Opacity of relativistically underdense plasmas for extremely intense laser pulses M. A. Serebryakov

2025-05-02 0 0 698.79KB 8 页 10玖币

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Opacity of relativistically underdense plasmas for

extremely intense laser pulses

M. A. Serebryakov

E-mail: serebryakovma@ipfran.ru

A. S. Samsonov

E. N. Nerush

E-mail: nerush@ipfran.ru

I. Yu. Kostyukov

Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov

St., Nizhny Novgorod 603950, Russia

Abstract. It is generally believed that relativistically underdense plasmas is

transparent for intense laser radiation. However, particle-in-cell simulations

reveal abnormal laser ﬁeld absorption above the intensity threshold about 3×

1024 W cm−2for the wavelength of 1µm. Above the threshold, the further

increase of the laser intensity doesn’t lead to the increase of the propagation

distance. The simulations take into account emission of hard photons and

subsequent pair photoproduction in the laser ﬁeld. These eﬀects lead to onset

of a self-sustained electromagnetic cascade and to formation of dense electron-

positron (e+e−) plasma right inside the laser ﬁeld. The plasma absorbs the

ﬁeld eﬃciently, that ensures the plasma opacity. The role of a weak longitudinal

electron-ion electric ﬁeld in the cascade growth is discussed.

Keywords:

arXiv:2210.01606v1 [physics.plasm-ph] 4 Oct 2022

Opacity of relativistically underdense plasmas for extremely intense laser pulses 2

1. Introduction

Propagation of laser radiation through electron-ion

plasmas have been studied for decades. For weak laser

ﬁeld plasmas become opaque if its electron density, ne,

exceeds the critical density, ncr =mω2/4πe2, with

ω= 2πc/λ the laser cyclic frequency and λthe laser

wavelength, mand eare the electron mass and absolute

charge value, respectively. Overdense plasmas, ne&

ncr, reﬂects weak laser pulses. However, if the laser

pulse is relativistically intense, a0&1, the overdense

plasma can become transparent due to relativistic mass

increase of plasma electrons [1]; here a0=eE0/mcω

is the dimensionless amplitude, E0is the amplitude

of the laser electric ﬁeld. In this case — the case

of relativistic self-induced transparency (RSIT) — a

circularly polarized laser radiation can propagate in

dense plasmas (ne&ncr) over a ﬁnite length which

increases with the incident intensity [1,2]. RSIT

have been investigated in simulations and experiments

including the case of linear polarization [3,4].

The criterion for RSIT is that the eﬀective plasma

density is lower than the plasma critical density,

ne/γ .ncr, with γthe electron Lorentz factor. Plasma

electrons are pushed by the laser pulse hence necan

diﬀer signiﬁcantly from the initial plasma density, n0.

Heating and acceleration of the electrons depend on

the laser polarization, on the density gradient at the

boundary, etc., however, the Lorentz factor can be

roughly estimated as a0, that corresponds to the energy

that a motionless electron gains in the oscillating or

rotating electric ﬁeld E0. Therefore, RSIT occurs for

ﬁeld intensity

a0&κn0/ncr,(1)

with κa numeric coeﬃcient of the order of unity.

Analytics [5] and simulations [6,2,1,4,3] show that

κis not more than 2.

The criterion (1) has a simple electrodynamical

meaning: in RSIT regime, the current produced by

all the electrons involved in the interaction cannot

generate the ﬁeld which quenches the incident ﬁeld

inside the plasma, even if the electrons are accelerated

up to the speed of light and the skin layer width

is about the wavelength [7]. Therefore, nor ion

motion [6,1] nor radiation reaction [8,7] can change

the RSIT criterion signiﬁcantly. Thus, in the general

sense the plasma which density fulﬁls criterion (1) is

called relativistically underdense for the given laser

light.

The eﬀect of quantum electrodynamics (QED), i.e.

pair photoproduction in electromagnetic cascades [9,

10,11], can change the plasma density dramatically.

Namely avalanche-like QED cascades can generate

electron-positron plasma which density is above the

opacity threshold (1), hence the plasma absorbs the

laser radiation eﬃciently. This scenario is observed in

simulations for counter-propagating laser beams and

seeded cascades [12,13], where the laser beams form

a standing wave which is suitable for the cascades.

For laser beams interacting with plasmas for counter-

propagating [14] and single [15,16,17] laser pulses the

QED eﬀects also inﬂuence the laser energy absorption

and the plasma opacity. However, avalanche-like

QED cascades do not develop in ordinary plane-wave

geometry and need quite dense plasma — to develop

in the sum of the incident and the reﬂected ﬁeld, or

to develop on the plasma-vacuum interface without

reﬂection [17]. Alternatively, noticeable transverse

ﬁeld gradient is needed for cascade development in the

ﬁeld of a single laser pulse [18].

In relativistically underdense plasma the laser

pulse pushes electrons out (as well as ions at high

intensities) thus a channel is formed. This regime

diﬀers signiﬁcantly from the quasi one-dimensional hole

boring or light sail regimes which occur at higher

densities, and where QED processes have been studied

recently [15,17]. The previous simulations of the

channelling regime performed for a0.103revealed

that the laser pulse can trap plasma electron which

ﬁeld drags ions, hence dense electron-ion bunch is

formed right in the laser pulse [19,20,21]. Radiation

reaction plays a crucial role in this electron trapping

and plasma transparency [20,21], however, the laser

pulse still can travel a long distance despite of the

electron trapping and “snow plough” eﬀects. Also,

pair photoproduction for such ﬁeld strength lead to

a small number of positrons whose ﬁeld is not enough

to inﬂuence the laser pulse propagation.

In this paper propagation of spatially limited laser

pulses of a0= 300 −3000 in a plasma half-space of

density n0= 50ncr is investigated. It is demonstrated

that at higher intensities (a0&1000) vast amount

of electrons and positrons can be generated in the

QED cascade. The e+e−pairs are generated not at

the laser front, but right inside the pulse, and absorb

the laser energy very eﬃciently. Similar process have

been studied in preplasma attached to a dense plasma

slab [16], however, the cascade mechanism can be

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OpacityofrelativisticallyunderdenseplasmasforextremelyintenselaserpulsesM.A.SerebryakovE-mail:serebryakovma@ipfran.ruA.S.SamsonovE.N.NerushE-mail:nerush@ipfran.ruI.Yu.KostyukovInstituteofAppliedPhysicsoftheRussianAcademyofSciences,46UlyanovSt.,NizhnyNovgorod603950,RussiaAbstract.Itisgenerallybelieve...

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Opacity of relativistically underdense plasmas for extremely intense laser pulses M. A. Serebryakov

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