J. Plasma Fusion Res. SERIES, Vol. 9 (2010)                    
M,eM,
nnnEnnn,n,,,n(Received: 20 November 2009 / Accepted: 17 February 2010)e e en e n ee () n  ne 
neenen (B) en  ee  n e Bnnen (B) en een, n n αe ne. n e ne e n nn  αe,ene3.21MeVγenee9Be(α,nγ)12Ceneeee.Bnene3.21MeVγeneeneeeenee,enenn9Beneee.enenenennnn9Be(α,nγ)12Cγeneneene.
eαe,ene,γ,ennn,nenne
eeeneeeeee[15].      ne,3.21MeVγen 9Be(α,nγ)12C
en  nee   n   e
 nenn n   ne 
nen   nenee ee e. e
3.21MeV γ  ee  e nn 
eneee(7.65MeV)eee(4.44
MeV)12C. 

  e nn  n ee ()
nn[16]eenen e
n nn  ne e en ()
[7,]  ne αe. e nn  eneenen(B)en[4,5]
nnnneeen(C)en[9].e e  nn  n en nnneeeenBene[4,5].
n   enee , e αe enee  ene e e n  n 
 e nen n enee αe (3.5
MeV) nee. n Bnnen (B)
e n nen ne e n een, n n αe n nn, eeeeeαeene[10]. e ee,e
en nee  e ne e. n ne,   ee  nen eeen 
n  e e e en nnn,nen
ne n en  n 
ne en [11].  e e e  n  [1214] n  e ee ene,n
e nenn n nn   eenee.ne e n n e  ne ee nenn  e n e ,e  n n e e

α + 9 Be→12 C * [7.65] + n,
C * [7.65]→12 C * [4.44] + γ ( E γ = 3.21MeV)e  en   e  n n . 1



300
9

12

Be(α,nγ) C

200
150



[]

250

100
50
0
3000

4000 5000 6000 7000
αeene[eV]
9



12

. 1  e  en  Be(α,nγ) C en3.21MeVγen[1214].ٛ n

64©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

S. Hirayama et al., Diagnostic Scenario for Beryllium Impurity Concentration Utilizing Modified Alpha-Particle Emission Spectrum in DT Fusion Plasmas

oe n V  800 3 s sse. or ron he NBInecon er hs no een nce, n he sorce nossersreescresohenre,rnsoross,nheosseo(d,n)4ereconrencn.
or αrce, he sorce er e o (d,n)4e
reconswrens (dE / dv ) dN a .
Sa (υ ) =(2)4πυ 2 dE
1214. Snce he cross secon o hs recon r
ncreses n he ener rne oe 3.8 e, heesson re o 3.21e r ro 9Be(α,nγ)12recon wo sense reson o he ocon ohe αrce esson secr whch s roeneowrhhenerreonNBIhen. e ccre ee he enerec (3.8 e)
coonen o he αrce eoc sron ncon
consern he ocon o αrce essonsecr on he ss o B oe. sn he one
αrce sron ncon, he 3.21e resson re  9Be(α,nγ)12 recon s ee. B
cornheone3.21eressonrewhheoneeerenesre,heconcenrono 9Beons co e ese.  scenro o nose he
concenron o 9Be sn 9Be(α,nγ)12 r en
reconsresene. ereN areresensheαrceeneronre.Isenersecrsescres dNα(E ) = f D  υ D  fT  υ T  dσ

 
 d
dE

∫∫∫

× δ (E − Eα ) υ D − υ T dυ D dυ T d ,     (3)

wheredσ/d s he eren cross secon o (d,n)4e
recon n Eα reresens he αrce ener nororssemn1Eα = mα Vc2 +(Q + E r )2
mα + m n

he eoc sron ncon or on seces a(a ,  n αrce) re ee  son heoownBeon.CNES
1 ∂  υ 3 f a  ∂f a  ∂f a 
+
+ 2




∂t 
∂t i
υ ∂υ  2τ c* (υ ) j i     (1)+ Sa (υ ) − La (υ ) = 0 ,where fa(υ) s he eoc sron ncon o heseces a. or scons, s s sse o es nor. he rs er n he ehn se o
.(1)reresensheeecoheoocosons.hesonsenoercronseces,.e.j,, αrce n eecron. he coson er s hencenonner, renn cosons eween ons o he seseces.heseconercconsorheNSosecesacronons.econserNSeweenαrcen,neweenαn,.e.,(a,i)(,α),(,α),(α,)
n(α,).heNScrossseconsreenroheworoernsnen8.
he hr er n he ehn se o .(1)
reresens he son n eoc sce e o herconcon. o ncorore he nnown oss echnso enerec ons no he nss, we se heeoceenence o he eneross e o herconconnherceosse(seee.46). hesorceSa(υ)nossLa(υ)erseerenor or eer on seces. or eeron, he sorce nossersreescresohheen,enecon,rnsor oss n he oss e o (d,n)4e recon re
ncnechoher.heNBIreernoeSNBIseressesnheeenerENBInneconower
PNBI,.e.,SNBIPNBI/(ENBIV).ereVreresenshes

∑∑2mα m n(Q + E r ) ,        (4)mα + m n+ Vc cos θ cwhere mα(n) s he αrce (neron) ss, Vc s he
cenerosseocoheconrces,θcshene eween he ceneross eoc n he
αrce eoc n he ceneross re. he Er
reresenshereeener2
1 m D mT
υ D −υT .            Er =2 m D + mT
()


he crosssecon o (d,n)4e recon s en ro hewororos16nBosch1.
ro he one eoc sron
ncon oαrce, esson re o 3.21e r ro
9Be(α,n)12reconcneeeYγ (3.21) = 8π 2V dυ α υ α f α (υ α )

∫

∫

(

× dυ Beυ Be f Be υ Be
9

9

9

9

)

 υα +υ2dυ r υ r σ Be (α , n ) C (υ r )×
 υα −υ




∫

9 Be

9

12




(6)

9 Be


where υr s ree eoc eween 9Be n αrce.
heeocsronnconoerssseo e wen  he eerre se s  oneerre. Becse he ss o 9Be s rer hn e65

S. Hirayama et al., Diagnostic Scenario for Beryllium Impurity Concentration Utilizing Modified Alpha-Particle Emission Spectrum in DT Fusion Plasmas10keV
ENBI

1

10

100

60
40
20

/oNBI1.0eV

2

10

(a)

3

10

10

8
ENBI1eV
19

5

10

2000

4000

6000


14

10



10

11

(b)

10

10

10

Te10keV

9

10ENBI1.0eV

8

0

2000

4000

6000

20

40
60
PNBI[]80100a e relaie onenraion o e enerei (3.8 eV)
αparile omponen) eome larer i inreaineam ineion poer. In i. 3, e 3.21eV γra
emiion rae rom 9Be(α,n)12 reaion i on a anionoeamineionpoerPNBIoreeraleleronemperare. e allaion parameer eepemperareandeamineionpoerareameaoeini. 2. e onenraion o erllim i amed o e
n Be = 0.005 × (nD + nT ) = 3.0 × 1017 m −3 .eemiionraeo
3.21eV γra eome larer i inreain PNBI andTe.e ne o (a) e αparile emiion perm
and (b) e αparile diriion nion or eeraldeerim (riim) deniie in i. 4. In i allaion,eleron emperare Te 10 keV, ener and parileoninemen ime τE  (1/2)τp  3 e, eamineionpoer PNBI  40  and eamineion ener ENBI 
1eV are amed. I i ond a e αparile enerperm i roadened o i ener reion and eenerei omponen o αparile diriion nioneome larer i dereain deeron deni. i ieae e loindon o a eamion i eakenedorloakronddeni[4]enonaellianailindeeron diriion nion reaed  NBI eaineome lare and e αparile emiion perm irerroadenedoardienerreion.    Ini.5,eoe3.21eVγraemiionraea a nion o el ion deni or eeral eleronemperare. e allaion parameer eepemperareanddeerimdeniareameaoeini.
4. e onenraion o erllim i amed o e
n Be = 3.0 × 1017 m −3 . In e lo deni reion, eeneraion o αparile rom  reaion dereae ande γra emiion rae rom 9Be(α,nγ)12 end o e100

60

40

20

/oNBI120
i. 3  Emiion rae o 3.21eV γra rom
9Be(α,nγ)12reaionanionoPNBIoreeralTe.

PNBI

13

10

10

10

8000

−3

nDnT3.0×1 m

110αparileener[keV]

1

10
13

12

10

3

10

10

4

(4πv/mα)fα[m keV ]Te20keV

141(dNα/dE)normalized

0

10

10

PNBI

Te

Y31[ ]

10



15



1

8000

αparileener[keV]


i. 2  (a) αparile emiion perm and (b)αparilediriionnionoreeral
NBIpoeraTe10keV.
ion,diorionoeloidiriionnion,e..deoNE,oldeneliile. 9


In i. 2, e o (a) e αparile emiionperm and (b) e αparile diriion nionen 20, 40, 60 and 100 NBI eain i applied.Ini allaion, eleron emperare Te 10 keV, iondeniie nD  nT  31019 m3, ener and parileoninemenimeτE(1/2)τp3eandeamineion
ener ENBI  1 eV are amed. I i ond a eαparile ener perm i roadened o i enerreion  NBI eain and a enerei omponen (3.8 eV) are ormed in αparile diriion nion.
e old line repreen e diriion nion in eae io NBI eain. I i ond a e enerei(3.8eV)omponenareormedoinoeNEoionproded αparile [1] een i e eam i noineed.eroadneoeemiionperm(aell

9



66

S. Hirayama et al., Diagnostic Scenario for Beryllium Impurity Concentration Utilizing Modified Alpha-Particle Emission Spectrum in DT Fusion Plasmas


19

PNBI403.05.0

1

10

2

10

14

Te10keV



(a)

3

10
10

ENBI1.0eV

5

0

2000

4000

6000



10

8

12

5

10

19

10
10

11

10

3

a

Yγ/Yγ(3.21)

Te10keV

9

10ENBI1.0eV

8

0

2000

4000

6000

αarileener[keV]



4.0

5.0

3



i. 5  miion rae o 3.21eV ra rom
9Be(α,nγ)12 reaion a a nion odeerim(riim)deniandTe.

PNBI40

10

3.0

10

(b)

10

2.0

nD[10 m ]3.01.0

12

1.0

19

nD5.010 m

13

PNBI40

ENBI1eV



3

1

(4πv/mα)fα[m keV ]

13

11



14

ENBI1eV

10

10

8000

αarileener[keV]

10

10

10

4

10

Te20keV

110Yγ[ ]0(dNα/dE)normalized

103nD1.010 m



10



15

8000

PNBI40

8
6

19

3

nD2.010 m3.05.0

4



1

2



0

i. 4  (a) arile emiion erm and (b)arile diriion nion or eeraldeerim(riim)deniaTe10keV.ٛ 

5

10

15
Te[keV]20
i. 6  nanemen o 3.21eV ra emiionrae de o e modiiaion o arile
emiion erm a a nion o Te oreeraldeerim(riim)deni. diriion. inall e mmarize e orrelaion eeen 9Be
onenraion and ra emiion rae or eeral (a)eamineionoerPNBI(b)deerondeninDand(c)
eleron emerare Te in i. . en e eloidiriion niono 9Bei amedoeaelliane 3.21eV ra emiion rae i roorional o e
erllim onenraion. e orrelaion eeen 9Be
onenraion and ra emiion rae i deermined a anion o PNBI nD and Te. I e old meare eaial diriion o nD and Te and arael ealaee enerei (3.8 eV) omonen o e arile
diriion  omarin e 3.21eV ra emiionraeealaedieeerimenallmearedoneeonenraionoerllimoldeeimaed.

mall.aonini.4(b)oeereenerei(3.8 eV) omonen in e arile diriion
nion inreae i dereain deni. e ra
emiion rae i oneenl ke nearl onaneeiall in loemerare rane een i deerondenidereae.    In i. 6 e enanemen o e 3.21eV ra
emiion rae de o e arile emiion erm rom e ale en
modiiaion i.e. Y γ ( 3.21) / Y γGauss( 3.21 ))ireenedaaaianermiamed( Y γGauss( 3.21)nion o eleron emerare or eeral deerondeniie. e allaion arameer ee emerare
anddeerimdeniareameaoeini.5.Inloemerare (and lo deni) rane e enanemeneome iniian. n e oer and in iemerare rane e deree o e enanemen raidl
rede e.. a Te  20 keV and nD  5.01019
Y γ ( 3.21) / Y γGauss1.04. In  a ae e 3.21eV ra( 3.21 )emiion rae old e ealaed  amin aian

67

S. Hirayama et al., Diagnostic Scenario for Beryllium Impurity Concentration Utilizing Modified Alpha-Particle Emission Spectrum in DT Fusion Plasmas

10

ENBI1e193nD3.0×10 m

3Bee[m ]ee     ee e  
emss e  ese [10].  s  se eess.7ssesmeee. e ENBI eees 1.2 e e eeees(6e)meseseesmes  e e ese e ss se 
9Be(α,nγ)12 e  eeses  e eee e 6 e.  e eeme e
eee  emss e s mese.  esseemssseessesse s e ees e m [11] e emss e m    sm 
eesme.    




18

Te10e

17

10PNBI20
(a)

16

10

40

9

60

15

10

10

11

10

12

10
10
 1
Y[
s
]


13

10






[1]


18

. B .   . e s. e.  3358(1997).
[2] .ee.s.e.e1246(2000)
[3] . .  . e  . . es s.sms957(2000).
[4] . s  .  s. sms  062507
(2006).
[5] . s  .  s. sms  054504
(2007).
[6] me.....024801(2006).
[7] . . ee  . . e . . .  323(1971).
[8] . . es  . . e . . .  77
(1981).
[9] ..see.sms..s1747
(2007).
[10] .s  .  s. sms  042507
(2009).
[11] .eee..s1967(2001).
[12] ..e.s.e.e115001(2004).
[13] ..se.583(1990).
[14] ....e ..eesms..s59(2006).
[15] .ee..smses.1051(2003).
[16] . s  . ee   e   e 10273 83
(1987).
[17] ..Bs.e.s611(1992).

ENBI1e

PNBI40

3Bee[ m ]10Te10e



10

17

10

16

10

15

19

3

nD1.0×10 m
(b)

3.0

9

5.0

10

10

11

10
10
1
Y[s ]

12

10

13




18

ENBI1e193nD3.0×10 m

3Bee[ m ]10PNBI40

17

10

(c)

Te5e
10

16

10

9

20
15

10

10

10

11

12

10
10
 1
Y[ s ]



13

10



. 7  e eee 9Be e emssesee(a)PNBI(b)nD
()Te.ٛ e 3.21e  emss e s ees emeeeENBI.seeme
ee ENBI  1e s ssme. e ENBI eees 1e e e emss sem s eme68