for the Deductive Procedure of Fusion Reactor Design J Miyazawa National Institute for Fusion Science Japan USJapan Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea ID: 416178
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Slide1
Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design
J. MiyazawaNational Institute for Fusion Science, Japan
US-Japan Workshop on Fusion Power Plants and Related Advanced Technologies with participations of EU and Korea
（
22-24 Feb. 2011
）Slide2
J. Miyazawa, 第424回LHD実験グループ全体会議 （30 Aug. 2010）2/15Slide3
How Do You Estimate the Fusion Output?In general fusion reactor design activities…- Radial profiles: parabolic for both T and n- MHD equilibrium: vacuum config. is often useed in helical reactor design- Density: density limit scaling- Temperature: energy confinement scaling
- Assumptions: T(r), n(
r
), equilibrium,
n
DL
, DL factor,
t
Escaling, H-factor, …In the DPE method proposed here…- Profiles and equilibrium obtained in the experiment are directly used- Gyro-Bohm type parameter dependence is assumed- Degree of freedom in determining profiles is largely reduced (= high reliability)
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）
3
/14Slide4
A New Procedure of Fusion Reactor DesignJ. Miyazawa, US-J Workshop （22-24 Feb. 2011）4/14Conventional procedure (inductive approach) New procedure using DPE (deductive approach)Slide5
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）DPE: Direct Profile ExtrapolationFrom the definition: fb = fT f
n fB-2
f
T
=
fb fn-1 fB2
(1)Gyro
-Bohm:
t
E
GB
a
2.4
R
0.6
B0.8 P-0.6 n0.6 n T a2 R / P a2.4 R0.6 B0.8 P-0.6 n0.6 T a0.4 R-0.4 B0.8 P0.4 n-0.4 fT = g fa/R0.4 fB0.8 fP0.4 fn-0.4 (2) delete fT from Eqs. (1) and (2) fP = g-2.5 fb2.5 fa/R-1 fB3 fn-1.5 (3) Then, fa is determined so as to satisfy Preactor = fa3 fa/R-1 fn2 (z Pa’ – PB’) (dV/dr)exp dr = g-2.5 fb2.5 fa/R-1 fB3 fn-1.5 Pexp(in this study, fa/R = z = Zeff = 1)
5
/14
fX : enhancement factor of X（e.g. fT = Treactor (r) / Texp(r), fn = nreactor (r) / nexp(r), fP = Preactor / Pexp）
Equilibrium in LHD
Volume integration of (alpha heating – Brems.)
One can calculate the alpha heating power per unit volume by assuming
f
B, fn, and fb
fa (= fR) is obtained if fB, fn, fb and g are given
Plasma volume × fa3
fa/R = 1 (fa = fR)
g : confinement enhancement factor
Independent of a and R
I
ndependent of a and RSlide6
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）fa （= fR） is determined so as to fulfill the power balancefn
=2, fb=5 and
g
=1.3 reproduce the profiles assumed in FFHR2m2
Example
6
/14
×
fn×
fT
×
f
b
Heating power ×
f
P
Mag. Field ×
f
B
Exp.ReactorConfinement × gPlasma volume × fa3Slide7
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）Mag. Field Strength Determines the Plasma Size
7/14
What is this lower envelope?
Design window for
f
n
= 1
B
reactor is scanned for various fn
(f
b
and
g
are fixed to
1
)
The
minimum
R
reactor is given as a function of BreactorSlide8
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）Rreactor ∝ Cexp Breactor-4/3Preactor = fa3 fa/R-1 fn
2 (z
P
a
’ – P
B
’
) (
dV/dr)exp dr ∝ fa
3 fa/R
-1
f
n
2
f
T
X
∝ fa3 fa/R-1 fn2 (fb fn-1 fB2)X ∝ g-2.5 fb2.5 fa/R-1 fB3 fn-1.5 Pexp fa3 ∝ g-2.5 fb2.5-X fB3-2X fn-3.5+X Pexp .(X = 3.5) fa ∝ g-5/6 fb-1/3 fB-4/3 Pexp1/38/14 Eq. (3)fn dependence disappears… Rreactor = Cexp g-5/6 fb-1/3 B-4/3CexpA small Cexp results in a compact reactorTemp. dependence: f
TX Slide9
輻射損失の効果
輻射損失の効果
J. Miyazawa, US-J Workshop
（
22-24 Feb. 2011
）
C
exp
is Given at a Fixed Temperature (z Pa’ – P
B’) (dV
/
d
r
)
exp
d
r
∝
f
TX <sv> ∝ TX(X =3.5 @ T ~ 7.1 keV w/o Bremsstrahlung) 9/14Actually, the plasma size becomes minimum at T0 ~10 keV (due to Brems. and volume-integration) Temp. dependence of DT fusion reaction rateTemp. dependence of an index X (<sv> ~ TX)<sv> ~ T3.5BremsstrahlungBremsstrahlungSlide10
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）How to Get Cexp 10/14Cexp１）Set fn = f
b = g = 1: f
T
= f
B
2
２）
Scan Breactor = fB Bexp:
Heating power: f
B
3
P
exp
Volume-integration:
(P
a
’ – PB’) (dV/dr)exp drRreactor = [(Heating power) / (Volume-integration)]1/3 Rexp３）The minimum of Rreactor / Breactor-4/3 is the Cexp (Note: in some cases, fn = 1 might be inadequate!)Slide11
Cexp is a Good Measure of Plasma Performance11/14
J. Miyazawa, US-J Workshop （
22-24 Feb. 2011
）
C
exp
can measure the plasma performance, like the fusion triple product of
nT
tAlthough an inverse correlation between Cexp and
nTt is recognized…
The maximum of
nT
t
does not necessarily correspond to the minimum of
C
exp
nT
t
is given by the averaged (or, the central) values, while the whole profiles of n and T are used to get Cexp Cexp that directly shows the design window is a better index than nTt!!Rreactor = Cexp g-5/6 fb-1/3 B-4/3FFHR-d1FFHR-d1Slide12
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）Seek the Minimum Cexp12/14
To design a helical DEMO reactor FFHR-d1 of (Rc,
B
c
,
C
reactor
) ~ (14 m, 6.5 T, 170), we are now trying to get the minimum
Cexp in LHD (Cexp ~ 225 in the 14th cycle exp.)How can we minimize the
Cexp?
magnetic
config
., high beta, high density, …
FFHR-d1
FFHR-d1Slide13
J. Miyazawa, 第424回LHD実験グループ全体会議 （30 Aug. 2010）13/15Slide14
Magnetic Configuration is ImportantJ. Miyazawa, US-J Workshop （22-24 Feb. 2011）14/14Cexp* is smaller in the vertically elongated magnetic configurationThe optimum magnetic field strength is ~ 1.5 T Slide15
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）How Large Enhancement is Needed?Rreactor = Cexp g-5/6 fb-1/3 B-4/3
If the design point is already fixed and the experimetal result is not enough, the beta should be increased with f
b
=
g
-2.5
(C
exp
/ Creactor)3 15/14
R
reactor
=
C
reactor
B
-4/3Slide16
DPE: a new method to predict the fusion out put- Using “real” profiles and equilibrium- Gyro-Bohm is assumed - fa (= fR) is estimated for assumed fB, fn, fb, g
The plasma (device) size is proportional to
C
exp
-
R
reactor
∝ Cexp Breactor-4/3 Seek the minimum C
exp
-
C
exp
is a better index than
nT
t
A new procedure of fusion reactor design
- Deductive approach is possible with DPE
Summary
J. Miyazawa, US-J Workshop
（22-24 Feb. 2011）16/14Slide17
FFHR-2m2
17
/14
J. Miyazawa, US-J Workshop
（
22-24 Feb. 2011
）Slide18
J. Miyazawa, US-J Workshop （22-24 Feb. 2011）ベータ値増大は出力増大を伴うfP = g-2.5 fb2.5 fa/R-1 fB3 fn-1.5 に fT = fb f
B2 fn-1 = const を適用
f
P
∝
g
-2.5 fa/R fb◎ エンベロープでの加熱パワーは fB と f
n には依らず、
f
b
に比例
◎
閉じ込め改善度
g
によって大幅減
◎ fb ~ 5 で磁場を低減、g ~ 1.2 で加熱パワーを低減できればFFHR2m2は可能FFHRの仕様で閉じ込め改善なしならば 1.3 GW の加熱パワーが必要（全核融合出力 6.5 GW）fb = 8 で中心βは 16 % (!)ベータ限界は？18/11