24F03
Interference Effects of Laser Beams for Fast Electron Generation
高速電子生成におけるレーザービームの干渉効果
Hitoshi Sakagami, Tomoyuki Johzaki1, Atsushi Sunahara1 and Hideo Nagatomo2
坂上仁志, 城崎知至1，砂原 淳1，長友英夫2
Fundamental Physics Simulation Research Division, National Institute for Fusion Science322-6, Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所 基礎物理シミュレーション研究系 〒509-5292 岐阜県土岐市下石町322-6
1
Institute for Laser Technology
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan（財）レーザー技術総合研究所 〒565-0871 大阪府吹田市山田丘2-62Institute of Laser Engineering, Osaka University
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan
大阪大学レーザーエネルギー学研究センター 〒565-0871 大阪府吹田市山田丘2-6
Four beams of LFEX will be combined to maximize the heating energy for next incorporated FIREX-Iexperiments. Overlapping four beams, however, would introduce a beam-interference pattern, which could
affect core heating. Thus interference effects of laser beams for fast electron generation is investigated withthe use of 2D PIC code. When the scale length of the preformed plasma is 1 µm, the beam-interference
causes enhancement of fast electron divergence. On the contrary, the beam-interference suppresses thefilamentation, hence the divergence if the scale length is 4µm.

1. Introduction
FIREX-I(FastIgnition
Realization
EXperiment project, Phase-I) [1] aims todemonstrate that the imploded core could beheated up to 5 keV, and incorporated experiments
for FIREX-I, in which heating is combined withimplosion, have started at Institute of Laser
Engineering, Osaka University. Efficient heating
mechanisms and achievement of such hightemperature have not been, however, clarified yet,and we have been promoting the Fast Ignition
Integrated Interconnecting code (FI3) project toboldly explore fast ignition frontiers [2,3]. First
series of the incorporated experiments wasperformed in 2009, and only 30-fold enhancementin neutron yield, which was ~ 1/30 smaller thanthat in 2002 experiments [4], was achieved andlower energy coupling from the heating laser tothe imploded core was expected [5]. The heating
laser LFEX (Laser for Fast ignition EXperiment)
was designed to consist of four beams, but only
one beam was actually used and lack of theheating energy was serious problem in 2009
experiments. Next incorporated experiments will
use four beams to maximize the heating energy.
Combining four beams, however, wouldintroduce a beam-interference pattern, which
could affect the coupling rate from the heating
laser to the core. Thus we have been investigatinginterference effects of laser beams for fastelectron generation with the use of 2D PIC code.

2. Interference of Laser Beams
Four beams can be combined with two differentways. One way is a train of four pulses in time, andthe other is an overlap in space. The time train
method has no interference of beams, but maximum
energy that we can get is limited by a damage
threshold of laser media for one beam even we wantas much energy as possible. If we use the space
overlap method, we can get 4 times higher
maximum energy than that by the time train methodwith the same damage threshold, but the beaminterference occurs. Therefore we must decide
which beam combining method is better, namely
lower energy without interference or higher energy
with interference. Amplitudes of laser electric field
are shown in Fig. 1 for two Gaussian beams (λL=1Fig. 1. Typical interference patterns

µm, φFWHM=5 µm and θ=±15°) that are injected
toward the origin, and typical interference patterns
can be seen. Assuming two beams with incident
angles of +θ and -θ are injected, interference
patterns are stably built up like as a standing wave.
The pattern length L can be calculated by!

!

! = !    !"#!! .

(1)

Parameters for Fig. 1 leads to L=1.89 µm and it
agrees well with the length in the figure.
As one beam of LFEX must be shifted with 20
cm by 4 m to aim the target and λL=1.06 µm, it
leads that θ=2.86º and L=10 µm. This length is lessthan an expected spot size 40 µm, and fast electron
generation would be affected.
3. Characteristics of Fast Electrons
In 2D PIC simulations, the Au (A=197, Z=30)
cone tip is introduced as a 10 µm thickness,
35(±17.5) µm wide, 20ncr flat profile with apreformed plasma, which has a exponential profileof the scale length (Lpre=1 or 4 µm) with densityfrom 0.1 up to 20ncr. The proton-electron mass ratio
is set to1836, and initial temperatures of electrons
and ions are set to 10 and 1 keV, respectively. The
heating laser is set to λL=1.06 µm, IL=1020 W/cm2,φFWHM=10 µm, τrise/fall=5 fs, τflat=600 fs and θ=0º as
a single beam, and IL=5×1019 W/cm2 and θ=±7°(This leads to L=4.3 µm) as double beams. Fastelectrons are observed at 4.5 µm from the rightplasma edge. To ignore a circulation of fastelectrons, we introduce three artificial cooling
regions, in which fast electrons are gradually cooled
down to the initial temperature, behind theobservation point and at top/bottom plasmaboundaries (2 µm width).
Electron density profiles with Lpre=1 µm at 500 fs
are shown in Fig. 2 for (a) single beam and (b)double beams. In the case of the single beam,
plasmas near the center (y=0 µm) are strongly
pushed by the Ponderomotive force because theFig. 2. Electron density profiles with Lpre=1 µm
for (a) single beam and (b) double beams

laser beam is Gaussian, and hole boring is clearlyfound. On the other hand, the interference of double
beams makes individual beams with narrow width(~4 µm) corresponding to L and higher peakintensity than that of the single beam. They deeply
drill plasmas and make holes with a small diameter.
Fast electrons generated at the wall of smaller holes
should have larger divergent angle. Thus the double
beam irradiation causes lower energy coupling ratefrom the heating laser to the core than that of thesingle beam.
Electron density profiles with Lpre=4 µm at 500 fs
are shown in Fig. 3 for (a) single beam and (b)double beams. In the case of the double beams,
interference patterns are still imprinted onto
preformed plasmas and holes that have almost same
size with the Lpre=1 µm case are drilled. As the laser
must propagate longer distance in underdense
plasmas than the Lpre=1 µm case, the filamentationof the single laser pulse occurs. The size of eachbroken up filament is smaller than that of theinterference patterns, so fast electrons diverge much
more compared to the double beam case. It leads toworse coupling efficiency than that of double
beams contrary to the Lpre=1 µm case.
To compare the core heating properties between
the single and double beams, we will perform
integrated simulations by FI3.
Acknowledgments
This work is partially supported by JSPS
Grant-in-Aid for Scientific Research(C)(22540511).
References[1] H. Azechi, et al.: J. Phys.: Conf. Series 112 (2008)
012002.
[2] H. Sakagami, T. Johzaki, H. Nagatomo, and K.
Mima: Nucl. Fusion 49 (2009) 075026.
[3] T. Johzaki, H. Nagatomo, A. Sunahara, H. B. Cai, H.
Sakagami, and K. Mima: J. Phys.: Conf. Series 244(2010) 022040.
[4] R. Kodama, et al.: Nature 418 (2002) 933.
[5] K. Mima, et al.: Plasma Phys. Control Fusion 52(2010) 124047.

Fig. 3. Electron density profiles with Lpre=4 µm
for (a) single beam and (b) double beams