Transcript FRC History, Physics, & RPPL Program Redmond Plasma Physics Laboratory University of Washington Review for TV George & Sam Barisch (September 18, 2007)

FRC History, Physics, &
RPPL Program
Redmond Plasma Physics Laboratory
University of Washington
Review for TV George & Sam Barisch
(September 18, 2007)
1
FRC Geometry
rc
Bo






rs
Be
xs  rs/rc
Bz(r)
ne(r)
Compact toroid with ‘non equilibrium affecting’ toroidal field.
Axial equilibrium requires high beta:  = 1 - ½xs2 .
Flux conservation: Be = Bo/(1 – xs2) .
Simple radial pressure balance: p + B2/2o = Be2/2o .
Field null at R = rs/2 .
Since generally highly elongated (prolate), usually shown with z-axis
horizontal - then talk of ‘reversing’ external Bz field.
2
Promise of Very Attractive
Compact Fusion Reactor
13 . 5 m
Fi r s t Wal l
Conf i nement Coi l s
Neutral beams
B l ank et
RM F A nt enna Leads
T ~ 10 keV ne ~ 1020 m-3
p ~ 4 Wb
B ~ 1 T rs ~ 2 m
s ~ 20
3
Ideal Propulsion Geometry
(should have NASA interest)
Mirror
Coil
Direct
Energy
Converter
RMF Sustainment Antenna (1 of 2) Magnetic Nozzle
FRC
Plasma
Exhaust
Specific Impulse
103 - 106 sec
External Magnetic Field Confinement
and Heating Coils
Idealized Fusion Propulsion
Utilizing D-3He Fuel
(quick stop at Moon or Jupiter to gas-up)
4
FRC Advantages & Problems
Advantages

Simplest possible cylindrical
geometry.

High  allows for low field
confinement magnets.

Natural divertor out ends.

Advanced fuel potential.

Fusion reaction ions will provide
much of current drive.

Translatability allows for
separation of generation and burn.

Natural geometry for space
propulsion.
Problems




Physics different from other
toroidal configurations. (Maybe
not as different as first thought.)
Stability uncertain due to lack of
strong toroidal field (reliance on
kinetic and flow effects - perhaps).
All currents diamagnetic – difficult
to sustain; transport may be rapid.
Amount of poloidal flux is key
scaling component for compact
toroids and achieving high flux has
been technologically difficult.
5
Outline

History – ‘Achieving Field Reversal’

FRC Physics
– Pulsed & steady-state

RPPL Program & TCS Results
– Non-RMF sustained translation experiments
– RMF formation & sustainment experiments

TCS-Upgrade (TCSU)

Long Term Opportunities for Significantly Better Reactor, and
Extremely Versatile Plasma Physics Facility
6
HISTORY
7
Attempts at Field Reversal have a Long
History – supra-thermal ring currents




First tried at LLNL in ASTRON Program in 1960s using electron beams.
Next tried in Mirror Program using Tangential Neutral Beam Injection (TNBI).
Finally achieved by Hans Fleishmann at Cornell using pulsed electron ring.
Ion ring needed for fusion application – but much more difficult.
8
Field Reversal in a -Pinch –
plasma currents
Iplasma
Icoil
Icoil
+
-

End View


Theta-pinches (rapid rise of 
current in external single turn coil
using high voltage capacitor
bank) produced some of the first
thermonuclear plasmas.
Lifetime was short due flow out
ends.
To ‘close-up’ the ends, start with some
negative bias flux and reconnect with added
forward flux.
Some original demonstrations done in Germany
and USSR, with FRC (name given by Rulon
Linford) experiments started at LANL (~1978)
as part of Mirror enhancement program.
9
Original Russian TOR
(Kurtmallaev group ~ 1970s)
Developed high energy
FRCs by delaying
reconnection at ends and
producing strong axial
implosions.
Program also included
imploding liners
10
FRX/C-T at LANL (~1980s)
Studied translation &
adiabatic compression
Interferogram taken
on FRX-C using
holography
11
LSX at STI Optronics (1990)
rs
rdr
s  
r
R s i
Kinetic # of
internal gyro-radii
parameter
Construction:
$14M over 4 years
(1986-1990)
12
FRC PHYSICS
13
Most Studied Problem - Stability
Rotational
n=2

Ion diamagnetic rotation drives n=2
mode due to centrifugal forces.
–
It has been stabilized by weak
multipoles with Bm2/2o >
centrifugal pressure
End View
Internal Tilt
Side View

Internal tilt is more insidious starts out as an axial n=1 shift.
– Most studied mode with various
ideas proposed for observed
stability
14
Stabilization of n=2 Rotational mode
No Stabilization
Octopole Stabilization
•
First calculated experimentally by Ishimura and demonstrated experimentally by
Ohi at Osaka University in 1982.
•
Since then shown in many experiments with many external field configurations.
15
Growth Rate of Tilt Mode
(from 3D HYM simulation)
1.0
S*/E < 3.5
E=4
E=6
E = 12
/mhd
0.8
Kinetic calculations
generally show reduction
of tilt rate at low s, but not
positive stabilization, at
least in linear phase.
(Elliptical)
0.6
Other effects may be
important, such as strong
flow, residual toroidal field,
ion viscosity, Hall effects.
0.4
0.2
0
0
0.2
0.4
0.6
0.8
E /S*
1.0
Most recent calculations
show FRC can be
completely stabilized by
fast ion component!
Calculations by E. V. Belova et al.
16
FRC Confinement
(for decaying FRC)
a ~ rs/4
d
s  a/io
w = d/io
l

At high  flux and particle diffusion are the same phenomenon: D = /o
–  = a2/D = rs2/16D : sets absolute ‘L/R’ lifetime of configuration
– N = xsa2[1 + w/2s]/D : open field line ‘bottleneck’ only slight help


Diffusivity inferred over very limited density range in theta pinch formed
FRCs appeared favorable to high density operation (but not seen in recent
high and low density experiments).
– D ~ 5/n1/2(1021 m-3) m2/s
RMF can completely reverse particle diffusion!
17
Measured FRC Particle Confinement in
Theta-Pinch Experiments (ne = 1-51021 m-3)
1000
LSX
TRX-1
General
N  xsrs2/i
TRX-2
Time
(sec)
FRX-B
5 m2 /s
D 
ne (1021 m3 )
FRX-C
LSM
100
LSX
N  (rs/i)3
No tilt
instability
seen in LSX
up to s = 4
10
1
10
rs/2i
100
(cm1/2)
18
Two Major FRC Reactor Approaches

Pulsed - High Density
– Most historical research – theta pinch formation yields high Ti and ne.
– Range of reactor scenarios
» Adiabatic compressor – moving rings (oldest reactor design approach)
» RACE type accelerator – use TRAP type moving wave FRC acceleration
» Liner compression – MTF

Steady State - ~1020 m-3 Density
– Tangential Neutral Beam Injection (TNBI) – first tried in Mirror program.
» Japanese design: ARTEMIS D-3He reactor
» FIX (FRC Injection Experiment) at Osaka U. - first to apply TNBI to translated
FRC.
– Rotating Magnetic Field (RMF) drive – adapted from rotamak research.
» TCS program: using RMF to form, build up flux, and sustain current
– Ultimate program: combine RMF to form and drive edge to enhance particle
confinement, NB to drive center. Torques balanced.
19
High Density Pulsed Approaches
(For non-sustained plasma probably need n ~ 1021m-3s
at T = 10 keV for economical reactor)
Using optimistic -pinch density scaling:
(s) = n1/2(1021m-3)rs2(cm) n(1021m-3) = 0.1B2(T)
p(mWb)  0.1rs2(cm)B(T) (s) = 3p(mWb)
s = p(mWb)/rs(cm) n = 3p(mWb)B2(T) 1014 m-3s
Non Destructive Wall
At B = 100 T need p = 300 mWb
n = 1024m-3 rs = 5.5 cm s = 55
 = 1 ms (requires D = 0.2m2/s)
Inertial Confinement
At B = 1000 T need p = 3 mWb
n = 1026m-3 rs = 0.2 cm s = 15
 = 10 s (requires D = 0.025m2/s)
(for  = inertia must have high )
20
Low Density Steady-State Approach
(For -heated plasmas n can probably be less than
1021 m-3s but will still need several Wb flux levels)
Formation Methods
Theta Pinch Formation and
Translation/Expansion
(LSX limited to p ~ 10-20 mWb)
(Formation power input ~ 10s of GW)
Merging Spheromak Formation
(slower formation – flux limits unknown)
(Formation power input ~ 100 MW)
Rotating Magnetic Field Formation
(also current drive mechanism – no
fundamental flux limit)
(Formation power input ~ 1 MW)
21
‘LSX’ Lifetime Scaling Not Seen in
Extended Density Range Experiments
1
TRX-1
low density
(~4x1019 m-3)
translated FRCs
TRX-2
/(2xs)1/2 (msec)
FIX
0.1
FRX-B
moderate density (LSX)
(~1021 m-3) scaling:
FRC-C
 = 0.47xs1/2(rs/I)2.14
LSX
TCStrans
0.01
FIXtrans
high density
(~4x1021 m-3)
FRX-L
0.001
6
8
10
20
30
40
50
rs/i1/2 (cm1/2)

Lower density (translated, expanded) FRCs have better lifetimes and
recent high density MTF (FRX-L) FRCs have poorer lifetimes.
– D  1/n is not correct over wide density range!
22
ARTEMIS Design (D-3He)
-pinch translation/expansion formation
TNBI flux build-up and sustainment
23
RPPL PROGRAM
& TCS RESULTS
24
RPPL Program




Develop technologically simpler formation method without
limits on achievable flux.
Conduct studies of basic FRC equilibrium, stability,
confinement, & recycling physics in steady state
environment.
Present focus is on RMF formation and sustainment, but will
eventually include TNBI.
Next few years emphasis is on controlling recycling
impurities and achieving high steady-state temperatures.
– (Great progress already made!)

High s, and low vde/vs studies would be future focus.
25
Previous RPPL Group Devices
20 cm
TRX,
(1980-1986)
1m
LSX
80 cm
(1991)
5m
40 cm
27 cm
80 cm
2.5 m
LSX/mod
(1993 -
)
TCS
(2000 - 2005)
26
TCS Device
RMF
Antennas
TCS Chamber
LSX/mod
(confinement & RMF drive)
(formation & ‘acceleration’)
Study Formation & Sustainment of RMF driven FRCs.
Either form FRCs directly using RMF alone, or translate and
expand theta-pinch formed FRCs from LSX/mod.
27
TCS Accomplishments





5 years of highly fruitful experiments - numerous important
journal articles. 4 PhDs graduated.
Basic theory of flux sustainment and density scaling well
developed both analytically and numerically.
Many additional facets, such as RMF acting as strong
stabilizer, use of odd-parity drive to maintain closed field
lines, and toroidal field appearance and Minimum Energy
States (MES) explored.
Main problem of low temperatures limited by radiation
barriers identified. TCSU program proposed.
Collaboration started with Materials Sciences Dept.
28
Sampling of Important Papers

Detailed examination of translated and RMF generated plasmoids to show selforganization into high- state.
– H.Y. Guo, et. al., “Flux conversion and evidence of relaxation in a high- plasma formed by
high-speed injection into a mirror confinement structure”, PRL 92, 245001 (2004).
– H.Y. Guo, et. al., “Evidence of relaxation and spontaneous transition to a high-confinement
state in high- steady-state plasmas formed by RMF”, PRL 97 235002 (2006).

Extensive development of RMF current drive theory for flux confined FRCs.
– A.L. Hoffman, “RMF current drive of FRCs subject to equilibrium constraints”, NF 40, 1423
(2000).
– R.D. Milroy, “An MHD model of RMF current drive in an FRC”, POP 7, 4135 (2000).
– H.Y. Guo, et. al., “Formation and steady-state maintenance of FRCs using RMF current
drive”, POP 9, 185 (2002).
– A.L. Hoffman, et. al., “Resistivity scaling of RMF current drive in FRCs”, NF 43, 1091 (2003).
– R.D. Milroy, et. al., “Edge-driven RMF current drive of FRCs”, POP 11, 633 (2004).
– H.Y. Guo, et. al., “Sustainment of elongated FRCs with localized RMF current drive”, POP 11,
1087 (2004).
– A.L. Hoffman, et. al., “Principal physics of RMF current drive of FRC", POP 13, 012507
(2006).
29
Additional Important Papers

Long term FRC sustainment demonstrated with spontaneous toroidal field
development leading to enhanced performance.
– A.L. Hoffman, et. al., “Long pulse FRC sustainment with enhanced edge driven RMF current
drive”, NF 45, 176 (2005).

Interchange mode stabilization with implications well beyond FRCs.
– H.Y. Guo, et. al., “Stabilization of interchange modes by RMF”, PRL 94, 185001 (2005).

Use of anti-symmetric RMF to eliminate FRC field line opening.
– S.A. Cohen & R.D. Milroy, “Maintaining the closed magnetic field line topology of an FRC
with the addition of static transverse magnetic fields”, POP 7, 2539 (2000).
– H.Y. Guo, et. al., “Observations of improved confinement of FRCs sustained by antisymmetric RMF”, POP 12, 062507 (2005).

Ti coating experiments to identify scrape-off layer flow and recycling impurity sources.
– G.C. Vlases, “TCS edge studies final technical report”, RPPL-UW (2005).
30
Non-RMF Driven FRC
Translation Experiments
31
Radius (cm)
FRC Translation Demonstrates
Robustness (at least at low s)
Axial distance (cm)
Used to reduce ne from 5x1021 m-3 in formation section (Be~ 0.5-1.0 T) to 5x1019
in TCS sustainment chamber (Be ~ 50-100 mT) without significantly degrading
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 end
mirrors.
32
Disorganized Plasmoid Transitions to
Preferred FRC State
Initial and Final Flux
Measurements
Rigid rotor: p =
0.31xs
2.0
1.0
60
Internal probe measurements
0
0
50
100
150
Bz
30
200
250
Time (sec)
Internal Field (mT)
 (mWb)
3.0
Bx
Rear
0
1st pass
-30
Front
60
30
0
2nd pass
-30
60
30
0
Captured
-30
0
2-D MHD Calculation of Reflection Process
10
20
30 0
10
20
30
Radius (cm)
33
Low Density Lifetimes Considerably Exceed
Values Inferred from High Density Scaling
300
Well centered
(a)
#6371 (probe)
2
200
1
 s)
#6114
#6135
0
70
it
100
ens
hD
Hig
ling
Sca
C
R
yF
60
0
50
0
LSX
100
150
3
200
s = 9x10 xsrsm/rLcm
2.14
40
High energy
1.0
50
100
150
Time s)
200
250
300
30
20
hg2005.st-frc.03
0
(b)
Low energy
D m2/s
0.5
0
50

1.5
hg2005.st-frc.02
ndl (1020 m-2)
Be (mT)
p
RR
(mWb)
3
10
Translated FRC
Lifetime Measurements
0
0
10
D
20
m2/s
30
40
LSX
34
Translated FRC q Profile

FRC will be high  as long as
B << Bz .
Due to high Elongation & small
Aspect Ratio actually have safety
factor above unity and significant
field shear even with low B/Bz .
B dl
q   
 rB
p
60
(a)
Bz
30
B (mT)

B
0
rs
-30
0
0.2
0.3
(b)
Y  1  / o
q
1
0
hg2005.st-frc.05
Amount of shear satisfies
cylindrical Suydam criterion based
on centrifugal force. (Other than
lack of center column, B profile
appears very much like ST)
r (m)
3
2

0.1
0
0.25
0.50
0.75
1.00
Y
35
Rotating Magnetic Field
Current Drive
36
RMF Current Drive
driven electron current
rotating field Bw
RMF antenna
Iz = Iocoswt
RMF antenna
Iz = Iosinwt
Bz field coils

‘Drag’ Electrons Along With Rotating Radial Field
– Must have wci < w << wce for electrons, but not ions, to follow rotation

Electrons Magnetized on Rotating Field Lines (wce >> 1)
– Necessary for efficient current drive
– Absolutely necessary for rotating field penetration
37
Flinders 50 l Rotamak
Now at PrairieView A&M
RMF flux drive pushes FRC
against plasma tube wall
38
Schematic of TCS Confinement
Coils and RFM Antennas
RMF Antennas
60
H
40
20
hg2001.1.2b
End Coils
Main Bias Coils
Mirror Coils
V
0
-20
-40
Induced axial oscillation of electrons, vez,
combined with RMF radial component, Br,
produces azimuthal drive, Fe.
Flux conserving wall is key!
-60
-60 -40 -20
0
20
40
60
X (cm)
39
Formation of FRC Inside Flux Conserver
Compresses Initial Bias Flux
Bo
rc
Add RMF
Be
rs
R
xs  rs/rc




RMF forces produce flux and generates FRC.
Use of flux conserving coils yields Be = Bo/(1-xs2).
FRC will expand radially until limited by high Be. p  (xs/2)1.3R2Be.
Compressed bias field keeps FRC off wall.
40
FRC formed by RMF alone
200
100
0
-100
-200
40
20
Pulse: 3569
Be
Bint
Wall
r
Up to 60 kA of current
is driven by RMF, and
maintained in steady
state for the entire
duration of RMF.
0
2
1
0
40
20
0
10
0
nem
Ttot
Iant
-10
alhaps2001.4a
0
500
1000
1500
2000
3
2
Pabs 1
0
2500 3000
Operating space:
Ttot: 20 ~ 100 eV
ne: 0.5 ~ 4 1019 m-3
Be: 5 ~ 20 mT
Bw: 1 ~ 6 mT
Time (s)
41
10
10
ne
5
5
ne
0
0
Bz
-5
Bz
Density (1018m-3)
Magnetic Field (mT)
RMF Sustained FRCs Significantly
Different than non-Sustained FRCs
rs
rs
-10
0
5
10
15
Blue – conventional FRC
Bz only partially reversed
ne(rs) fairly high
Red – RMF driven FRC
Bz fully reversed
ne(rs) very low
20
Radius (cm)

rs driven close to flux conserving wall: xs  rs/rc  0.8 .
Outward radial diffusion reversed, ne(rs) [and ne(0)] very low.

p greatly increased – better thermal insulation.

42
RPPL Development of RMF
Current Drive Theory for FRCs
43
Previous Static Calculations based on
Fixed Density and Resistivity
Calculations for stationary plasma based on RMF drive and penetration
parameters. Non-linear penetration, with no penetration beyond simple
skin depth d until  exceeds , and then full penetration.
 
wce
 ei
 
wce 

eBw
me
rs
d
d

2
ow
me ei
ne e 2
Penetration occurs due to near synchronous
rotation of electrons, we  w,  = w - we very
small.
d* 
2 
o
1
 = I/Isynch

0
=40
0
20
40
60

 rs
44
MHD Model of RMF Current
Drive in FRCs
d p
dt
Trmf
 2 RE ( R) 

rs

we

I line
2 Be /o 


 


I sync
w
0.5 ne w rs2 

2 rs2 Bw2

f ( )l ant
o
rs
2
Trmf  T 
2
neers l s
RMF Force
ne-vezBr
d*

T   2rme   newe r 2 drl s  0.5 (nmers ) 2 we rs2l s
0

The RMF parameters and underlying plasma resistivity determine ne.
nm (1019 m 3 ) ~ Bw (mT ) /  (m)w(10 6 rad/s )rs2 (m)


The temperature is determined independently by power balance.
The penetration distance d* adjusts automatically dependent on  and is
less than rs for  < 1. (RMF drive ceases if  > 1)
45
Torque Based Model Accounts
for Resistive Torque Everywhere
RMF Antenna
Plasma flow can distribute the RMF drive
forces throughout the FRC, both radially
and longitudinally. An FRCs length is
determined by particle and energy
balance.
B
Vr
VZ
RMF2003.15
RMF Antenna
0.7 m (#10512)
40
30
~
E   j   ~
v ezBr  Vr Bz  Vz Br
10
Midplane
0
40
1.6 m (#8990)
30
20
R MF2003.12
r (cm)
20
10
0
3.0
3.5
4.0
4.5
5.0
Under Antenna
Outer:
Inner:
FRC Ends
Outer:
Inner:
5.5
Z (m)
46
RMF Penetration Movies
Vacuum calculation in
lab frame of reference
Plasma calculation in
RMF frame of reference,
with uniform resistivity.
Plasma measurement in
RMF frame of reference
(Calculation starts from
already formed FRC)
47
Edge Driven Mode
(due to very non-uniform resistivity profile)
fe
Calculation based on  = 30 + 1000/(1+e(a-r)/d)
-m, with a = 35 cm, d = 1 cm.
fd
fw
Experimental measurement of internal
probe (aligned at 45) frequency content
for fw = 258 kHz.
Inner structure rotates at we and tearing and
oscillating torque occurs at wd = w - we.
48
RPPL RMF Current Drive
Experiments
49
Illustration of Impurity Radiation
Limiting Temperature in TCS
Operation at High w = 1.62x106 s-1 and Low Bw
The plasma density is seen to be
proportional to Bw, independent of
other factors.
ne ~
Bw
wrs2
120
12
Be (mT)
8
4
40
0
6
0.6
4
The magnetic field is proportional to
Tt1/2. The initial temperature is high
before recycling brings in impurities
and radiative energy losses dominate.
Higher fields and currents are
accommodated without increases in
Bw or Pabs.
0.2
0
3
0
2.0
2o nemkTt
#9729
#9751
2
praddl
(MW/m2)
0.4
2
Pabs
(MW)
1.5
Bw (mT)
1.0
1
0
Be 
nedl (1018m-3)
Tt (eV)
80
0.5
0
0
0.4
0.8
1.2
TIME (msec)
1.6
0
0.4
0.8
1.2
TIME (msec)
1.6
50
Axial Magnetic Field (mT)
15
5.0
Bext
10
3.7
Bext(vacuum)
Bw
Bw(vacuum)
5
1.3
0
0
-5
RMF Magnitude (mT)
Long Time FRC Sustainment
Bint
-10
brawc31 12967
brawc31 12974
-15
0



2
4
Time (msec)
6
8
10
Long terms sustainment without any active refueling.
No sign seen of any tilt instability.
After ~4 msec, transition occurs to higher performance mode.
– Spontaneous toroidal field development.
– RMF penetration profile changes.
– Lowering of interior resistivity.
51
5
Bz
0
-5
BRMF
(Shot 12964 – 2.5 ms)
Bx
-10
-15
0
10
20
30
40
15
10
5
Bz
BRMF
(Shot 12964 – 4.1 ms)
-5
-10
-15
0
10
20
RADIUS (cm)
20
15
30
40
Shot No: 12964
10
5
0
(with/out 10 kHz filter)
2
r = 24 cm
0
-2
0
2
4
6
8
10
hg2004.tf.1
Be (mT)
(Shot 12968 – 5.22 ms)
Bx
0
RADIUS (cm)
Btor (mT)
After
Transition
hg2004.24
10
(Shot 12968 – 2.63 ms)
Before
Transition
INTERNAL FIELD (mT)
15
hg2004.23
INTERNAL FIELD (mT)
Spontaneous Toroidal Field
Generation & Profile Changes
TIME (ms)
52
Rotational n=2 Instability Can Occur
No n=2


With n=2
The n=2 rotational instability is ubiquitous in -pinch formed FRCs due to ion spin-up in ion
diamagnetic direction.
It should always occur in RMF driven FRCs due to torque on plasma in electron diamagnetic
direction.
53
RMF Can Stabilize Interchange Instabilities
(This has applicability well beyond FRCs)
Fr (r , )   j z B
 rs  r 

d* 
2 Bw2 rs 2
 
e
 o d* r
 
1  
 r
1.0
Wall
0.8
0.6
0.4
0.2
0
hg2004.sta.6a
The radial inward force
produced by a partially
penetrated dipole RMF with an
elliptical distortion  is given
by,
2
r /(Be /2µ0)

90
180
270
360
The condition for interchange stability is that the radial force response to
the perturbed ‘interchange’, Fr1, exceed the centrifugal term 2, which
amounts to requiring Bw2/o > 1.32rs2 .
54
Experimental Demonstration of RMF
Stabilization of Rotating n=2 Interchange
40
40
rs = 36 - 39 cm
30
r
(cm)
35
30
0.35-m gap
(#13863)
1.0
20
10
6
6
6
0
hg2004.sta.2
0.5
0
1.0
2.0
3.0
Time (ms)
Use of separated RMF antennas,
which produce same ion spin-up, to
illustrate instability development when
central RMF is not present
6
s-1
s-1
s-1
s-1
hg2004.sta.7
19 m-2)
20
1.5 0.05-m gap
(#13709)
B2/o (Nt/m2)
25
0
0
10
20
30
40
1.32rs2 (Nt/m2)
Correspondence of distortion
development (open data points) or
non-development (filled data points)
with simple calculation.
55
Possible effect on tilt mode

No tilt modes have been
observed for FRCs lasting over
500 tilt growth times:
1/tilt ~ ls/2VA ~ 20 µs

RMF may also have some
influence on tilt stability since it
acts inside the separatrix.

Axial variation in RMF fields
seem beneficial
in experiments with both
shorter antenna lengths and
anti-parallel antennas.
Kinetic effects are not
important as Ti is low.
56
Anti-symmetric RMF Current Drive
(Effective even at large Bw/Be when RMF d*/rs is small)
1.2
Iant
RMF antennas
start point
(a)
start point
(b)
Iant
0.8
0.4
0.4
0.3
0
1.2
r (m)
0.5
0.8
hg2005.antiRMF.15a
0.4
0.1
0
-1.0
-0.5
0
0.5
z (m)
Anti-Symmetric RMF
Field Pattern in Vacuum
1.0
RMF Antenna
0
-4
-2
0
z/r
2
hg2005.antiRMF.18a
0.2
4
s
Field Line Tracings for
Symmetric (top) & AntiSymmetric RMF (bottom)
Bw/Be = 0.25, d*/rs = 0.15
57
Large Reduction of Convection/Conduction Losses
with Anti-Symmetric RMF Current Drive
Anti-// (#13904)
// (#13709)
10
// RMF
Anti-// RMF
B
5
200
0
1.5
1.0
150
0.5
cc
0
1.0
r
100
0.5
0
2
50
Pabs
hg2005.antiRMF.04
(MW)
250
Be
1
0
hg2005.antiRMF.03c
(MW m-2)
(1019 m-2)
(mT)
15
0
0.5
1.0
1.5
Time (ms)
2.0
2.5
Experimental comparison of
data symmetric and antisymmetric RMF current
drive.
3.0
0
0.1
0.11
0.12
0.13
2
0.14
0.15
2
rs (m )
Comparison of intrinsic conduction
and convection based lifetimes for
symmetric and anti-symmetric RMF
current drive.
58
Ti-Coating Experiments
0.12


0.95< time <1.05
0.1
Oxygen III (a.u.)

Ti-coating covering quartz entrance tube
has greatly reduced silicon impurities.
Ti-coating end-cones temporarily reduces
oxygen impurity, but H and C radiation
increase, actually reducing performance.
Data implies that recycling comes from
normal scrape-off layer end points despite
RMF.
Densities were the same for all data points,
in agreement with RMF theory, but excess
gas lowers Tt, presumably due to excess
fueling and charge exchange losses, which
lowers resultant Be.
0.08
0.06
0.04
Be (mT)
15.2
0.02
13.0
0
12040
12060
12080
12100
12120
12140
12160
12180
Shot Number
10.7
0.4
0.95< time <1.05
0.35
8.4
0.3
Silicon III (a.u.)

0.25
6.1
0.2
3.8
0.15
0.1
0.05
0
12040
12060
12080
12100
12120
12140
12160
12180
Shot Number
59
TCS-UPGRADE
60
Original TCSU Plans & Goals

Reduce impurity levels, and possibly recycling, to allow temperature limits
to be set by fundamental transport.
– Build UHV vacuum chamber with clean surfaces and minimal leakage and
outgassing.
– Bake to remove H2O and allow effective discharge cleaning.
– Glow discharge cleaning with H2 and then He.
– Wall coating with – either Ti-gettering or siliconization.

Switch to odd-parity antennas to measure effect of better field line closure.
– Try to approach temperature limits set by   1 limit.
– Illuminate RMF current drive scaling laws and underlying plasma resistivity.
– Add new diagnostics to reach better understanding of RMF current drive and
FRC physics under steady-state operation.

Use LSX/mod, if necessary, to reach high temperatures.
61
TSC/upgrade Schematic
Transition mirror
End/Pumping Section magnet
capture
Chamber
Central Confinement Section
(Quartz For RMF Drive)
cmp
cp
magnets
magnets
magnets
diagnostic
ports
48 cm
I.D.
60 C M
80 C M
32 C M
diagnostic
48 cm
ports
flux rings, tantalum I.D.
clad, 76 cm I.D.
80 cm
I.D.
75 C M
Transition Original
Section
Source
fast gate
Section
coil
125 C M
75 C M
32 C M
40 cm
I.D.
80 C M

Larger, metal input section to eliminate translated FRC contact with quartz.

Protective tantalum covered flux rings under quartz RMF drive section.

Elimination of “O-rings” to allow bakeout and discharge cleaning.

Combination of Ti-gettering and boronization wall conditioning.

Control of scrape-off layer end-point with ‘divertor’ armoring and pumping.
62
Additional RMF Drive Physics
 Maximum
 
we
w
possible temperature set by   1
1/ 2
 Tt (eV) 

I line
2 Be /  o
5.67 10





2
6 1
2
19
3 

I sync
0.5 ne ewrs
w(10 s )rs (m)  ne (10 m ) 
3
 Maximum
possible temperature to density ratio
(with ne set primarily by RMF magnitude Bw)
depends on key RMF/FRC parameter, wrs2.

Te (eV)
2
6
2
 176wrs (10 m /s)
19
3
nm (10 m )

2
63
First TCSU Results (fw = 117 kHz)
(baking & discharge cleaning only – external flux rings)
300

Radiated power reduced.
Recycling (as indicated
by D line radiation) also
strongly reduced.


Temperature already
close to 1 limit.
Tt (eV)
Prad l (MWm-2 )
200
1.5
1.0
TCSU (#21214)
100
0.5
TCS (#10393)
0
20

hg2007.high-zeta.5
Be (mT)
0
D (a.u.) 1.0
0.5
10
Be nearly doubled due to
higher Tt for similar Bw.
0
6
4
1.0
Pulse lengths kept short for
best, vibration limited,
interferometry.
2
0.5
B (mT)
0
0 0.5 1.0 1.5 2.0 2.5
Time (ms)
0
1.5
ndl (10 m-2 )
19
0
0 0.5 1.0 1.5 2.0 2.5 3.0
Time (ms)
64
Measurements of Be versus Bw
35
30
25
20
15
10
hg2007.high-zeta.6

Ran TCSU in
Argon, in addition
to Deuterium, to
simulate TCS
radiation dominated
results.
Be/Bw ~ 5.6 for
TCSU (Deuterium)
versus 2.8 for TCSU
(Argon) or TCS.
Be (mT)

TCSU - D2
TCSU - Ar
TCS - D2
*
5
0
0
1
2
3
B (mT)
4
5
6
65
Achievable Ratio of Be/Bw Depends on
Temperature and Overall Resistivity
2
0.4
2
s

Equate the torques with f() = 0.1,
0.3
analytic
0.2
hg2007.high-zeta.3a
1/ 2
  o e nm   Be 
    l s
T  r 
 2kTt    o 
2
2  2 Bw 
f ()l a
Trmf  rs 
 o 
2
0.1
ls/la = 1.25.
1/ 4
 Tt (eV ) 
Be

 0.0131
19
3 
Bw
 ne (10 m ) 

0
0.2
1
 (m
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1/ 2
At w = 0.735106 s-1, rs = 0.36 m; Tt/nm = 2802.
66
MHD Calculations Leading to f()
1.5
B / B , F / (2B
2
ors)
2.0
1.0
0.5
(a)
B
Br
F
B
Br
F
B - analytic
Br - analytic
F - analytic
0
0.5
0
(b)
Bz
n

Bz
n

Bz - rigid rotor
n - rigid rotor
hg2007.high-zeta.2ab
Bz / Be, n / nm, 
1.0
-0.5
-1.0
0
0.2
0.4
0.6
r / rs
0.8
1.0

Calculated Be(r) and ne(r) profiles
are nearly Rigid Rotor (RR) (also
as measured in TCS), but with 
 we/w  1 near edge, and
depressed near field null.

This leads to azimuthal force
localized near RMF penetration
point (in sharp contrast with nonMHD analytic calculation) and
RFM torque nearly independent
of  until  approaches unity.
1.2
67
Measured Be/Bw Ratios verses Tt/nm
in Deuterium & Argon
7

Old TCS Tt/nm ratios of ~25
the same as for TCSU
results in Argon, except for
experiments run at higher w
and very low Bw where nm
was very low*.
Central  ~ 26 -m at
lower Tt and ~17 -m at
higher Tt (also lower
Bw/Be). [assumes e = 10i ].
TCSU - D2
TCSU - Ar
TCS - D2
6
*
5
4
3
2
hg2007.high-zeta.7

Maximum experimental
Tt/nm ratio of 250 in
Deuterium close to  = 1
limit of 280.
Be / B

1
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
(Tt / nm)1/4
0
1
16
Tt/nm
81
256
68
Measuring absorbed power at two temperatures
allows separation of ohmic and RF induced
power absorption
2.5
Calculation
2.0
rs
1.5
hg2007.high-zeta.8
1.0
0.5
*
0
0
200
400
600
2
800
2
{
  1000Be2 (mT)  40,000Bw2 (mT) W/m
EXP: Pabs
P
PRF
2
 
The absorbed power due to
j2 yields a central resistivity
of   23 -m, essentially
the same as calculated from
torque balance!
1000
Be (mT )
{
P’abs (MW/m)
2
 2B 
P    j 2rdr  1.4 e   l s
0
 o 
P  10Be2 (T)  (m) MW/m
TCSU - D2
TCSU - Ar
TCS - D2
RF related heating is dominant
(and useful) at low values of Be/Bw,
but becomes insignificant at reactor
level values.
69
Experimental Comparisons
Device
OPrmf
rw (m)
0.04
fw (kHz)
14,000
Bw (mT)
1.0
rs (m)
0.03
wrs2 (106 m2/s) 0.078
nm (1019 m-3)
0.15
Tt (eV)
165
Be (mT)
10

(2.4)
Be/Bw
10
Tt/nm
1100
i (-m)
17
Pabs (MW/m) 0.05
eff (-m)
46
Pabs/A (MW/m3) 18
STX
TCS*
TCS
0.2
350
2.5
0.18
0.071
0.4
50
9
0.9
3.6
125
43
0.2
230
2.0
0.4
258
1.0
0.37
0.222
0.19
47
6
0.4
6
246
22
0.11
280
0.25
0.4
114
4.6
0.37
0.098
1.7
23
12.4
0.2
2.7
14
26
1.0
600
2.3
TCSU
0.4
117
5.1
0.37
0.101
0.9
175
25
0.8
4.9
195
29
1.6
236
3.7

All successful
experiments operate at
similar values of wrs2.

Pabs is independent of
device size, so larger
devices will have better
current drive efficiency
(however, smaller
devices will have higher
power inputs per unit
volume).
 (W/m) / 10Be2 (mT)
eff (μΩ  m)  Pabs
70
Revised TCSU Plans






Operate at higher RMF frequency to raise limit of allowable
temperature.
Switch to odd-parity antennas to test effect on radial losses.
Use wall coatings (TI-gettering and siliconization) to see if
can further reduce recycling impurities.
Replace external flux rings with internal ones for more
uniform flux conserver, and as DVT for larger device.
Make spatially resolved measurements, including Te(r) using
Thomson Scattering.
Study effects of directing open field line edge flow in
‘natural’ FRC divertor (end tubes),
71
Summary

The TCS program was highly successful in developing the RMF formation
and sustainment method of FRCs.
– Development of partial penetration theory and scaling analysis.
– Long sustainment times without refueling.

Discovery of many additional features
– RMF stabilization of rotational modes.
– Development of toroidal fields and tendency toward Minimum Energy States.
– Demonstration of transport improvement using odd-parity RMF drive.

TCSU has already met most basic goal of reducing impurity levels.
– Unexpected ability to reach  limited Tt without wall coatings or odd-parity RMF.
– Switching to higher frequency to increase temperature limit.

An exciting future opportunity exists for building a world-class facility for
both basic plasma physics research and significantly improved fusion
reactor development.
72
PROPOSED NATIONAL
COMPACT TOROID FACILITY
73
Project Organization
Principal
Investigator
FRC
Leader
FRC front end
Analysists
Advisory Group
T. Jarboe
A. Hoffman
……
Spheromak
Leader
Experimental
Operations
Sph. front end
Analysists
Controls
Data Acquisition
Power Supplies
Vacuum Systems
Neutral Beams
Diagnostics
Interferometers
Bolometers
ICCD – profiles
Thomson Scattering
…..
74
Two Front Ends
 FRC
front end based on TCSU
 Spheromak
front end based on HIT-SI
75
Rationale for FRC Front End

Make vde/vs < 1 where theory predicts large improvements in anomalous .
– Base only on extrapolations of present results without neutral beams.
– (Automatically has large enough p for high energy ion confinement.)

Purchase RMF supply powerful enough to ensure good performance under
most pessimistic projections.
– Mostly need higher voltage to drive higher inductance antennas (somewhat compensated
by lower RMF frequency).
– Need higher antenna currents due to larger radius (pulser currents depend on FRC
resistance).

Purchase neutral beam sources with ~10-50 A capability.
– 10-25 keV capability to match FRC conditions.
– Expect ~ 10 kA ion ring current per A beam current (will do detailed calculations).

Base power supply size on 50 -100 msec operation.
76
Sketch of FRC Front End
TCSU (rc = 0.4 m, la = 1.2 m)
Neutral beam port
3m
Internal flux rings
5m

vde/vs < 1 stipulation requires ~2.5 times scale-up of TCSU to flux
conserver radius of rc = 2 m. (vde/vs  Ai/n1/2R)
77
Projected Performance

Vacuum Chamber Parameters: rc = 1.0 m, lc = 6 m, Bmax = 1.2 kG (1.3 MJ)

FRC & RMF Parameters: rs = 0.9 m (xs = 0.9), ls = 5 m, wrs2 = 0.14106 m2/s
fw = 27 kHz (w = 0.17106s-1), Bw = 10 mT

Projection based on already achieved Be/Bw = 6,  = 0.8 (p = 45 mWb)
–

Be = 60 mT :
If can reach
Be = 120 mT :
nm = 1.4x1019 m-3
Tt = 650 eV
Be/Bw = 12,  = 0.8 (p = 90 mWb)
nm = 2.8x1019 m-3
Tt = 1300 eV
78
RMF Pulser Requirements
antenna

–
–
–
–
–
–
Present LANL triode pulser
rant= 0.6 m, lant = 1.25 m
Lant = 1.5 h, w = 1 mHz, wLant = 1.5 
Bw = 0.6 mT/kA; Bw = 5 mT, Iant = 8.3 kA
Ipulser = 0.7 kA, Vpulser = 12.5 kV
Pabs = 1.5 MW, Ppulser = 5 MW
pulser = 10 msec, Epulser = 50 kJ
[6 Machlett ML8616 giant triodes]

–
–
–
–
–
–
IGBT Based Pulser fw = 27 kHz
rant = 1.2 m, lant = 3.5 m (// fed)
Lant = 3.8 h, w = 0.17 mHz, wLant = 2.5 
Bw = 0.15 mT/kA; Bw = 10 mT, Iant = 66 kA
Ipulser = 3 kA, Vpulser = 40 kV
Pabs = 20 MW, Ppulser = 25 MW
pulser = 100 msec, Epulser = 2.5 MJ
[1 string of advanced 3 kA - 3 kV IGBTs]
79
Important Scaling Parameters
Parameter
TCSU
Proposed FRC
Reactor
fw (kHz)
150
27
8
rs (m)
0.37
0.9
0.9
2.0
Be (T)
0.03
0.06
0.12
1.3
p (Wb)
0.0035
0.045
0.090
4.5
Ti, Te (keV)
0.12
0.32
0.65
10
ne (1020m-3)
0.1
0.15
0.3
2.0
s
1.0
3.0
4.2
22
ii (m)
25
150
300
10,000
ci (m)
0.06
0.04
0.03
0.013
vde/vs
3
0.65
0.47
0.07
Ai
1
2
2
3
Eic (keV)
1.3
18
72
24,000
Ei (keV)
5.9
70
280
100,000
}
Without any
contribution
from TNBI
} governs 

}
?
TNBI parameters
(optimal to be at
Eic or below)
80
Tangential Neutral Beam Injection
(TNBI) can Counteract RMF Torque
Poloidal Flux (mWb)
FIX
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0 100 200 300 400 500 600
80
60
Te (eV)
•TNBI can balance RMF torque, adjust toroidal
flow profile, and provide kinetic ions.
with NBI
with NBI
40
•With tangential injection it can drive the
toroidal current and provide flux enhancement.
•FIX FRCs had p < 1 mWb which required
mostly axial injection with fast ions oscillating
outside separatrix.
20
r = 0.1 m
0
150 200 250 300 350
Time (s)
81
Collaboration with Ricardo Farengo
on TNBI Calculations (Eb = 10 keV)
Need at least 6.6 mWb
even for Eb = 10 keV
rs
R
Critical
orbit:
0.0144  p (m Wb) 


 ic (keV) 
Ai  rs (m) 
2
Ideal energies < Eic, but can operate
with Ei ~ 2Eic.
vb  s
I beam
2r

0.02  Te (keV) 

 sec
s 
ne (1020 m 3 )  0.27Eb (MeV) 
I ring 
p (mWb)
6.6
Be (T)
0.08
rs(m)
0.3
Te (keV)
0.14
ne(1020 m-3)
0.5
Ai beam
1
Eic
5 keV
Ei(rs)
25 keV
Calculated current drive
efficiency is 0.7 kA/A,
which scales as Te3/2/ne.
82
Ratio of vde to vs is Important Parameter For
Turn-On of Anomalous Cross-Field Resistivity
vde/vs < 1
vde/vs >1
Non-linear 2-fluid calculations of instabilities in a Z-pinch by Loverich &
Shumlak for various vde/vs.
v de
Tt1/ 2
1 Bx
 we r 
 1/ 2
ne eo r
n R
vs 
kTt
Tt1/ 2
 1/ 2
mi
Ai
83
Progress with spheromak research justifies a POP exp.




Steady-state inductive methods have formed and sustained
spheromaks (30kA) on HIT-SI (Invited talks at up coming APS/DPP)
Spheromaks can be formed at low power (3MW)
Theory of equilibrium, formation, and sustainment have been proven
by experiment
High power pulsed formation methods have produced spheromaks that
heat to Te = 0.5 keV showing spheromaks can have good confinement.
Vacuum wall of possible spheromak
front-end based on HIT-SI
Injectors
Spheromak
flux conserver




Jarboe 9-18-07
Injectors makes spheromak rotate to stabilize the RWM
Injectors removed from the equilibrium (more like a reactor)
Still in the brain storming phase (more data will help)
Flux conserver diameter is 2 m – 3 m
The power to sustain a small spheromak
experiment may be nearly the same as a reactor









20MW sustainment power is certainly acceptable in a reactor.
Scaling at constant n, j/n, and β yields a sustainment power
independent of size.
Spheromaks seem to require j/n>10-14Am which is the same as the
Greenwald limit in a tokamak. So constant j/n is a reasonable scaling.
Constant β is reasonable and the hope.
Constant n leads to a reactor and means constant j.
Assume the resistivity η scales as T-3/2 (Spitzer)
Since B = oj: B  R so Magnetic energy ( B2R3)  R5
At constant β and n: T  B2  R2 , η  R-3 so τmag.eng.  R2/η  R5
Thus, sustainment power [ (Mag. Energy)/ τmag.eng] is constant with R
Jarboe 9-18-07
Scaling from HIT-SI goals gives a
reasonable POP experiment
Jarboe 9-18-07
HIT-SI (goal)
HIT-POP
a
0.2 m
0.6 m
T
110eV
1 keV
mag axis
0.2
0.2
n
2.4 x 1019 m-3
2.4 x 1019 m-3
Itor
150 kA
1.4 MA
j/n
3 x 10-14Am
3 x 10-14Am
pulse
10 ms
1.0 s
Some Projected Costs

Basic Construction & Operating Cost - ~$7,500,000 per year.
– Based on 1986-1990 LSX construction effort ($3.5M/year in 1987 dollars).

Major Procurement Items.
–
–
–
–

RMF power supply - $3,000,000
Short pulse neutral beams - $2,000,000
FRC front end (based on TCSU experience) - $5,000,000
Spheromak front end - $5,000,000
Schedule - 4 year construction.
–
–
–
–
Includes power supplies, neutral beams, diagnostics, and FRC front end.
Operate TCSU for first two years of construction for developmental tests.
Operate HIT-SI until decide on front end design
Alternate operation of FRC and spheromak front ends.
88