global energy connement scaling predictions for tandem mirrors

KSTM TBD – slide 1

Global Energy Confinement Scaling Predictions for TandemMirrors

W. Horton, J. Pratt, H.L. BerkUniversity of Texas at Austin, IFS

March 9, 2006

Relation between Radial and Axial Losses in Tan-dem Mirrors


� The tandem mirror still remains a potentially attractive magneticconfinement geometry. The absence of toroidal curvature and internalplasma parallel current gives the system strongly favorable stability.

� GAMMA-10 experimental results demonstrate that sheared rotation cansuppress turbulent radial losses.

� For an MHD stable system, we investigate the interplay between drift wave(ITG, ETG and Bohm) radial transport and axial losses.

� Using empirical energy confinement scaling laws from large ITER and ISSdatabases as upper bounds on the radial loss rates, we simulate radialtransport for burning plasma.

� Our simulations show that high core temperatures result in long Pastukhovloss times; drift wave radial transport dominates, except at the plasmaedge, where pitch angle scattering losses dominate.

� We consider 3 sets of machine data: the Gamma-10 hot ion (G10-HI) mode,Gamma-10 high potential (G10-HP) mode [4], and the KSTM fusion reactor.

Machine Concepts


Figure 1: On the left is the KSTM fusion reactor (

� �� ) [1],on the right is a schematic of the Gamma-10 (

� �� ) [4]

Table of Machine Parameters


Parameter G10-HI G10-HP KSTM-FR valuea .36 m .36 m 1.5 mL 6 m 6 m 30 m��

�� .3 .3 7�� .4 T .4 T 3 T�� ! " .49 T .49 T 18 T#%$ 1 keV (2003) 300 eV (corr.) 60 keV#'& 4 keV (2005) 1 keV (corr.) 15 keV

Table of Machine Parameters continued...


Parameter G10-HI G10-HP KSTM-FR valuegas type D-D D-D D-Tvolume 2.44 � � 2.44 � � ( ( � �surface area

� � � � � � () � � �

* & � + & � #'& � � , )

* $ � + $ � #%$ ( � � � � ) �

+�

kV (2003)

�

kV (corr.) 117 keV+'- ( �

kV

�kV 510 keV.0/ 12 � � 3 � , 3 � 3

465 � ( � ( 7

8 � � � 7 � �

Outline of Scaling Work


1. We derive scaling laws for confinement time and stored energy vstotal power input from alpha and ECH, using Bohm, gyro-Bohm andETG turbulent diffusion models and the power balance equation.

2. We calculate Bohm and ETG dimensionless transport coefficents( * 9

and * /: ;

respectively) using theory and simulation as well ascomparison with experimental data from toroidal machines.

3. We compare results from KSTM scaling laws with severalexperimental databases for tokamaks and stellarators (a proxy forexperimental data).

4. We evaluate Lawson’s Criterion and fusion power amplificationfactor Q for these scaling laws.

5. We solve radial transport equation for the profiles to thermal stabilityand prepare for drift wave stability calculations.

Summary of Global Scaling laws for Radial LossTimes <>= (s) Adapted to the Tandem Mirror


Table 1: Summary of Global Scaling laws for Radial Loss Times ? / (s)

? 9/ � � � � ( � � @ � � � @ � � � � � @ � . � � @ �

? A 9/ � � � �CB � �B D � �B E �B D . � B D

? /: ;/ � � ( � F �B � � � �B D D � � . � B � �

?HG � I � � � �CB � � �B � � � �JB � D �B E . � B I �

?2 � � � � , � � B � � �B E D � �B E E �B E � . � B D�

?HK L L�M � � � �CB � � �B � DM � �B � � � � BM � . � BM �

?HK L L� E � � � �NB � � �B D � �B � � �BM � . � B D E

We estimate dimensionless transport coefficients for the Bohm (B), gyro-Bohm(gB) and ETG models using a simple matching technique. In the NSTXexperiment, shot 106194 LeBlanc et al report

OQP RTS R

MW and U / P S VW XZY

which matches the L97 prediction [5]. We require that our Bohm, gyro-Bohm,and ETG scaling laws for confinement time match the L97 prediction atO P RTS R

MW as well; this matching determines the diffusivity coefficients.

Power Amplification Factor: Q


The measure of success of a magnetic confinement machine is thepower amplification factor

[

. The formula for

[

is simply power-outdivided by power-in:

[ �.0\ ] ^`_a

. ^a b`cd ec fg

(1)

In steady state:

[ih jk � � .6l � .h jk (2)

The more general transient formula for[

is:

[ m � � . l �n .h jk Fo

opq

(3)

� � . l �n .c a f r .6s t fvu h w x F .6l q

(4)

KSTM-FR Confinement Times


Radial Confinement Time in the KSTM

Palpha+ PECH(MW)

t E(s)

0 20 40 60 80 100 120

0.0

0.5

1.0

1.5

2.0

ETGBohm

gyro−Bohm

L97

H98

ISS04

Calibration with NSTX Shot 106194

Classical drift wave scaling laws (Bohm, gyro-Bohm, and ETG) are normalizedto match empirical L97 results from NSTX at 3.3 MW of radial power loss.

Confinement Times for the Gamma-10


Radial Confinement Time − Gamma 10 (Hot Ion Mode)

PICH + PECH(kW)

t E(ms)

0 100 200 300 400 500

05

10

15

20

25

30

cho ’05 data

ETG

Bohmgyro−Bohm

L97 H98

ISS04



Radial Confinement Time − Gamma 10 High Potential Mode

PICH + PECH(kW)

t E(ms)

0 100 200 300 400 500

05

10

15

20

25

30

ETG

Bohm

gyro−BohmL97

H98

ISS04

Calibration with NSTX Shot 106194



Radial Confinement Time vs density− Gamma 10

density [1018m −3]

t E(ms)

0 1 2 3 4 5

510

15

yatsu ’03 data

ETG

Bohmgyro−Bohm

L97

H98

PECH = 140 kWφc= 0.6 kV

Breakeven Scaling Law Results – KSTM-FR


0 50 100 150 200

02

46

8

Breakeven in the Fusion Reactor

Te (KeV)

Q

0 50 100 150 200

02

46

8

Q (fus/ECH)

Here we use only

O / 12 for external heating power – this makes an optimisticestimate for when breakeven is achieved. For

y $ P R W S z

KeV theO / 12 P W { V

MW,

O l P R XMW and

|h jk P } O l ~ Oh jk P W

.

Pastukov End Loss Times for the KSTM


0 20 40 60 80 100 120

050

100

150

Ratio of Pastukov/confinement time (KSTM−FR)

Te(keV)

past−loss/radial−loss/100

ETGBohm

gyro−Bohm

L97

for

� & P W W {

keV,

� $ P } W VkeV. and � $ P W V ��

.

Pastukov End Loss Times for the Gamma-10


Ratio of Pastukov/confinement time (G10−hot ion mode)

Te(keV)

past−loss/radial−loss

0 0.5 1 1.5

01

23

ETG

Bohm gyro−Bohm

L97

PECH = 170 kW

Pastukov End Loss Times for the Gamma-10


Ratio of Pastukov/confinement time (G10−high pot. mode)

Te (keV)

past−loss/radial−loss

0 0.5 1 1.5

24

68

10

ETGBohm gyro−Bohm

L97PECH = 170 kW

Power Ramp for the KSTM Reactor


Conclusions


1. Core plasma is burning with ?� � � ? s t f ^ t � g g

. Thus radial turbulentlosses dominate in the core of the central cell.

2. Confinement similar to straight cylinder confinement with axis toopen field line biasing for

�6� .3. Edge plasma is parallel-loss dominated from pitch angle scattering

into the velocity space loss-hyperbola.

4. The tandem mirror geometry provides natural divertor configurationto make use of the annulus of end losses.

5. ?� � � ? /: ;� � � � . � � � � � � � stable thermal temperature

# m .6. Steady State

[ h j k up to 5.0 for

#%$ � ( �

keV,

#'& � ��

keV.


[1] R. F. Post, T.K. Fowler, R. Bulmer, J. Byers, D. Hua, L. Tung.“Axisymmetric Tandem Mirrors: Stabilization and Confinement Studies”.Innovative Confinement Concepts Workshop. May 25-28 2004. MadisonWisconsin.

[2] Hua, D.D. and T. K. Fowler. SYMTRAN - A Time-dependent SymmetricTandem Mirror Transport Code.

[3] Fowler, T. K. Correspondence. 6/21/04.

[4] T. Cho, J. Kohagura, M. Hirata, et al. Nuclear Fusion. 45 (12), 2005.

[5] B.P. LeBlanc, R.E. Bell, S.M. Kaye, et al. Nuclear Fusion. 44 (4), 2004.

[6] K. Yatsu, T. Cho, H. Higaki, et al. Nuclear Fusion. 43 (5), 2003, p358.

global energy connement scaling predictions for tandem mirrors

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