B C A – p. 1/26

26
– p. 1/26

Transcript of B C A – p. 1/26

Page 1: B C A – p. 1/26

�� ��� � �� � � �

�� � ��� � ��� � ��

� ��

� � � ! " #$% & ' ! () *+ " #,

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 1/26

Page 2: B C A – p. 1/26

� � ��� �� �� � � � �� �� � ��

=⇒

�� � �� ��� � �� � � � �� !" #$ %

� � �� & '

=⇒

() *+ � ,-

�. / 0 1� 2� 34 � 5

(

βp

4 � 5)67 8 9: ; <

7 8 9 : => � ?@ AB CD E(

F G D E

)� �H I

s

� 6J

K � �H I E L

; < � MN O P

7 8 9 : => � ?@ AB CD E

(

F G D E

)� �H I # K � A� > Q � R S

() *+ � ,-=⇒

=> () TU

(ITB)

� R S-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 2/26

Page 3: B C A – p. 1/26

� � � �� �� � � �� �

� / 0 1� � �

)

� � � < () * + � ,-

� / 0 1� � � � C H I � � ?

� � ;� � � � � �

E × B

� � � C H I � � ?

ITB

� � � ;� Q� � � , � �� � !" @ � # � � #$�&% � � ;�

Er =1

Zieni

dpi

dr+ VφBθ − VθBφ

' (�) () *+ � ,� � � / 0 1� � �- . � / � 0 %

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 3/26

Page 4: B C A – p. 1/26

� � � �� �� � ��

MHD

� � �� �

� � � � � � � �

ρ(V · ∇)V

- . � � �%MHD

� � � � �

∇ · (ρV ) = 0 ∇× B = j

ρ(V · ∇)V = j × B −∇p E + V × B = 0

∇× E = 0 B · ∇T = 0

∇ · B = 0 p =ρT

m� J � �� � � �- ��%� ��� �(R, φ, Z)

!" #%$ &' ( )*+

φ

,- . " / 01 23 465789 :;+ <= > ?@ AB9 C D B " # " E5-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 4/26

Page 5: B C A – p. 1/26

Grad-Schlüter-Shafranov

�� �

�� �

MHD

� � � � �� ��� � � � �� � �Grad-Schlüter-Shafranov

� � - �� �&%GSS

� �

R2∇ ·(∇ψR2

)

+ T T ′ +R2

{

p′T + pTR2

2

(

mω2

T

)′}

exp

(

mR2ω2

2T

)

= 0

ψ

. / 0 1� � � +T (ψ)

7 8 9: B C

R

?� �ω(ψ)

� � �+

pT (ψ)

7 8 9: F GB

� � C

m

�� � ��T T = BφR

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 5/26

Page 6: B C A – p. 1/26

� � � �� � � � �� � �� � �� ��

7 8 9: � � 8� � 3

R = 3 m p0 = 0.1 MPa κ = 1.6

a = 1 m T0 = 6 keV δ = 0.25

B0 = 3 T Ip = 1.6 MA Vφ0 = 5 × 105 m/s

� / 0 1� � � � C # � � � �� � � ; < � C � � �

# �� � � �� �" � �� � � �� # � � � H � � �&%

1-/ 1-3 1-5 2-1 2-4 3-//-/

/-1

/-3

/-4

/-5

0-/

,78;*:+<96.>1=

,8A?A*:+

,*8A?A,8@?A+

,8@?A*:+0.140.160.18

0.20.220.240.260.28

0.30.320.34

0 0.2 0.4 0.6 0.8 1 1.2

Rax

is−R

0a

M0-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 6/26

Page 7: B C A – p. 1/26

�� � �� �

:

� �� �

. / 0 1� � �+

ψ(R,Z)� ; < � C

j(R,Z)

� � � Q�

1.1 1.4 2./ 2.3 2.5

-0./

/./

0./

796*8,:+

1.1 1.4 2./ 2.3 2.5

-0./

/./

0./

679*8,:+

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 7/26

Page 8: B C A – p. 1/26

�� �� � � �

1

ω(ψ)

T (ψ)

� � �

ω2

T= constant

pT , T 2

-

ψ

�� �+ " � �pT =

P

R40

(ψ − ψ1)

T 2= T 20 + 2

M

R20

(ψ − ψ1)

ψ1

� 7 8 9: � " �ψ

" $� � ψ1 = 0� � � J " �

Grad-Schlüter-Shafranov

� �

∇ ·(∇ψR2

)

+M

R20

+P

R40

R2 exp

(

mR2ω2

2T

)

= 0

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 8/26

Page 9: B C A – p. 1/26

�� �� � � �

2

7 8 9: �� -

D-shape

" � A� � � R � �%κ = 1, δ = 0+ � * ) *+ * �

ψ

� 8 �

(at Z = Zaxis)

� 09 � + $ �

Rnuma =

3.16280m$ Ranala = 3.16275m

.9 �$ �9 � �+ �� �� � � � 1� #

|Rnuma −Ranal

a |a

≈ 0.005%

� � E5

*+1+/53.,

*140-2.,+/

-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC

– p. 9/26

Page 10: B C A – p. 1/26

�� �� �

7 8 9: 4 ��� �� � � �� � � �� � �� Zeff = 1

, � �%q(0)

#

1

� J � A� � /� � � # $� � & � # � /

� A � � �- �� �%�� � () � �

∂t(nsV ′) = −

∂ρ

V ′〈|∇ρ|〉nsVs − V ′〈|∇ρ|2〉Ds∂ns

∂ρ

�+ SsV ′

∂t(msnsusV ′) = −

∂ρ

V ′〈|∇ρ|〉msnsusVus − V ′〈|∇ρ|2〉msnsDus∂us

∂ρ

+ SuV ′

∂t

3

2nsTsV ′5/3

= −V ′2/3∂

∂ρ�

V ′〈|∇ρ|〉3

2nsTsVEs − V ′〈|∇ρ|2〉nsχs

∂Ts

∂ρ

+ SEV ′5/3

∂Bθ

∂t=

∂ρ

η‖

µ0

F

V ′〈R−2〉

∂ρ�

V ′

F

�|∇ρ|2

R2

−η‖

FR0

〈|∇ρ|〉

〈R−2〉〈JCDB〉

JCD :� ���

F : F = BφR

V ′ : dV/dρ � V

� ! "# $%

η‖ :

&'(-. /0 1 23 4567 89 :;<=> ?@A 89 BC

– p. 10/26

Page 11: B C A – p. 1/26

� �� � �

() H ��� �� H� �" � � �� � �� *+ �� � � �

� * +

χNC

� < () *+

χTB

� " � %χe = χNC,e + 12χTB

χi = χNC,i + 12χTB

CDBM

� �� � � � <� �� � � �� � �� *+

χTB = F (s, α, κ)α3/2 c2

ω2pe

vAqR

� �H Is ≡ r

q

dq

drF G D Eα ≡ −q2Rdβ

dr� �� �

κ ≡ − r

R

(

1 − 1

q2

)

-. /0 1 23 4567 89 :;<=> ?@A 89 BC

– p. 11/26

Page 12: B C A – p. 1/26

� � � � �� � � �

� �

F (s, α, κ)

� *+ � A � � �� + �� � ��� �

� �� � � �% (κ� 1)

F =1

2(1 − 2s′)(1 − 2s′ + 3s′2)for s′ = s− α < 0

F =(1 + 9

√2s′5/2)

2(1 − 2s′ + 3s′2 + 2s′3)for s′ > 0

7 8 9: � � 8� � 3R = 3 m B0 = 3 T

a = 1.2 m Ip = 3 MA

κ = 1.5 ne0 = 5 × 1020m−3

Pin = 10 MW PHe = PHi = Pin/2

-. /0 1 23 4567 89 :;<=> ?@A 89 BC

– p. 12/26

Page 13: B C A – p. 1/26

� �� �� � � � � � �� �

(CDBM)

� �

2

� �� � �� � �� � �� � �� ���� � � �� � � !� "# �$ �% � &' � � �� () � * +, - ) � � " �.0/ 1 � 234

(

&' �

= 0)

5 6 �� () � 3. "# � $ � �78 ' � %9 : ; � " < �� = >? = : @A " B C �� #

=⇒ λk2⊥ � η‖ (λ = µ0(c

2/ω2pe) :

� D � � ( )

)� E� FG HI : JLK " %9 ��/ 1 � M � : JLK " N D�� O PQ ����� R S T : JLK " N D �� < UV

=⇒

2 3W

CDBM

< %9 � &'X Y/ N D � � � M �

=⇒ Z 2 3W[\ ]^ _ `��

��abcd e fg hijk lm nopqr stu lm vw

– p. 13/26

Page 14: B C A – p. 1/26

�� ��

TASK/TR

�� � �� �� � � � :� / � � � �� � ��� �� ���� � ��� �)� �

ns (s=D,T,He,Impurity)�� ! " #

us (s=D,T,He,Impurity)$ �

Ts (s=e,D,T,He,Impurity)% &' (*) � �Ws (s=α,

+) , -. /

)01 23 � �nfs, nss (s=D,T)45 - 6' 7Ψ8 ) 9 : ;<=> ?@A % &' (*) B ?

RFCD A : EF ? abcd e fg hijk lm nopqr stu lm vw

– p. 14/26

Page 15: B C A – p. 1/26

TASK/TR & TASK/EQ 1

TR

� � �� C� � � # "

EQ

� � � � ��/ 1 � � 6

� � � C� � � :

TR

� � �� O� � � � Q ���TR

�� � � :� / � � � �� � :TR

� � 5 6EQ

� � �� � � � �� � Q $ � � �� � � � � �� � "# ���

TR

: �# " � � D! " C� � #$ � . :/ % � " � �, & : &# " '( � % � F G H I � D) 5 6 *+ : � W � ,

$ "# �/ -. / � � � D! " C� � , &Q ���

TR/EQ

� � 01 < 2 3 � �� 4 56 F � 7 � $ � � � ���

� � � � <TR

: 8K " � �jmax

% � "9 :Q � ; � <

= >� 7? � ���

abcd e fg hijk lm nopqr stu lm vw

– p. 15/26

Page 16: B C A – p. 1/26

TASK/TR & TASK/EQ 2

�. :

TR

<

R, a, κ, δ,B, Ip

� / p, j

� �

ρ

� - ) �EQ

:

#$/ � � � � � 7 � $ � � FG HI , � � , � =/ FG HI

��

(V )

R

q

� � �

ψ

� -) � � � Q ��TR � <

ρ

� -) � � " �) � � X � ���1 � � � � : � � � �) � � ; 5� ; � < � � � � =

� % ��

TR EQ

Ip, p(ρ), j(ρ), u(ρ), T (ρ) � q(ψ),metric(ex.V ′(ψ))

� � � �/ �� � � � � �� � < � ; � "# � # . /

u(ρ)

� � � < 7? � "# � # �

abcd e fg hijk lm nopqr stu lm vw

– p. 16/26

Page 17: B C A – p. 1/26

βp

�� �

: 2s

� �� �� �

1

� � �� ��� �� �

: ne ∝ (1 − r2/a2)1/2� �� �� �A � � � Ts(r = 0) = 1.0keV �ne,D(r = 0) = 0.5 × 1020/m3 � Ip = 1MA

� �� ���> #���� � ! C D "# �$ � �� % & "# �$' � ( ! )$* + , !- � . / �

r = 0.1m

'

ICRH13.5MW

� CD � 021 ���3 � 4

1

+ , !- ��CD5 67 489 : ;<= > �8 ?' � : ;� @ A' �� �� # �

abcd e fg hijk lm nopqr stu lm vw

– p. 17/26

Page 18: B C A – p. 1/26

βp

�� �

: 2s

� �� �� �

2

r < 0.6 m

� �� 8 $ �� � �� � � �< � � � r = 0.3− 0.4 m

BS

: E� � < � / 8 # �$ � � : E� �� �) � � �# � 3 � ��q �' :� � < % & � � � � �� �

s

� ��A � � �α

� � �' 1�

F (s, α)

< ! "' # � / 8 $ � D % &' (< � � "# �

-*,+

-,*/+

-.*/+.1/1*2+./-*2+

.,0*2+

*+/,

0+/,

.+0-*,

,*-+ */+2,

*-0+2,

*1.+2,

abcd e fg hijk lm nopqr stu lm vw

– p. 18/26

Page 19: B C A – p. 1/26

βp

�� �

: 2s

� �� �� �

3

*+.-/,

Raxis : 3.354

Zaxis :−1.481 × 10−14

Saxis : −5.204 × 10−1

βt : 3.964 × 10−3

βp : 1.914

qaxis : 2.794

qsurf : 1.713

abcd e fg hijk lm nopqr stu lm vw

– p. 19/26

Page 20: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

1

� � � �� � � �� ���� �� �� �A � � � Ts(r = 0) = 1.0keV �ne,D(r = 0) = 0.5 × 1020/m3 � Ip = 1MA

� �� ���> #���� � ! C D "# �$ � �� % & "# �$' � ( ! )$* + , !- � . / �0� '

NBI1MW � r = 0.3m

'ICRH10MW

� C D �5 6 " #A ?' � �� ! : E�1

+� �1 MA

!

3 MA

� � � C� - ��CD5 6 !

1

+ 4 � r = 0.7m

'LH4MW

� CD � 0� � 3 �4

2

+ , !- ��CD5 67 489 : ;<= > �8 ?' � : ;� @ A' �� �� # �

abcd e fg h�jk lm nopqr stu lm vw

– p. 20/26

Page 21: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

2

CD �5 6 "#A � r = 0.6m

� � �� 8 $ �� � < % & � � 6$ # �� �� �� � �� � < 1 � : E � �� �) � < � &� � 8 < ! ' 3� �' B ? �� � / � $' � � 1 � � # � � � � 3 � � � > �' (< �� � � � � �� � � �< % & � �# �-*,+

2/0*4+

20,*4+21.*4+

23-*4+/1*4+

/,3*4+

/0.*4+

/2-*4+

-1

,1

/.*0+

*,

+,

.*/+

,0

-0

abcd e fg h�jk lm nopqr stu lm vw

– p. 21/26

Page 22: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

3

CD5 6 4

3s

�� �� � � � ( # � $ �' . � � �

ITB

� % & < � !� � < � � � �� � ! �8 1 ��� > �' (< / �� � � #A � � � �D % & ' (< �� �� . $ � � �� � � �� �A �� 8 � � � �' 1� % & � �� � # �A < # �

-,*/+

-.*/+ /414*5+

/1.*5+/0,*5+

/2-*5+

/,3*5+

,*-+

.-*/+

.,*/+

-*/,0+0*.+

/*.+

*/+2,*-0+2,

*1.+2,

abcd e fg h�jk lm nopqr stu lm vw

– p. 22/26

Page 23: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

4

*+.-/,

Raxis : 3.251

Zaxis :−7.366 × 10−14

Saxis : −1.067 × 10−1

βt : 1.046 × 10−2

βp : 5.777 × 10−1

qaxis : 2.412

qsurf : 4.917

abcd e fg h�jk lm nopqr stu lm vw

– p. 23/26

Page 24: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

5

: E� � �� ?� ��

abcd e fg h�jk lm nopqr stu lm vw

– p. 24/26

Page 25: B C A – p. 1/26

�� �� � � �

: 4s

� �� �� �

6

> �' ( �� ?� ��

abcd e fg h�jk lm nopqr stu lm vw

– p. 25/26

Page 26: B C A – p. 1/26

� � �

� 5 - 6' " #� �� C � # �A ' 1 � � � � " #' # �� �' 1 � � � � < � �' � � " # �A < $ ! � ����

βp

� ) � � � � �� � � �' . # �) �$ �� � �� � ( #�� �� % &� �� � ��� � ) �� / � �� � ���: ;A � ! - # �A ' 1 � � � �� "� � � # # (� � ! �� � ��� � ) �� / "# $ <% & ��' 4 � ( )� � �' . #

ITB

� % &�* + "���, ) �' � 5 - 6' " #� - � � C � # �

ITER

� .) /0 ) 9 � 1 � � 23 .) /A 4 5 " # �= 67 � 01 2 3 � 89 !: ; � - � � C � � � .' � �< �0= �

abcd e fg h�jk lm nopqr stu lm vw

– p. 26/26