Proceedings of International Conference on Physics in ... - KEK

Abstract
Flying Mirror as a tool to access ultra-high fields ∗
M. Kando, A. S. Pirozhkov, T. Zh. Esirkepov, T. Nakamura, J. Koga, H. Kotaki
Y. Hayashi, S. V. Bulanov
JAEA, Kizugawa, Kyoto 619-0215, Japan
Thanks to the recent progress <strong>of</strong> laser technology, there
are growing interests to explore ultra-high fields (electromagnetic
fields) by focusing intense, ultra-short laser
pulses down to a few micron sizes. Presented here is a
study to possibility reach (or boost) such ultra-high fields
using a new concept employing the interaction <strong>of</strong> intense
laser pulses with plasma. The concept uses breaking waves
excited by ultra-short, intense laser pulses in plasma. We
present example parameters to reach the Schwinger field
and review the recent experimental progress <strong>of</strong> the flying
mirror concept.
INTRODUCTION
Since the innovation <strong>of</strong> the chirped pulse amplification
(CPA) technique [1], the peak power <strong>of</strong> lasers has been increasing
and the focused irradiance has reached as high as
10 22 W/cm 2 [2, 3]. The extreme light infrastructure (ELI)
project[4] is being promoted and the goal is to reach 10 26
W/cm 2 . The unprecedented irradiances allow us to explore
a new regime <strong>of</strong> physics, which has previously not been
accessible experimentally. Theoretically there are challenging
tasks which can be done in the high electromagnetic
fields. One example is to explore the so-called quantum
electrodynamics critical field or the Schwinger field,
at which vacuum breaks down and therefore non-virtual
electron-positron pairs are created from vacuum. Assuming
a direct-current (DC) electric field the QED critical
field Ec = 1.3 × 10 18 V/m is obtained. The associated
laser irradiance is Ic = 2.3 × 10 29 W/cm 2 , which is 7 orders
<strong>of</strong> magnitude higher than the world record and still
3 orders <strong>of</strong> magnitude higher than that at the planned ELI
project. Can we use the present laser technology to reach
the Schwinger field?
The answer might be ’Yes’. There is theoretical work indicating
lowering <strong>of</strong> the limit <strong>of</strong> electron-positron creation
from vacuum[5, 6, 7]. Here in addition to the work, we recall
the proposal that an plasma device –relativistic flying
mirror– can be used to intensify the laser pulse as shown in
Fig. 1[8]. Flying mirrors are electron density cusps propagating
almost at the speed <strong>of</strong> light in tenuous plasma.
Such electron density cusps are formed when plasma wake
waves excited by intense, ultrashort laser pulses are breaking.
The flying mirror reflects an incoming laser, and the
reflected pulse is upshifted due to the double Doppler effect
∗ Work in part supported by JAEA and KAKENHI No. 20244065
and is compressed as well. In addition, the flying mirror
may focus the laser pulse. Thus, the flying mirror can be
a novel device that enhances the laser focused irradiance
drastically. In this paper, we discuss the possibility to access
ultra-high electromagnetic fields employing the flying
mirror.
THEORY
We shall consider a mirror moving at the speed vM =
βMc, where βM denotes the ratio <strong>of</strong> the mirror speed to the
speed <strong>of</strong> light c. The reflected frequency in the laboratory
frame <strong>of</strong> reference is expressed as
ωr = ωs
1 + βM cos θ
, (1)
1 − βM cos θr
where ωs is the frequency <strong>of</strong> the incident source pulse and
π −θ and θr are angles in the laboratory frame <strong>of</strong> reference
between the wave propagation direction and the mirror velocity
for the incident and reflected waves, respectively. If
the incident angle satisfies the condition −π/2 < θ < π/2,
the frequency <strong>of</strong> the reflected pulse is upshifted. The maximum
upshift is achieved when θ = θr = 0. In this case the
reflected frequency is approximately equal to ωr ≈ 4γ 2 M ωs
for γM ≫ 1, where γM = 1/ √ 1 − β 2 M .
The electric field amplitude in the reflected wave is ex-
pressed as
Er = R 1/2 Es
( ωr
ωs
)
, (2)
where R is the reflectivity <strong>of</strong> the moving mirror in terms <strong>of</strong>
the photon number. For a mirror with a paraboloidal shape,
the reflected light can be focused down to a spot equal to
λs/(2γM). In this case the focused irradiance is given by
Ir = 64Rγ 6 M
( D
λs
) 2
Is. (3)
Here Is is the irradiance <strong>of</strong> the incident source pulse on
the mirror with a waist <strong>of</strong> D. As explained in the previous
section flying mirrors are created during the interaction <strong>of</strong>
intense, utra-short laser pulses with tenuous plasma. The
velocity <strong>of</strong> the flying mirror is equal to the phase velocity
<strong>of</strong> the plasma wave, i.e. βMc = βphc. The phase velocity
<strong>of</strong> the plasma wave is approximately equal to the group velocity
<strong>of</strong> the laser in the plasma βphc = c[1−(ωpe/ω) 2 ] 1/2 ,
where ωpe = (4πnee 2 /m) 1/2 , m and e are the electron
mass and charge, and ω is the laser angular frequency.