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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
17
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
19
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
20
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
)