Review about acceleration of plasma by nonlinear forces
from picoseond laser pulses and block generated fusion
flame in uncompressed fuel
H. HORA,1G.H. MILEY,2K. FLIPPO,3P. LALOUSIS,4R. CASTILLO,5X. YANG,2B. MALEKYNIA,6
AND M. GHORANNEVISS6
1University of New South Wales, Sydney, Australia
2University of Illinois, Urbana-Champaign, Illinois
3Los Alamos National Laboratory, Los Alamos New Mexico
4Institute for Electronic Structure and Lasers IESL/FORTH, Heraklion, Crete, Greece
5Campbelltown Branch, University of Western Sydney, Sydney, Australia
6Plasma Physics Research Center, I. A. University of Poonak and Coordinated Research Project IAEA Vienna, Austria
(RECEIVED 1 June 2011; ACCEPTED 22 June 2011)
In addition to the matured “laser inertial fusion energy” with spherical compression and thermal ignition of deuterium-
tritium (DT), a very new alternative for the fast ignition scheme may have now been opened by using side-on block
ignition aiming beyond the DT-fusion with igniting the neutron-free reaction of proton-boron-11 (p-11B).
Measurements with laser pulses of terawatt power and ps duration led to the discovery of an anomaly of interaction, if
the prepulses are cut off by a factor 108(contrast ratio) to avoid relativistic self focusing in agreement with preceding
computations. Applying this to petawatt (PW) pulses for Bobin-Chu conditions of side-on ignition of solid fusion fuel
results after several improvements in energy gains of 10,000. This is in contrast to the impossible laser-ignition of
p-11B by the usual spherical compression and thermal ignition. The side-on ignition is less than ten times only more
difficult than for DT ignition. This is essentially based on the instant and direct conversion the optical laser energy by
the nonlinear force into extremely high plasma acceleration. Genuine two-fluid hydrodynamic computations for DT are
presented showing details how ps laser pulses generate a fusion flame in solid state density with an increase of the
density in the thin flame region. Densities four times higher are produced automatically confirming a Rankine-
Hugoniot shock wave process with an increasing thickness of the shock up to the nanosecond range and a shock
velocity of 1500 km/s which is characteristic for these reactions.
Keywords: Fast ignition; Fusion flame; Hydrogen-boron fusion; Laser driven fusion energy; Nonlinear (ponderomotive)
Catastrophic climatic change by excessive emission of
carbon dioxide is evident and expansion of nuclear energy
generation is an essential alternative (Hora, 2010). The fact
is evident that nuclear energy is about 10 million times
more efficient than chemical energy from combustion of
fossil fuels. Use of fossils is limited by the amount of
carbon dioxide emission to the atmosphere to avoid climatic
changes; the problem of nuclear energy is to master the con-
trol of generating very dangerous radioactive radiation.
Nuclear fission has reached a matured perfect level offering
the lowest cost energy production compared with any other
large scale energy source despite of its comparably short his-
tory of development since its discovery by Hahn and Strass-
mann (1939) and Miley et al. (2010). Fission energy is today
the second largest energy generation after burning carbon
containing resources. On top, fission energy includes many
more options for further reductions of costs and further im-
provements, e.g., by underground thorium breeders (Teller,
2005; Rubbia, 2010) and small reactors (Guinnessy, 2010)
apart from the otherwise reached very high safety levels.
In a not yet sufficient state, is the development to reach
fusion energy as energy source in view that all energy pro-
duction from the sun is of this kind. Enormous expenses
Address correspondence and reprint requests to: Heinrich Hora, Depart-
ment of Theoretical Physics, University of New South Wales, Sydney,
Australia. E-mail: firstname.lastname@example.org
Laser and Particle Beams (2011), 29, 353–363.
©Cambridge University Press, 2011 0263-0346/11 $20.00
for research is well justified because this is promising further
options for very dramatic reduction of cost, it is everywhere
available, safe and a never exhaustive energy generation in
the future. The problem is that at present the sufficiently
well known fusion reactions work at very high temperatures
while the fission reactors work at or near room temperature.
The problem is to confine the reacting fusion plasma where
magnetic fields are tried to be used. Despite some techno-
logically achieved success in the past on which further very
expensive projects are on the way, this all is insufficiently
based on linear physics concepts running in contradicting
wasessentiallyopened(Hora,1981,1991) whenstudying the
particle beams will solve the ignition problem of fusion
energy (Hora, 2000, Section 6.3).
The problem with the controlled generation of nuclear
fusion was most competently summarized by Edward
Teller (2001). He knew from the beginning with his
decisions about this research topic for the Lawrence Liver-
more National Laboratory in 1952 that this is an extremely
difficult task because the plasma properties can nearly
impossibly be tamed by hydrodynamics for a correct des-
cription in physics. This refers not only to the later
discovered more or less realized instabilities, but the problem
is the entire state of the plasma with its microscopic
statistically-uncertain behavior and the long time ignored
internal electric fields (Hora, 1991, p. 159) where hydrodyn-
amic description had basic limitations, corrected by the gen-
uine two-fluid hydrodynamics (Lalousis & Hora, 1983; Hora
et al., 1984). This isthe samewith all the attemptsto describe
the weather by the well known immense hydrodynamic
models for predictions. Only when all is going so fast as in
uncontrolled nuclear reactions, the times are short enough
before the complex processes may develop. A basically
new situation was reached by the fast ignition (Tabak
et al., 1994) where the timing at ps interaction excludes the
mentioned problems with plasmas where the advantage is
used by the direct conversion of laser energy into plasma
dynamics without the need of thermal processes by the
nonlinear force interaction (Hora & Miley, 2005; Hora
et al., 2007, 2010; Hora, 2003, 2009) or by laser driven
extremely intense relativistic electron beams (Nuckolls &
Woods, 2002; Hora et al., 2005, p. 13; Nuckolls, 2010).
In the following, we summarize first for comparison, the
present traditional way of laser driven fusion using spherical
compression of fusion fuel where the necessary laser has
been built with more than megajoule (MJ) energy of nanose-
cond (ns) pulses (Moses et al., 2006; Moses, 2008, 2010;
Glenzeret al., 2010, 2011), forconditionsthat exothermic re-
actions of DT may be reached next. Parallel to these ignitions
byspherical compression, afast ignition scheme is under dis-
cussion (Tabak et al., 1994), which led to develop of ps laser
pulses (Mourou & Tajima, 2001). These laser pulses led to
unexpected extreme relativistic interaction effects (Cowan
et al., 1999), however, from some few very exceptional
experiments led to the discovery of a significant anomaly
(Hora et al., 2002b, 2007), which could be understood
using earlier numerical results about nonlinear force driven
block acceleration producing ion current densities of 1011
Amp/cm2, which is about a million times higher than accel-
erators can reach. This permitted the application of the
side-on ignition of solid state density fusion fuel (Chu,
1972; Bobin, 1974). This scheme was impossible to be
achieved then, but the conditions of the PW pulses based
on the new effect (Hora et al., 2002b, 2007) permitted to
expect ignition of DT with gains of 10,000 similar to another
modification of fast ignition using electron beams (Nuckolls
& Woods, 2002). As a surprise, it was possible to conclude
the ignition of p-11B at similar conditions as DT in contrast
to the spherical compression where exorbitant conditions
2. TRADITIONAL LASER FUSION WITH
The discovery of the laser in 1960 initiated immediately the
vision that its extreme concentration of energy in space and
time may lead to the solution of producing nuclear fusion
energy. Initially, it was evident that fusion energy generation
by laser driven ignition needs high compression DT fuel
(Nuckolls, 2010). To achieve this, a significant milestone
was reached (Moses, 2008) by commissioning of the largest
laser in the world, the national ignition facility (NIF), produ-
cing laser pulses of more than MJ energy of about nanose-
cond (ns) duration. Indirect drive by conversion of the laser
radiation into X-rays within capsules for smooth fuel
irradiation on spheres of DT for heating and compression
to more than 1000 times the solid state density nsis aiming
to achieve spark ignition (Lindl, 2005; Glenzer et al.,
This highly sophisticated process is to reach gains (G) of
50 up to 100 of generated fusion energy per input laser
energy producing 1019or more fusion neutrons per shot
(Nakai, 2008). The difficulties to achieve conditions of
spark ignition (central ignition) are well known and the ap-
plied techniques are well developed to achieve this goal.
Confidence is given by comparing earlier results (Fig. 1),
indicating an increase of the fusion neutrons on nearly the
square of the laser energy ELsuch that the 1012fusion neu-
trons with kJ laser energy may reach 1018neutrons at MJ
The confidence to reach such neutron numbers may be es-
timated also from the alternative compression scheme of
volume ignition (Hora & Ray, 1978), which schemewas con-
firmed (Kirkpatrick & Wheeler, 1981) by evaluation of the
“Wheeler modes” and applied with inclusion of self-heating
by the generated neutrons (He & Li, 1994; Martinez-Val
et al., 1994), and clarified as a rather uncomplicated
“robust” method (Lackner et al., 1994). It was rather surpris-
ing that the highest measured laser produced yields (Hora
et al., 1998, see Fig. 6) were exactly following this volume
H. Hora et al.
reaction process (Hora & Ray, 1978), measured in 1985 at
Osaka (Yamanaka et al., 1985) and in 1986 at Livermore,
and with the ever highest reported values of 2×1014neutrons
at Rochester (Soures et al., 1996). From the line shown in
Figure 2 (Hora et al., 1998, see Fig. 1) drawn from the exper-
super-linearityforgainsG>8 perenergyE0incorporated into
the compressed plasma will produce a faster achievement of
the 1019neutrons per shot if the volume ignition (Amendt
et al., 2005) will be followed up at the NIF experiments. The
line in Figure 2 was drawn in 1991 (Hora, 1991, see
Fig. 13.15) before the Rochester results at 1995 (Soures
et al., 1996) were known noting the remarkable coincidence
of these measurements with the earlier drawn line.
If the verification of the expected reactions using the com-
plex spark ignition (Lindl, 2005) may need a longer time
with the experiments, a faster solution for fusion energy
may use volume ignition of pellets with ingeniously im-
provement of (Amendt et al., 2005) double shell com-
pression of targets (see Fig. 2). Even at room temperature
this may lead to the gains of 50 or more and to 1019neutrons
with NIF. This may at least lead in principle to the conditions
for building laser driven inertial fusion energy (Storm et al.,
2009; Moses, 2010) as prototype of afusion power station by
2020 where the solid state laser drivers are diode pumped
with more than 15 times higher efficiency for a much more
compact laser than NIF. This would be a highly serious
and reliable contribution in the fight against the climatic
catastrophe using fusion energy.
A reflection may be given to statements by Edward Teller
(2001). “Research on controlled fusion means … hydrodyn-
amics of plasmas … for the fearsome nature … where every
little volume does its own thing … How fast does each move
on the average? What is the electric force … acting on them?
The same complications occur in planning a thermonuclear
explosion. But an explosion occurs in so short time that
many of the complicate phenomena have no chance to devel-
op … It took a decade from Fermi’s first suggestions … that
the theoretical calculations for thermonuclear explosions
were reasonably complete. I had no doubt that demonstrating
controlled fusion would even be more difficult.”
Our new direction — as mentioned in the Introduction —
is that fast ignition (Tabak et al., 1994) has the same advan-
tage to “occur in so short time.” On top when getting rid of
the delaying thermal processes by instantly working with the
nonlinear forces as generalization of ponderomotion for
direct conversion of laser energy into motion, this is the
new advantage. This is so well documented since Sauer-
brey’s (1996) measurement of the ultrahigh acceleration
after this was long time expected and in full agreement
with the theory — confirmed just from hydrodynamics
(Hora et al., 1979)! This operation in the picoseconds or
shorter range is well guiding, while the large scale laser-
fusion experiment in the nanosecond range may just help
to explore the open gap of plasma physics formulated by
Edward Teller. Simplification may be the key as seen from
Figure 1, where the highest measured gains were all with
volume ignition and direct drive (Hora et al., 1998;
Amendt et al., 2005) to lead to the aimed very high neutron
gains with the megajoule lasers. Some relaxation of the dif-
ficulties of spherical compression and thermal ignition of
HB11 was possible using the latest resonance correction of
the fusion cross sections (Kouhi et al., 2011).
3. NEW FAST IGNITION WITH NONLINEAR
It was necessary for the new developments on laser fusion
with ps laser pulses (Tabak et al., 2004) that powers above
terawatt (TW) had to be generated. This was achieved by dis-
covering the chirped pulse amplification (Mourou et al.,
2002) or the amplification of sub-ps dye laser pulses, e.g.,
Fig. 1. (Color online) Measured and projected neutron gains at DT fusion
using ignition by spherical laser compression depending on the energy of
the laser pulse following Nakai (2008).
Fig. 2. Measured DT neutron gains from spherical laser compression for
direct and indirect drive with single and double shell targets depending on
the measured maximum compression, (Hora et al., 1998).
Ultrahigh acceleration of plasma by nonlinear forces
in Schäfer’s inverted excimer laser media (Szatmari et al.,
1988). The second new aspect is to depart from the usual
lets in favorof a side-on ignition of modestly (e.g., by chemi-
cal explosives) compressed or uncompressed solid density
et al., 2002) or the Chu-Bobin scheme (Chu, 1972; Bobin,
1974) used in the here presented work (Hora, 2002).
Irradiating (TW to PW)-ps laser pulses (Cowan et al.,
1999; Maksimchuk et al., 2000; Ledingham et al., 2002;
Kaluza et al., 2004; Flippo et al., 2010) usually results in ex-
treme relativistic effects as generation of highly directed elec-
tron beams with more than 100 MeV energy, in highly
charged GeV ions, in gamma bursts with subsequent photo-
nuclear reactions and nuclear transmutations (Magill et al.,
2003), in positron pair production (Cowan et al., 1999),
and high intensity very hard X-ray emission. In contrast to
these usual observations, very few different anomalous
measurements were reported. What was most important in
these few cases, is that the laser pulses with TW and
higher power could be prepared in a most exceptional way
to have a suppression of pre-pulses by a factor of 108(con-
trast ratio) or higher for times a few dozens of ps before
the main pulse is hitting the target. These very clean laser
pulses were most exceptional only and especially possible
by using the Schäfer-Szatmari-method (Szatmari et al.,
1988) with excimer lasers by Sauerbrey (1996) or with
chirped pulse amplification using titanium-sapphire lasers
by Zhang et al. (1998) and by Badziak et al. (1999) using
neodymium glass lasers. These exceptional conditions
could be understood from the many years earlier derived
results of very detailed one-dimensional computations of
laser-plasma interaction with dominating nonlinear (ponder-
omotive) forces (Hora et al., 2002b; Hora, 2003). It was
shown (Fig. 3) that irradiation of a deuterium plasma block
of specially selected initial density (bi-Rayleigh profile)
with a neodymium glass laser intensity of 1018W/cm2re-
sulted within 1.5 ps in a thick plasma block moving against
the laser light with velocities above 109cm/s and another
similar block moving with the laser direction into the
plasma interior. However, such a generation of plasma
blocks was never observed because in all experiments, a
minor prepulse produced plasma in front of the target
where the laser beam was shrinking to about one wavelength
diameter with extremely high intensities due to relativistic or
ponderomotive self-focusing (Hora, 1975).
The acceleration was dominated by the nonlinear force fNL
given by the time averaged values of the amplitudes of the
electric field E and the magnetic field H of the laser in this
simplified geometry at perpendicular incidences in the
x-direction as (Hora, 1991, 2000)
fNL= (n2− 1)(∂/∂x)(E2/16π)
= −(∂/∂x)[(E2+ H2)/(8π)],
where n is the complex index of refraction in the plasma. The
first expression is the ponderomotive force derived Kelvin for
electrostatics before the Maxwellian theory while the second
expression represents the force density as gradient of the
energy density given in general by the Maxwellian stress
tensor. Despite these theoretical predictions since 1981 for pi-
cosecond laser pulses of very high intensities (Hora et al.,
1979; Hora, 1991, see Fig. 10.18b) it was never possible to
measure this process. It was then an important discovery in
1996 thanks to the clean laser pulses of the Schäfer-Szatmari
(1988) method, that Sauerbrey measured this process for the
very first time. It was essential to use the clean ps laser
pulses avoiding the self-focusing (Hora, 1975, 1991, see Sec-
tion 12.2) and to measure the generated plane plasma block
moving against the laser light with an acceleration determined
by the Doppler shift. The measured acceleration was very ac-
curately reproduced by the nonlinear force theory (Hora,
1981; Hora et al., 2007) and had a value of
Such a high acceleration is due to the instant and direct
conversion of the electromagnetic energy of the laser pulse
into kinetic energy of plasma motion without intermediary
heating process where the thermokinetic pressures are gener-
ated in much longer times than that of the ps pulse duration.
The comparable thermokinetic accelerations using the very
extreme conditions of the NIF laser are in the range of
(Parket al., 2010) for use to studyacceleration in high energy
density astrophysics HEDLA.
two. For the comparison of the experiments with the theory, it
has to be taken into account that the dynamically changing di-
electric swelling of the energy density in the plasma had to be
taken from several other similar experiments, which average
value is between 2 and 3 with a similar error bar as the exper-
iment. Apart from this rather complex detail, it is evident that
Fig. 3. Nonlinear (ponderomotive) force driven plasma block generation at
laser-target interaction (Hora, 2003).
H. Hora et al.
in contrast to thermokinetic pressures with delay times of ther-
malization and equipartition is significantly larger than ps
modified nonlinear force of the laser radiation on the electrons
for acceleration of space charge quasi-neutral plasma blocks.
was performed with clean laser pulses of about 30 wavelength
diameter by Jie Zhang et al. (1998) irradiating the target with
300 fs laser pulses. It was very abnormal that there was only
a modest X-ray emission, and not the usually very intense
hard X-rays. When taking out a weak pulse and pre-irradiate,
this at times t∗few ps before the main pulse, the X-rays were
unchanged. But as soon as t∗was increased to 70 ps, the
usual hard X-rays were observed. It was estimated (Hora
et al., 2002b, 2007) that the 70 ps were just needed to build
up the plasma plume before the target, which is necessary for
providing relativistic self-focusing with the subsequent usual
very low beam diameter and very high intensities.
A third crucial observation was by Badziak et al. (1999)
with irradiation of copper targets with half TW very clean
laser pulses of few ps duration. Instead of the expected and
usually measured 22 MeV fast copper ions, the fast ions
had only 0.5 MeV energy. Furthermore, it was observed
that the numberof the fast ions (in difference to the slow ther-
mal ions) was constant when varying the laser power by a
factor of 30. From this it could be concluded (Hora et al.,
2002b, 2007) that the acceleration was from the unchanged
volume of the skin layer at the target surface where the non-
linear force produced the generation of a highly directed
plane plasma block moving against the laser. This skin
layer acceleration by the nonlinear force with avoiding self-
focusing was then confirmed experimentally in all details,
especially from high directivity of the fast ions and the gen-
eration of a plasma block towards the plasma interior, as
measured at irradiation of thin foils (Badziak, 2006).
Most significant wasthe result (Hora et al., 2002b) that the
generated directed space-charge neutral plasma blocks have
an ion current density of
j > 1011Amps/cm2,
2006). The generation of the nonlinear force driven plasma
blocks was studied on a broad level (Hora et al., 2002b,
2002a, 2004; Badziak, 2006; Miley et al., 2006; Hora, 2003;
Hora et al., 2007, 2009) where the initially resulting up to 20
vacuum wave length thick plasma blocks (Hora, 1981,
Fig. 10.18a and Fig. 10.18b) were re-confirmed numerically
(Cang et al., 2005; Hora et al., 2007; Sadighi et al., 2010).
4. COMEBACK OF THE FUSION FLAME USED
FOR A RADICAL NEW LASER SCHEME BY
Ion current densities, Eq. (4), of directed DT ions of about
100 keV in the space charge neutral plasma blocks are
million times higher than accelerators can produce. This
led to reconsidering the Chu (1972)-Bobin (1974) scheme
of side-on direct ignition of solid state or modestly com-
pressed DT by the plasma blocks (Hora, 2002) for fusion
energy production similar to the Nuckolls-Wood scheme
(Nuckolls et al., 2002) using very intense 5 MeV electron
beams generated by 10 PW-ps laser pulses. The only diffi-
culty for igniting solid-state density DT is that there is the
need of an exorbitantly high energy flux density E∗
E∗> 4 × 108J/cm2
derived by Chu (1972) and confirmed by Bobin (1974). This
enormous high threshold Eq. (5) seemed to be prohibitive for
laser fusion and the classical way of spherical laser com-
pression was followed up (Moses et al., 2008; Moses,
2008). At the new measurements by Badziak et al. (1999),
values of E∗were well reaching nearly 106J/cm2. However,
the need to generate wide spread, high contrast ratio laser
pulses for the highly directed ps ion blocks for side on
ignition, only the nowavailable PW pulses will be interesting
after the TW pulses at least could demonstrate the basically
new conditions for the side-on ignition.
It wasthen necessary to reproduce the hydrodynamic com-
putations of Chu (1972) and to improve them in view of later
discovered phenomena. One of these phenomena is the
strong reduction of thermal conduction in laser produced
plasmas. This was first observed indirectly from fitting
experimental values at laser fusion and led to an empirical
inhibition factor which for DT is 69 for the decrease of ther-
mal transport. This reduction could directly be explained by
electric double layers (Hora, 1991, 2000, 2009) due to the
strong inhomogeneous plasma structures. Another phenom-
enon for adding to the studies of Chu (1972) was to use
the reduced stopping lengths based on the collective effect
following Gabor (1952) at the high plasma densities for the
generated alpha particles. Without these two additions, the
same results of Chu were received (Ghoranneviss et al.,
2008) as seen from the temperature T of the detonation
front on time t which characteristics depend on E∗as
parameter. For reasons of comparison E∗was given in
erg/cm2. An example where both added phenomena were
included is shown in Figure 4. When the characteristic
were decaying for long time t, no ignition happened. If not
decaying, ignition occurred and the threshold Et∗had to be
determined. Without the additions, the value of
Et∗= 4.8 × 108J/cm2
resulted in agreement with the results of Chu (1972, see
Fig. 2 ). With inclusion of the inhibition factorand the collec-
tive effect (Fig. 4) the threshold was reduced to
Et∗= 2.4 × 107J/cm2
Ultrahigh acceleration of plasma by nonlinear forces
with an uncertainty of estimated 50% (Hora et al., 2008). It
was estimated that ps laser pulses with more than 108contrast
ratio and about 10 to 30 PW power should ignite solid state
5. GENUINE TWO-FLUID COMPUTATIONS FOR
It had been shown in principle how the drastic difference of
nonlinear force acceleration of plasma by lasers is in contrast
to thermal pressure acceleration and how laser pulses of ps
duration may ignite a fusion flame in uncompressed solid
density nuclear fusion fuel if the pulses have a power in
the range of PW to exawatt (EW). In order to study the details
of the fusion flame generation, one hasto apply instead of the
one-fluid plasma hydrodynamics of Chu (1972) and the fol-
lowing here mentioned studies, to apply the genuine two
fluid model (Lalousis et al., 1983; Hora et al., 1984) in
order to evaluate the generated extremely high longitudinal
electric fields in the highly inhomogeneous plasma fronts
of the flame, and to study its propagation during the inter-
action with the fuel together with the generation of fusion
products. These studies are interesting also for evaluation
of shock waves and the shock ignition for fusion (Betti
et al., 2007) and impact fusion ignition (Azechi et al.,
2009). Studies with advanced PW to EW laser pulses are
important also for exotic conditions of shock waves in astro-
physics (Park et al., 2011) for experiments on high density
laboratory astrophysics HEDLA with ultrahigh accelerations
and for related interactions including nuclear mechanisms. It
should be mentioned that the genuine two-fluid plasma
hydrodynamics (Lalousis et al., 1983; Hora et al., 1984)
was well used for studying the block acceleration (Glowacz
et al., 2004; Badziak et al., 2004) and optical plasma proper-
ties (Cang et al., 2005; Sadighi et al., 2010), but only the
following described first results led to the general evaluation
of the processes involved. What was important with the
ultrahigh acceleration, was that the directed space charge
neutral plasma blocks arrived at 1011Amps/cm2or more
ion current densities. This is again more than a million
times higher than accelerators could provide for ion beam
fusion, and permitted a comeback of the ignition of solid
state — uncompressed or modestly compressed — fusion
fuel by side-on ignition of a fusion flame. Following the
initial computations of Chu (1972), this seemed to be com-
pletely impossible but this has changed now with the
greater-than PW-ps laser pulses. It is potentially possible
for energy production in power stations to achieve gains of
10,000 similar to the Nuckolls-Wood scheme (Nuckolls
et al., 2002) using ps-laser produced very high density rela-
tivistic electron beams instead of the here treated nonlinear
force driven plasma blocks.
For laser fusion of DT, extremely clean ps laser pulses
with a contrast ratio above 108may drive the controlled reac-
tions in power stations with pulses in the range of a few
dozens of PW power. These are close to technical realization.
Avoiding the need of extremely high fuel compression in the
usual thermally ignited laser-fusion schemes, the side-on
ignition is simplifying the process, and it can be expected
that power production can be at considerably low cost.
The updated computations of Chu (1972) were based on
one-fluid hydrodynamics (Hora et al., 2008; Hora, 2009)
while the genuine two-fluid hydrodynamics (Laousis et al.,
1983; Hora et al., 1984) with evaluation of the very high
electric fields within the extremely inhomogeneous plasmas
were well used to see the dielectric effects at the laser-plasma
interaction (Hora et al., 2007; Hora, 2009; Sadighi et al.,
2010). We report here about the first extension of the updated
Chu (1972) computations by using the genuine two-fluid
model including the fusion reactions and the details of the
generation of the fusion flame. This is done also for prep-
aration of specific experiments with PW-ps laser of sufficient
contrast to explore the revolutionary new scheme (Hora et al.,
2010). Figure 5 shows results of the ion density of the fusion
flame when developing into solid density DT fuel after a ps
laser pulse initiated the fusion flame. It is very interesting to
see that the local ion density in the thin flame front moves
with a velocity of 1.55 × 108cm/s and the density in the
flame front is four times higher than the untouched cold
DT. This is an automatic result of the genuine two-fluid com-
putation and agrees with the Rankine-Hugoniot theory of
Figure 6 shows the computation for a 2 ps irradiation of
2× 108J/cm2laser pulse into 5 μm deep surface area of a
solid state DT target at the time of 2000 ps after irradiation.
The reaction rate showsthe successful ignition and the plot of
the ion density show the compression to four times the initial
solid state fuel in the flame region of about half mm thick-
ness. Behind the flame, the density of the plasma is less
than the solid state due to the thermal expansion where the
reaction had gone over. From comparing the point of the
Fig. 4. Dependence of DT plasma temperature T on time t with collective
E∗compared with the decaying curves with inhibition factor only.
H. Hora et al.
hit of the flame in the cold fuel at times 1 ns and 2 ns, the
propagation velocity of the flame is 1300 km/s at this
time. The same computation for a laser irradiation with 2 ×
106J/cm2does not show ignition though an initial reaction
as a kind of an impact fusion has been shown in the calcu-
lations. This case was evaluated for the generally more favor-
able conditions to use KrF laser pulses (Teubner et al., 1996;
Osman et al., 2007; Sadighi-Bonabi et al., 2010), which
Sauerbrey (1996) had used for his experimental discovery
of the ultrahigh plasma block acceleration.
The shock velocity of around 1400 km/s for later times of
the fusion flame shows more and more a deviation of the
density profile differing from the simplified shock wave
theory. This is evident from the output of the fast velocity
of the generated alpha particles when moving into the un-
touched solid DT by gradually changing there the conditions
of densities and temperatures. However, the velocity of the
entire flame is nearly unchanged. The genuine two-fluid
computations arrive at many more details than known from
the one-fluid computation. It is important to note that these
studies are aimed to apply ps laser pulses in the range of
30 PW up to nearly EW. Generalizing the preceding compu-
tations (Hora, 2009; Hora et al., 2010), the genuine two-fluid
hydrodynamics is used in order to follow up the details of the
generated very high electric fields in the shock fronts and to
confirm some modifications while most of the other results
calculated before with the usual one fluid hydrodynamics
are rather unchanged. The results are interesting for astrophy-
sical cases and for shock ignition of fusion (Betti et al., 2007)
where in contrast to the thermal pressure process used in
these computations, the new research now was generalized
to non-thermal nonlinear force direct conversion of laser
energy into plasma motion to reach the ultra-high
6. FUSION ENERGY WITHOUT DANGEROUS
From the beginning of fusion energy research, a dream reac-
p +11B = 34He + 8.664MeV(9)
because no neutrons are produced and the resulting alpha
particles are mono-energetic of 2.888 MeV for irradiating
protons with energies up to 200 keVas used in the following.
Strong deviations for higher energies were measured only re-
cently in agreement with the Breit-Wigner theory (Stave
Fig. 5. Genuine two fluid hydrodynamic computations (Lalousis et al.,
1983; Hora et al., 1984) of the ion density in solid DT after irradiation of
a laser pulse of 1020W/cm2of ps duration at the times 22 ps (dashed)
and 225 ps after the initiation.
Fig. 7. CharacteristicsofthekindofFigure 4 for p-11B under the assumptions
most similar to Chu (1972)forcomparisonwith DT fusion(Hora et al., 2010).
Fig. 6. (Color online) Genuine two-fluid hydrodynamic computation for the
time of 2000 ps after a 2 ×108J/cm2laser pulse irradiated a 5 μm deep sur-
face area of a solid density DT fuel. The reaction rate (highest curve) con-
firms that the fusion flame has penetrated 4.2 mm into the cold fuel; the
flame has a plasma compression by a factor 2.6 (second highest line)
which is a long time alteration of the Rankine-Hugoniot theory and a thick-
ness of about 1.4 mm, and the curve of the ion temperature.
Ultrahigh acceleration of plasma by nonlinear forces
et al., 2009). The result (Eq. (9)) is ideal for high-efficient
direct conversion into electricity with minimum heat pol-
lution or after redirecting of the alphas with magnetic fields
for space propulsion. Secondary reactions lead to radioac-
tivity but this is less per produced energy than burning
coal due to its natural contents of 2 parts per million of
uranium (Weaveret al., 1973) and may be considered as neg-
ligible. However, it was evident from the beginning that this
fusion reaction is very much more difficult than using DT
fusion fuel, as seen from the spherical laser compression of
p-11B needing densities of 100,000 times the solid state
(Hora, 2002) and input laser pulses of several 10MJ energy
to produce modest energy gains per laser energy of less
than 25 (Scheffel et al., 1997). These conditions are exorbi-
tant and excluded any hope for laser driven p-11B fusion by
spherical compression. The factor 100,000 is based on the
100 times higher compression than the about 1000 solid den-
sity for DT, the necessary 100 times higher input energy of
the laser and the 10 times lower gains.
To be consistent with the results of Chu (1972) with DT
fuel, computationswere first performed based on hisassump-
tions. The p-11B fusion reaction rates given by the reaction
cross section σ averaged for a temperature T over a Maxwell
distribution of the velocity v of the particles are shown in
Figure 6. Using the <σv > -values for p-11B reaction rates in-
stead of DT, results in the time dependence of the plasma
temperature T shown here in Figure 6 in analogy to Figure 4
for DT. The parameterof the curves isthe energy flux density
E∗. What is important is to find the value of Et∗of the
ignition threshold where the plasma temperature T merges
into a constant value in the dependence on time t. In order
to define the threshold Et∗for p-11B, the computation of
the temperature T in Figure 6 was going to rather long
times (15 ns) in order to see the stationary values. It can
only be estimated that the final value is
E0∗= (1.5) × 109J/cm2± 30%,
These results seem to be very remarkably modest com-
pared with the values of DT (Eq. ((4)) according to Chu
(1972). In view of the exorbitant difference between DT
and p-11B for volume ignition based on spherical pellet com-
pression, it is really surprising how much easier the ignition
of p-11B works for a side-on generated thermonuclear reac-
The correctness of the shown hydrodynamic results may
be seen in the derived proof of consistency shown in the re-
sulting temperatures. In the case of DT, the ignition without
reheat and without partial X-ray re-absorption dropped from
the (energy averaged value) of about 12 keV for spherical
compression to 7.2 keV even under the simplified conditions
of Chu (1972) only. There is a clear similarity to the case of
p-11B. In this case, the temperature for the spherical com-
pression without reheat and without partial self-absorption
is in the range up to about 150 keV (Scheffel et al., 1997),
while the here reported side-on ignition of solid fusion fuel
arrived at 87 keV temperature for the side-on ignition with
the assumptions of Chu (1972) only (Fig. 6 and Eq. (11)).
The problem of re-absorption for spherical compression
with thermal volume ignition is well including whether the
bremsstrahlung is re-absorbed by collisions or additionally
by Compton scattering (Meyerhofer et al., 2008). For the
volume ignition case, neglecting the Compton process may
result in lower fusion gains (Scheffel et al., 1997) only as a
lower, pessimistic level of gains. The situation is basically
different for the case of the fusion flame at side-on ignition
by nonlinear force driven plasma blocks, where the inclusion
of bremsstahlung in the code is for a complete energy loss
has been well included, but any re-absorption within the
thin front of the fusion flame can be neglected.
The basic result of this work is to confirm that side-on
ignition of uncompressed p-11B fuel is not very much more
difficult than DT fusion and estimated to be possible with
laser pulses in the range of ps duration and several dozens
of PW power if not some slight pre-compression or the
inclusion of other effects will permit a further reduction of
these well feasible conditions.
Details of the computations clarified that the radiation
losses were sufficiently low for DT and p-11B reactions.
Otherwise no ignition at all could have been seen beginning
with the plots of Chu (1972) (Fig. 2), and finally for the
p-11B reactions. Bremsstrahlung is not nuclear radiation, its
nature is x-radiation up to about 100 keV which will not pro-
duce nuclear reactions, and may be eliminated by sufficient
screening in power stations as known from the usual handling
For the here described modification of fast laser ignition by
nonlinear force produced plasma blocks, a much more de-
tailed analysis is needed but at least the basic characteristics
for side-on ignition are clearly visible. Most significant are
the very surprising results that uncompressed p-11B can be
ignited. This fusion energy generation with laser pulses in
the range of several dozens of PW power and ps duration
can achieve p-11B power production (Hora et al., 2009,
2010). Theremarkable fuel avoids neutron generation,results
in negligible radioactivity, and allows direct energy conver-
sion, which in turn reduces heat pollution. Such a power
plant is ideal for stationary electrical generation in a power
station or for space propulsion. Modest pre-compression by
chemical driving (Nuckolls et al., 2002) or with high density
cluster methods (Holmlid et al., 2009; Yang et al., 2011)
could improve the performance even further, especially for
p-11B. The X-ray radiation produced in the reaction chamber
is ≤ 200 keV which can be screened off and does not lead to
nuclear reactions in the power stations (Guyot et al., 1971;
Miley, 1970, 1971, 1976, 2005). This provides an exciting
vision of a very attractive sustainable future power plant for
H. Hora et al.
worldwide use. Its achievement will depend on continued ad-
vances in laser optics, target physics and power conversion
technology. However, the studies reported here show that
such a system is rather close at hand — something not rea-
lized before, since p-11B ignition had always been viewed
as virtually impossible. This development was in principle
favorably acknowledged in an IAEA review by Tanaka
(2009). The results of the side-on ignition of p-11B were de-
scribed in more details (Hora et al., 2010). It was mentioned
by Steve Haan, from the National Ignition of Fusion NIF pro-
ject in an interview by the Editor (Li, 2010) of the Royal
Society of Chemistry in London, that the result “has the
potential to be the best route to fusion energy.”
Support for PhD projects under the main supervision by
M. Ghoranneviss through the Coordinated Research Project No.
13508 of the International Atomic Energy Agency IAEA is grate-
fully acknowledged. Special thanks are expressed to Dr. Guenter
Mank at IAEA for his helpful attention. Discussions about these re-
sults at the ICONE 2010 conference in Xian/China and at the Fast
Ignition Workshop 2010 in Shanghai/China are appreciated with
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