1

FRC on the Path to Fusion Energy(Moderate Density Steady-State Approach)

Alan Hoffman

Redmond Plasma Physics LaboratoryUniversity of Washington

(FPA Meeting on Fusion Pathways to the Future)(September 27-28, 2006)

2

Outline

History – ‘Achieving field reversal’, -pinch

formation.

What is an FRC? Why are we interested?

Recent developments, particularly for steady-state.

Ultimate promise.

3

Attempts at Field Reversal have a LongHistory – supra-thermal ring currents

ASTRON & Reversed Field Mirrors at LLNL in the 1960s.

Achieved with pulsed electron rings; ion rings being pursued.

4

Field Reversed Configurations (FRCs)(plasma currents producing field reversal)

Compact toroid with ‘negligible’ toroidal field - 0.5 < < 1.0

Simple cylindrical geometry – natural divertor.

Low magnetic fields – inexpensive reactors & experiments.

Low field region – kinetic physics applies.

High voltage -pinch formation – best for pulsed approach.

rcrsBo

Bexs rs/rc

= 1 - _xs2

Be = Bo/(1-xs2)

5

LANL FRXC/T - (1980s)

FRCs extremely robust – survive dynamic translation, reflection, & capture.

Translated FRCs develop moderate toroidal fields.

Evidence of high minimum energy state in more recent TCS experiments.

Pulsed plasmas with only ~100s of µsec lifetimes.

Interferogram taken on FRX-C

using holographic interferometry

6

Concerns About Stability

2-D interchange typeinstabilities, driven by plasmarotation, have been stabilizedby weak multipoles withBm

2/2µo > centrifugal

pressure Internal tilt is more insidious –

kinetic effects are important.

End

view

Interchange Tilt

Side View

/m

hd

E/S*0.2

0.2

00 0.4

0.4

0.6

0.6

0.8

0.8

E = 4

E = 6

E = 12

1.0

1.0

S*/

E <

3.5

Typical kineticcalculations by

E. V. Belova et al.

more kinetic

7

Large s Experiment (LSX) Built at STI to StudyExtrapolation to non-Kinetic Regime – (1990).

=sr

R isr

rdrs

Kinetic # of

internal gyro-radii

parameter

10

100

1000

1 10 100

LSX

TRX-1

TRX-2

FRX-B

FRX-C

LSM

Tim

e (µ

sec)

N (rs/ i)3

LSX

General

N xsrs2/ i

rs/2 i (cm1/2)

Stable FRCs formed with s up to ~ 4,

n ~ 1021 m-3, n ~ 1018 m-3s

Ti up to 2 keV Te up to 0.5 keV

N E _ N

8

What is needed for steady-statecompact toroid (CT) reactor?

Ideal ne ~ 1-2 1020 m-3, Te = Ti ~ 10 keV, Be ~ 1-1.5T

Continued stability up to s ~ 20-30

Sufficient energy confinement - n E > 1020 m-3s.

Reactor relevant formation methodology

Efficient sustainment of cross-field diamagnetic current I

– is anomalous.

– It is actually the poloidal flux which must be sustained; (I = 2Be/µo

simply due to diamagnetism)

9

Techniques for Sustaining FRCs(also enhance stability)

Tangential Neutral Beam Injection (TNBI)

– Kinetic ions should be stabilizing (low s particles).

– Studied in Japan and proposed by PPPL & UW. No current experiments.

Rotating Magnetic Fields (RMF) can drive electrons in same

manner as induction motor. (Also formation technique.)

– Provides stabilizing inward radial force

– Developed in Australia and adopted by UW. Recently demonstrated in TCS.

Key parameter is anomalous cross field resistivity, , since it

determines current drive (or flux sustainment) power

requirements.

– All transport may be related to this parameter.

10

RMF Current Drive (dipole fields)

Simple loop antennas with ~10-200 kHz RF phased 90° apart

‘Drag’ electrons along with rotating radial field

RMF antennaIz = Iosin t

RMF antennaIz = Iocos t

Bz field coils

driven electron current rotating field B

11

TCSTCS(Translation, Confinement, Sustainment)(Translation, Confinement, Sustainment)

LSX/mod(formation & ‘acceleration’)

TCS Chamber(confinement & RMF drive)

RMF

Antennas

Primarily interested in FRC formation & sustainment by RMF alone.

12

Partial RMF Penetration isPartial RMF Penetration isNatural OccurrenceNatural Occurrence

Vacuum calculation in

lab frame of referencePlasma calculation in

RMF frame of reference.(Calculation needs to start

from already formed FRC)

Plasma measurement in

RMF frame of reference

so

s

RMF

r

BrT

*222

µ=

*

13

2D Interchange Stability Providedby Partially Penetrated RMF

Wall

0 90 180 270 360h2004t6

0.4

0.2

0.6

0.8

1.0

r/(Be

2

/ 20)

Calculations show strong restoring forces to

rotationally driven interchange instabilities,

such as the ubiquitous rotating n=2.

00

0.5

1.0

1.520

30

25

35

40

1.0

Time (ms)

2.0

h2004

t2

3.0

19

m-2

)r

(cm

)

0.05-m gap

(#13709)

0.35-m gap

(#13863)

Observation of stabilizing effect on

rotational n=2 instability when RMF

antennas extend over central region

14

RMF also reverses radial particle diffusion& results in long particle lifetime

Nominal ‘ N’ extended by at least factor of 10.

‘Steady-state’ sustainment due to recycling with

pulse length only limited by RMF power supply.

RM

F M

agn

itu

de

(mT

) 15

10

5

0

- 5

-10

-15

Ax

ial

Mag

net

ic F

ield

(m

T)

0Time (msec)

5.0

3.7

1.3

0

brawc31 12967brawc31 12974

Bext

Bext(vacuum)

Bint

B B (vacuum)

2 4 6 8 10

Collisional plasma but

no sign of tilt instability

15

Also see spontaneous toroidal field development:further evidence for a minimum energy state (MES)

(Shot 12968 – 2.63 ms)

(Shot 12964 – 2.5 ms)

0

0

5

-15

15

-10

10

-5

10 20

RADIUS (cm)

INT

ER

NA

L F

IEL

D (

mT

)

30 40

hg2004.2

3

Bz

Bx

BRMF

Before

Transition

(Shot 12968 – 2.63 ms)

(Shot 12964 – 2.5 ms)

0

0

5

-15

15

-10

10

-5

10 20

RADIUS (cm)

INT

ER

NA

L F

IEL

D (

mT

)

30 40

hg2004.2

3

Bz

Bx

BRMF

Before

Transition

0

0

-2

2

0

5

10

15

20Shot No: 12964

(with/out 10 kHz filter)

2 4TIME (ms)

Be (m

T)

Bto

r(m

T)

6

r = 24 cm

8

hg2004

tf1

100

0

-2

2

0

5

10

15

20Shot No: 12964

(with/out 10 kHz filter)

2 4TIME (ms)

Be (m

T)

Bto

r(m

T)

6

r = 24 cm

8

hg2004

tf1

10

After

Transition

(Shot 12964 – 4.1 ms)

0

0

5

-15

15

-10

10

-5

10 20RADIUS (cm)

INT

ER

NA

L F

IEL

D (

mT

)

30 40

hg2004.2

4

Bx

BzBRMF

(Shot 12968 – 5.22 ms)After

Transition

(Shot 12964 – 4.1 ms)

0

0

5

-15

15

-10

10

-5

10 20RADIUS (cm)

INT

ER

NA

L F

IEL

D (

mT

)

30 40

hg2004.2

4

Bx

BzBRMF

(Shot 12968 – 5.22 ms)

16

Plasma density depends on

Also see rapid reductions in with increasing temperature.

(In calculations with constant , nm decreases with Tt, while experimentally it increases).

Observed dependencies are characteristic of decreasing with vde/vsound, as seen in

all empirical scaling, and supported by recent two-fluid numerical calculations.

0

0.5

1.0

1.5

2.0

2.5

3.0

0 1 2 3 4 5 6 7 8 9

RMF Drive Parameter: B ( */rs)1/2/( r/0.15)1/2rs

Pe

ak D

en

sity:

nm (

10

19m

-3)

114 kHz83 kHz

152 kHz

258 kHz

Calc

nm = 0.044{Bw( */rs)1/2/rs r

1/2}4/3

44

3659

25

28

41 24

36

39

30

60

Tt

Resistive Torque

T ne3/2Tt

1/2rs2.

m)m10(

50~

3192/1µ

mn

Same as seen in high density -

pinch formed decaying FRCs

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Relative current drive power alsodecreases with temperature

Effective ‘ p’

0

0

10

150

100

50

114 kHz

152 kHz

258 kHz

20

(Be/B )2 ~ Tt

30

hg

20

05

.alh

.f1

0

40

Pab

s/6.8

(2B

e/µ

o)2l

s (µ

-m)

10,000 in

reactor

18

Experimental results described well by empirical‘Chodura’ formula, dependent on vde/vs.

Provided best numerical match to

formation and translation experiments( ) m1)m10(

1050 v/v

3192/1Chod µ= tideene

Strong vde/vs scaling supported by recent

numerical calculations.

vde/vs < 1 vde/vs >1

*Non-linear 2-fluid calculations of instabilities in a Z-pinch by

Loverich & Shumlak for various vde/vs.

0.11.54vde/vs

10100100f (kHz)

2.50.350.4rs (m)

1.00.060.02Be (T)

250.30.05Tt (keV)

1.00.30.2ne (1020m-3)

ReactorTCSU(goals)

TCS

Projected vde/vs ratios

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TCS Temperature (and Flux) Limited inPresent Experiments – at least partially byimpurities

#9729

0 0.4 0.8 1.2 1.6

TIME (msec)

Be (mT) 18

12

6

0

nedl (1019m-3)

0.6

0.4

0.2

0

Tt (eV)

0 0.4 0.8 1.2 1.6

TIME (msec)

120

80

40

0

praddl

(MW/m2)

0.6

0.4

0.2

0

Pabs

(MW)

2.0

1.5

1.0

0.5

0

B (mT)

3

2

1

0

#9751

Operation at High = 1.62x106 s-1 and Low B with symmetric RMF current drive

& -pinch vacuum technology

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TCS/upgrade Built to Reduce Impurity Leveland Radiative Losses

Larger, metal input section to avoid translated FRC contact with quartz.

Protective tantalum covered flux rings under quartz RMF drive section.

Elimination of Viton “O-rings” to allow bakeout and discharge cleaning.

Ti-gettering or siliconization wall conditioning.

80 CM 32 CM 75 CM 125 CM 32 CM 80 CM60 CM 75 CM

cp magnets

cmp magnets

mirror magnet

fast gate coil

capture magnets

Original Source Section

Transition Section

Central Confinement Section(Quartz For RMF Drive)Transition

SectionEnd/PumpingChamber

48 cm I.D.

80 cm I.D.

40 cm I.D.flux rings, tantalum

clad, 76 cm I.D.

diagnostic portsdiagnostic

ports48 cm I.D.

80 CM 32 CM 75 CM 125 CM 32 CM 80 CM60 CM 75 CM

cp magnets

cmp magnets

mirror magnet

fast gate coil

capture magnets

Original Source Section

Transition Section

Central Confinement Section(Quartz For RMF Drive)Transition

SectionEnd/PumpingChamber

48 cm I.D.

80 cm I.D.

40 cm I.D.flux rings, tantalum

clad, 76 cm I.D.

diagnostic portsdiagnostic

ports48 cm I.D.

21

TCS/upgrade

22

Recent Interesting Results

Anti-symmetric RMF (originally proposed theoretically)

results in completely closed field lines and, hopefully, good

thermal confinement.

h20

05

tiR

MF

15

-1.00

0.2

0.1

r (m

)

0.4

0.5

0.3

0

z (m)

0.5 1.0-0.5

Iant IantRMF antennas

-4 0-2

z/r s

42

(a)start point

start point (b)

0

0.4

0.8

1.2

0

0.4

0.8

1.2

h2005

tiR

MF

18

RMF Antenna

Time (ms)

(101

9 m

-2)

(MW

m-2

)(M

W)

0 0.5 1.0 1.5 2.0 2.5 3.00

1

20

0.5

1.00

0.5

1.0

1.50

5

10

15Anti-// (#13904)

// (#13709)Be

B

r

Pabs

h2005

iRMF04

(mT

)

23

Recent PPPL kinetic calculationsshow promise of complete stability

HYM simulations for oblate FRCs (E~1) with a close-fitting

conducting shell and energetic beam ion stabilization:- Linearly stable with respect to the n=1 tilt mode and the n=2 modes

- Residual instabilities saturate nonlinearly at small amplitudes

- Configuration remains MHD stable, if current is sustained.

|Vn|2

n = 1

no stabilization

conducting shell

conducting shell & ion beam

t ci

|Vn|2

n = 2

no stabilization

conducting shell

conducting shell & ion beam

t ci

24

Summary

FRCs are a simple, surprisingly robust confinement scheme.

Unique plasma configuration:– Ideal reactor attributes (high , simple geometry with natural divertor, advanced fuel

potential).– Interesting plasma studies of and high- MES in simple geometry.

Formation and sustainment has been demonstrated by RMF.

RMF with TNBI could provide stability and efficient current drive.

scaling with vde/vs is favorable for reactor.

If TCSU is successful, the next step would be a larger device, including TNBI.– with lower vde/vs.

RMF current drive is simple, robust, and now relatively inexpensive!

Blanket

RMF Antenna Leads

Confinement CoilsFirst Wall

13.5 m

Neutral beams

25

ARTEMIS Design (D-3He)

-pinch translation/expansion formation

TNBI flux build-up and sustainment

26

FRC Translation DemonstratesRobustness (at least at low s)

Wanted to reduce ne from 5x1021 m-3 in formation section (Be~ 0.5-1.0 T) to5x1019 in TCS sustainment chamber (Be ~ 50-100 mT) without significantlydegrading temperature.

This is made possible by non-isentropic recovery of high (~ 400 km/s)translation energy.

FRC exhibits remarkable robustness in surviving violent reflections off endmirrors.

Axial distance (cm)

Ra

diu

s (

cm

)