Electron-Positron Pair Production by
Ultra-Intense Lasers
K. Nakashima*, T. E. Cowan* and H. Takabet
* General Atomics, San Diego, CA 92122 USA
^Institute of Laser Engineering, Osaka University, Osaka, 565-0871 JAPAN
Abstract. Pair production by ultra-intense lasers are studied by use of numerical code based
on Fokker Planck equation. Using ultra-intense laser with the intensity more than 1019W/cm ,
electron-positron pairs are produced from hot electrons accelerated by the laser field. The number
of positrons reaches 10~4 t the number of hot electrons. To analyze the physical processes of laser
pair production, a numerical code based on relativistic Fokker-Planck equation are developed. The
results from this simulation agree with the theoretical studies and experimental studies. The positron
yield is 1010 when the laser intensity 1020W/cm2, laser energy 280J, wave length 1 ^tm. The number
of pair production increases at 1019W/cm2, and starts to saturate at 1021 W/cm2.
INTRODUCTION
The pair production by ultra-intense lasers are shown in this paper. A positron is an
anti-matter of an electron, which has the mass, 0.511 MeV, exactly same quantity of
an electron. To produce an electron-positron pair, more than IMeV energy is needed.
Ultra-intense laser can load this energy into plasmas.
The energy of electrons quivering in laser electro-magnetic field is expressed as
follows[l],
2
0)
where e is the energy of electron, m is the electron rest mass, c is the velocity of light,
e is the electron charge, and A is the electro-magnetic potential. When a laser intensity
exceeds the 1019W/cm , the electrons have relativistic energy, that is, e > me2. The
electron energy reaches about 7MeV with an laser intensity 1021 W/cm2. This energy is
enough to produce an electron-positron pair.
There are many electron acceleration mechanism not only quivering but beat wave,
wake field, and self-modulated wake field accelerations etc. [2-4] The energy of electrons reaches higher energy region using these mechanisms. These effects increase the
number of pair productions.
The well-known plasma simulation method is particle in cell method (PIC). The studies using PIC method have brought many remarkable results[5, 6]. But PIC simulation
cannot treat electro-magnetic waves with very short wave length like x-ray or y-ray because the mesh width on numerical space has the order of Debye length. Therefore we
directly solved the transport equation for electrons, photons and positrons.
CP634, Science of Super strong Field Inter actions, edited by K. Nakajima and M. Deguchi
© 2002 American Institute of Physics 0-7354-0089-X/02/$ 19.00
323
PAIR PRODUCTION BY ULTRA-INTENSE LASERS
It was noticed that intense lasers with more than 1019W/cm2 is needed to produce
electron-positron pairs in the previous section. These high intensity laser have been
realized using CPA method|7, 8] from early '90. So the experimental study is just started
recently.
There are mainly two processes to produce electron-positron pairs from laser energy.
One is to produce them directly from laser energy. The potential energy within the
Compton length of electron becomes comparable to two times of the electron rest mass.
= 2mc2
(2)
The laser intensity which satisfies this equation is about 1028W/cm2. If the laser is a
plane wave, the pair production does not occur because of the violation of momentum
conservation. Bunkin et al. estimated pair production in case that a Gaussian laser is
focused with 45° cone angle in the vacuum[9]. This laser has a curved wave surface.
In this case, the laser power to produce pairs is 1019W. This laser intensity at the beam
waist is almost same with 1028W/cm . However, it is too high intensity to construct the
lasers with recent technology.
Another process is pair production from high energy electrons which generate in
the laser-plasma interactions. The threshold intensity relatively low in comparison with
direct pair production. The threshold is 1019W/cm2[10, 11]. In addition, there are two
pair production processes from high energy electrons. One is an interaction between an
electron and a nucleus (Trident pair production).
e~ + Z —> e++ 2e~ -{-Z,
(3)
where e~ is electron, e^ is positron, and Z is nucleus. The other process is the interaction
between Bremsstrahlung photon and nucleus (Photo pair production).
Liang et al. showed that Trident process becomes dominant when a target thickness is
about a few micron, and derived positron production rate[12]. The positron yield reaches
10~4 times of the number of produced hot electrons.
At the same time, Gryaznykh et al. estimated the positron yield by ultra-intense lasers
independently, they showed that photo pair production becomes dominant when the
target thickness is a few milli-meters[13]. One can find the dominant pair production
process alters if the target thickness changes from the order of micron to milli-meter.
The cross point is at 20jum[14].
There are also several studies on pair production by ultra-intense lasers in Refs[1519].
So far theoretical studies are more advanced than experimental studies, but the intense
lasers with capability of pair production can be built using CPA technology now. So a
few pair production experiments were done. Cowan et al. carried out this first experiment
using NOVA laser system in Lawrence Livermore National Laboratory[20]. In this
experiment, the number of positrons estimated are 10~4 of hot electrons.
324
¥
1014
|1012
|io10
11°8
I 106
0
5
10
15
20
25
30
35
40
Momentum [MeV]
FIGURE 1. The electron, photon, and positron momentum spectrums are plotted. The feature of each
spectrum is shown around l-5MeV. The electron number is about 1014, the photon number is about 1012,
the positron number is about 1010. The thickness of gold foil is 125pm, the laser intensity is 1020W/cm2.
Other experiment performed by Gahn et al. showed that continuous positron source
can be realized using ultra-intense lasers. They chose He gas as a target of laser irradiation, many hot electrons are successively produced from the interaction region. Electrons
were guided to Pb target, then hot electrons are converted to electron-positron pairs.
The other experiment was quite different from previous ones. In this experiment, laser
photons are converted to pairs directory. At first, the head-on collisions between laser
and 47GeV electrons were occurred. High energy y-ray with 29GeV were created in
this interaction. This y-ray proceeds in the laser field, then y-ray and multi-photon of
laser interaction was realized.
+ e~
y -f nco
(5)
where co is a photon of laser. The energy of laser photon is several eV. Multi-photon
interaction is important experiment in the point of non-perturbation theory of quantum
electrodynamics.
As we said above, the pair production by ultra-intense lasers are hot topics in view
of theory and experiment. But the spatial distribution, energy distribution, and higher
order quantum dynamical processes have never studied yet. We are developing a numerical simulation code based on Relativistic Fokker-Planck equation to investigate these
unknown problems.
NUMERICAL SIMULATION BASED ON RELATIVISTIC
FOKKER-PLANCK EQUATION
Electrons generated by ultra-intense lasers have the energy up to several MeV. These
electrons proceed in a plasma or solid target with the velocity of light. The electron
with MeV energy feels the interaction of Coulomb scattering, bremsstrahlung, and pair
production in the target. Especially Coulomb scattering is a long range interaction, so
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6x10
* 5x101'
14X1010
3xio
2x101'
1019
102°
a
Laser Intensity [W/cm ]
1021
FIGURE 2. Total number of created positrons versus intensity of ultra-intense laser are plotted. The
positron yield increases dramatically around 1019W/cm2, and saturates around 1021W/cm2. Total energy
of the laser is fixed at 280J. The thickness of gold foil is 125jum.
this force must be treated statistically. Fokker-Planck equation is the equation derived
from this statistical view. We reduced Relativistic Fokker-Planck equation[21, 22] as
follows under the condition that the velocity of back ground electron and ions are small
enough in comparison with hot electrons,
-^
.=z4.1T
7(1-M 2 )^ ,
(6)
-
where ne t is electron and ion density, p is the hot electron momentum, Tee ei is the
Coulomb logarithm, ]U = cos0, f ( x , p , d ) is the distribution function of hot electron.
This equation has 1-D real space and 2-D momentum space with spherical symmetry.
In addition to Coulomb scattering, Bremsstrahlung and pair production are set in the
numerical code[14].
Target condition in the simulations are used in the parameters of the experiment
of Cowan et al.[20] The target is gold. The thickness of the target is 125]um. The
intensity of laser is 1020W/cm2. We initially put the hot electrons with Maxwellian.
The temperature of hot electrons is given by Ponderomotive potential[23]. That is, this
simulation shows the hot electron beam transport produced by ultra-intense lasers. We
got hot electron, photon and positron spectrum from this simulation(FIGURE.l). The
results show that the number of positron is 1010, and the ratio of each particles are,
electron : photon : positron = 1 : 10"1 :10~4. These results agree with the experiment.
We derive the relation between laser intensity and the number of electrons(FIGURE.2). The theoretical studies said that there is a threshold around
1019W/cm . Our simulation shows the rapid increasing of positrons at 1019W/cm2.
One of the remarkable results is the saturation of the positron yield at 1021 W/cm2.
326
fpnj
WJ IpsJ
FIGURE 3. Initial temperature of hot electron is 4MeV. This temperature is the same temperature of
electrons produced by ultraintense laser with 1020W/cm2. The electrons are injected from the left side of
simulation area.
We are also developing higher dimensional simulation code. That has 2-D real space
and 3-D momentum space. The basic equation is as follows,
P
dt
——
ray
•9(rf)
df
dr
dz
d(j)
)
One of the results from this 2-D simulation is shown in FIGURE.3. Photons go long
distance (mean free path) in the target before creating pairs. So the density peak of
positrons goes on ahead in comparison with the density peak of electrons. Other results
are now being analyzed.
CONCLUSION
The pair production by ultra-intense laser is considered in this paper. The threshold of
pair production is around 1019W/cm2 according to the theoretical studies. This was
confirmed from our simulation.
Recently, some experimental studies were carried out. The experimental study by
Cowan et al. showed the electron and positrons spectrum. The ratio of electrons and
327
positrons is 10 4. The results of our study agrees with it.
Then, we are developing the 2-D simulation code to investigate the spatial distribution
and electro-magnetic effects. One of the results shows the positron density peak is
disagree with the electron density peak.
We continue to study the electron-positron dynamics to apply particle sources, relativistic plasma, and astrophysical plasma research.
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