Title Review of progress in Fast Ignition
Author(s)
Tabak, M.; Clark, D.S.; Hatchett, S.P.; Key,
M.H.; Lasinski, B.F.; Snavely, R.A.; Wilks,
S.C.; Town, R.P.J.; Stephens, R.; Campbell,
E.M.; Kodama, R.; Mima, K.; Tanaka, K.A.;
Atzeni, S.; Freeman, R.
Citation Physics of Plasmas. 12(5) P.057305
Issue Date 2005-05
Text Version publisher
URL http://hdl.handle.net/11094/3277
DOI 10.1063/1.1871246
rights
Note
Osaka University Knowledge Archive : OUKAOsaka University Knowledge Archive : OUKA
https://ir.library.osaka-u.ac.jp/
Osaka University
Review of progress in Fast Ignition
a…
M. Tabak,
b兲
D. S. Clark, S. P. Hatchett, M. H. Key, B. F. Lasinski, R. A. Snavely,
S. C. Wilks, and R. P. J. Town
Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, California 94550
R. Stephens and E. M. Campbell
General Atomics, P. O. Box 85608, San Diego, California 92121-1122
R. Kodama, K. Mima, and K. A. Tanaka
Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka, Japan 565-0871
S. Atzeni
Dipartimento di Energetica, Università di Roma, “La Sapienza,” and INFM, Via A. Scarpa,
14 00161 Roma, Italy
R. Freeman
425 Stillman Hall, The Ohio State University, Columbus, Ohio 32210-1123
共Received 15 November 2004; accepted 20 December 2004; published online 5 May 2005兲
Marshall Rosenbluth’s extensive contributions included seminal analysis of the physics of the
laser-plasma interaction and review and advocacy of the inertial fusion program. Over the last
decade he avidly followed the efforts of many scientists around the world who have studied Fast
Ignition, an alternate form of inertial fusion. In this scheme, the fuel is first compressed by a
conventional inertial confinement fusion driver and then ignited by a short 共⬃10 ps兲 pulse,
high-power laser. Due to technological advances, such short-pulse lasers can focus power equivalent
to that produced by the hydrodynamic stagnation of conventional inertial fusion capsules. This
review will discuss the ignition requirements and gain curves starting from simple models and then
describe how these are modified, as more detailed physics understanding is included. The critical
design issues revolve around two questions: How can the compressed fuel be efficiently assembled?
And how can power from the driver be delivered efficiently to the ignition region? Schemes to
shorten the distance between the critical surface where the ignitor laser energy is nominally
deposited and the ignition region will de discussed. The current status of Fast Ignition research is
compared with our requirements for success. Future research directions will also be outlined.
© 2005 American Institute of Physics. 关DOI: 10.1063/1.1871246兴
I. INTRODUCTION
Fast Ignition
1
is a form of inertial fusion in which the
ignition step and the compression step are separate pro-
cesses. The invention of chirped pulse amplification
2
of la-
sers spurred research in this area because these lasers can, in
principle, supply energy to the fusion ignition region as fast
as the convergence of stagnating flows can for the conven-
tional ignition scheme. In the original concept, the delivery
of this ignition laser energy is mediated by the transport of
relativistic electrons produced in the laser-plasma interac-
tion. Another variant of this scheme uses protons
3
driven by
these fast electrons to deliver the energy to the fuel. Fast
Ignition offers the possibility of higher gains, lower driver
energy and cost required to achieve economically interesting
gains, flexibility in compression drivers 共lasers, pulsed
power, and heavy ion beam accelerators兲, innovative reactor
chamber concepts, and lower susceptibility to the effects of
hydrodynamic mix than the conventional inertial fusion
scheme. Researchers around the world have studied this fu-
sion scheme intensively for the past dozen years. The chal-
lenging physics and opportunities motivated Marshall
Rosenbluth to encourage and to contribute to Fast Ignition
research. This report will review the Fast Ignition scheme,
the progress made over the past decade, and possible direc-
tions for the future. The plan of this paper is as follows:
Section II describes ignition requirements and a simple gain
model. Section III describes a typical implosion used to as-
semble fuel, its consequences for Fast Ignition, and how this
implosion might be modified. Section IV presents results on
the coupling of high-intensity laser light and plasmas, the
generation of fast electrons, and the subsequent transport of
these electrons. Section V describes various techniques to
improve the efficiency of the transport of energy between the
nominal critical surface where the ignitor laser energy is de-
posited and the compressed fuel where ignition occurs. Sec-
tion VI summarizes
4
and concludes this paper.
II. IGNITION REQUIREMENTS AND GAIN MODELS
Ignition requires that a sufficiently large region of fusion
fuel be heated to the ignition temperature. This ignition tem-
perature depends on the ignition region size given by its
a兲
Paper HI1 6, Bull. Am. Phys. Soc. 49,175共2004兲.
b兲
Invited speaker.
PHYSICS OF PLASMAS 12, 057305 共2005兲
1070-664X/2005/12共5兲/057305/8/$22.50 © 2005 American Institute of Physics12, 057305-1
Downloaded 17 Jun 2011 to 133.1.91.151. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions
column density, h=兰
dR⬇
R. The hotspot energy require-
ment in megajoules is then: E
ign
=144关共Z
¯
+1兲 /A
¯
兴MT, where
M=4
/3共
R兲
3
/
2
and
is given in g/cm
3
, T in keV. Z
¯
,A
¯
are the average atomic number and atomic weight, respec-
tively. For an equimolar deuterium–tritium 共D–T兲 plasma Z
¯
=1 and A
¯
=2.5. In conventional inertial fusion, a low density
hotspot and ignition region is surrounded by a relatively cold
and dense main fuel region, where the bulk of the yield is
produced. The heating of the hotspot and the compression of
the main fuel to high density happen simultaneously as the
kinetic energy of the imploding shell is converted into inter-
nal energy of compressed fuel during stagnation. Because the
hotspot and the main fuel are sonically connected, their pres-
sures are approximately equal 共⬃200 Gbar兲. The minimum
ignition requirements 共in terms of T and h兲 depend on how
well energy is confined in the hotspot. The losses can include
radiation, electron conduction, and hydrodynamic work. In
an isobaric configuration, the hotspot is tamped and its hy-
drodynamic losses are limited during ignition. In addition,
some self-heating during the implosion reduces the energy
that must be delivered to the hotspot for ignition. In contrast,
in the isochoric configuration used in Fast Ignition, the igni-
tion region is far out of pressure balance with the surround-
ing fuel, so hydrodynamic losses can be significant.
Atzeni and collaborators
5
by performing a series of two-
dimensional 共2-D兲 simulations where energy is injected into
precompressed D–T fuel found that the ignition energy in an
isochoric configuration was approximately 5 times greater
than that for isobaric ignition. This corresponds to h
=0.6 gm/cm
2
and T=12 keV. Figure 1 shows the ignition
windows in energy, power, and intensity for various fuel den-
sities. The minima for these quantities, for deposition ranges
between 0.3 and 1.2 g/cm
2
, can be parametrized as functions
of
:
E
ign
共kJ兲 = 140
冉
100 g/cm
3
冊
−1.85
,
W
ign
共W兲 = 2.6 ⫻ 10
15
冉
100 g/cm
3
冊
−1
,
I
ign
共W/cm
2
兲 = 2.4 ⫻ 10
19
冉
100 g/cm
3
冊
0.95
.
The coupling efficiency will determine the ignitor laser re-
quirements. Preliminary results show that if the ignition en-
ergy is used to drive an ultrahigh pressure reimplosion of the
compressed ignition region instead of directly heating it, the
ignition energy can be reduced by at least a factor of 2 with
an associated increase in spot size and delivery time.
6
By combining these ignition requirements with models
of directly driven implosions
7,8
that supply the hydrody-
namic efficiency,
hyd
; the relation between ignition laser
intensity and the temperature
9
of the hot electron distribu-
tion:
T共MeV兲 =
冉
I
ign-laser
1.2 ⫻ 10
19
共W/cm
2
兲
冊
1/2
for an ignition laser with wavelength 1.05
m; and the par-
ticle range, R共g/cm
2
兲=0.6 T共MeV兲, we can derive model
gain curves.
10
The nominal model assumes a 25% coupling
efficiency,
ign
, from the ignition laser to the fuel with dura-
tion and spot size inferred from the ignition requirements
given above. We also take the fuel to be Fermi-degenerate
during the implosion, although entropy will be generated
during stagnation leading to a higher fuel adiabat. Using
cones and/or proton beams to deliver energy to the ignition
region 共see below兲 breaks the correlation among the ignition
intensity, the laser intensity and the particle deposition range,
because the laser energy is deposited over a larger area and
then concentrated into the ignition spot. Direct illumination
produces particles with the longest ranges and hence the
largest ignition requirements. Figure 2 shows the dependence
of the gain curve on the minimum laser spot size. Note that
the nominal model produces gain 100 at about 10% of the
FIG. 1. 共a兲 Isochoric ignition window in energy-power space for a variety of
compressed fuel densities; 共b兲 ignition windows in energy-intensity space.
FIG. 2. 共Color兲. Gain vs total laser energy for capsules directly imploded
with 0.35
m lasers for a variety of ignition energy deposition radii. The
model assumes 25% coupling from ignition laser to compressed fuel.
057305-2 Tabak
et al.
Phys. Plasmas 12, 057305 共2005兲
Downloaded 17 Jun 2011 to 133.1.91.151. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions
energy required from a conventionally ignited directly driven
capsule. Table I shows examples of the sensitivity of the gain
to various changes in model assumptions including utilizing
a 0.5
m wavelength laser as the implosion driver rather
than the nominal 1/3
m laser. All of these variations show
gain 100 occurring with a lower laser energy requirement
than conventionally ignited capsules.
III. IMPLOSION RESULTS
The Fast Ignition concept requires an implosion to as-
semble the fuel into a compact and dense mass. Typical in-
ertial confinement fusion implosions are designed to produce
a central high entropy region where ignition occurs. Figure
3共a兲 shows density profiles produced during various mo-
ments of a typical direct drive implosion. There are two sa-
lient features: the critical density 共above which the laser can-
not propagate兲 is located almost a millimeter from the high
density region and the compressed fuel assembles into a high
density shell surrounding a central region with 10% of the
peak density. This thin shell will be difficult to ignite by
injecting heat because it can disassemble in two directions
during the ignition phase. In addition, the burn efficiency of
the fuel, once ignited, is reduced because its column density
共兰
dR兲 is smaller when distributed as a shell than as a uni-
form sphere of the same mass. We can eliminate the central
low density region in several ways: 共1兲 introduce a high-Z
seed 共e.g., Xe with 3⫻ 10
−5
atomic fraction兲 into the center
and radiate away the entropy 关see Fig. 3共b兲兴. For the implo-
sion shown in Fig. 3, this a 10% energy cost. 共2兲 Expel the
central gas through openings 共either preformed or produced
during the implosion兲 in the shell. 共We discuss this below.兲
Or 共3兲 design the implosion so that with proper pulse-
shaping, a shell can be imploded to form a uniform sphere.
Figure 3共c兲 shows a sequence of snapshots in time of the
self-similar implosion of a shell, driven by pressure applied
to its outer surface, that upon stagnation becomes a uniform
sphere. Producing the initial state shown in the figure from a
uniform shell at rest will require a sequence of well-timed
shocks and remains to be accomplished. The final design will
be ablation driven and hence will also have an extensive
coronal plasma surrounding the compressed fuel.
IV. LASER COUPLING TO FAST ELECTRONS AND
SUBSEQUENT TRANSPORT
The generation of the ignitor electrons is accomplished
through the absorption of the laser via collisionless
mechanisms,
11
such as resonance absorption, J⫻B heating,
and Raman scattering. Figure 4 shows the conversion effi-
ciency of intense light to forward-going relativistic
electrons.
12
These data were inferred from experiments
TABLE I. Total laser energy required for gain 100.
Parameter E
laser
共MJ兲
Nominal model 0.3
E
ign
⫻1/2 0.1
ign
⫻0.25 1.7
hydro
⫻0.5 0.95
range
ign
⫻3 0.75
0.5
m drive 0.55
FIG. 3. 共a兲 Snapshots of
vs r for directly driven implosion with critical
surface marked; 共b兲 like 共a兲 but central fuel has Xe introduced into central
gas; 共c兲 snapshots of self-similar implosion taking shell into uniform sphere.
057305-3 Review of progress in Fast Ignition Phys. Plasmas 12, 057305 共2005兲
Downloaded 17 Jun 2011 to 133.1.91.151. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions
where targets composed of varying thicknesses of aluminum
followed by 50
m molydenum K
␣
fluor layers and then
2-mm-thick equimolar carbon–hydrogren 共CH兲 beam stops
were illuminated by intense laser light. The K
␣
signals were
then compared to those obtained by ITS,
13
a Monte Carlo
particle tracking code, using Maxwellian distributions for the
injected electrons. Because this analysis did not include the
self-consistent electric and magnetic fields, the quoted results
represent lower estimates for the coupling efficiencies.
Physics at multiple scales affects the transport of the
intense relativistic electron beams produced by the laser. For
Fast Ignition applications the beam electron temperature is in
the range 0.5–3 MeV, the forward current is a giga-ampere
and the forward current density, j, is about 10
14
A/cm
2
. This
current leads to large space-charge and magnetically induced
electric fields that draw a return current approximately equal
to the forward current. The return current is composed, in
part, of low energy electrons. Scattering of these returning
electrons produces a resistive E field=j/
⬃10
8
V/cm in
aluminum below 100 eV temperature, where
is the con-
ductivity. For existing experiments in aluminum or CH, Joule
heating produced by the return current dominates the heating
of the background plasma. In the Fast Ignition regime, where
the fuel has been compressed to a density of hundreds of
g/cm
3
, the temperature is 10–100 times larger and Z, the
atomic number, equals unity, Joule heating is unimportant.
Because the current densities are so large, coherent
scattering
14
of pairs of relativistic electrons off background
electrons and ions may increase stopping and multiple scat-
tering relative to incoherent single particle scattering.
15
On the scale of the collisionless plasma skin depth
共0.01–10
m兲 the collionless and collisional version of the
filamentation instability for cold beams have growth rates
that scale like
␣
1/2
e
; where
␣
=n
b
/n
e
, n
e
is the background
plasma density, n
b
is the beam plasma density and
e
is the
background plasma frequency. Finite transverse beam tem-
perature, T, and reduced values of
␣
lead to reduced linear
growth rates.
16
Silva et al.
16
found, using a waterbag beam
distribution, that there is 共Fig. 5兲 a threshold for instability
growth that depends on
␣
and T. Large values of T/E
beam
,
where E
beam
is the beam particle kinetic energy, have been
inferred from measurements of bremsstrahlung radiation pro-
duced during illuminations of high-Z targets by intense laser
beams. The radiation was distributed within a cone half angle
of 1 rad about the beam centroid, much more than would be
produced by multiple scattering off nuclei.
17
This large ap-
parent T/E
beam
may be a result of the electron acceleration
process in the laser-plasma interaction as seen in particle-in-
cell 共PIC兲 code calculations or may be produced as the in-
stability evolves. For typical experimental conditions this
graph implies that there will be no growth of the collisionless
filamentation instability. However, finite background plasma
resistivity and more general beam distributions allow growth
below the thresholds plotted in Fig. 5. In addition, for Fast
Ignition
␣
ranges from 1 共at the critical surface兲 to 10
−5
in
the ignition region. For sufficiently gentle plasma density
profiles, there is a window where this instability can grow.
Figure 6
18
shows idealized 2-D PIC predictions of the
scaled energy loss during the nonlinear phase for cold mo-
noenergetic relativistic electron beams as they propagate
through background collisionless plasmas with
␣
varying
from 0.1 to 0.02. When
␣
=n
b
/n
e
=0.1, the energy loss rate
corresponds to stopping in a range of 5⫻ 10
−5
g/cm
2
, a stop-
ping power 10
4
larger than classical. The stopping power
decreases as
␣
decreases. Magnetic trapping causes the satu-
rated magnetic field value to depend on the linear growth
rate.
16
Winding the electron paths by magnetic deflection
will also increase the apparent stopping power due to colli-
sions.
FIG. 4. Conversion efficiency into forward going electrons as a function of
laser intensity for 1
m light.
FIG. 5. Instability boundaries in the space of beam transverse temperature
and ratio of beam to background density for the Weibel instability for vari-
ous electron beam kinetic energies.
FIG. 6. Fraction of incident beam energy as a function of time in units of
inverse plasma frequency for three ratios of plasma to beam particle density:
关50,30,10兴. The highest ratio corresponds to the uppermost curve. The num-
bers on each curve are the number of filaments at any given time.
057305-4 Tabak
et al.
Phys. Plasmas 12, 057305 共2005兲
Downloaded 17 Jun 2011 to 133.1.91.151. Redistribution subject to AIP license or copyright; see http://pop.aip.org/about/rights_and_permissions
