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Secondary electron emission from solid surface in an oblique magnetic field
ELSEVIER
Journal of Nuclear Materials 220-222 (1995) 488-492
Secondary electron emission from solid surface in an oblique magnetic field S. Mizoshita a, K. Shiraishi b, N. O h n o a, S. Takamura a a Department of Energy Engineering and Science, School of Engineering, Nagoya University, Nagoya 464-01, Japan h Department of Electrical Engineering, School of Engineering, Nagoya University,Nagoya 464-01, Japan
Abstract It is numerically demonstrated that the electric field in the sheath and its finite thickness have a great influence on the release of secondary electrons from the surface of the target plate with a grazing incident magnetic field, although usually the Lorentz force is said to make almost all the electrons return to the plate. The magnetic sheath was found to have little effect on the emission fraction due to the weakness of its electric force. A distribution of the ejection angle for emitted electrons is considered in the analysis. A measure for determining the emission fraction is given.
I. Introduction Control of impurities generated by physical and chemical sputtering, radiation enhanced sublimation and evaporation from divertor target plate is quite important for improvement of plasma performance in magnetic confinement fusion devices. The sheath formed upon the divertor plate gives essential influences on the impurity generation and the edge plasma property because the sheath voltage determines the ionic incident energy and heat flux to the target plate [1,2]. The secondary electron emission due to particle bombardment on the target plate has a significant effect on the sheath formation [3-6]. Moreover, a large amount of secondary electron emission leads to a cooling of the edge plasma [7]. As the magnetic field lines are obliquely incident to the divertor plate, it is required to study whether a suppression of secondary electron emission really takes place since Larmor gyration inhibits those electrons from leaving the plate surface and, on the other hand, a strong electric field in the sheath makes an acceleration of electrons to go away from the surface. In this article we give the fraction F of really emitted electrons into the plasma by subtracting reabsorbed secondary electrons from all the originally emit-
ted ones. Although a rough sketch of reabsorption of emitted electrons has been reported, no detailed numerical analysis has been presented so far considering realistic conditions. The strength of the electric field, the finite thickness of the sheath, and the energy of secondary electrons are the key factors influencing the above mentioned emission fraction. In addition, we have to take into account the distribution of the ejection angle and the effect of magnetic presheath.
2. Model for numerical analysis A series of orbit tracings of electrons emitted from the target surface with a given energy and direction of emission has been performed with the R u n g e - K u t t a Gill method. The following collisionless equation of motion is employed, me/:= - e ( E + v × B ) ,
(1)
with the initial speed of c o = (2eEs/me) 1/2, where E~ is the energy of secondary electrons in eV units. The model configuration is shown in Fig. 1 where the magnetic field line makes an angle 0 with respect to the surface normal, x-axis. The electric field associated with electrostatic or magnetic sheath has a component perpendicular to the plate surface. It produces an
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00509-5
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
Fig. 1. Model configuration for electron emission from the target surface on which the magnetic field line makes an oblique incidence. The electric field associated with the elec-
trostatic and magnetic sheaths, perpendicular to the target surface, causes an acceleration away from the surface.
acceleration of electrons so that they leave the target surface. The energy distribution of those ejected electrons is composed of a very small fraction of reflected ones with almost the same energy of primary electrons and a majority part of electrons with an energy of 5-15 eV [8]. The distribution of the ejection angle is well represented by a cosine dependence over the wide ranges of incident energy and direction [9]. Therefore, the fraction of electrons which do not come back to the surface, F, is written by, F= a/
d0 cos a f(a, p),
where f(a, p) = 1 when the electron emitted in the direction determined by (Y and @ goes to the plasma, while f(a, p) = 0 when the electron wmes back to the surface. The electric fields in the electrostatic and magnetic sheaths are approximated as shown in Fig. 2. It is shown that the sum of the potentials drops in the sheath @,,, and in the magnetic presheath @,,, is wn-
489
1 -0.01
1
0.1
10
B lT1
Fig. 3. Ratio of sheath thickness to the electron Larmor radius in the parameter space of the electron density and the magnetic field strength. An electron temperature T, of 10 eV and a secondary electron energy E, of 10 eV are assumed.
stant over the change in 8, e(@, + @,,,)/T, = 2.8 (for hydrogen plasma), and a,,, is given by [lo],
In the fusion environment the thickness of electrostatic sheath d = 5A, is much less than the magnetic sheath length _ C,/W,~, where C, is the sound velocity and oJ27r is the ion cyclotron frequency, so that the magnetic sheath has only a minor contribution to the fraction F due to its weakness of electric force. However, we note that the electrostatic sheath voltage decreases when 0 approaches 90”. The ratio of the sheath thickness d to the Larmor radius pe of emitted electron with the energy Es is written by, T,(eV)B*(T) d - = 1.1 x 10’0 ES(eV)n,(m-3) &
“* I
’
and is shown in Fig. 3 where the sheath thickness is found to be usually larger than the electron Larmor radius in the divertor layer of fusion devices, otherwise the effect of electron acceleration by the sheath field is greatly suppressed since the electric field force works in only a part of the Larmor gyration.
3. Numerical results 3.1. Orbit tracing of emitted electrons
Fig. 2. Schematic profile of the electric field over the electrostatic and magnetic sheaths.
A typical example for release of the suppression of electron emission in the presence of a sheath electric field is shown in Fig. 4, where the orbit without electric field is drawn by the thin solid line, while the thick
490
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
m c way of the first half period of the cyclotron motion. It m e a n s that the electrons r e t u r n to the surface. O n the o t h e r h a n d , we see that the electric field cause an acceleration of the e m i t t e d electrons so that they leave the surface. W h e n we have no electric field, t h e fraction F is uniquely d e t e r m i n e d by the angle 0 which is i n d e p e n dent of m a g n e t i c field a n d electron energy, a n d is shown by the thin solid line in Fig. 5a. In this case the electron emission is suppressed by a factor of 2 at 0 = 60 ° a n d F is limited to only 17% at 0 = 80 °.
E =k
-~u
u
~u
"+u
or)
ou
y [ u m] 60.,,,i,,,I,,,1,,,i,,,
~
3.2. The case o f a uniform electric field 40
. . . . . . . . . . . .
•
E 20
. . . . . ~. . . . . . . . . . . .
~. . . . . . .
×
o
~
~
9n'.,,i,.,i,.,i.,,i..
--:80
As m e n t i o n e d before, the s h e a t h thickness is usually larger t h a n the electron L a r m o r radius in the fusion e n v i r o n m e n t , so that it is not u n r e a s o n a b l e to assume t h a t the electric field is c o n s t a n t in semi-space b o u n d e d by the target surface. T h e n u m e r i c a l results are summarized in Fig. 5 showing t h a t t h e emission fraction F increases substantially w h e n E S d e c r e a s e s from 10 to 1 eV, a n d the d e p e n d e n c i e s on B and E x are p r e s e n t e d at 0 = 80 °. Fig. 5b shows t h e energy d e p e n d e n c e of F; decreasing approximately as Es - ) / 2 a n d a p p r o a c h i n g to 17% at the limit of large energy since the L o r e n t z force b e c o m e s g r e a t e r t h a n the electric field force. A similar r e d u c t i o n d u e to the L o r e n t z force a p p e a r s in Fig. 5c, b u t m o r e strongly, say inversely p r o p o r t i o n a l to B. T h e strong d e p e n d e n c e also a p p e a r s for E x making
,"
-60
-40 -20 0 20 z [/z rn] Fig. 4. Examples of electron orbit with (thick solid line) and without (thin solid line) sheath electric field. B = 1 T, n c = 5 × 1019 m - 3 , E~ = 10 eV, T e = 10 eV, 0 = 80°, a = 30°,/3 = 270°.
solid line indicates the orbit w h e n the s h e a t h electric field is t a k e n into account. T h e area occupied by t h e s h e a t h is shown by t h e gray b a n d . W i t h o u t electric field the x-coordinate of t h e orbit b e c o m e s negative on
1 0.8 0.6 rr
0.4
I \ \',q
0.2
I
[0=80d0g I B=IT
.
.
.
.
.
.
]
.
00L 1 0 2 0 30 40 5 0 6 0 7 0
80 90
0,
0.1
1
1
10
100
E s [eV]
0 [deg] I
I iii1~
i iii1~
i iin
i iiiii
i ,,Hml
t iH*ul
i
rr
(c) 0.1
0.1
1
B [T]
10
100
0."
I
02
r,*a*~
10 3
10 4
i ip**ml
10 5
*
10 6
ii,*m
10 7
E x [V/m]
Fig. 5. Dependencies of the angle 0 (a), the ejection energy E~ (b), the magnetic field B (c) and the electric field E x (d) on the fraction F in the case of a uniform electric field.
491
S. Mizoshita et aL /Journal of Nuclear Materials 220-222 (1995) 488-492
the approach to F = 1 in the limit of a strong electric field. Over the parameter range in which F changes rapidly, the measure for the parameter dependence of F was found to be
Ex ~ [ nJo ],/2
v ,B te,
rE×. or
the relatively weak magnetic field. A similar situation appears in the range of high density for n~ dependence in Fig. 6d. The T~ dependence in Fig. 6c is well represented by Eq. (5) since the sheath thickness increases as T~~/2 so that the electric field increases also a s Te]/2.
(5)
Vo
~
4. Discussions and conclusion 3.3. The case o f a more realistic configuration
In the present numerical analysis, the electric field in the sheath was found to reduce substantially the well known suppression of secondary electron emission from the target surface with grazing incident magnetic field due to the electron cyclotron motion resulting from the Lorentz force. As a measure to determine if the electric field is influential, we present the ratio of the electric field force to the Lorentz one. The measure also equals to the ratio of the E x B drift velocity to the ejection speed of secondary electrons. It scales to (neTe/EsB2) ]/2. In the high density plasma with low magnetic field the finite sheath thickness makes the effect of the electric field small. It is found that the electric field in the magnetic sheath is too weak to pull the electrons away from the target surface. Throughout this article the structure and the electric field in the sheath are fixed independently of secondary electron emission. In reality the self-con-
The spatial profile of the electric field in the electrostatic and magnetic sheaths is now considered as shown in Fig. 2 where the thickness of the electrostatic sheath is assumed unchanged against 0. The reduction of the electrostatic sheath potential drop and the alternative increase of the magnetic sheath potential drop are taken into account by Eq. (3) when 0 increases. The fraction F is summarized in Fig. 6 for the following dependencies: the angle 0, the magnetic field B, and the temperature T~ and density n~ of the plasma electrons. The E s dependence not shown here is very similar to that in Fig. 5b since the sheath structure is fixed for the change in Es. The B dependence is different from that in Fig. 5b in the range of weak magnetic field because the sheath thickness becomes smaller than the electron Larmor radius. It means that the effect of electric field is greatly suppressed even in
1., 0.8
i ']--',6.-
I '
'~'
:i •
~._~
; ~ + 'N
" ne=SX 019m -3
0.4
I ~ X ~ "~ I[ i i "_1 J
-,:
li
0"2 I~----e==,*v s=,ol- ~ ~, '
i
i ,,~
i , i , i , i , i , i , i , i
-0 10 20 30 40 50 60 70 80 90 0 [deg] 1
(C) ,
I
10
I a =80deg I
i E,=l°°v I I B=IT
I
I T'=l°ev I I
l B =80deg Es-10eV
~"
(d)
[ he=5X lO"m-' I .......
I
10
,
{
(b)
I P '''~1
1
B [T]
1
/
0.1
, m n,,.nl
0.1 0.1
1
J
.......
I
Te=I0eV I he=5X 1019m'3I
/
/ ~
Es=lOeV
i i • i
~
.-1 Es=I0eV,B=IT : i - - - - - - Es=IeV,B=IT
0,',
o :8odog .... i'
:I
H
i,,<\, I
Te=10eV
0.6 . . . . . . . .
LI.
I '~1 'd
!\~ i =.-----;--..----.i...-..--.-.--..~....~........~.-..I~ ...........t •(ai
. . . . . .
I
100
T e [eV]
'
' It"
N
I
.... HI .... el .... -J .... el .... i l
1000 ""1016
1010
1020
.....
1022
n e [m -3]
Fig. 6. Dependencies of the angle (a), the magnetic field (b), the electron temperature (c), and the electron density (d) on the emission fraction F when the structure of the electrostatic and magnetic sheaths is taken into account.
492
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
sistency between the secondary electron yield and the sheath formation, such as the space charge effect, the presence of nonthermal energetic electrons, etc., should be considered. Here, we do not concern the incidence of primary electrons. However, the grazing incidence of primary electrons on the target surface enhanced by the oblique incidence of the magnetic field makes the secondary electron yield large [11]. Such an effect is not included in the present analysis, although this must be taken into account to determine the concrete sheath voltage across the p l a s m a - m a t e r i a l interface.
Acknowledgement The authors would like to thank Dr. K. Sato of Himeji Institute of Technology for his helpful discussions.
References [1] P.C. Stangeby, in: Physics of Plasma-WaU Interactions in Controlled Fusion, Nato Advanced Science Institute Series, eds. D.E. Post and R. Behrisch (Plenum, 1986) p. 41. [2] R. Chodura, ibid, p. 99. [3] K. Shiraishi and S. Takamura, J. Nucl. Mater. 176/177 (1990) 251. [4] K. Shiraishi and S. Takamura, Contrib. Plasma Phys. 32 (1992) 243. [5] K. Shiraishi et al., J. Nucl. Mater. 196-198 (1992) 745. [6] K. Shiraishi, N. Ohno and S. Takamura, J. Plasma Fusion Res. 69 (1993) 1371. [7] N. Ohyabu et al., J. Nucl. Mater. 196-198 (1992) 276. [8] E. Rudberg, Phys. Rev. 50 (1936) 138. [9] J.L.H. Jonker, Philips Res. Reports 6 (1951) 372. [10] K. Sato, H. Katayama and F. Miyawaki, Contrib. Plasma Phys. 34 (1994) 133. [11] K. Ohya et al., J. Nucl. Mater. 196-198 (1992) 699.
Journal of Nuclear Materials 220-222 (1995) 488-492
Secondary electron emission from solid surface in an oblique magnetic field S. Mizoshita a, K. Shiraishi b, N. O h n o a, S. Takamura a a Department of Energy Engineering and Science, School of Engineering, Nagoya University, Nagoya 464-01, Japan h Department of Electrical Engineering, School of Engineering, Nagoya University,Nagoya 464-01, Japan
Abstract It is numerically demonstrated that the electric field in the sheath and its finite thickness have a great influence on the release of secondary electrons from the surface of the target plate with a grazing incident magnetic field, although usually the Lorentz force is said to make almost all the electrons return to the plate. The magnetic sheath was found to have little effect on the emission fraction due to the weakness of its electric force. A distribution of the ejection angle for emitted electrons is considered in the analysis. A measure for determining the emission fraction is given.
I. Introduction Control of impurities generated by physical and chemical sputtering, radiation enhanced sublimation and evaporation from divertor target plate is quite important for improvement of plasma performance in magnetic confinement fusion devices. The sheath formed upon the divertor plate gives essential influences on the impurity generation and the edge plasma property because the sheath voltage determines the ionic incident energy and heat flux to the target plate [1,2]. The secondary electron emission due to particle bombardment on the target plate has a significant effect on the sheath formation [3-6]. Moreover, a large amount of secondary electron emission leads to a cooling of the edge plasma [7]. As the magnetic field lines are obliquely incident to the divertor plate, it is required to study whether a suppression of secondary electron emission really takes place since Larmor gyration inhibits those electrons from leaving the plate surface and, on the other hand, a strong electric field in the sheath makes an acceleration of electrons to go away from the surface. In this article we give the fraction F of really emitted electrons into the plasma by subtracting reabsorbed secondary electrons from all the originally emit-
ted ones. Although a rough sketch of reabsorption of emitted electrons has been reported, no detailed numerical analysis has been presented so far considering realistic conditions. The strength of the electric field, the finite thickness of the sheath, and the energy of secondary electrons are the key factors influencing the above mentioned emission fraction. In addition, we have to take into account the distribution of the ejection angle and the effect of magnetic presheath.
2. Model for numerical analysis A series of orbit tracings of electrons emitted from the target surface with a given energy and direction of emission has been performed with the R u n g e - K u t t a Gill method. The following collisionless equation of motion is employed, me/:= - e ( E + v × B ) ,
(1)
with the initial speed of c o = (2eEs/me) 1/2, where E~ is the energy of secondary electrons in eV units. The model configuration is shown in Fig. 1 where the magnetic field line makes an angle 0 with respect to the surface normal, x-axis. The electric field associated with electrostatic or magnetic sheath has a component perpendicular to the plate surface. It produces an
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00509-5
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
Fig. 1. Model configuration for electron emission from the target surface on which the magnetic field line makes an oblique incidence. The electric field associated with the elec-
trostatic and magnetic sheaths, perpendicular to the target surface, causes an acceleration away from the surface.
acceleration of electrons so that they leave the target surface. The energy distribution of those ejected electrons is composed of a very small fraction of reflected ones with almost the same energy of primary electrons and a majority part of electrons with an energy of 5-15 eV [8]. The distribution of the ejection angle is well represented by a cosine dependence over the wide ranges of incident energy and direction [9]. Therefore, the fraction of electrons which do not come back to the surface, F, is written by, F= a/
d0 cos a f(a, p),
where f(a, p) = 1 when the electron emitted in the direction determined by (Y and @ goes to the plasma, while f(a, p) = 0 when the electron wmes back to the surface. The electric fields in the electrostatic and magnetic sheaths are approximated as shown in Fig. 2. It is shown that the sum of the potentials drops in the sheath @,,, and in the magnetic presheath @,,, is wn-
489
1 -0.01
1
0.1
10
B lT1
Fig. 3. Ratio of sheath thickness to the electron Larmor radius in the parameter space of the electron density and the magnetic field strength. An electron temperature T, of 10 eV and a secondary electron energy E, of 10 eV are assumed.
stant over the change in 8, e(@, + @,,,)/T, = 2.8 (for hydrogen plasma), and a,,, is given by [lo],
In the fusion environment the thickness of electrostatic sheath d = 5A, is much less than the magnetic sheath length _ C,/W,~, where C, is the sound velocity and oJ27r is the ion cyclotron frequency, so that the magnetic sheath has only a minor contribution to the fraction F due to its weakness of electric force. However, we note that the electrostatic sheath voltage decreases when 0 approaches 90”. The ratio of the sheath thickness d to the Larmor radius pe of emitted electron with the energy Es is written by, T,(eV)B*(T) d - = 1.1 x 10’0 ES(eV)n,(m-3) &
“* I
’
and is shown in Fig. 3 where the sheath thickness is found to be usually larger than the electron Larmor radius in the divertor layer of fusion devices, otherwise the effect of electron acceleration by the sheath field is greatly suppressed since the electric field force works in only a part of the Larmor gyration.
3. Numerical results 3.1. Orbit tracing of emitted electrons
Fig. 2. Schematic profile of the electric field over the electrostatic and magnetic sheaths.
A typical example for release of the suppression of electron emission in the presence of a sheath electric field is shown in Fig. 4, where the orbit without electric field is drawn by the thin solid line, while the thick
490
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
m c way of the first half period of the cyclotron motion. It m e a n s that the electrons r e t u r n to the surface. O n the o t h e r h a n d , we see that the electric field cause an acceleration of the e m i t t e d electrons so that they leave the surface. W h e n we have no electric field, t h e fraction F is uniquely d e t e r m i n e d by the angle 0 which is i n d e p e n dent of m a g n e t i c field a n d electron energy, a n d is shown by the thin solid line in Fig. 5a. In this case the electron emission is suppressed by a factor of 2 at 0 = 60 ° a n d F is limited to only 17% at 0 = 80 °.
E =k
-~u
u
~u
"+u
or)
ou
y [ u m] 60.,,,i,,,I,,,1,,,i,,,
~
3.2. The case o f a uniform electric field 40
. . . . . . . . . . . .
•
E 20
. . . . . ~. . . . . . . . . . . .
~. . . . . . .
×
o
~
~
9n'.,,i,.,i,.,i.,,i..
--:80
As m e n t i o n e d before, the s h e a t h thickness is usually larger t h a n the electron L a r m o r radius in the fusion e n v i r o n m e n t , so that it is not u n r e a s o n a b l e to assume t h a t the electric field is c o n s t a n t in semi-space b o u n d e d by the target surface. T h e n u m e r i c a l results are summarized in Fig. 5 showing t h a t t h e emission fraction F increases substantially w h e n E S d e c r e a s e s from 10 to 1 eV, a n d the d e p e n d e n c i e s on B and E x are p r e s e n t e d at 0 = 80 °. Fig. 5b shows t h e energy d e p e n d e n c e of F; decreasing approximately as Es - ) / 2 a n d a p p r o a c h i n g to 17% at the limit of large energy since the L o r e n t z force b e c o m e s g r e a t e r t h a n the electric field force. A similar r e d u c t i o n d u e to the L o r e n t z force a p p e a r s in Fig. 5c, b u t m o r e strongly, say inversely p r o p o r t i o n a l to B. T h e strong d e p e n d e n c e also a p p e a r s for E x making
,"
-60
-40 -20 0 20 z [/z rn] Fig. 4. Examples of electron orbit with (thick solid line) and without (thin solid line) sheath electric field. B = 1 T, n c = 5 × 1019 m - 3 , E~ = 10 eV, T e = 10 eV, 0 = 80°, a = 30°,/3 = 270°.
solid line indicates the orbit w h e n the s h e a t h electric field is t a k e n into account. T h e area occupied by t h e s h e a t h is shown by t h e gray b a n d . W i t h o u t electric field the x-coordinate of t h e orbit b e c o m e s negative on
1 0.8 0.6 rr
0.4
I \ \',q
0.2
I
[0=80d0g I B=IT
.
.
.
.
.
.
]
.
00L 1 0 2 0 30 40 5 0 6 0 7 0
80 90
0,
0.1
1
1
10
100
E s [eV]
0 [deg] I
I iii1~
i iii1~
i iin
i iiiii
i ,,Hml
t iH*ul
i
rr
(c) 0.1
0.1
1
B [T]
10
100
0."
I
02
r,*a*~
10 3
10 4
i ip**ml
10 5
*
10 6
ii,*m
10 7
E x [V/m]
Fig. 5. Dependencies of the angle 0 (a), the ejection energy E~ (b), the magnetic field B (c) and the electric field E x (d) on the fraction F in the case of a uniform electric field.
491
S. Mizoshita et aL /Journal of Nuclear Materials 220-222 (1995) 488-492
the approach to F = 1 in the limit of a strong electric field. Over the parameter range in which F changes rapidly, the measure for the parameter dependence of F was found to be
Ex ~ [ nJo ],/2
v ,B te,
rE×. or
the relatively weak magnetic field. A similar situation appears in the range of high density for n~ dependence in Fig. 6d. The T~ dependence in Fig. 6c is well represented by Eq. (5) since the sheath thickness increases as T~~/2 so that the electric field increases also a s Te]/2.
(5)
Vo
~
4. Discussions and conclusion 3.3. The case o f a more realistic configuration
In the present numerical analysis, the electric field in the sheath was found to reduce substantially the well known suppression of secondary electron emission from the target surface with grazing incident magnetic field due to the electron cyclotron motion resulting from the Lorentz force. As a measure to determine if the electric field is influential, we present the ratio of the electric field force to the Lorentz one. The measure also equals to the ratio of the E x B drift velocity to the ejection speed of secondary electrons. It scales to (neTe/EsB2) ]/2. In the high density plasma with low magnetic field the finite sheath thickness makes the effect of the electric field small. It is found that the electric field in the magnetic sheath is too weak to pull the electrons away from the target surface. Throughout this article the structure and the electric field in the sheath are fixed independently of secondary electron emission. In reality the self-con-
The spatial profile of the electric field in the electrostatic and magnetic sheaths is now considered as shown in Fig. 2 where the thickness of the electrostatic sheath is assumed unchanged against 0. The reduction of the electrostatic sheath potential drop and the alternative increase of the magnetic sheath potential drop are taken into account by Eq. (3) when 0 increases. The fraction F is summarized in Fig. 6 for the following dependencies: the angle 0, the magnetic field B, and the temperature T~ and density n~ of the plasma electrons. The E s dependence not shown here is very similar to that in Fig. 5b since the sheath structure is fixed for the change in Es. The B dependence is different from that in Fig. 5b in the range of weak magnetic field because the sheath thickness becomes smaller than the electron Larmor radius. It means that the effect of electric field is greatly suppressed even in
1., 0.8
i ']--',6.-
I '
'~'
:i •
~._~
; ~ + 'N
" ne=SX 019m -3
0.4
I ~ X ~ "~ I[ i i "_1 J
-,:
li
0"2 I~----e==,*v s=,ol- ~ ~, '
i
i ,,~
i , i , i , i , i , i , i , i
-0 10 20 30 40 50 60 70 80 90 0 [deg] 1
(C) ,
I
10
I a =80deg I
i E,=l°°v I I B=IT
I
I T'=l°ev I I
l B =80deg Es-10eV
~"
(d)
[ he=5X lO"m-' I .......
I
10
,
{
(b)
I P '''~1
1
B [T]
1
/
0.1
, m n,,.nl
0.1 0.1
1
J
.......
I
Te=I0eV I he=5X 1019m'3I
/
/ ~
Es=lOeV
i i • i
~
.-1 Es=I0eV,B=IT : i - - - - - - Es=IeV,B=IT
0,',
o :8odog .... i'
:I
H
i,,<\, I
Te=10eV
0.6 . . . . . . . .
LI.
I '~1 'd
!\~ i =.-----;--..----.i...-..--.-.--..~....~........~.-..I~ ...........t •(ai
. . . . . .
I
100
T e [eV]
'
' It"
N
I
.... HI .... el .... -J .... el .... i l
1000 ""1016
1010
1020
.....
1022
n e [m -3]
Fig. 6. Dependencies of the angle (a), the magnetic field (b), the electron temperature (c), and the electron density (d) on the emission fraction F when the structure of the electrostatic and magnetic sheaths is taken into account.
492
S. Mizoshita et al. /Journal of Nuclear Materials 220-222 (1995) 488-492
sistency between the secondary electron yield and the sheath formation, such as the space charge effect, the presence of nonthermal energetic electrons, etc., should be considered. Here, we do not concern the incidence of primary electrons. However, the grazing incidence of primary electrons on the target surface enhanced by the oblique incidence of the magnetic field makes the secondary electron yield large [11]. Such an effect is not included in the present analysis, although this must be taken into account to determine the concrete sheath voltage across the p l a s m a - m a t e r i a l interface.
Acknowledgement The authors would like to thank Dr. K. Sato of Himeji Institute of Technology for his helpful discussions.
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