High brilliance -rays generation from the laser interaction in a carbon plasma channel Christian Heppe and Naveen Kumar

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High brilliance γ-rays generation from the

laser interaction in a carbon plasma channel

Christian Heppe and Naveen Kumar ∗

Max-Planck-Institut f¨

ur Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg,

Germany

Correspondence*:

Naveen Kumar

naveen.kumar@mpi-hd.mpg.de

ABSTRACT

The generation of collimated, high brilliance γ-ray beams from a structured plasma channel

target is studied by means of 2D PIC simulations. Simulation results reveal an optimum

laser pulse pulse duration of 20 fs, for generating γ-photon beams of brilliances up to

1020 s−1mm−1mrad−2(0.1 %BW)−1and photon energies well above 200 MeV in the interaction of

an ultra-intense laser (incident laser power PL≥5PW) with a high-Z carbon structured plasma

target. These results are aimed at employing the upcoming laser facilities with multi-petawatt

(PW) laser powers to study the laser-driven nonlinear quantum electrodynamics processes in

an all-optical laboratory setup.

Keywords: Laser-plasma interaction, Particle-in-cell, γ-rays generation, Laser-driven QED processes, Radiation generation in plasmas

1 INTRODUCTION

Plasma based short-wavelength radiation sources have attracted signiﬁcant attention in past decades,

since plasmas enable not only a compact size but also a wide range of physical mechanisms to generate

short-wavelength radiations; be it high-harmonic generation, synchrotron radiation, or betatron radiation

mechanisms; Mourou et al. (2006); Rousse et al. (2004); Kumar and Tripathi (2006); Liu et al. (2018);

Yu et al. (2018); Ji et al. (2014). These highly energetic photon sources have numerous applications

for the fundamental research of radiation-reaction force, generation of electron-positron (e−e+) pairs,

photospectroscopy, radiotherapy and radiosurgery; Mourou et al. (2006). The main advantage of using

laser-plasma interaction for generating short-wavelength radiation sources is to only require an all-optical

setup for the experimental realization. With a continued push for increasing the laser intensity further

in a regime where radiation reaction and pair-production effects become important, the possibility of

generating highly-energetic γ-ray in an all-optical setup is becoming an exciting experimental prospect.

Recently, it has been shown that the use of structured plasma targets e.g. a cylindrical target acting as

an optical waveguide, is optimum for accelerating electrons and consequently generating γ-photons; Zhu

et al. (2015); Stark et al. (2016); Vranic et al. (2018); Jansen et al. (2018); Wang et al. (2020); Luedtke

et al. (2021); Huang et al. (2017). This scheme is analogous to the betatron radiation generation in an ion

channel; Rousse et al. (2004); Corde et al. (2013); Ji et al. (2014); Mangles et al. (2005); Ji et al. (2018).

However, here the self-generated magnetic ﬁeld of the electron beam accelerated in the channel not only

causes the generation of γphotons but also enhances the yield of these photons, especially in the so-called

arXiv:2210.06050v1 [physics.plasm-ph] 12 Oct 2022

Heppe et al. MeV photons generation in a carbon plasma channel

radiation-dominated regime. Thus, this scheme not only produces higher yields of γ-photons but also the

self-generated magnetic ﬁeld helps in collimating the generated photon beam in a 10◦lobe around the laser

propagation axis. This high-directionality of the photon beams can be exploited for producing electron-

positron pairs by the Breit-Wheeler process in colliding two γ-rays beams setup in a laboratory; Wang

et al. (2020). Key ﬁndings of the scheme are that for high-Z e.g. carbon plasmas at incident powers in the

range PL≤5PW, the laser to photon energy conversion efﬁciency drops for incident laser power in the

excess of PL≈5PW; Wang et al. (2020). Also, the efﬁciency of the γphotons generation seems to peak

around τ∼45 fs laser pulse duration for laser powers PL≤10 PW at laser intensity IL= 5 ×1022

W/cm2; Wang et al. (2020). At this laser intensity, radiation reaction can be modeled classically and

stochastic effects involved in quantum radiation reaction are negligible; Kumar et al. (2013).

The upcoming laser facilities such as ELI and others; Al´

eonard et al. (2011); Papadopoulos et al. (2016);

xce (2017); vul (2022) are expected to provide multi-petawatt laser systems. These multi-petawatt laser

systems are to rely on short laser pulse durations τ∼20 fs as signiﬁcantly increasing the energy contained

in the laser pulse is challenging due to technical reasons associated with material damage etc. Thus,

it is instructive to examine the generation of γ-photons with much shorter laser pulses e.g. τ≤45

fs. Also these multi-petawatt laser pulses can be focused to smaller beam radii ≤10µm resulting in

laser intensities (IL≥1×1023 W/cm2) that can enter the so-called quantum-electrodynamic regime,

in which radiation reaction has a stochastic nature and it signiﬁcantly affects the electron dynamics and

consequently γ-photons generation. Moreover, generation of pair-production can also be important in

this regime. Motivated by these considerations, we study the generation of γ-photons in a laser-plasma

channel, for the laser power exceeding PL= 5 PW. The plasma channel used is a structured carbon

plasma target and the laser pulse has the intensity IL= 2.65 ×1023 W/cm2. Further, we also chose

a conical plasma channel to optimize the generation of γ-photons since conical shaped targets provide

higher laser to plasma electron energy conversion efﬁciencies; Vranic et al. (2018). We carry out all

simulations for both target geometries for 20 fs and 40 fs pulse durations.

The remainder of this paper is organized as follows: in Sec.2 we discuss the simulation setup and plasma

dynamics and the physical process of γphotons generation. In sections 3.2 and 3.3, we show results

from planar and conical plasma channels, respectively. In Sec.3.4, we compare our results with previous

simulations results. Finally we conclude the discussions in Sec.4.

2 MATERIALS AND METHODS

We carry out 2D particle-in-cell (PIC) simulations, employing the open source PIC code

SMILEI; Derouillat et al. (2018). The simulation domain is 120 ×8µm(x×y) with a cell size of

0.02 ×0.01 µmsimulating a time period of Tsim ≈2500 fs, divided into timesteps of ∆t≈0.02 fs.

A linearly polarized laser pulse with wavelength λL= 0.8µmimpinges on a structured carbon ion

plasma target located at x≥10 µmfrom the left-boundary. We use 16 particles per cell for electrons

as well as ions. To ensure quasi-neutrality in our simulation, the ion density is chosen to be ni=ne/6,

where neis the plasma electron density. Open boundary conditions are used in x-direction while

periodic boundary conditions are employed in y-direction. The laser pulse has a normalized amplitude

a0=eE0/mω0c=eA0/mec2= 350 (corresponding laser intensity IL≈2.65 ×1023 W cm−2)and a

pulse duration of τ= 40 fs as well as τ= 20 fs (measured at FWHM), where eis the electronic charge,

cis the velocity of light in vacuum, E0(A0) and ω0are the laser electric ﬁeld (vector potential) and

frequency, respectively. The core of the plasma channel has density ne,ch = 37 ncr while the surrounding

bulk plasma is denser ne,B = 184 ncr, as also simulated before; Stark et al. (2016); Jansen et al. (2018).

Frontiers 2

Heppe et al. MeV photons generation in a carbon plasma channel

Here ncr =meω0/4πe2is the non-relativistic critical plasma density. This type of plasma channel can

either be created using modern techniques; see Fischer and Wegener (2013) or they can arise dynamically

due to the action of ponderomotive force associated with the laser pre-pulse. The laser pulse has a 2D-

Gaussian spatial distribution and it was focused on the center of the channel’s opening at x= 10µm

and y= 4µmfrom the left-boundary of the simulation box. To maximize the energy conversion from

the laser pulse to plasma electrons, the waist of the pulse w0in the focal plane was chosen to be equal

to the channels entrance radius w0=R0. On increasing the laser waist-radius, one can scan the power

dependence PL=πw2

0I0/2 = πR2

0I0/2, in our simulations, where I0is the peak laser intensity. The

ﬁrst set of simulations was carried out for a planar target that represents a longitudinal cross-section of

a cylindrical target with a constant channel radius R(x) = R0. For a conical target the radius varies as

R(x) = R0−(R0−Rexit)(x−10µm)/L, for x≥10µm, where L= 110µmis the channel length

and R0and Rexit = 0.25µm for all incident laser powers. In total the experiment consists of two sets of

four simulations. We scanned the incident power for PL= [5,10,15,20] PW for laser pulse durations of

τ= 20 and 40 fs.

The laser pulse parameters chosen to be broadly consistent with the upcoming laser systems at ELI

facility, which aim to investigate laser-driven quantum-electrodynamic processes. SMILEI employs a

fully stochastic quantum Monte-Carlo model of photon emission and pair generation by the Breit-Wheeler

process; see bre (2022); rad (2022). The probability of photon generation and pair-creation can be

simpliﬁed considerably if some assumptions can be enforced, e.g. ultra-relativistic particle motion, the

electromagnetic ﬁeld experienced by particles in their rest frames are lower than the critical Schwinger

ﬁeld and varies slowly over the formation time of a photon, and radiation emission by particle is

incoherent; Nikishov and Ritus (1964). These assumptions are always satisﬁed in the PIC simulations

carried out here. The photon-emission and pair-creation are fundamentally a random-walk process;

Duclous et al. (2010); Kirk et al. (2009); bre (2022); rad (2022). One assigns initial and ﬁnal optical

depths (between 0and 1) to a photon. This optical depth is allowed to evolve in time following particles

motion in the laser ﬁeld. The time evolution of the optical depth is equal to the production rate of pairs in

the laser ﬁeld; bre (2022). When the ﬁnal optical depth is reached, a photon is allowed to be emitted by

the algorithm. The parameters of emitted particles can be obtained by inverting the cumulative probability

distribution function of the respective species; see Duclous et al. (2010); Lobet et al. (2015). Production

of e−e+pairs from photons also utilizes a similar procedure and pairs are expected to be emitted along

the photon propagation direction; see bre (2022).

2.1 Filamentation of the laser pulse in a plasma channel

As one increases the incident laser power at a ﬁxed laser intensity, the focal spot of the laser pulse

increases. For high laser power (and large laser spot-size), the laser pulse becomes susceptible to the

laser ﬁlamentation instability; Kaw et al. (1973); Sheng et al. (2001); Kumar et al. (2006). This issue

hitherto has not been discussed in the previous studies so far, even though the ﬁlamentary structures in

electron plasma density are visible and they are attributed to the current ﬁlamentation instabilities; Jansen

et al. (2018). Transverse laser pulse ﬁlamentation can also affect the generation of γ-photons in a plasma

channel. Thus, it is instructive to estimate the laser ﬁlament and choose the laser spot size which is smaller

than the ﬁlament size due to the ﬁlamentation instability. For the purpose of estimating the ﬁlament size

of a laser pulse in an underdense plasma, we use the well-know formalism of laser-driven parametric

instabilities and employ the envelope model of the laser pulse propagation. For including the radiation

reaction force on the instability analysis, we follow the approach developed in Kumar et al. (2013) by

including the dominant term of the Landau-Lifshitz radiation reaction force. Equation of motion for an

Frontiers 3

Heppe et al. MeV photons generation in a carbon plasma channel

electron in the laser electric and magnetic ﬁelds including the leading order term of the Landau-Lifshitz

radiation reaction force is

∂p

∂t +υ· ∇p=−eE+1

cυ×B−2e4

3m2

ec5γ2υ"E+1

cυ×B2

−υ

c·E2#,(1)

where γ= 1/√1−υ2, e is the electronic charge, meis the electron mass, and cis the velocity of light in

vacuum. The other terms of the Landau-Lifshitz radiation force are 1/γ times smaller than leading order

term;Landau and Lifshitz (2005).

For theoretical calculations, we employ the circularly polarized laser pulse propagating in a plasma.

The relativistic motion of an electron in a linearly polarized laser pulse involves generation of high-

harmonics at the fundamental laser frequency. Due to this reason, the Lorentz factor γof an electron is

not constant in time and analytical treatment of any laser-driven plasma processes becomes intractable in

ultra-relativistic regime. For circularly polarized laser pulse, the gamma factor is constant in time and it

enables analytically tractable results to showcase the inﬂuence of radiation reaction on the ﬁlamentation

instability of a laser pulse in a plasma. This has been also done by others in the past while investigating

the parametric instabilities of laser pulse in plasmas. A quick comparison with the linearly polarized laser

pulse can be made by rescaling the normalized vector potential a0as aLP

0=aCP

0/√2. We express the

electric and magnetic ﬁelds in potentials employing Coulomb gauge in Eq.(1), and write the CP laser

pulse as A=A0(x⊥, z, t)eiψ0/2 + c.c., where ψ0=k0z−ω0t. We have assumed that the laser pulse

amplitude varies slowly i.e. |∂A0/∂t|  |ω0A0|,|∂A0/∂z|  |k0A0|, and |φ|  |A|, ω2

p/γω2

01,

and γ= (1+e2|A|2/m2

ec4)1/2,φbeing the electrostatic potential. We then write the transverse component

of the quiver momentum from Eq.(1) as

∂

∂t p⊥−e

cA=−eµω0

cAγ|A|2,(2)

where ωp= (4πnee2/me)1/2the non-relativistic plasma frequency, and µ= 2e4ω0/3m3

ec7. We have

assumed |µγ|A|2|  1, which is valid for laser intensities IL≤1023 W/cm2, for which the inﬂuence of

radiation reaction force has to be taken into account. The wave equation then reads as

∇2A−1

∂2A

∂t2=ω2

γc2

ep⊥,(3)

where A0is the amplitude of the envelope. On collecting the terms containing eiψ0, Eq.(3) yields the

dispersion relation for the equilibrium vector potential as ω2

0=k2

0c2+ω02

p1−iµ|A0|2γ0/2, where γ0=

(1 + e2A2

0/2m2

ec4)1/2is the equilibrium Lorentz-factor, and ω0

p= (4πnee2/meγ0)1/2is the relativistic

electron plasma frequency corresponding to the equilibrium propagation of the laser pump. It is evident

from the dispersion relation that the radiation reaction term causes damping of the pump laser ﬁeld. This

damping can be incorporated either by deﬁning a frequency or a wavenumber shift in the pump laser by

deﬁning a frequency shift of the form ω0=ω0r−i∆ω0,∆ω0ω0r(real part of ω0) with the frequency

shift ∆ω0being ∆ω0=ω02

pεγ0a2

0/2ω0r, where ε=reω0r/3c, and re=e2/mec2is the classical radius of

the electron. Eq.(3) in the envelope approximation can be expanded as

2iω0

∂A0

∂t +c2∇2

⊥A0+ω2

γ01−iµ|A0|2γ0

2A0=ω2

γ1−iµ|A|2γ

2A, (4)

Frontiers 4

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Highbrilliance-raysgenerationfromthelaserinteractioninacarbonplasmachannelChristianHeppeandNaveenKumarMax-Planck-Institutf¨urKernphysik,Saupfercheckweg1,D-69117Heidelberg,GermanyCorrespondence*:NaveenKumarnaveen.kumar@mpi-hd.mpg.deABSTRACTThegenerationofcollimated,highbrilliance-raybeamsfromastruct...

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High brilliance -rays generation from the laser interaction in a carbon plasma channel Christian Heppe and Naveen Kumar

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