J. Plasma Fusion Res. SERIES, Vol.5 (2002) 63-68

Magnetitzed Target Fusion:
Prospects for Low-cost Fusion Energy
SIEMON Richard E., TURCHI Peter J., BARNES Daniel C., DEGNAN James H.l
PARKS Pau12, RYUTOV Dmitri D.3 and THIO Francis y.a
Los Alamos National lttboratory, Los Alamos, New Mexico 87545, USA
t Air Force Research Laboratory,
2
3

Kirtland AFB, NM 87117-5776, USA

General Atomics, San Diego, CA, 92121-1194, USA

Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
4 NASA Marshall Space Ftight Center, Huntsville,

AL 35812, USA(Received: ll December 2001 / Accepted: 6 August 2002)

Abstract
Mrlgnetized Target Fusion (MTF) has attracted renewed interest in recent years because of its
potential to resolve one of the major problems with conventional fusion energy research - the high costof facilities to do experiments and in general develop practical fusion energy. The requirement for costly
facilities can be traced to fundamental constraints. The Lawson condition implies large system size in thecase of conventional magnetic confinement, or large heating power in the case of conventional inertial
confinement. The MTF approach is to use much higher fuel density than with conventional magnetic
confinement (corresponding to mega bar pressures), which results in a much-reduced system size toachieve Lawson conditions. Intrinsically the system must be pulsed because the pressures exceed thestrength of any known material. To facilitate heating the fuel (or "target") to thermonuclear conditions
with a high-power source of energy, magnetic fields are used to insulate the high-pressure fuel frommaterial surroundings (thus "magnetized target"). Because of magnetic insulation, the required heating
power is reduced by many orders of magnitude compared to conventional inertial fusion, even withrelatively poor energy confinement in the magnetic field, such as that characterizedby Bohm diffusion.
This paper shows semi-quantitatively why MTF should allow fusion energy production without costly
facilitios within the same generally accepted physical constraints used for conventional magnetic andinertial fusion. We also report on the exploratory research underway, and the interesting physics issues
that arise in the MTF regime of parameters.

Keywords:
fusion energy, inertial fusion, magnetized target fusion, pulsed power

1. lntroduction

thinking of 82 as pressure. By considering pressure as a

During the years that John Clarke headed DOE's
Office of Fusion Energy, he sometimes quipped: "Betais beautiful, but B is better." He was referring to the factthat magnetic fusion power density is proportional toB2B4.In this paper we intend to generalize that point by

wide-ranging variable rather than a given quantity basedon conventional magnet technology, we argue that
fusion has important unexplored possibilities. Eventually
the technology requirements for working with the high@2002 by The Japan Society of Plasma
Science and Nuclear Fusion Research

C orresponding author' s e -mail : siemon@ lanl. gov

63

Siemon R.E. et al., Magnetized Target Fusion: Prospects for Low-cost Fusion Energy

approach to burning-plasma tokamak experiments would
be the use of pulsed copper magnets as selected in thepressures considered here will determine the practicalityof this pathway. From a physics perspective, oncepressure is specified, it is somewhat surprising how

IGNITOR and FIRE designs. The FIRE design [4]operates with 10 T (400 atmospheres) and achieves themuch can be calculated given a small number of otherrelatively well-established and fixed parameters. In fact,
for thermonuclear fusion. ie.. fuel ions with a thermalvelocity distribution, pressure seems to be the only

same Q-10 with a smaller less-expensive facility.

The main reason for this trend is that smaller size
becomes possible as pressure is increased. Although
thermal diffusivity 7 and normalized plasma pressure B
tend to stay constant as pressure changes, density andtherefore fusion reaction rate increases for given beta

variable available for sienificant variation of fusion
systems and cost.

Arguments for magnetic fusion systems operated athigh pressure have been made and generally rejected formany years, probably in part because the technology forpulsed mega-gauss magnetic fields is unfamiliar and lessdeveloped than for conventional magnets. This appears
to be a good time to reexamine this type of systembecause 1) pulsed high-field technology has advanced,
2) plasmas such as compact toroids appropriate to thisand temPerature:n = Bp/27.

(1)

Temperature is necessarily - l0 keV for DT fusion, andwe use Z to represent kL Pressure in eq. 1 is P = Br2/2pt in a tokamak. We consider a nominal tokamak witha circular plasma cross section of radius a. We can thenwrite the pressure dependence of the radius as:

approach have been developed, and 3) fusion researchhas been called into question by skeptics. The skepticso = (r x)t,, = 12Tnr fl Bltt2lPtt2

ask whether practical fusion is possible given the(2)

expense and complexity of facilities needed for progressin the parameter regime of burning plasmas. Such costs

For given values of nt and /8, the required minor radius decreases as the square root of pressure. For a burn-are sometimes claimed to be generic to fusion.
According to the arguments in this paper, one should

ing tokamak we take nr = 5xlOzo s/m3 corresponding to

Q-r0.
The toroidal magnets are the largest-coststate more carefully that high-cost facilities are intrinsic

component for a tokamak. For the present purpose we
assume that costs for the balance of the facility also
increase in proportion to the amount of magnetic energy.
According to four contemporary tokamak designs(ITER-FEAT, FIRE, PCAST, and ARIES-RS), the ratioof total facility cost to magnetic energy is reasonably
constant (0.16 + .07) for magnetic energy ranging from
5 to 85 GJ, so we will use $0.16 per joule to estimate
tokamak facility cost based on energy.

to conventional fusion. Indeed, a large and expensive
tokamak is needed for progress on burning plasma
issues. However, expensive facilities might not beneeded for the unexplored regime of pressureintermediate between conventional magnetic and inertial
fusion. With this issue in mind we will estimate the costof an MTF facility capable of energy gain (Q = fusionenergy output/ liner kinetic energy - l), whichcorresponds to the Lawson condition of nt = 3x1020 sec/
m3. For the purpose of doing a broad survey covering

For our nominal tokamak, the plasma radiusten orders of magnitude in pressure, we will adopt arough approximation that cost is proportional to twoquantities: a constant times total system energy plus a
different constant times system power (system energy/r). The constants of proportionality and the generaltrend for costs will be derived from costs of existing

estimated from eq. 2, and the aspect ratio allow us tocalculate the plasma volume V = 2 n2 A a3. W e define aparameter x, equal to the ratio of plasma radius tomagnet inner radius, and calculate the magnet volume as
Vlf .The system energy is then calculated as follows:

E=\tf+B|2)PV

facilities and projected costs for new facilities such as= 1lf + Bl2)2n2A(27 X nrlByrz,r''t

ITER-FEAT.

= 200 GJ / P(atm)t/2(3)

2. Cost Estimates for Nominal Tokamaks
This numerical example for the dependence of .E upon P
is based on the numbers in Table 1 below. We see here,
as noted by Sheffield [5], that the ratio Blyis a figure of
merit for physics performance of a magnetized plasma.
The larger that ratio, the smaller the magnet energy and

The range of parameters available for conventional
magnetic fusion is strongly constrained by the fieldstrength available from steady-state magnets. The ITER
design has a toroidal field of 5.5 T, corresponding to amagnetic pressure of l2O atmospheres. An alternative64

Siemon R.E. et al., Magnetized Target Fusion: Prospects for Low-cost Fusion Energy

has not demonstrated a very large improvement in Bly.

3. Cost Estimates for Generic Magnetized
Target Fusion (MTF)

So we next consider what might be possible with significantly increased pressure.
The point of developing eq. 3, is to show how
magnet energy in a tokamak with fixed nt dependsof any material, and involve pulsed technologies ofsome type. Liner technology [6] has demonstratedpressures in the megabar range and corresponding

strongly upon the magnetic pressure. Then themagnetic fields of up to about 200 T. The liner approach

approximation of cost proportional to magnetic energy
allows an estirrate of the tokamak cost. Such a crude
approximation ignores significant differences, like those

involves rapid compression of a metal cylinder, often by
the use of the pinch effect from an axial current applied
to the outer surface of the liner. Inward motion proceeds
until pressure inside the cylinder stops the implosion.

facility cost. However, alternate concept research so fiu

We consider now pressures that exceed the strength

between superconducing and copper magnet technology,

Another MTF approach called LINUS involved

nuclear shielding requirements, and so forth. The
approximation is not unreasonable as seen in Fig. 2

compression of a cylindrical chamber by the use of thickrotating liquid metals [7]. In laser fusion, the final hot
spot that initiates fusion is compressed by the rapid
implosion of a "pusher" material from the outside. In
Fig. 1 we show parameters for a generic MTF system.
All such approaches have in common the feature that

below. But for the purpose of this paper, cost variationsof less than a factor of two are considered as anonessential detail, even though such differences are
obviously important when choosing between competing
tokamak technologies and proposing an experiment.

a pressure pulse is sustained for a limited time given by:

r=6Rl(Plp)t''
Pusher material

We take eq. 4 to be the defining feature of generic MTF.
This is a quite general relationship that can be derived
by thinking of the shock and rarefaction waves that must
propagate through the pusher material at peak compression, or by considering the impulse (Pr) that must balance the momentum change of incoming pusher (liner)
mass [2,8]. Fusion reactions stop when the pressure

a= 6R/R

thickness

B+6F

Magnetic field

drops, so this characteristic time must satisfy the same
Lawson criterion, as does the energy confinement time.
The energy confinement time, estimated as x2R2l7, wlll
be larger than the dwell time of eq. 4 so long as 7 issmaller than the followine:

l0 keV plasma mixed
with maenetic field

Fig. 1 Parameters p, x, a, R,6R for a generic liner-imploded MTF system.

/ (maximum) = 2x2\nrlT/p\d(5)

The value is about 10 m2ls independent ofpressure. Fortunately this is a rather high diffusivity, which gives
hope we can find acceptable magnetic configurations.
Specific ways this might be achieved will be discussed
in the next section.
The parameters we have defined for the nominal

6' rooo€tokamak and the generic MTF system are listed in Table
I along with typical values used in calculations.

6

$

(4)

roo

Assuming a pusher efficiency e, the required
pusher kinetic energy, KE, is the magnetic plus plasma

thermal energy inside the chamber divided by e:'1.E+04 1.E+06 'l.E+08 1.E+'10 1.E+12

Kn=(l+Bx2/Z)pV/t

Pressure (atmospheres)= ( + Px2 /Dl6ne(nr)373 lfea3 p3 p3t2 p1/21= 23 GJ / P(atm)tt2

Fig. 2 Facility cost vs. pressure for nominal tokamak andgeneric MTF systems
65(5)Siemon R I. et al., Magnetized Target Fusion: Prospects for Low-cost Fusion Energy

inertial dwell time, with the opposite below thetransition pressure. For a rough estimate of ICF

Power requirements are also an important consideration
for MTF. We calculate facility cost divided by output
power for the following state-of-the-art pulsed power

parameters inside the central hot spot where burning
begins, thermal diffusivity can be taken as X - hV",
where i, is the mean free path and V" is the electron
thermal speed. For the Field Reversed Configuration,
heat loss by particle diffusion is observed to have aneffective thermal diffusivity of y - vo pio, where vo is anempirical constant equal to 4x104 m/s. and p;o is the ion

devices: NIF $6/megawatt; Z machine $3/megawatt; andAtlas $l2lmegawatt. We expect that Atlas or Z technology are the most likely to be useful for MTF, so weadopt $l/joule for energy and $10/megawatt as the characteristic energy and power costs for the generic modeland estimate facility cost as follows:

gyroradius calculated with the central temperature andGeneric MTF facility Cost ($)= $l * KE(J) + $10 * Power(MW)the external magnetic field. In the expressions fortransition pressure, ro is the classical electron radiusused for dimensional simplicity. There are interesting(6)

The justification for this crude approximation is thesame as for the nominal tokamak. We investigate how

new theoretical results suggesting that experimentallyobserved FRC stability can indeed be explained byelongation [9], as considered in earlier analysis [0]. In
the FRC model of this paper, elongation was adjusted atcost depends upon major parameters, and ignore impor-tant issues such as cost for nuclear shielding as a detail.
We chose liner kinetic energy and pulsed power level
because existing large pulsed power facilities show
those to be major characteristics, just as magnet energy
is the most important parameter for a tokamak. Neither
the nominal tokamak cost, nor the generic MTF facility

Table 1 The oarameters used to characterize a nominal

tokamak and a generic Magnetized Target
Fusion system.

cost, represent the full cost of a fusion reactor. We focus

Quantity

SymbolNominal tokamak

Generic MTF

here on the cost of the nuclear island, not the costs for
power conversion, fuel processing (tritium breeding),and so forth. Such a focus is reasonable because themain technical uncertainties and remaining development
cost concern the nuclear island.
The results are shown in Fig. 2. The potential for
considerable cost savings in the intermediate pressure
regime is immediately obvious. We emphasize that thisconclusion is based on costs of representative pulsed-

PressureP

Br212po103- 10r2 atm.

100-400 atm.
Temperature

T_T

Lawson ptrameter

nx

Beta

p

-T

Ratio of plasma radius
to masnet inner radius

power facilities and the implications of eq. 4, not upon
plasma physics. We next consider particular possibilities

l0 keVl0 keV

5xl02o sec/m3

3x1020 sec/m3

.o4

0.'1

0.5

0.8

Thermal diffusivityx

I m2ls

10 m2ls

Aspect ratio

A

3.5

Not.applicable

Pusher densityp

Not applicablel0

Thickness ratio 6R /Ra

Not applicable

3

Pusher elongation L/2Re

Not applicable

5

Pusher efficiencya

Not applicable

0.5

=E/KE

for plasma targets.

4. Potential Plasma Targets and the Influenceof Thermal Diffusivity

Table 2 Parameters and relationships to be substituted
in the generic MTF model for three potential
MTF plasma targets

We examine here three possible MTF targets:conventional inertial fusion, Field-Reversed Configurations, and a less explored idea of wall-confinement with
Bohm diffusion. In these cases we change some generic
MTF parameters as listed in Table 2.
Pressure is still the major variable as before, butthere is now an important transition pressure, P1, forwhich the maximum allowed thermal diffusivity (eq. 5)
becomes equal to the thermal diffusivity applicable to

Quantity
D

66

FRC

Wall confined Bohm

dfl,v"trv.2 Bzpzaa(m,1m,\l

tlf ll[24 nr,(n'r)2Tx4l

f212 nm"r.(l-p)(nt)2nT

10 keVl0 keV3 x 1020 sec/m3 3 x l02o sec/m3

p

1.0

0.8

x

1.0

0.8

1.0

x

Lv,

v" Pi"

vi pil 16

p

3

20

20

d

3

e

I

Determined from S*

I

0.5

0.5

0.5

I

the particular plasma target. Above the transitionpressure the dominant time constant is given by the

ICF

10 keV

3 x l02o sec/m3
0.953Siemon R.E. et aI., Magnetized Target Fusion: Prospects for Low-cost Fusion Energy

each pressure to meet the stability requirement:

points where the slope of these curves is discontinuous

The idea of high-beta wall confinement has been exam-

are at the transition pressure in each case. Above thetransition pressure, the generic scaling resembles thecurve shape in each case as expected, although the exact

ined theoretically and computationally [,ll]. The pvalues depend upon the p.uameter variations associatedused in this paper is the plasma pressure relative to total

with specific plasma targets.

pressure, which does not exceed unity. Imagine that in-

The typical sizes and energies associated with the
FRC and Bohm examples are shown in Fig. 4. The
strong variation of FRC length with pressure resultsfrom the stability requirement. Magnetic fields range
from 10-1000 T, and KE ranges from 10-1000 MJ.
While all parameters are not of interest in a practicalsense, the variation with pressure is instructive. One of
the critical physics issues is how rapidly high Z wallmaterial will mix with low Z fusion fuel. Another issue
is the acceptable range of liner thickness (alphaparameter). Large alpha increases the dwell time, butwould also reduce efficiency if the equation of state forg,rls = fxRl(clt\i)Ue= 3.5.

(7)

side the confinement chamber, that a uniform B and nT
are compressed, then the local internal beta would be

PIQ-\, or 19 for 0=0.95. While this regime has notbeen studied experimentally so far, the results from themodel of this paper support earlier work [2] suggestingthat such a system would indeed allow larger Q in a rcasonably small system, compared for example with the
FRC when the required elongation is considered. The
estimated cost for these various systems are shown in
Fig. 3 and compared with the generic MTF model. The

compressed pusher material were taken into account. As

discussed in ref. 2, scaling of gain with energy in abatch-burn MTF system is proportional to 1KE;r/3.
However, as the examples here show, the proportional-

ity constant depends upon details of confinement, which
are obviously very important for the ultimate applicationof this technology.
Present US DOE efforts are focused on producing

o

o

o

an FRC target plasma at Los Alamos [3,13], andexperiments at the Air Force Research Laboratory [14]show that the Shiva Star facility would allow interesting

10

integrated liner-on-plasma experiments as funding
permits. Cost of facilities is also related to the mass ofequipment required to produce fusion energy. Specificpower (power per unit mass of power supply) is a key
parameter for space applications, and MTF has attracted
interest in the US NASA space program [2]. The MTF
web page http://fusionenergy.lanl.gov is available for

Pressure (atmospheres)Fig. 3 Cost estimates for specific plasma targets compared with the generic MTF estimate.

additional information.

5. Conclusions
While the status of MTF research is immature atthe present time, and many unresolved issues can be
identified, the results shown by Figs. 2 and 3 provide agood rationale for investigating the intermediatepressure regime. The cost of facilities needed fordevelopment is emphasized here because of its
importance to cost of development, a major impedimentto achieving practical fusion energy. Other importantunresolved issues remain for fusion energy, such as
materials to survive the first-wall neutron damage.
While it remains to be seen whether alternative concepts

P(dno.phr.r)

Fig. 4 Radius, magnetic field, KE and FRC length varia-

tion with pressure for FRC confinement and wallconfined Bohm confinement.
67

Siemon R.E. et al., Magnetized Target Fusion: Prospects for Low-cost Fusion Energy[7] P.J. Turchi, Proc. Third International Conferencesuch as MTF provide useful solutions, the study ofqualitatively different approaches to fusion seems highly

on Megagauss Magnetic Field Generation and Related Topics, Novosibirsk (1983).

prudent at the present time.

t8l F.L. Ribe and A.R. Sherwood, Fusion, E. Teller,
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68