andEm depend on a material. Table I gives their values
for tungsten (W) and molybdenum (Mo) for probe
electrodes.

 (E )v exp(m v /2k T )dv
2p



v0e

B e

 v exp(m v /2k T )dv2e

B ev0 2.72 m2Table I. Values of  m and Em for tungsten (W) andmolybdenum (Mo).

k BTe eEm 0k T   2  B e   E m  d .
(2)

WMo

mEm (eV)

1.35
1.25

650375Here,me Boltzmannis an electron mass,constant,k B is the1andme v02  eVs  Vb 2

1Ep  me (v 2  v02 ) with an elementary charge e , a2
space potential Vs and a bias potential applied to aprobe electrode Vb . It is easily seen that  doesn’t

depend on Vs Vb but Te [2]. Figure 1 shows of tungsten and molybdenum, as functions of Te . It
might be worth to mention that there is theconditionof   0.81 for the existenceof a
monotonic sheath [3].

3. Experiment
An argon plasma was filled in a pyrex glass tube
with a diameter of 100 mm and a length of 800 mm,
where a structure similar to a double plasma device
was constructed. By decreasing a wall potential of adriver side against a wall potential of a target side, aplasma with two Maxwellian electron velocity
distributions, the temperatures of which are Tec(  2 eV) and Teh (10-40 eV), respectively, wasproduced in the target side. In such the plasma withtwo electron components, the electron current of aprobe electrode, Ie , is composed by two parts asfollows:

I e / S  I ec / S  I eh / S






 1   (Tec ) nec

 1   (Teh ) neh

secondaryelectronemission.
Specifically,nec ' [1 (Tec )]nec and neh '  [1   (Teh )]neh . Then, wedefine two ratios of the density of the component
with Teh to that of the component with Tec , i.e.,f n  neh / nec and f n '  neh ' / nec ' . Between the tworatios, we have the relation of

fn 
1  (Tec )fn ' .
1  (Teh )(4)

Probe measurements were madewith
consideration that different values of f n ' might be but almost the same value of f would beobtained
nobtained using probes with electrodes made ofdifferent materials. Since we used probes withelectrodes made of tungsten and molybdenum, wecan compare f n -W with f n -Mo and f n -W ' withf n -Mo ' . The results are shown in Fig. 2, whereand f n-Mo ' / f n-W ' are plotted as
f n-Mo / f n-Wfunctions
 of Teh byclosed circles
 and open circles,
respectively. Consequently, we find the validity ofusing  from the facts that f n-Mo / f n-W  1 andf n-Mo ' / f n-W '  [1   Mo (Teh )] /[1   W (Teh )] , because ofTeh  Tec , where the subscript of  indicates the material (W or Mo) of an electrode.

 eV kBTecexp  b 2me kBTec  eV kBTeh
exp  b ,2me kBTeh (3)where S is the area of the surface of the probe
electrode; and n ec and n eh are densities of thecomponents with Tec and that with Teh ,References
[1] E. W. Thomas: Nuclear Fusion Special issue(1984) p.
94.
[2] G. Fuchs and B. Schlarbaum: Journal of Nuclear
Materials 145-147 (1987) p.268.
[3] G. D. Hobbs and J. A. Wesson: Plasma Physics 9(1967) p.85.

 respectively. Note that  (Tec ) represents  for (Teh ) represents  for Teh .
Accordingly, both Tec and Teh are determined
from the usual logarithmic plot of the electroncurrent. Using the logarithmicplot of Ie withhigher voltages
 of Vb , Teh is determined since theTec and that

contribution of the component with Tec to Ie issmall. Then, using the logarithmic
 plot of theremaining electron
current
afterthecomponent withOn
Teh is subtracted from I e , Tec is determined.
the other hand, the usual treatment gives densitiesof the two components, nec ' and neh ' , which are densities
smaller than true
we want to obtain, n ec
and n eh , respectively, due to the effect of

Fig.2 f n-Mo / f n-W and f n-Mo ' / f n-W ' are plotted asfunctions of Teh by closed circles and open circles,respectively. Solid line represents f n-mo / f n-W  1and Broken curve represents f n -mo '/ f n -W '[1  Mo (Teh )]/[1  W (Teh )].
