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!"#$%&'()*+,&!-
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!"#$+®+¯°±²d³´&µe¶·¸¹yºg
Te
ne
Particle/
Heat Flux
Gas
Density
~50eV~10eV
~1eV
Separatrix Divertor Plate
!"#$
H2,CH
4 %&Ne,Ar %&
»¼½¾Y~M³´&µ¿®À&ÁÂÃÄ&Å]ÆÇÈ
Molecular Assisted Recombination
(MAR) '()*+ v ! 4,-.
/012345678'9:;00 ?@
H2(v) + e ->0H2- -> H- + H
H- + H+ ->H + H*
H2(v) + H+ ->0H2
+ + H
H2+ + e ->H + H*
IC
DR
DA
MN
(1)
(2)
É'(»¼½¾YcÊËÌqM'(ÍεÏ()*пÑ+
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1
rot
1
sin"
#
#"sin"
#
#"
$
% &
'
( ) +
1
sin2"
# 2
#* 2+ , -
. / 0 rot =
1
vib
h2
2µ
#
#r
$
% &
'
( ) 2
1V (r) + E+ , -
. / 0 vib =
h2J(J +1)
2µr2
.kÝ*Þeß/g%Vàáâãäh
ÙåÝ*ÞeæÙgVVçè鲯êë[ìÕ(
&Æíî¶ïy»:Ý*Þ&%+[\ðKqMñÁòóyÆô8h
õ('(&Æíî¶ïy»:Ý*Þ&ö'²eæÙ{ß/g
!
!
Erot
=h2J(J +1)
2µr2
rot =YJM(",#)
ß/6789:34(÷ø`S(TU~ch
ß/ùÙä&úûÎVàáâãäY~Mh
ü8y{·ýyþ$:(BO)ÿ!
eñÁÿ!gRç&ØÙ¯+Q\hÕ(&"#¯"$`,%[\j±ì&%&ç&ØÙ¯'QMRæÙß/ØÙR(R1~10 ps Õ(&ØÙRRR(R0.1-1 fs
6
'(&6789:;<
!
H = H0
+ HSO
+ HB
+L
!
" = elecvib
rrot
" Hel " = Eel (R)
v Hvib v =#e (v +1/2) $#e%e (v +1/2)2
+#e ye (v +1/2)3
+L
rot Hrot rot = BvJ(J +1) $DvJ2(J +1)
2+ HvJ
3(J +1)
3
)*Ù&'(þ+8º¤,y(Õ(-+æÙ-.ß/-)
!
H0
= Hel
+ Hvib
+ Hrot
Hel
= Tel(r) +V (r,R)
/0¯+^*Ù
!
Bv
= Be"#
e(v +1/2) + $
e(v +1/2)
2+L
Dv
= De
+ %e(v +1/2) +L
ü8y{·ýyþ$:(BO)ÿ!2ñÁÿ!
'(ë2¶:1:¼~c
ñÁòóyÆô82¢ea^PjBOÿ!&3g
4§ß/ 56TY~M78
âãæÙ( Morse9
¼:y:;<
=:$y
-
7
þ+8º¤,y&ú.µ+Vm
!
H" = E"
H11
H12
H21
H22
#
$ %
&
' ( "1
"2
#
$ %
&
' ( =
E1
0
0 E2
#
$ %
&
' ( "1
"2
#
$ %
&
' (
ABCDEFGHI2JKLMNOP;QRSTUVWXI2'YZ'[\]^;_'==I2`abcdABCDEFG'[\]^He?U+fgehijkjWXI2'[\]^'$lmZ,nopU;,V?KI2qPirSsWtuCvw`xy?z{+|}'~!OHW2]^`xy?z{+'2]^'$lmZ'^`xy?z{H,V?i0I2JU;,>W[\]^`',WdABCDEFG`~!Oo?EwN|}`xyW[\[\DC`xy?pU;,V?i
ABCDEFG`|}njTUVW[\+tuCvw`W_'UV'[\DC;K2]^P`noi
'(&6789:;]?c@pV`*ÙAY~Mh
Õ(-&³ú. '2:RBÕÚ*Ù
æÙ-&³ú. '2:R³ñÁòóyÆô8`
ß/-&³ú. '2:Rß/*Ù
Cl-R2:R¼:y:;
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'(&'=">
n2S+1LJ
[XABCD.....abcd....]2S+1!+/"#(g/u)
'(2
LVZpS(jV]p
'(2[c¯\]ØÙ
#=!+"!
S
NR
Hund’s case (b)
N=R+!
J=N+S
"
Hund’s case(a)
#=!+"
J=#+R
L = 0, 1, 2, 3, 4 ,,,,
-2S, P, D, F, G....
! = 0, 1, 2, 3, 4 ,,,,
-2", $, %, &, '....
Õ(GH;<
GH+÷^_Uk
`]M_Uk
S
UÚYV`]Mcasej_GH&ö
a¯btr÷¡Y]Mh
iClebsh-Gordan¬, Wigner symbol
(
'(
¼:y_Uk
2S+1: ¼:y_Uk
cdÎ
10
eóï`Æy¹º:
|el> &úûÎ
fõ('({{'(2¯ghij&áklYmp\`RR"=0e#-g{{nö(op+)Jq>r/(op-)JpsqJRR"9õU-&&`3Ý¿(op+)_%3Ý¿(op-)
f¡çõ('({{dt\&Õ(¯4Yä[\r/dM+±hRR|el> &q>¿JLK]pRc"#(even) = g (gerade) q>¿JLMR d"#(odd) = u (ungerade)
#g, $u¡
|el> +|rot>j±PM
|rot>=YJM(%,&)~c`uvr/Ymp\VJw+YSTdMhJ=0jVnöh
uvr/=z2ß/(|el>nö)i'(2¯ghár/x(cJ)op+/- +÷^
¡çõ('(&çSaeyX(4r/iÕ(&84r/gYmp\
|el> |rot>R&q>nöRiRsym. RR{(+) , g } {(-), u }
RRRRRRq>r/Ri@antisym. RRzXY
e-parity : (-1)J f-parity -(-1)J j{|dM"A_
-
11
34'(#AB$CDEFGH&æÙß/}~
12
Õ(ÏÒ¾Ð&æÙß/}~
(n’, v’, J’) iÏn”, v”, J”)
!
I = h" # $ N A $ n % $ $ n
A $ n % $ $ n = 2.026 &10'6" 3
$ n $ v $ J µe$ $ n $ $ v $ $ J
2
2 $ J +1
$ n $ v $ J µe$ $ n $ $ v $ $ J
2
= $ v $ n µe$ $ n $ $ v
2
$ J $ $ J 2
= $ v Re(r) $ $ v
2
$ J $ $ J 2
!
" v Re (r) " " v 2
= Re2(r " v , " " v ) " v " " v
2
= Re2(r " v , " " v )q " v , " " v
Õ(£:¹yº&öµ¿”J”]&`
!
A " n # " " n =$%3Re2q " v " " v
S " J " " J
2 " J +1
S " J " " J " J
& = 2 " J +1
q " v " " v " v " " v
& =1 Franck-Condon (
Hönl-London (
P(branch) J’-J”=-1
Q(branch) J’-J”=0
R(branch) J’-J”=+1
-
13
34'(Ë{=)*&æÙß/}~
hijklmnoVUVp
-
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z;
-
17
5x10-3
4
3
2
1
0
Sig
na
l in
ten
sit
y[a
rb.
un
it]
660640620600Wavelength [nm]
Q
R
(0-0)P
(1-1)P
(2-2)P(3-3)P
1 5 1 5 1 5 1 5 1 5 1 1(0-0) (1-1) (2-2) (3-3) (4-4) (5-5) (6-6)
4 0 4 0 4 0 3 0
2 6
2 6
2 6
2 5
J''
(0-0) (1-1)
!H
(b)
1m-Czerny-Turner (2400 G/mm), PMT(Hamamatsu R928)
Wavelength resolution(FWHM) < 0.03 nm @50 µm slit
#AB$CDE@89¥:@;¦D$§E9
18
!
RX ,vd,v'"qvv'
X #dexp{
#Ev(0) + Ev(v)
kTe}
tukl×¹ØÙÚBÊ˱Á,ÌÍ®ÚBÛÜsÝÞ8(MAR)
ØÙÚB9:@ßhoFulcher-!²,àF-CAðÍüý¹¼ã
case: d -> a : G Staszwska 1999
case: X -> d: Meneses, 1995
ÃBkl¡¢@ÈÉkl2þÆÇÿ!¼ã
X1"+g
d3#-u
a3"+g
!
Aa,v"d,v '"qvv '
d# a
!
R2(X " d) = Re
2#qvv'X "d
# SJJ 'X" d
Ãklòó®vw".#,î$%ª&'()*ã
Ã
-
19
#B9¥$¨F¼(G Staszwska 1999)
Fulcher-!@vw".#,Re(r)
'"kg#«xy?¬$;?@
Franck-Condon¡¢`:j
TYZ' *(F-C®8)U¯°`|±@
²%³´ *@@)^@±@@@:?$AF9?"²RÏ=³>E©¥³$Ð
-
21
The comparison of qv’v” / R2 for d3$u – a
3"g
.268/.43261%
.555/.64386%
.154/.117137%
.015/.006250%
v'=3
.003/.00743%
.204/.32363%
.671/.74390%
.115/.08144%
v'=2
.137/.21364%
.79/.8494%
.064/.04160%
v'=1
.069/.10566%
.93/.93100%
v'=0
v"=4v"=3v"=2v"=1 v"=0 ad
2¦§¨'Schrödinger§©ª'^"+µ¶·¸@
Franck-Condon®8+ Spindler(1971)'¹wHº»o?@
./vw£@01»¼®23@45î678mnÜ*9
Ó./ÍÚ@5":
@:?$AF9?"²@812Ï=³>E©¥³$Ð *U#F
-
23
#AB$CDEFG!-&·¸
24
:¹º»¼()@F--Y~M½¾
;j: %&'(?6'ABÚBCDî·@'ã
Arc discharge: 70-100V, 30-45AB = 0.02Tne ~ 2x10
12 cm-3, Te ~ 0.05-15 eVTi ~ 0.5 eV (@target chamber)
5uAB: on--> -CDEÉ off --> F-CDmn
MAP-II
-
25
¿:ÀÁ:}: Õ@2%Î(ÂÃ&¥¦¯8M
Discharge Condition:
230-270 V, 70 mA, 20-3000 Pa(300 Pa in this work)
ne~109 cm-3, Te = 2-5 eV
26
!
Ia " " v " " J d " v " J
=hc
#a " " v " " J d " v " J
Aa " " v " " J d " v " J
Aa " " v " " J d " v " J
v",J "
$% ne RXvJ
dv 'J 'Cv (2J +1)gas
Jexp &
FX (J,v)
kTrotX
&GX (v) &GX (0)
kTvibX
'
( )
*
+ ,
- . /
0 1 2 v,J
$
#AB$CDEF!Ï:?$!"#AF9?#²ÄÐ@Å©E@§CD@A.#²
ÄÏ=ÆBÐ@ÇD9ÈAEDÇD¥§
!
RX ,vJ
d ,v'J 'N
vJ
X{ }J
"v
" = Nv'J 'd Ad ,v'J 'a,v"J "J '
"•d GQX :
•d ÊQa¦
!
Id ,v 'J '
a,v"J"= h" # A
dv 'J '
av"J"N
vJ
d
Assuming X(vJ) is characterized by Boltzmann Tvib,Trot
!
Nv'JX
= Cv (2J +1)gasJexp "
FX (J,v)
kTrotX
"GX (v) "GX (0)
kTvibX
#
$ %
&
' (
measurement Reliable database required Fitting Parameter
X1#+g
d3$-u
a3#+g
Coronal
equilibrium
spin-changed
Fulcher)(
!
RXvJdv'J '
= qXvdv'
< Qv '"vGryzinski
ve > a0J1J '#
gas
g'as
a$K$ 'K '
K '
% =K '
% Q r' (2K '+1)K '
$'
r
$ & $'
K
&$
'
( )
*
+ ,
r
%2
=1
Multi-polar Q’r=1-4 :{0.76, 0.122, 0.1, 0.014}.
r = 1 ---> dipolar = Hönl-London factor
Excitation rate (adiabatic)
!
SJ 'J "
Q=
2J '+1
2,
SJ 'J "
P+ S
J 'J "
R=J'
2+J '+1
2=
2J'+1
2
Radiative transition ratio
Hönl-London factor
P,RHHLÅ伦Anomaly
-
27
!
"eH2
(Te) : e +H
2(v)# H
2
-( )*
#H +H$
"eH$(Te ) : e +H
$ # e + e + H
"H+H$(Ti) : H
++H
$#H + H
*
Ï.Ð#AB$CDEG!-Y~Myk&Éë[µ, ÊË]
!
0 =d H
"[ ]dt
= ne
H2(v)[ ]#eH2
0$v$9
% " H"[ ](ne#eH" + H+[ ]#H+H") "H
"[ ]&
transport
!
H2(v)[ ] = N0 exp "G(v) "G(0)
kTvib
#
$ %
&
' (
Tvib : Fulcher-band spectroscopy
Te¦/double probene¦/double probe[H-] ¦Laser photodetachmentdeg. dissociation¦H-H2 intensity ratio
=ne
dissociative attachment (DA)
e-impact electron detachment00
mutual neutralization ( = NI-MAR)
vibrational distribution of H2
depletionproduction
We first discuss w/o transport.
QcIPIZJQ_bKZbLQMGONOPRMOLPQcQQIWHSSQRSQGHRKIePTZQQSOUQdaXP\QMOMOSHRMOL
28
Ï5ÐC©ÈÈFD=D¥§@Ì@¦C©§©¥
!
H2" Loss" events
H# " photon=$ H
2" Loss( )
% H#( )=
ne[H2](S + D+ CX + DA )
ne[H2](X1&3diss + FX
1&3
dir)B H#( )
!
H2" Loss" events
Fulcher " photon=# H
2" Loss( )
$ H2(d% a)( )
=ne[H2](S + D+ CX + DA )
ne[H2]Xd&X (Te )
!
" H2(d# a)( )" H$( )
=Xd%X (Te )
X1#3
diss(T
e)B(H$ )
H!YTÛÌqM(¼ýzº8&'(&©ª
§ÍY½[\^M((H{'((H2= )(H:H!), )(H2:H!), )(H2:Fulcher-!)
ÎRkÏ&ÐF
ÃkÑÒ : Õ¡Ywp\RkÏJKTe¯ðMÈF=0
F=[H]/[H2]
!
" H#( )" H$( )
=(X
1%4
diss + FX1%4
dir)B H#( )
(X1%3
diss + FX1%3
dir)B H$( )
F!-Ókj%²Ë¿Ì^]M+Ôk¿ÕÖM
-
29
Ï?ÐGDÄG5໼!"#$&%²ke()@F--gFµH
!
" H#( )" H2(d$ a)( )
=ne[H]X1$6
eff(ne,Te )B(H# )
ne[H2]Xd%X (Te )F/(2+F)%²k
F=[H]/[H2]Kado et. al., Journal of Nuclear Materials 337-339 (2005)116.
·Ø2He!"#$3.1 mTorrYH2»¼¯exene
-
31
ÏOÐæÙk{ß/k&âè'e¢¨'Sg[µ]
6
5
4
3
2
1
0
Te [
eV
]
-4 -2 0 2 4Position [cm]
3
2
1
0
ne [1
0-1
1 cm
-3 ]
Te
en
(3.8mTorr)
4000
3000
2000
1000
0
Tv
ib [
K]
-4 -2 0 2 4Position [cm]
800
600
400
200
0
Tro
t [K]
Tvib
Trot
(3.8mTorr)
Ð5678'ÑÒÇ [ÓÔ¼ 1 km/s]/[ÕÖ 10 cm] = 100's
Ð1234×7Ø'6Ù©'ÈÚÇ 1/[H2,ne] ~ 10 ms
ÛÜÅÆ(X)'1234+ºÝ'+Þß
àáÅÆ'âã+40 ns ©¼
0/_'Y'äå,?@
à12347Á;æCçèG7Á,éǺÝ,>WTe;ºÝ,ehUhêehKëìP/íTe'¿9H&'@
Tvib@ÓÕVWÜo§$¾Úìp@mnÜîXY×8ã
4000
3000
2000
1000
0
Tv
ib [
K]
-4 -2 0 2 4Position [cm]
800
600
400
200
0
Tro
t [K]
Tvib
Trot
!"#$%&'%(#)*+,-./
32
col
colpre
4'
30'
exp
fit
KA
KDA
N
Nf
v
v
X
+
++==!
=
"=
#
#
pre
col
1
1
D
KA
f
+=
!
16.7
-
33
%56&'(è )*¾56+Z&'(è
, 16.7nsîï
Ð 19.0nsîï
! îïej
!8ÛÜ'12-(.¼kg/´
0
¿À0
Kcol`X),V?MAP-II'12&'(èHîï^`34
56
78w9:w;¿À
TvibX=3945[K]
TvibX=2044[K]Tvib
X=1693[K]
TvibX=4871[K]
æç¬&£I[äå`µ]
* D. Yamasaki, S. Kado et
al., J. Phys. Soc. Jpn. 75
044501 (2006).
34
P+Q
Ð5678'1234+WG?£W@ûAG`BCT×mZHû?¹"D'E£Hû¤WFGkgHIJHK>´T&'(è'ÓL1MHNo?OÚ;?@
Ð)þÿ'Fulcher-!P(QQ)+*9;RS,?T+;?@
à¹ww÷+UUVjh;W@@WXYZehÎÏ[;\SsVsh?i
ÐFulcher-!P(P,Q,RQ)'7å+]^'Ý_e)4'OÚ`\jsh?i
èé&êë
Ð78'34`¹CUFulcherPU'¯°
ÐaÓbcÚKdThóeö÷'fÒP',gWéÇhi'j´@
Ð-ékl÷mDC(Lyman, WernerP)U'¯°en
-
35
ìsíî
[-] S. Kado, Y. Iida, S. Kajita, D. Yamasaki, A. Okamoto, B. Xiao,
T. Shikama, T. Oishi and S. Tanaka,
“Diagnostics of Recombining Plasmas in Divertor Simulator MAP-II” (Review)
J. Plasma Fusion Res. 81, 810 (2005) .
[-] S. Kado, S. Kajita, D. Yamasaki, Y. Iida, B. Xiao, T. Shikama, T. Oishi, A. Okamoto and S. Tanaka
“Experimental study of negative ion profiles in H2-MAR plasmas in divertor simulator MAP-II”
J. Nucl. Mater. 337-339, 166-170 (2005).
[-] B. Xiao, S. Kado, S. Kajita and D. Yamasaki,
“Rovibrational distribution determination of H2 in low temperature plasmas by Fulcher-! band spectroscopy” Plasma Physics and Controlled Fusion 46, 653-668 (2004).
[-] !"#$% &'()*+,-./012324 56!7819:23;?5@ -./0A'()BCD80, 749-756E2004F
[-] !"#$GHIJKGLMNOGP"Q, &9:23FulcherRS4TUVWP,RX1YZ[@\]^%_(8), (15) -./0A'()BCD80, 783-791(2004).
[-] B. Xiao, S. Kado, S. Kajita, D. Yamasaki and S. Tanaka,
“Rovibrational distribution of H2 in low temperature plasma: the dependence on plasma parameters”
J. Nucl. Mater. 337-339, 1082-1086(2005) .
[-] S. Kado, D. Yamasaki, B. Xiao, Y. Iida, A. Okamoto, S. Kajita, T. Shikama and S. Tanaka,
“On the Anomalous Characteristics in the P and R Branches in a Hydrogen Fulcher Band”
J. Plasma Fusion Res. SERIES, 7, 54 (2006) .
[-] Daisuke Yamasaki, Shinichiro Kado, Bingjia Xiao, Yohei Iida, Shin Kajita and Satoru Tanaka,
“Experimental Evaluation of Predissociation Rate in v = 4 State Usable for Analysis of H2 Fulcher-”
J. Phys. Soc. Japan, 75, 044501 (2006).
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