Magnetized Target Fusion:
Prospects for low-cost fusion energy
Richard E. Siemona,
Peter J. Turchia, Daniel C. Barnesa, James H. Degnanb,Paul Parksc, Dmitri D. Ryutovd, Francis Y. Thioea) Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USAb) Air Force Research Laboratory, Kirtland AFB, NM 87117-5776, USAc) General Atomics, San Diego, CA, 92121-1194, USAd) Lawrence Livermore National Laboratory, Livermore, CA 94550, USAe) NASA Marshall Space Flight Center, Huntsville, AL 35812, USA

ITC-12
Dec 12, 2001
Toki, JapanFusion physics: 107 - 108 oCMTF

1012 bar

106 bar
1 bar

Partial ionization

Maximum pressure depends
upon technology• Superconducting magnets (steady state)
B < 15 Teslap < βB2 ~ 100 atmospheres• Liner technology (pulsed)
B ~ 200 Teslap ~ βB2 ~ 106 atmospheres• Laser compression (pulsed)
p ~ 1011 atmospheres

Liner technology
Bθ ~ 100 tesla (40,000 atmospheres)

107 amps< 10 µs“Liner” is thin-walled
aluminum cylinderRadiograph of liner implosion
Initial 1-mm thickAluminum liner

Flash xrays
Side-on viewof liner moving
4 mm/µs

Stationary 6-mm probejacket

Elastic-plastic deformed 7-mm
thick liner at 12:1 radialcompression

How might MTF be done?

0.5 m

Thin metal
wall implodes

Pulsed current~ 107 AMTF requires energy to preheat thetarget and separately to implode the liner
Liner implosion~ 10-100 MJ

Target formationand preheating~ 0.1-1.0 MJ

Los Alamos FRX-L experiment
3 meters

100-kV, 200-kJ
Capacitor bank

Current collector
plate

Theta-pinch coil
36-cm long;
12-cm diameter

Predictn ~ 1017 cm-3
T ~ 300 eV

Shiva Star liner implosion (Qeff ~ .01)80 kV, 5 MJ

The Field Reversed
Configuration

End-on FRC interferogram

R. Siemon et al.,Fusion Tech. 9, 13 (1986)
M. Tuszewski,
Nuc. Fusion 28, 2033 (1988)
with 416 references.

Time history of interferograms

Equilibrium theory up to E ~ 5Conducting boundary
rsL/2<β> = 1 – xs2/2
xs = rs / Rwall

E = L / 2rs

Stability appears to depend upon elongation
FRC Operating Regime
100

Size Parameter, S*LSXCTORARTEMIS
FRX-L
FRX-C

10TRX
PIACE
S* = 3.5 E
S* = 5.8 E
1110100

Elongation ES* = rs / (c/ωpi) ~ rs / ρi

E = Ls / 2 rs

Profile of long FRC determined by equilibrium alone
D.C. Barnes, Phys. Plasmas 8, 4864 (2001)

Combining p = p(ψ) with uniform elongation (∂/∂z << ∂/∂r)gives solutionp = p0 [ψ ; pop] + ε 2 p1 [ψ ; r s ( zˆ)]
Depends on: open p ; elongation ; shape30

16 curves essentiallythe same

20

0.8

p0 - psr

10
0

0.6
0.4
0.2

-0.6

-0.4

ψ

-0.2

Universal closed pressure000510z1525:1 2D solution

2025

Stability with Hall terms agrees withempirical good parameter regime*
E100[CB FRX[P TRX
HHP
E H
BH
B B
HHB BPBBBPPP B
P PPPPPPP PBB

S*[F PIACE

E

H LSX

[10[52P

C ARTEMISE FRX-LFFE

E CTOR

10[4.543.5
32.5
S */E
21.5
10.5
030LocalVolume average

Eql. 1 Eql. 2 Eql. 3 Eql. 4Empirical analysis (Tuszewski) shows S*/E < 3.5for good plasma flux confinement.
Theory shows S*/E < 2 - 4 for stability

S* = rs /(c/ωpi)
E = ls/ds*D. C. Barnes, Phys. Plasmas, accepted Nov. 2001

Los Alamos FRX-L team

Goal: Compress an FRC inside
a liner to achieve T ~ 10 keV

Los Alamos Atlas facility (Qeff ~ 1)

240 KV
25 MJ

Summary of introductory points•The field-reversed configuration provides one method
to position 300-eV plasma inside a conducting cylinder•Recent theoretical work suggests that the long-standing
paradox of FRC stability might now be resolved•Liner implosions with 10:1 radial compression are feasible
B ~ 50 kG → ~ 5 x 106 G
P ~ 100 bar → ~ 106 bar (1 bar = 1 atmosphere)•One should ask: Why is this important to fusion research?

High pressure cavity
Pusher materialwith density ρ10 keVplasma
mixed withmagnetic
fieldxRRdR

BnTr

α = dR/R

Lawson triple product requirement½ n2 <σv> Ef ≥ 3nT/τE; ρ = n minTτE ≥ 6T2/ <σv> EfTemperature and fusion cross section σdetermine required product of pressureand energy confinement time

System size tends to decrease aspressure increases
Suppose τE is determined by thermal
diffusivity; then size must be large enoughto meet Lawson condition:

τE = a2/χ
Define an engineering β = nT / Pa = sqrt(τE χ) = sqrt(nTτE χ/β) / sqrt(P)Variation of size with pressure depends upon
specific loss processes
Approximate
Upper-limit “Bohm”

Fuel Mass (grams)

ITER
1

Advancedconcepts

109

MTF

10-3

10-6

Diffusion-limit
Zero magnetic
field

106

NIF

Diffusion-limit“classical” magnetic confinement

103

106

Pressure (atm.)

103

109

Fuel Energy (joules)

103Dwell time
Pressure (P) lasts for a pulse time τlimited by inertia of liner (density ρ).

τ = dR / (P/ρ)1/2
Pulse duration τ must separately satisfy
the Lawson condition.

Liner kinetic energy and power
Can show:
E = Eplasma + Efield = (1+βx2/2) PV
Kinetic Energy is related to E by anefficiency ε
KE = E/ εCharacteristic Power = E / τCost estimate
State-of-the-art pulsed power devices:
NIF$6 / megawatt
Z machine $3 / megawatt
Atlas$12 / megawatt
Adopt $1/joule and $10 / megawatt for thistype of pulsed-power supply
Make estimate:
MTF cost ($) = $1 * KE(J) + $10 * Pwr(MW)Generic MTF facility cost vs. pressure

Cost ($Millions)

10000
ITER-FEATFIRENIFZAtlas
Generic MTF
Generic Tokamak
High pressure tokamak

1000

100

10
1.E+02

1.E+04

1.E+06

1.E+081.E+10Pressure (atmospheres)

1.E+12

Energy confinement – specific targets
ICF: electron thermal conduction
χ = λ ve
λ = m.f.p.,ve = elec. thermal speed
Field Reversed Configuration: empirical scalingχ = ρi vo

ρi = ion gyro radiusvo = 4x106 cm/s

Wall-confined Bohm thermal conductionχ = ρi vi / 16

Facility costs - specific plasma targets

Cost ($Millions)

10000

1000

NIFZAtlas
Generic MTF
ICF
FRC Q ~ 1Bohm Q ~ 10100

101.E+04

1.E+06

1.E+081.E+10Pressure (atmospheres)

1.E+12

Wall-confined Bohm-like plasma
Pusher material
with density ρ

α = dR/RRdR

L≈R

10 keV plasma
mixed withmagnetic fieldComputations show wall-confinedplasma cools at acceptable rate
5x1019 cm-3

1 keVnTZB

θθr50 TZ

Z pinch Bθ

3 cm

3 cm

2x104 barZPθ pinch Bzθ

3 cm

3 cm

Russian MAGO has wall-confined plasma

Inverse pinchacceleration

Nozzle action

GroundConceptual experiment
to study wall-confined plasma
T ~ 0.5 keVn ~ 1017 cm-3I
1 MA~ 0.1 µs

Inverse pinch
current sheet
Insulator
Aluminum

5 cmCenter-line

Program plans
DOE Office of Fusion Energy Sciences Exploratory Research• Develop FRC target plasma
FY 2002-2003 $2-4 M / year
Proposed:• Liner implosion Shiva Star
FY 2003-2004 $4-6 M / year
• Liner implosion Atlas
FY 2005-2008 $10-20 M / year
NASA Marshall Space Flight Center• Plasma-gun implosion system
FY 2002 – 2004 $2-3 M / year
Actual budgets in black
Anticipated budgets being proposed in red

Technical issues• Plasma target formation, stability, andenergy confinement at high density• Wall-plasma interactions and impurity
mixing with fusion fuel• Gain limitations using batch-burn mode
• Practicality of pulsed operation

Conclusions• MTF warrants exploration given its potential as a
low-cost approach to fusion• The cost results are derived from simple
considerations and experience with pulsed-power
facilities; not plasma physics.
• Plasma physics will determine the detailed behavior
and ultimate optimization of an MTF system.
• Experimental facilities already exist that allow testingof many critical MTF issues• This research is just beginning; interested scientists
are encouraged to contact any of the authors (moreinformation at http://fusionenergy.lanl.gov).