Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design

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 ）

J. Miyazawa, 第 424 回 LHD 実験グループ全体会議（ 30 Aug. 2010 ） 2/15

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, nDL, DL factor, tE

scaling, 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 ） 3/14

　 A New Procedure of Fusion Reactor Design


Conventional procedure (inductive approach)

New procedure using DPE (deductive approach)

Plasma Experiment Confinement improvement Self-ignition

ScalingsRadial

profilesMHD

equilibrium

Density limit

Engineering Parameters

Fusion output

Mag. field

strengthDevice

size

Engineering Parameters

Fusion output

Mag. field

strengthDevice

size

DPEEnhance

ment factors

Self-ignition Cexp

Plasma Experiment

Radial profiles MHD equilibrium

J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ）

DPE: Direct Profile Extrapolation

From the definition: fb = fT fn fB-2 fT = fb fn

-1 fB2 (1)

Gyro-Bohm: tEGB a2.4 R0.6 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 fB

0.8 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 fb

2.5 fa/R-1 fB

3 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 fB, fn, and fb

fa (= fR) is obtained if fB, fn, fb and g are given

Plasma volume × fa

3

fa/R = 1 (fa = fR)

g : confinement enhancement factor

Independent of a and R

Independent of a and R


fa （ = fR ） is determined so as to fulfill the power balance

fn=2, fb=5 and g=1.3 reproduce the profiles assumed in FFHR2m2

Example

6/14

× fn

× fT

× fb

Heating power × fP

Mag. Field × fB

Exp. Reactor

Confinement × g

Plasma volume × fa

3


Mag. Field Strength Determines the Plasma Size

7/14

What is this lower envelope?

Design window for fn = 1

Breactor is scanned for various fn (fb and g are fixed to 1 )

The minimum Rreactor is given as a function of Breactor


Rreactor ∝ Cexp Breactor-4/3

Preactor = fa3 fa/R

-1 fn2 (z Pa’ – PB’) (dV/dr)exp dr

　　∝ fa3 fa/R

-1 fn2 fT

X

∝ fa3 fa/R

-1 fn2 (fb fn

-1 fB2)X ∝ g-2.5 fb

2.5 fa/R-1 fB

3 fn-1.5 Pexp

fa3 ∝ g-2.5 fb

2.5-X fB3-2X fn

-3.5+X Pexp .

(X = 3.5) fa ∝ g-5/6 fb

-1/3 fB-4/3 Pexp

1/3

8/14

Eq. (3)

fn dependence disappears…

Rreactor = Cexp g-5/6 fb-1/3

B-4/3

Cexp

A small Cexp results in a compact reactor

Temp. dependence: fT

X

輻射損失の効果

輻射損失の効果


Cexp is Given at a Fixed Temperature

(z Pa’ – PB’) (dV/dr)exp dr ∝ fTX <sv> T∝ X

(X =3.5 @ T ~ 7.1 keV w/o Bremsstrahlung)

9/14

Actually, the plasma size becomes minimum at T0 ~10 keV (due to Brems. and volume-integration)

Temp. dependence of DT fusion reaction rate Temp. dependence of an index X (<sv> ~ TX)

<sv> ~ T3.5

Bremsstrahlung

Bremsstrahlung


How to Get Cexp

10/14

Cexp

１） Set fn = fb = g = 1: fT = fB2

２） Scan Breactor = fB Bexp:

Heating power: fB3 Pexp

Volume-integration: (Pa’ – PB’) (dV/dr)exp dr

Rreactor = [(Heating power) / (Volume-integration)]1/3 Rexp

３） The minimum of Rreactor / Breactor-4/3 is the Cexp

(Note: in some cases, fn = 1 might be inadequate!)

0

1

Cexp is a Good Measure of Plasma Performance

11/14J. Miyazawa, US-J Workshop （ 22-24 Feb. 2011 ）

Cexp can measure the plasma performance, like the fusion triple product of nTt

Although an inverse correlation between Cexp and nTt is recognized…

The maximum of nTtdoes not necessarily correspond to the minimum of Cexp

nTtis 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-4/3

FFHR-d1

FFHR-d1


Seek the Minimum Cexp

12/14

To design a helical DEMO reactor FFHR-d1 of (Rc, Bc, Creactor) ~ (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-d1

J. Miyazawa, 第 424 回 LHD 実験グループ全体会議（ 30 Aug. 2010 ） 13/15

Magnetic Configuration is Important


Cexp* is smaller in the vertically elongated magnetic configuration

The optimum magnetic field strength is ~ 1.5 T


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 fb = g-2.5 (Cexp / Creactor)3 15/14

Rreactor = Creactor B-

4/3

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 Cexp - Rreactor ∝ Cexp Breactor

-4/3

Seek the minimum Cexp - Cexp is a better index than nTt

A new procedure of fusion reactor design- Deductive approach is possible with DPE

Summary


FFHR-2m2

17/14J. 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 fB2 fn

-1 = const を適用 fP ∝ g-2.5 fa/R fb

◎ エンベロープでの加熱パワーは fB と fn には依らず、 fb 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

Direct Profile Extrapolation Method for the Deductive Procedure of Fusion Reactor Design

Documents