J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)341–344
000–000

Integrated Simulations for Fast Ignition Targets
JOHZAKI Tomoyuki, NAGATOMO Hideo, MIMA Kunioki,
SAKAGAMI Hitoshi1 and NAKAO Yasuyuki2
Institute of Laser Engineering, Osaka University, Suita 565-0871, Japan
Department of Computer Engineering, University of Hyogo, Himeji 671-2201, Japan2
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka 812-8581, Japan
1(Received: 9 December 2003 / Accepted: 20 March 2004)

Abstract
The basic issues of fast ignition scheme are radiation-hydrodynamics from implosion to fusion burning, relativistic
laser-plasma interactions and core heating by fast electrons. For investigating the physics phenomena of fast ignition,“Fast Ignition Integrated Interconnecting code project” (FI3 project) has been proposed, where the each phenomenon
is simulated with individual code and each code is collaborating with the others through the data transfer via thecomputer network. In the first step of the FI3 project, we carried out the integrated simulations for a cone-guided
target and examined the implosion dynamics, the fast electron generation, and the core heating.
Keywords:
fast ignition, FI3 project, ALE hydro code, collective PIC code, relativistic Fokker-Planck code,
cone-guided target

1. Introduction

evaluate the core plasma profile at the maximum compression.
Using this profile, the collective PIC (particle in cell) code
[6] evaluates the time-dependent energy distribution of fastelectron generated by the relativistic laser-plasma interactions.
Finally, on the basis of a coupled Eulerian hydrodynamics
and the RFP (Relativistic Fokker-Planck) code, the coreheating process are simulated using both profiles (implodedcore plasma and fast electron).
In the present paper, we will demonstrate the first resultsof overall FI simulations and discuss the implosion dynamics
oh a cone-guided target, time-dependent fast electron energy
distribution, and core heating profiles.

In Fast Ignition (FI) scheme [1], an ultra-intense shortpulse laser is focused on pre-compressed plasma to heat it up
to ignition temperature. Compared with the standard central
hot-spark ignition scheme, the FI scheme would mitigate therequirement on uniformity of implosion and could obtain ahigh gain with a small-driver energy. Recent integrated
experiments [2,3] for cone-guided targets demonstrated
efficient fast heating of imploded cores.
For understanding the physics phenomena and proving
fusion burning in the FI scheme, overall calculation, which
includes the implosion dynamics, generation of fast electrons
in relativistic laser-plasma interactions, core heating, andfusion burning processes, is indispensable. Each of physics
phenomena, however, has different time and space scales andcomplicatedly interacts one another, so that it is practically
impossible to simulate all phenomena with one code. In ILE(Institute of Laser Engineering), Osaka University and therelated group, hence, “Fast Ignition Integrated Interconnectingcode project” (FI3 project) [4] has been started, where theeach phenomenon is simulated with individual code and theeach code is collaborating with the others through the datatransfer via the computer network.
In the first step of the FI 3 project, we carried out
integrated simulations, where each of processes is separatelysimulated, and the obtained results are transferred to the othercodes. First, the ALE (Arbitrary Lagrangian Eulerian)radiation-hydro code [5] simulates the implosion process to

2. Implosion dynamics of cone-guidedtargets
In FI scheme, a cone-guided target has been proposed tokeep the propagation path of ignition laser free from thecoronal plasma. We carried out 2-D (two dimensional)
implosion simulations to study the implosion dynamics ofsuch a none-spherical shell target. For the conventional multidimensional integrated implosion code, where Lagragianbased ALE (Arbitrary Lagrangian Eulerian) methods arecommonly used, it is very difficult to treat this kind ofsimulation because of the complex geometry which requires
a sophisticated rezoning / remapping method and many timesof trial and error during the execution. Therefore, we haveextended CIP method [7] into ALE-CIP code “PINOCO” [5],©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: tjohzaki@ile.osaka-u.ac.jp1341

Johzaki T. et al., Integrated Simulations for Fast Ignition Targets

which enables to simulate the problem without any rezoning/remapping difficulty.
In the 2-D implosion code “PINOCO”, two temperatureplasma, Spitzer-Harm type thermal transport, radiationtransport, LTE (local thermodynamic equilibrium) and CRE(collisional radiative equilibrium) opacity and emissivity,equation of state, laser ray-trace, laser absorption areconsidered. For the thermal diffusion equations and multigroup diffusion type radiation transport equation, the implicit
9-point difference equations are solved by ILUBCG method.
For the laser ray-trace, a simple 1-D (one-dimensional) raytracing method is applied.
A target shell of polystyrene (ρ = 1.06 g/cm3) has auniform thickness of 8 µm and an inner radius of 250 µm.
The cone with an opening angle of 30 degree is attached tothe shell. The similar experiment was performed at GXII laser
facility of ILE to demonstrate the FI [2,3]. The target isuniformly irradiated by 6 kJ (on target) Gaussian-pulseshaped green laser (λ = 0.53 µm). In these simulations, wehave ignored the radiation transport for the limitation of theCPU time.
In Fig. 1, Density contours at 1.93 ns when themaximum average ρR was measured is shown. Although theedge of the shell was delayed under the influence of theconical target, the shell target was compressed to more than
200 g/cc at the maximum. Because of the pressure imbalance
due to the existence of Au-cone, the hot spot was moved to
the left-hand side. In the spherical implosion, the shell target
was rebound by the hot spot located at the center after themaximum compression at 1.90 ns [Fig. 2]. In non-sphericalcase, however, the shell continued to be imploded due to theloss of hot spot at the moment, and then the dense main fuelpart is concentrated at the center. As the result, the averageρR of the cone-guided target reached the maximum at
1.93 ns, and the value becomes twice larger than that of thespherical case.

laser to the forward directed fast electrons (Efe > 50 keV) are
19% and 21% for the case of IL = 1019 and 1020 [W/cm2],respectively. The energy spectrum of fast electrons passing
through the 100 ncr point per unit time at every 100 [fs] fromFig. 1

Mass density (g/cc) contours at t = 1.93 ns when themaximum average ρR is measured.

Fig. 2Time history of average ρR. Solid line indicates thesimulated result of non-spherical implosion with conetarget, and dotted line indicates the spherical implosion
case.

Fig. 3

Temporal profiles of intensity of forward-directed fastelectrons.

3. Relativistic laser-plasma interactions
For evaluation of fast electron generation due torelativistic laser-plasma interactions, we use the 1-D collective
PIC code [6], where collective particles are used to represent
many normal particles and then total number of particles andcomputations are drastically reduced. The density profile in
the inner side of Au-cone at the maximum compression wasobtained from ALE hydro code and was introduced as an
initial plasma into the PIC system. The Gaussian pulse ofwavelength λL = 1.06 [µm] and FWHM (full width at halfmaximum) = 300 [fs] was assumed as the ignition laser. We
carried out the collective PIC simulations for the laser
intensity of IL = 1019 and 1020 [W/cm2] and evaluated timedependent energy spectrum and intensity of forward-directed
fast electrons every 20 [fs] at 100 ncr point.
The temporal evolution of fast electron intensities areplotted in Figure 3. In both cases (IL = 10 19 and 10 20[W/cm2]), the electron beam pulse length is almost the sameas the laser pulse length. The energy transfer rates from the2342

Johzaki T. et al., Integrated Simulations for Fast Ignition Targets

Fig. 4

Momentarily energy spectrum of forward-directed fast electrons passing through the 100 ncr point per unit time at every 100[fs] from t = 500 to 1,500 [fs].

t = 500 to 1500 [fs] are plotted (a) for IL = 1019 [W/cm2] and(b) for IL = 10 20 [W/cm2] in Fig. 4. (In this and the next
sections, the time t was set to be 0 at the beginning of ignitionlaser.) The average energy of fast electrons estimated fromtime-integrated spectrum are 1.7 and 5.3 [MeV] for IL = 1019
and 1020 [W/cm2]. It is found, however, that the momentarilyenergy spectrum changes with time. At the beginning of theelectron beam pulse, the energy of generated electrons isrelatively low (Efe < a few [MeV]). At t = 500 [fs], the averageenergies of fast electrons Ēfe are 0.5 and 1.0 [MeV] for thecases of IL = 1019 and 1020 [W/cm2], respectively. The highenergy component gradually increases with time. At the time
when the intensity of electron beam pulse becomes themaximum (t ~ 1100 [fs]), the average energy of fast electrons
also becomes the maximum (Ēfe = 2.6 [MeV] for IL = 1019
[W/cm2] and 8.8 [MeV] for IL = 1020 [W/cm2]). After that,the high-energy component decreases with time, and thenbecomes 0.6 [MeV] for IL = 1019 [W/cm2] and 2.3 [MeV] for
IL = 1020 [W/cm2] at t = 1500 [fs].
For core heating analysis, not the time integrated, but
the time-dependent energy spectrum of fast electrons isimportant.

sources. The fast electrons were injected at the inner side of
Au-cone by assuming the Gaussian profile of FWHM =15 µm in the perpendicular direction. The simulations werealso carried out for mono-energy electron beams (E0 = 1, 2and 5 MeV) with Gaussian profile (τFWHM = 300 [fs]). The
peak intensity of these electron beams was assumed almost
the same value as that obtained in the PIC simulations for
IL = 1020 W/cm2, i.e. IREB = 3×1019 W/cm2.
Figure 5 shows the contours of the heating rate by fastelectrons when the heating rate in the dense core becomesthe maximum (t = 800 fs). (The density contours are alsoplotted by lines.) It is found from this figure that the fastelectrons injected at the inner side of the cone propagate into
the dense core and they deposit some fraction of their kinetic
energy there due to the Coulomb interactions.
In Fig. 6, the temporal profiles of (a) the heating rateand (b) the ion temperature averaged over the dense coreregion are plotted as a function of time for five different
electron beam conditions, i.e. PIC sources of IL = 1019 and1020 [W/cm2], mono-energy sources of E0 = 1, 2 and 5 [MeV]with peak intensity of 3×1019 [W/cm2]. The energy deposition
rate per unit path length of a fast electron decreases with theelectron energy. In addition, the number of injected fastelectrons decreases with the beam electron energy under thefixed beam intensity. Thus, in the 1-MeV mono-energy beam4. Imploded core heating by fast electrons
A 1-D RFP code [8] has been developed for analysis of
the fast electron transport and energy deposition processes indense core plasma. Recently, this code was extended to 2-D
one and coupled with a Eulerian hydro code to examine coreheating properties. In this code, cold bulk electrons and ions
are treated by a 1-fluid and 2-temperature hydro model, andthe fast electrons generated by the ignition laser-plasmainteractions are treated by the RFP model. In the coupled
RFP-hydro code includes magnetic field generated by fastelectron current, gradient of plasma resistivity and pressure
gradient.
Using the RFP-hydro code, we examined the coreheating properties in a cone-guided target. As an implodedcore profiles, we use results of the ALE radiation-hydrosimulation (shown in Sec. 2). The time-dependent momentum
distribution of fast electrons evaluated by the 1-D collective
PIC code (shown in Sec. 3) was used as the fast electron

Fig. 53343

Contours of heating rate by fast electrons, pdep [W/cm3](black and white) and core density [g/cc] (lines) when
the core heating rate becomes the maximum (t = 800fs) in the case of IL = 1020 [W/cm2].

Johzaki T. et al., Integrated Simulations for Fast Ignition Targets

Fig. 6

Temporal profiles of (a) Core heating rate, pdep,av and (b) ion temperature, Ti,av averaged over the core region (ρ > 50 g/cc).

since the energy of fast electrons was too high for IL = 1020
[W/cm2] and the intensity of fast electron beam was too lowfor IL = 1019 [W/cm2].
For more realistic estimations, each of the code isrequired the model improvement (e.g. consideration ofmagnetic field generation during implosion, multidimensional effect in the fast electron generation and recirculation of fast electrons due to the sheath field generated
around the core. In near future, we will start “on-line”
integrated simulations.

case, the core heating rate is the largest among three monoenergy beam cases, and then the core temperature becomes
the highest. The electron beam obtained from PIC simulation
for IL = 1020 [W/cm2] has almost the same intensity as themono-energy beams. The average energy of electrons,
however, is excessively high (Ēfe = 8.8 [MeV] at the peakintensity, 5.5 [MeV] for the time-integrated spectrum), so thatthe range is too long. On the other hand, in the case of PIC
source of IL = 1019 [W/cm2], the average energy is relatively
low, but the intensity is also low. Thus, the core heating rate
obtained in both PIC source cases is too small to raise thebulk plasma temperature.

References
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[2]
[3]
[4]

5. Summary
In the first stage of FI3 project, we demonstrated theintegrated simulations for a cone-guided target and examined
the implosion dynamics, the fast electron generation, and thecore heating. The implosion simulations using CIP-based ALE
code showed that the areal density of cone-guided target
becomes twice larger than that of the spherical target becauseof loss of central hot spot. The time-dependent fast electron
momentum distribution was estimated by the 1-D collective
PIC simulations, in which the density profile of inner side of
Au-cone obtained from implosion simulations was used.
Finally, the core heating was simulated by the coupled RFPhydro code where we used the imploded core profiles andthe fast electron profiles obtained from the ALE hydro codeand the collective PIC simulations, respectively. We could not
obtained expected core heating in the present simulations,

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[6]

[7]
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