° 1。
‐ 25
1。
‐2,
l c ) , 2i
E( ev )
Fig. 4.2 Calculated electron and proton impact excitation cross sections, o, among fine structure levels of ArXV 2s2p3Py3Pz as a function of electron and proton impact energy. Solid and dashed lines are expressed electron impact (EI) and proton impact @I), respectively. Electron impact cross sections are calculated by Flexible Atomic Code [13] (solid line) and relativistic distorted-wave method [14] (closed circles) and proton impact cross section is calculated by close-coupling impact parameter method [15] (dashed line).
In magnetically confined toroidal plasmas, the radial densrty profile of a certain ionized stage impurity ion is mainly determined by the electron temperature profile. In order to determine the T" where ions in a selected ionization stage exist, a radtal line intensity distribution of the ions has been measured in the visible range with multi-viewing-chord observation using a Czerny-Turner type spectrometer and fiber arrays. Tlpical examples on the measured profiles are shown in Fig. 4.3 for Ml lines of ArX and ArXV. Since the
PI
・‐Ⅲ‐ 1・
・ , /
El
ArXV 2s2ptP,, -tP,
… 98‐
central electron temperature is high (-2.5keV), both the ArX and ArXV line emissions are located in the edge region of the plasma. In the discharges used for the prese,lrt analysis, slightly different locations are derived at p^O.8 between the two ions. The T" values for the calculation are determined to be 376eY and 646eV for ArX and ArXV, respectively. The Ti values for ArX and ArXV are estimated from those of ArXtr (991 eV) and ArXVI (1831 eV) shown in Fig. 4.3 assuming an appropriate T; profile. Consequently, the Ti values of 557eV and 1050eV are derived for ArX and ArXV, respectively. The proton temperature is assumed to be equal to the Ar ion temperaflre (Ti = To) io the following analysis.
６４２０８６４２０
が ３ ｏ 釧 ︐ り ｏ ∫ 一 Ｆ ︶ ぉ 廼 ︐ 三
‐‐‐
‐
、/ T e
iErx 5533A
Ar XV 594艤
3
︵＞０︶ ．ト
２ １
0
0 0. 2 0. 4 0. 6 0. 8 1 ρ
F'ig. 4.3 Vertical distributions of line-integrated ArX (5533A) and ArXV (59444) with solid lines and T" profile with dashed line measured from argon plasmas.
4。3。 Li ne r a■ o of F‐ hke i ons ( Ar X, T凶 V and FeXVI I I )
h o r d e r t o y z e a 皿 t h e d e n s i t y d e p e n d e n c e o f t h e Ml l i n c l iik e n t e n s ii o n s t t t a r et h e F ‐ s el ec t ed as t he s i mpl es t c onf l yat i on and t he l evel ‐popul at i on of Ar X has been c al c ul at ed
wi t h quas i ‐並∽ け
‐s t at e r at e equat i om, whi c h i nc l udё hi ま‐ener gy pЮt on mpac t exc i t t t i on
‐ 99‐
between the fine structure levels.
three levels model, because the considered to be relatively small.
This level-population calculation of ArX is applied to a influence of electron cascade from higher levels is The energy level diagram ofArX considered here is
2s2po 2s
2$22p5 2P
l r 2( 3)
l r 2( 2) 3 r 2 ( 1 )
Fig. 4.4 Partial energy diagram of ArX with Ml (5533A) and El (165.53A and 170.63A) mnsitions (EM: spontaneous emission, EI: electron impact collisional excitation and de-excitation, PI: proton impact collisional excitation and de-excitattion). Horizontal line with hatch above figure indicates ionization level. Integers in brackets at right hand denote states used in quasi-steady-state rate equations with J values of levels. Width of arrows represents relative amplinrdes of transitions.
illustrated in Fig. 4.4. The numbers in the parentheses are the labels used to identiff the levels in the following discussion. The atomic processes considered in the model are drawn with arrows and their width represeirts the magnitude of the population flow under a typical plasma condition. The population mechanism of the level I is rather simple and is explained with the corona equilibriurn, namely, the population is determined on a balance of the population inflow from the lower levels due to electron collisions and the outflow down to the lower levels due to spontaneous radiative transitions. Consequently, the level 3
こ う ０ ． ● 卜 ｒ
EM: 寺 E l : 企 ↓ P l : 合 ●
‐ 100‐
population proportionally increases with the electron densrty. On the other hand, the population mechanism of level 2 is rather complicated because several processes are competitive for the population determination owing to the small transition probability of the level 2 to level I (1.06x102s-1). The population inflow to the level 2 is always dominated by the collisional excitation from the level I and the radiative cascade from the level 3, and their transition rates are proportional to the electron density: for the latter process the level 3 density is proportional to the electron densrty though the transition probability is constant.
As for the population outflow from the level 2, inthe low densrty case it is dominated by the radiative transition to the level I and in the high density case the collisional processes predominate over the radiative process. As a result, in the low density case the level 2 population increases with the electron density similarly to the level 3 population, whereas in the high densrty case the level 2 population is saturated. The density depende'nce of the line intensity ratio of E1/1v11 is thus understood qualitatively.
Five processes are taken into account to arnlyze the level 2 population, i.e., electron and proton collisional excitation and de-excitation and radiative decay by Ml transition betwee'n the level 2 and level l, electron impact ionization fromthe level 2 andradiative decay from the level 3, as shown in Fig. 4.4. A set of quasi-steady-state rate equations in ArX (F-like) configuration is given by
n l= n g l,
n2[ ne( C' 21+Ce23+S2) 十npCp21+勁
, C●21+A21] =
n i( n e C9 1 2 + n p Cp 1 2 + 勁
,C・1 2 ) + n 3 ( A3 2 + n e Ce 3 2 ) ,
n3[ nc ( Ce31+Ce32+S 3) +A31+A32] =nl neCe13+n2neCち3,
where the subscripts of 1, 2, and 3 are the same meaning as Fig. 4.4. And n" and nn is the electron and proton de,nsities, respectively, q the population density of energy level i, A1 the spontaneous emission probability, C*ii the collisional-excitation rate coefficient when i < j or de-excitation rate coefficient when i > j and Si the electron impact ionization rate coefficient of level i. Here, the ng is normalized to l. The de-excitation rate is obtaind from the Klein-Rosseland formula as
( l a) ( l b)
( l C)
‐ 101…
% =i t t eも 等
,
( 2)wher e gi c i ) i s t h9飢試i t t i c d wei まt of t he 10wer i or upper j l evel , △耳J and Tx ar e t he t r ans i t i m ener gy and t he t emper ane of dec t r on or pr ot on, r es p∝t 市et t h t he Ar di s c har ges 6f LHD t he amount of hydr ogen i s l ar gel y r educ ed s i nc e Ar gl ow di s c har ge c l eani ng i s r epeat ed bef or e t he l mt t di s c har ge. The hydr ogen denSi t y i s det er ml ned s pec t r os c opi c al l y wi t h t hc hel p of t he i mpur i t y and 3‐di l nens i onal H di agnos t i c s and t t r mα eaSur ement .
Her e, t he val uc of 、 ‐ V5i s us ed. The s ubs c npt of ゎ expr eSSes a c ont r i but i on of c ol l i s i onal pr oc es s by f as t pr ot ons , whi c h ar e o五gi nal l y br ought by hi ま
‐ener gy neut r al beanl mJ ec t i on oBD. The bem ener gy of t he NBI us ed i n LHD i s 1800̲ Thes e f as t
pr ot ons r educ e t heむ ener gl es コ mml y t hr ouま t he c 01l i Si on wi t h t hemal el ec t r ons i n t he pl as I I l a and t he c ner gl es f l nal l y bec ol ne equal t o t he t h―
l i on t emper at we ai er t he c ol l i s i on wi t h t hemal i o郎 。 A nЮ no‐ener get i c beam of Eゎ =100keV i s t hen as s unl ed i n t he c al c ul at i ono A l i t t l e c hange of t hi s ener gy has no i nauenc e on t he c al c ul at i on r es ul t ( See Fi g。4. 2) . The eXCi t at i on r at e c oer l c i ent by t he f as t pr ot on mpac t i s gl ven by CわJ =vゎ び
わ 1, wher e vo i s t he vel oc i t y of f as t pЮt on and♂
J i s t he c xc t t at i on c Ю
s s s ec t i on f or t he pr ot ol l l
i mp a c t . T h e s p o n t a n e o u s t r a n s ■l o n p r o b a b 遺量i e s o f t h e Ml a n d E l l in e s a r e g i v e n i n t h e
at omi c dat abas e t abl e[ 17, 18] . The i nt ens i t y of t r ans i t i on k) mj t o i i s r pr es c nt ed by L=
、ヘト The F‐l i ke i ons of TⅨⅣ and FeXVⅢ ar e al s o c ac ul t t ed us l ng t he s ame mnl l er as
Ar X. At onuc dat a of Ar X, TⅨ I V and FeXVI I I us ed i n t hi s c al c ul at i on ar e l i s t ed i n Tabl e 4 。1 .
T h e c a c u l t t i o n r e s u l t s o n M1 / E l( L lA 3 D in t e n S it y r a t io s 1 6 5 Åo f A r X , T Ⅸ5 5 3 3 カⅣ 2218A/ 122A and FeXVI Ⅱ 975ノ聯94A ar e s l Юwn i n Fi g. 4. 5 as a mc t i on of t he dec t Ю n dens i t y h t hi s c al c ul at i on l l o c ont r i but i on of t he f a飢―
pr ot on i s t aken mt o a∝ol mt ( 恥 =0) .
T h e in t a s i t y o f t h e E l lin e e s s e n t i a l ly h a s a l in e a r d e p e n d e n c e o n t h e e le c t r o n d e n s h y in a ll d e n s i t y r a n g e .Ho we v e r 9 t h e i n t e n s it y o f t h e Ml l in e t e n d s t o ∝ d e n s is a t u r a t e t y t t h i ま
r ange s i nc e t he r adi at i ve dec ay i s l i mi t ed b∝aus e of t he wdl val uc of s p6nt aneous d∝ay
r at e. T hen, s t r ong el ec t r on dens i t y dependenc e i s appear ed i n t he l i ne r at i os of M1/ El . T h e d e n s i t y d c p e n d e n c e o f t h e r a t i, T Ⅸo s Ⅳ f o r 暉a n d F e X V Ⅲ a p p e a r s a b o v e 1 0 1 6 ml × ‐
3 ,
‐ 102‐
lxl0r8rn3 and lxl0rern3, respectively. This threshold density is mainly determined by the transition probability of the Ml line.
1 0 0
Ｆ ■ ざ 巨 10-1
10-2
10-3
\-_f_:-**....
\