B C A – p. 1/26
Transcript of B C A – p. 1/26
�� ��� � �� � � �
�� � ��� � ��� � ��
� ��
� � � ! " #$% & ' ! () *+ " #,
-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC
– p. 1/26
� � ��� �� �� � � � �� �� � ��
=⇒
�� � �� ��� � �� � � � �� !" #$ %
� � �� & '
=⇒
() *+ � ,-
�. / 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
� � � �� �� � � �� �
� / 0 1� � �
(φ
�
)
� � � < () * + � ,-
� / 0 1� � � � C H I � � ?
� � ;� � � � � �
E × B
� � � C H I � � ?
ITB
� � � ;� Q� � � , � �� � !" @ � # � � #$�&% � � ;�
Er =1
Zieni
dpi
dr+ VφBθ − VθBφ
∴
' (�) () *+ � ,� � � / 0 1� � �- . � / � 0 %
-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC
– p. 3/26
� � � �� �� � ��
MHD
� � �� �
� � � � � � � �
ρ(V · ∇)V
- . � � �%MHD
� � � � �
∇ · (ρV ) = 0 ∇× B = j
ρ(V · ∇)V = j × B −∇p E + V × B = 0
∇× E = 0 B · ∇T = 0
∇ · B = 0 p =ρT
m� J � �� � � �- ��%� ��� �(R, φ, Z)
!" #%$ &' ( )*+
φ
,- . " / 01 23 465789 :;+ <= > ?@ AB9 C D B " # " E5-. /0 1 23 4567 89 :;<=> ?@A 8 9 BC
– p. 4/26
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
� � � �� � � � �� � �� � �� ��
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
�� � �� �
:
� �� �
. / 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
�� �� � � �
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
�� �� � � �
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
�� �� �
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
�
Bθ
�
−η‖
FR0
〈|∇ρ|〉
〈R−2〉〈JCDB〉
�
JCD :� ���
F : F = BφR
V ′ : dV/dρ � V
� ! "# $%
η‖ :
&'(-. /0 1 23 4567 89 :;<=> ?@A 89 BC
– p. 10/26
� �� � �
() H ��� �� H� �" � � �� � �� *+ �� � � �
� * +
χNC
� < () *+
χTB
� " � %χe = χNC,e + 12χTB
χi = χNC,i + 12χTB
CDBM
� �� � � � <� �� � � �� � �� *+
χTB = F (s, α, κ)α3/2 c2
ω2pe
vAqR
� �H Is ≡ r
q
dq
drF G D Eα ≡ −q2Rdβ
dr� �� �
κ ≡ − r
R
(
1 − 1
q2
)
-. /0 1 23 4567 89 :;<=> ?@A 89 BC
– p. 11/26
� � � � �� � � �
� �
F (s, α, κ)
� *+ � A � � �� + �� � ��� �
� �� � � �% (κ� 1)
F =1
√
2(1 − 2s′)(1 − 2s′ + 3s′2)for s′ = s− α < 0
F =(1 + 9
√2s′5/2)
√
2(1 − 2s′ + 3s′2 + 2s′3)for s′ > 0
7 8 9: � � 8� � 3R = 3 m B0 = 3 T
a = 1.2 m Ip = 3 MA
κ = 1.5 ne0 = 5 × 1020m−3
Pin = 10 MW PHe = PHi = Pin/2
-. /0 1 23 4567 89 :;<=> ?@A 89 BC
– p. 12/26
� �� �� � � � � � �� �
(CDBM)
� �
2
� �� � �� � �� � �� � �� ���� � � �� � � !� "# �$ �% � &' � � �� () � * +, - ) � � " �.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[\ ]^ _ `��
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– p. 13/26
�� ��
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
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
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
�
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
�
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
�
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
�� �� � � �
: 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
�� �� � � �
: 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
�� �� � � �
: 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
�� �� � � �
: 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
�� �� � � �
: 4s
� �� �� �
5
: E� � �� ?� ��
abcd e fg h�jk lm nopqr stu lm vw
– p. 24/26
�� �� � � �
: 4s
� �� �� �
6
> �' ( �� ?� ��
abcd e fg h�jk lm nopqr stu lm vw
– p. 25/26
� � �
� 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