Dense GeV electron-positron pairs generated by lasers in near-critical-density plasmas

Abstract

Pair production can be triggered by high-intensity lasers via the Breit-Wheeler process. However, the straightforward laser-laser colliding for copious numbers of pair creation requires light intensities several orders of magnitude higher than possible with the ongoing laser facilities. Despite the numerous proposed approaches, creating high-energy-density pair plasmas in laboratories is still challenging. Here we present an all-optical scheme for overdense pair production by two counter-propagating lasers irradiating near-critical-density plasmas at only ∼10²² W cm^-2 . In this scheme, bright γ-rays are generated by radiation-trapped electrons oscillating in the laser fields. The dense γ-photons then collide with the focused counter-propagating lasers to initiate the multi-photon Breit-Wheeler process. Particle-in-cell simulations indicate that one may generate a high-yield (1.05 × 10¹¹ ) overdense (4 × 10²² cm^-3 ) GeV positron beam using 10 PW scale lasers. Such a bright pair source has many practical applications and could be basis for future compact high-luminosity electron-positron colliders.

ARTICLE

Received 13 Apr 2016 | Accepted 25 Oct 2016 | Published 14 Dec 2016

Pair production can be triggered by high-intensity lasers via the BreitWheeler process. However, the straightforward laserlaser colliding for copious numbers of pair creation requires light intensities several orders of magnitude higher than possible with the ongoing laser facilities. Despite the numerous proposed approaches, creating high-energy-density pair plasmas in laboratories is still challenging. Here we present an all-optical scheme for overdense pair production by two counter-propagating lasers irradiating near-critical-density plasmas at only B1022 Wcm 2. In this scheme, bright g-rays are generated by radiation-trapped electrons oscillating in the laser elds. The dense g-photons then collide with the focused counter-propagating lasers to initiate the multi-photon BreitWheeler process.

Particle-in-cell simulations indicate that one may generate a high-yield (1.05 1011) over-

dense (4 1022 cm 3) GeV positron beam using 10 PW scale lasers. Such a bright pair

source has many practical applications and could be basis for future compact high-luminosity electronpositron colliders.

1 College of Science, National University of Defense Technology, Changsha 410073, China. 2 Collaborative Innovation Center of IFSA (CICIFSA), Key Laboratory for Laser Plasmas (MoE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China. 3 SUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK. 4 School of Electronic Science and Engineering, Nanjing University, Nanjing 210023, China. 5 National Institute for Physics and Nuclear Engineering, ELI-NP, Str Reactorului, nr. 30, P.O.Box MG-6, Bucharest-Magurele 077125, Romania. 6 Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX, UK. 7 Institut fr Theoretische Physik I, Heinrich-Heine-Universitat Dsseldorf, 40225 Dsseldorf, Germany. Correspondence and requests for materials should be addressed to T.-P.Y. (email: mailto:[email protected]

Web End [email protected] ) or to Y.Y. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms13686 OPEN

Dense GeV electronpositron pairs generated by lasers in near-critical-density plasmas

Xing-Long Zhu1, Tong-Pu Yu1,2, Zheng-Ming Sheng2,3, Yan Yin1, Ion Cristian Edmond Turcu4,5,6

& Alexander Pukhov7

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686

Pair production is one of the fundamental quantum electrodynamics (QED) effects, which is potentially interesting for a variety of applications13, such as fundamental

nuclear and particle physics, laboratory astrophysics and plasma physics, radiography for material science and medical applications. For example, GeV and even TeV positron beams are required for studying highly energetic astrophysical phenomena in laboratories and realizing electronpositron (e e ) collider for high-energy particle physics3,4. Schwinger has predicted the critical electric eld5 EsE1.32 1018 V m 1 for

spontaneous creation of pairs out of vacuum by a laser beam. This eld corresponds to a light intensity roughly 1029 W cm 2, which is seven orders of magnitude higher than attainable in current laboratories4. It has also predicted that pairs can be produced via the Trident and BetheHeitler (BH) processes6,7 from lasers interaction with high-Z targets. So far, the major way of producing positrons with lasers in experiments relies upon the BH process, which is based on the decay of bremsstrahlung g-rays from electrons in high-Z targets. It is shown that energetic positrons could be obtained by direct lasersolid interactions810 or by laser-driven electrons colliding with solid targets1114. However, the positrons obtained have a low density of B1016 17 cm 3 with a laser energy conversion efciency to positrons around B0.02% only15,16. There is a need to signicantly enhance the positron yield, density and energy, as well as the laser energy conversion for the aforementioned applications.

Under extremely high laser intensities, the lasermatter interaction enters the near-QED regime and the following two critical processes are involved: (1) high-energy photons emission by relativistic electrons quivering in ultraintense laser elds17 (e ng

laser-gphoton e , where g

laser represents a laser photon); and (2) pairs creation by real photonphoton annihilation, that is, the multi-photon BreitWheeler (BW) process18 (gphoton mg

laser-e e ). The rst process is

essentially the nonlinear Compton scattering of laser photons by relativistic electrons, while the second generally occurs under extreme laser conditions by photons colliding with the electromagnetic waves, for example, the laser elds. The rst such an experiment was carried out by using the conventional paradigm at SLAC19. It is demonstrated that a 46 GeV linac-accelerated electron beam colliding with a 1018 W cm 2 laser is able to produce a few pairs (10614), which shows a relatively weak QED effect.

State-of-art laser systems20 are capable of delivering a laser pulse with intensity up to 2 1022 W cm 2. The next-generation

multi-PW lasers (for example, the XCELS and ELI facilities (the next generation of laser facilities, such as Exawatt Center for Extreme Light Studies (XCELS) and Extreme Light Infrastructure (ELI). Available at http://www.xcels.iapras.ru

Web End =http://www.xcels.iapras.ru and http://www.eli-np.ro

Web End =http://www. http://www.eli-np.ro

Web End =eli-np.ro )) are expected to reach B1024 W cm 2 and beyond.

This opens the door for studying lightmatter interactions as well as QED effects in unexplored domains1,4,21,22. Diverse schemes have been proposed for energetic e e pairs production via the

BW process using ultrarelativistic lasers2331. It is shown that using multiple colliding lasers25 for pair cascades in vacuum can reduce the required laser intensity down to B1026 W cm 2. This intensity is signicantly smaller than the Schwinger value. An alternative scheme26,27 relies on the energetic electrons from a laser-driven gas jet or thin solid target by using either two counter-propagating lasers or a single laser. The positron beam produced is very bright and energetic. However, the required laser intensity is as high as B1024 W cm 2, still two orders of magnitude higher than that of the available lasers. Another challenge is the target transparence27 to the incident super intense lasers, which leads to the low efciency of the BW process. By

comparison, the laser-hohlraum scheme28 invokes the single-photon BW process with a much lower laser intensity but achieves a positron yield at the 105 level only. More recently, it is proposed to combine the laser wakeeld acceleration (LWFA32) with the positron generation by colliding the accelerated electron beam with a counter-propagating laser pulse29,30. The resulting positron yield can be up to B109 (predicted by Blackburn et al.29), with a maximum density o1020 cm 3 (simulations by

Lobet et al.30). This conguration allows for a compact linac, while the extraction and application of the produced positrons depend on additional laser and beam facilities, which is of signicant importance for particle physics experiments, for example, a linear e e collider. To date, an all-optical collider based on laserplasma interactions for high-energy physics has yet to be realized.

For prolic pair creation via the BW process, high-energy and density g photons are essential. The latter can be obtained by nonlinear Compton scattering33,34, bremsstrahlung radiation of electrons in a solid target28 or synchrotron radiation of electrons in a laser beam reected from a thick foil27. Instead of using a solid or gas plasmas, here we present an efcient non-conventional scheme to generate extremely dense g photons and copious numbers of e e pairs by focusing two counter-propagating lasers at currently affordable laser intensity

B1022 W cm 2 onto two near-critical-density (NCD) plasmas. The proposed scheme requires two steps. First, bright g photons are produced by radiation-reaction trapped electrons in both NCD plasmas; second, the dense g photons emitted from one

NCD plasma collide with the focused counter-propagating laser in the other to initiate the multiple-photon BW process. We have carried out full three-dimensional (3D) particle-in-cell (PIC) simulations with collective QED effects incorporated. We demonstrate that the positron yield obtained is up to1.05 1011, which is 106-fold more than that obtained from the

laser-hohlraum scheme28 and is two orders of magnitude larger than those by using the LWFA-accelerated electrons29,30. The peak positron density is as high as 4 1022 cm 3 with a cutoff

energy of several GeV. This overdense e e pair plasma source may nd many practical applications and could serve as a compact linear collider with high luminosity.

ResultsOverview of the scheme. When an electron absorbs multiple laser photons in the nonlinear Compton scattering process, it can radiate a high-energy photon. The radiated photons propagate through the laser elds and interact with the laser waves to produce e e pairs via the multi-photon BW process. The probabilities of g-photon emission and positron creation are determined by two relativistic and gauge invariant parameters35 (see Methods): Z ge E? b cB

j j=Es and w o=2mec2

^

k cB

E?

=Es, where E> is the local electric eld perpendicular to the electron velocity b, Es m2ec3=e is the

Schwinger electric eld, and :k(:o) is the emitted photon momentum (energy). When a laser propagates parallel with an electron beam, it leads to ZD0, which is undesirable for high-energy g photon emission and positron production; If the laser counter-propagates with the energetic electron beam, there is

ZD1, which has been extensively investigated in past years19,26,29,30. Here we propose to use two lasers and two electron beams in an all-optical conguration realized simply by a pair of counter-propagating laser pulses in NCD plasmas. This enables one to have two sets of laser-electron beam colliding with Z1D1 and Z2D1 simultaneously (equivalent to a real Z larger than 1), which could signicantly enhance the g photon emission and the pair production via the BW process.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686 ARTICLE

Radiation-reaction effect and radiation trapping of electrons. In extreme laser elds, the radiation damping force3638 exerting on electrons could be expressed as fd 2e4=3m2ec4

g2eb E b B

2 E b

2 ,

where e is the charge unit, me is

the electron mass, and b is the normalized electron velocity by the light speed in vacuum c, B and E are the magnetic and electric elds. Here we keep only the main term proportional to g2e in the strong relativistic case. It is shown that the damping force fd becomes signicant enough to compensate for the Lorenz force fL q(E b B), under laser intensity 41022 W cm 2, and it

has to be taken into account in modelling laserplasma interaction. As a result, the electron motion is profoundly altered. Instead of being scattered off transversely, electrons are trapped inside the laser eld and perform extreme oscillations in the laser polarization direction. This is the radiation trapping effect39,40, which could lead to efcient synchrotron-like g-ray emission. However, the simple test electron model39 suggests a threshold laser amplitude required to enter this regime, that is,

a0th

3 2p2

s

3

0 ; 1

where r0 is the laser focal spot radius normalized by the wavelength l0 and re e2/mec2 is the classical electron radius. It is

shown that the threshold is dependent on the laser focal size. In order to excite the multi-photon BW process with synchrotron-like g rays, the threshold laser amplitude should meet a0th 650,

which is currently inaccessible. Therefore, in our scheme we rst employ two cone-targets to focus the lasers. Instead of using a gas plasma or solid, we choose NCD plasmas lled inside the cones to increase the laser energy absorption and conversion so that more background electrons are provided and accelerated to enhance the g-rays emission and positrons production.

The scheme takes advantage of the radiation damping and trapping effect in the near-QED regime39,40. Figure 1 presents the schematic drawing of our basic conguration, where two counter-propagating laser pulses interact with the NCD plasmas inside a double-cone-targets. In this scheme, high-energy-density g photons are emitted by the trapped energetic electrons in the

NCD plasmas at the laser axis, which are accelerated by the intense laser elds. When the g-photons collide with the focused counter-propagating laser waves from another direction, e e pairs are efciently produced via the multi-photon BW process. A positron beam produced in one NCD plasma can interact with the electron beam accelerated in the other NCD plasma, behaving like a microscopic e e collider.

Here we demonstrate the feasibility of the scheme by using full 3D PIC code EPOCH with QED effects incorporated (see Methods). To benchmark the simulation results, we also perform a series of reference simulations using the QED-PIC code Virtual LaserPlasma Lab. (VLPL37,41), which can reproduce the main results presented below.

3D PIC simulation results. Figure 2 illustrates the simulation results at t 36T0 (T0E3.3 fs is the laser cycle), when both lasers

overlap in the double-cone junction. It is shown that the laser intensity can be greatly boosted due to the coupling effect of nonlinear plasma effects and tightly focusing of the laser pulse in the cone4244. The strengthened laser ponderomotive force accelerates the electrons both radially and forward with considerable radiation emitted. When the radiation damping effect is taken into account, electrons undergo a strong backward damping force. This force increases with the time and becomes comparable to the laser ponderomotive force. As a consequence, a large number of electrons are kicked back to the laser elds radially and accumulate near the laser axis, forming a dense electron bunch as shown in Fig. 2a. These electrons are ultrarelativistic with a cutoff energy of B5 GeV (Fig. 3a) and are well collimated around the laser axis with a peak density up to 40nc (nc meo20=4pe2 is the critical density). Additional

simulations without the NCD plasmas and cone, respectively, indicate that the reduction of the laser threshold for the electron trapping is ultimately attributed to the nonlinear effect of the laser in the NCD plasmas-lled cone, which demonstrates the advantages of the cone structure over a plasma channel40. These trapped electrons travel almost along the laser-axis, inducing a strong poloidal self-generated magnetic eld40,43. This results in additional pinching effect on the electrons. Therefore, the electron trapping or pinching near the laser axis originates from the radiation damping force and is remarkably enhanced by the magnetic pinching effect.

The trapped electrons co-move with the focused laser in the cone and keep oscillating with an amplitude of B2 mm in the laser eld for a long time (Fig. 2a). During the process, two oxhorn-like electron bunches close to the cone mouths are also formed, resulting from the strong return currents in the cone. These trapped electrons emit a great deal of g photons. At t 36T0, the photon density is up to 850nc (Fig. 2b) and the

cutoff energy is about several GeV (Fig. 3b). The corresponding average photon energy density is around 1018 J m 3, which is 107 higher than the threshold for high-energy-density physics45. The production of such relativistic g photons is crucial to studying the plasma dynamics and collective QED effects in lasermatter interactions4648, which has many applications in diverse frontiers1,21,23, especially laboratory astrophysics.

The photon emission is mainly contributed by two processes:(1) the trapped electrons perform oscillations in the laser elds, like betatron oscillations in the bubble regime32,49,50; (2) the trapped high-energy electrons collide head-on with the opposite-propagating lasers, so that energetic photons are emitted by nonlinear Compton backscattering. Here the rst process dominates the radiation over the second because the photon spectrum as seen in Fig. 3b is a typical synchrotron-like spectrum, while the scattered photons in the ultrahigh laser eld limit via

Electrons

NCD plasma

e e +

Laser

#1

Laser

#2

Electrons

Figure 1 | Extremely dense electronpositron pair production from near-critical-density plasmas. Two counter-propagating ultraintense laser pulses are focused from two directions onto the near-critical-density plasmas lled inside two cones (purple). The quivering electrons in the ultraintense laser elds experience large radiation-reaction forces by emitting photons so that a large number of electrons are trapped in the laser elds. These trapped electrons perform extreme oscillations in the transverse direction and emit bright g rays (red- and blueyellow) around the laser axis. Finally, copious numbers of e e pairs are created via the multi-photon BreitWheeler process.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686

a

8

40

y(m)

0

n e (n c)

0

8 10

20

x (m)

30

40

50

8 0 8

z (m)

b c

4

0

4

0

4

850 36

y(m)

n (n c)

y(m)

n e+ (n c)

0

0

4 0 4

4

25

4 0 4

25

30

30

x (m)

35

z (m)

x (m)

35

z (m)

Figure 2 | Three-dimensional particle-in-cell simulation results. Density distribution of electrons (a), g photons (b) and positrons (c) at t 36T0. Both

lasers enter the simulation box at t 0T0 and arrive at the open mouths of the double-cone-target at t 5T0. Two dense electron bunches are formed

around the laser axis in the double-cone due to the radiation trapping effect, with high energy (B5 GeV) and a high density (B40 nc).

a 1012 b

1014

109

104

34T0

40T0

36T0

36T0

34T0

40T0

36T0

N e

N e +

108

104

1010

107

104 0 1.0 2.0 30 35 40 45 50

N

0.1 8 12

4

5

500 5,000

Ee (GeV) E (MeV)

c d

18

9

0

34T0

40T0

e

e+

50

Ee+ (GeV) t (T0)

Figure 3 | Evolution of the particle energy spectrum and the laser energy conversion efciency. The energy spectra of electrons (a), g-photons (b) and positrons (c) at t 34T0, 36T0 and 40T0. (d) The laser energy conversion to the trapped electrons re(%), g-photons rg(%) and positrons re (0.01%),

dened as the energy conversion efciency r, as a function of the interaction time t.

the second process would be only peaked at51 x/(1 x)Ee,maxE

1.5 GeV. Here the parameters are x 4Ee:o0/(mec2)2E0.18,

Ee,maxE10GeV at t 34T0, where :o0E1.2 eV is the laser

photon energy. However, the second process enhances the high-energy g-photon emission at later times (Supplementary Fig. 1;

Supplementary Note 1). On the contrary, the photon emission by

positrons created is a small fraction, since these positrons have a much smaller ux, energy, and density as compared with the trapped electrons in the laser elds.

These photons are distributed mainly around the laser axis with a cone angle ygB1/geo1 mrad with respect to the cone axis in both cones. Later, they collide with the focused

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686 ARTICLE

counter-propagating laser waves from the opposite directions, initiating the multi-photon BW process. Here, the BH process is intrinsically inefcient because of the low-Z NCD plasmas and the thin Al cone thickness814. Therefore, this process can be reasonably ignored in our simulations. Figure 2c presents the positron density distribution at t 36T0. A maximum positron

density of B4 1022 cm 3 can be obtained with energies up to

1.6 GeV (Fig. 3c). This peak density is much higher than that reported in the both BW and BH experiments as well as relevant simulations816,19,2731. The total positron yield is as high as1.05 1011, which is more than an order of magnitude larger

than that in laser foil interactions27, although our laser intensity is lower by more than an order of magnitude. As compared with the recent LWFA-aided scheme29,30, both the positron yield and density are two orders of magnitude higher.

Figure 3d presents the evolution of the laser energy conversion efciency to the trapped electrons, g photons, and positrons left in the simulation box. As the laser energy is soaked up and the electron energy grows, the damping process attenuates the laser wave and the laser energy is transferred to electrons and photons, and nally to positrons. At t 38T0, the positron energy

approaches a maximum and then decreases by emitting photons in a similar way to electrons in the laser elds. The laser energy conversion efciencies to the photons and positrons are peaked at14.9% and 0.14%, respectively. With the same laser parameters, the efciency of the positron production in our scheme is much higher than that of the LWFA-aided scheme29,30, making it very competitive as a compact positron source.

Parametric inuences and robustness of the scheme. The robustness of the scheme is further demonstrated by using different laser intensities and NCD plasmas, as summarized in Fig. 4. Here the laser duration is changed to 8T0to save time, while other parameters are kept the same except for a0 and ne. As expected, both the photon emission and positrons creation are

enhanced with the increase of the laser intensity. In the following, we compare our simulation results with theoretical predictions.

The quantum-corrected instantaneous radiation power by an electron is given by ref. 52, Prad (4pmec3/3lC)aZ2g(Z) PCg(Z),

where lC is the Compton wavelength, a e2/:c 1/137 is the

ne-structure constant, PC (4pmec3/3lC)aZ2 is the classical

power, and g Z

3

3

1 with F(Z, w) being

the quantum-corrected synchrotron spectrum function as given by Erber35. Figure 4a shows the evolution of the radiation power. For comparison, we also give in Fig. 4a the simulation result calculated by collecting all g photons energy and then dividing this by the total number of trapped electrons. The radiation time is estimated to be of order of several laser cycles. We see that our simulation results agree well with the theoretical predictions, considering the fact that we neglect the low energy photons (o1 MeV) in the simulations. The numerical scaling of the laser energy conversion efciency to the g photons with different laser intensities and NCD plasmas is shown in Fig. 4b. By increasing the laser intensity, the laser energy conversion to the g-photons increases at rst and then saturates when the laser eld amplitude a04800. This can be attributed to the rapid annihilation of the high-energy g-photons via the BW process. Note that the g-photon emission is signicantly limited by the number and energy of the trapped electrons.

In the simulations, we also observe a linear increase of the laser energy conversion to the positrons kinetic energy, as illustrated in Fig. 4c. This tendency is valid for all considered NCD densities and laser intensities with a04100. Qualitatively, the energy conversion efciency can be approximately written as

re f a0; ne a0t ath

; 2 where f(a0,ne) is a factor dependent on the laser and NCD plasmas, and is a constant under a given initial condition, a0(t) a0g(t), and g(t) is the temporal prole of the laser pulse.

This implies there exists a threshold laser intensity or eld amplitude, that is, athB120, for efcient pair creation in our

p =2pZ2

R

0 dwF Z; w

a

1

b

106

45 1.5nc

3nc4.5nc

30

g ( )

0.1

P rad(W)

(%)

g ( ) Theory Simulation

15

0.01

102 101 100 101

0 0 300 600 900

a0

c d

45 1.5nc 3nc4.5nc

1015

1012

109

0 300

Eq. (3) Simulation

30

15

0

e + ()

N e +

0

ath120

300 600 900

104

102

600 900

a0

a0

Figure 4 | Results of theoretical predictions and numerical simulations. (a) The electron radiation power (red line) and the function g(Z) (black dashed line) as a function of the parameter Z in our scheme. The red asterisks represent the simulation results. The laser energy conversion efciency to (b) the g-photons and (c) positrons with different laser intensities and plasma densities. Here the green dashed line in b shows the tted results. Note that there exists a laser threshold intensity in (c), athB120, for efcient positron production in our conguration. (d) The positron yield as a function of the laser intensity, based on the equation (3) and PIC simulations.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686

Magnetic spectrometer

Laser

Laser

EB

PB GB

NCD

Plasma

-ray

detector

Beam dump

e+

e

Parabolic mirror

Jet

Figure 5 | Schematic diagram of a possible experimental arrangement with strong lasers. Two counter-propagating 10 PW laser beams are focused by off axis parabolic mirrors on two gas or foam or cluster jets with near-critical-density, generating electron beams (EB), positron beams (PB) and g-ray beams (GB). The focusing mirrors have small holes in the centre to extract the electrons (e ), positrons (e) and g-rays (g), and to observe their interactions on axis.

conguration (Fig. 4c). We can understand the underlying physics simply in this way: when such a laser pulse is focused in the NCD plasmas-lled cone-target, its electric eld amplitude can be increased by more than three times (depending on its focusing location in the cone), which has been conrmed by additional simulations using the same cone conguration as above. As a result, one obtains an enhanced laser amplitude, which approximates the equivalent theoretical laser threshold for the electron trapping in our cone-target, a0th

3 r00=r0

p

650

p ,

3

0:3

assuming a focusing spot radius of r00E0.3r0.

We nally compare the laser energy conversion efciency in the simulations with theoretical predictions. Here the laser electric eld can be increased up to Ef 2:5 1015Vm 1 due to

the enhanced pinching and focusing effect of the cone. The corresponding two critical parameters are given by ZfB3 and

wfB2, which indicate effective excitation of both processes during the laser-NCD plasmas interaction. If we take w 0.1 for example

(see Methods), the required photon energy for pair creation is only 26 MeV, which is in reasonable agreement with the average energy of the g-photons in our simulations. Considering wf\1 in our case, the characteristic positron energy is given by53

Ee

mec2 E?=aEs

3=4

p

mec2= o0

, while the laser energy is

eL

cE2?r20tL=4. Thus we can estimate the nal maximum

positron yield by:

Ne ;m

re eL

mec2

3=4

o0 mec2

s ; 3

which is plotted in Fig. 4d. It is shown that our simulation results validate these theoretical estimations, especially for higher laser intensities. This further demonstrates the robustness of our scheme and validation of the simulations. If we scale our results to the upcoming lasers such as the XCELS (the next generation of laser facilities, such as Exawatt Center for Extreme Light Studies (XCELS) and Extreme Light Infrastructure (ELI). Available at http://www.xcels.iapras.ru

Web End =http://www.xcels.iapras.ru and http://www.eli-np.ro

Web End =http://www.eli-np.ro ), we can estimate the positron yield approaching B1014 with peak density of B1025 cm 3 and energy of tens GeV.

Schematic of a possible experimental arrangement. A possible experimental arrangement of the scheme with two 10 PW ELI-NP laser beams is illustrated in Fig. 5. Instead of using a double-cone-targets, we can focus the two laser beams on two gas, foam or cluster jets to produce NCD plasmas54,55. Carbon-Nano-Tube foams56 can be also used for NCD plasma generation, which has been extensively applied in laserplasma interactions. One can vary the gap between the two jets to optimize the g-photon emission and pair production. The focusing mirrors have small holes on the interaction axis in order to separate the electrons, g-photons, and positrons, and to diagnose their interaction dynamics on axis. The background radiation can be

reduced by burying the gamma detectors into the electron beam-dump23, which is positioned on the axis of the two laser interaction, as schematically shown in Fig. 5.

The femtosecond synchronization57 of the two femtosecond laser pulses can be obtained because both pulses are split from the same pulse in our conguration (after the laser oscillator), travel nearly identical optical paths (in the laser amplier chains) and the small temporal differences are compensated at the end. Indeed synchronization of 50 fs has already been demonstrated experimentally with the two 0.5 PW laser beams of the Astra-Gemini Laser at STFC in the UK57 and the method described can be further improved. Because of the copious numbers of positrons and electrons expected, the measurement of the number and spectrum of electronpositron pairs and of g-photons can be done in a single-laser-shot12,23, that is, there is no need to accumulate many shots as is typical in particle and nuclear physics experiments. The detectors could also be gated to the picosecond time-window of the laser shot in order to further increase the Signal-to-Noise ratio. Various interesting physics processes are likely to occur at the interaction area, including nonlinear Compton scattering, multi-photon BW process, e e collider and gg collider as discussed below.

DiscussionProduction of high-energy-density pair plasmas within a few tens of laser periods may open up new possibilities of studying astrophysical collective QED phenomena1,21 and high-energy particle physics3,4 in laboratories. Our scheme provides an efcient way to produce high-energy-density electrons and positrons, g photons, and potentially other particles through their interactions, resulting in many applications. For example, this conguration is particularly suitable for applications as a non-conventional table-top e e collider: the positron/electron beams and trapped energetic electron beams are generated in both NCD plasmas; when the electron beams in one NCD plasma collide head-on with the positron beams in the other NCD plasma (Supplementary Fig. 2; Supplementary Fig. 3; Supplementary Note 2), a compact e e collider is expected, as indicated in Fig. 5. In the case of the future ELI facility (the next generation of laser facilities, such as Exawatt Center for Extreme Light Studies (XCELS) and Extreme Light Infrastructure (ELI). Available at http://www.xcels.iapras.ru

Web End =http://www.xcels.iapras.ru and http://www.eli-np.ro

Web End =http://www.eli-np.ro ; assume I0B1024 W cm 2), the total positron number predicted is about 6 1013, with about 3 1011 positrons in the energy

range between 2 and 2.5 GeV. This number is million times higher than detectable in current laserplasma experiments so that the signal is strong enough to be detected in a single-laser-shot12,23. Assuming equal beams and Gaussian proles in all dimensions with a beam size, conservatively, for example, sx sy 1mm, it is estimated that the peak geometric

aEs

E?

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686 ARTICLE

luminosity of such a 4 5 GeV centre-of-mass (CM) e e

collider is as high as 1033 cm 2 s 1, which is comparable to the state-of-art colliders worldwide3. One may even scale the proposed scheme to TeV CM e e collision, which is a unique feature of our scheme as compared with the others816,2631.

In our scheme, the low-emittance high-energy-density g-photons in one NCD plasma can also collide with the other g-photons from the second NCD plasma, which is a second gg collider51 (Supplementary Fig. 1; Supplementary Note 1), an add-on to the e e collider. Compared with the conventional linear colliders3, these new conceptual colliders based on laser

plasma interactions have many advantages, such as pure e e collisions, low expense, compact size, and high luminosity, which may enable investigations in far-ranging scientic domains4,21,58 in future, for example, testing nonlinear phenomena such as mass-shift, spin-dependent effects, quantum gravity and so on.

In summary, we have presented a scheme on the generation of extremely dense e e pairs via the multi-photon BW process at affordable laser intensity B1022 W cm 2 with the upcoming 10s

PW lasers. In this scheme, bright g rays are rst produced by radiation-reaction trapped energetic electrons in the NCD plasmas. The photons then collide with the focused counter-propagating lasers to initiate the multi-photon BW process. A high-yield (1.05 1011) overdense (4 1022 cm 3) GeV posi

tron beam is thus produced with a laser energy conversion efciency as high as 0.14%. This highly energetic system may serve as a test bed for a variety of nonlinear QED physics and may be applied as a compact electron-position collider.

Methods

Two critical parameters in strong electromagnetic elds. The probability of photon emission and pair production can be written in terms of a differential optical depth35, dtg=dt 3

p acZ

=

lCge

R

Z=20 dwF Z; w

=w and

dt/dt (2pac/lC)(mec2/:o)wT(w), respectively. Here Z controls the photon

emissivity via the quantum-corrected synchrotron function F(Z,w), and w determines pair creation via the function T w

0:16K21=32=3w=w. In our case,

the two key parameters equals Z 2ge E?

j j=Es and w o=mec2

E?

j j=Es, since

k cB are parallel to the transverse laser eld E?. The Lorentz

factor for electrons in the cone is assumed to be

ge af eEf =meco0, where :o0 is

the laser photon energy and Ef is the focused laser transverse electric eld. Then, we obtain Zf 2 o0=mec2E2f=E20, where E0 meco0/e. The characteristic photon

energy can be described classically using the theory of synchrotron radiation as26 o 0:44Zf gemec2. Thus the parameter w is rewritten as wf 0:22Z2f. It is

shown that, as Z \1 and w\1, the BW process dominates the positron production and quantum effects intervene signicantly. Considering only w\0.1 in the photonphoton annihilation, the BW process also occurs, although it is relatively inefcient.

Numerical modelling. The open-source PIC code EPOCH27,59 is used to perform the 3D simulations. The code has been equipped with the synchrotron radiation module, the radiation-reaction module, and the pair creation module (BW process), allowing self-consistent modelling of laserplasmas interactions in the near-QED regime. In the code, the BW process is modelled by a probabilistic Monte Carlo algorithm52,59, which has been extensively applied recently. For simplicity, the e e annihilation is ignored in the code.

In the simulations, two counter-propagating linearly polarized laser pulses are incident from the left and right boundaries of the box simultaneously, which have the same temporal-spatial proles, that is, a transversely Gaussian distribution with a a0exp( r2/r02) and a square temporal prole with a duration of

tL

12T0. Here the laser parameters are, respectively, a0 150, r0 5l0,

T0 3.3fs, r2 y2 z2, and l0 1mm, which indicates a laser peak intensity

of I0E3 1022 W cm 2. Exposed in such a strong laser eld, both

electrons and protons can be pushed forward. The simulation box size isx y z 60l0 16l0 16l0, sampled by cells of 3,000 240 240 with 27

macroparticles per cell. For simplicity, two symmetric aluminium cones are used to focus the incident laser pulses, both of which have a length of 50l0 and a plasma density of n0 390nc. The left and right radius of each cone mouth are R 6 mm

and r 1.5 mm, respectively. To enhance the laser energy absorption, the double-

cone-targets are lled with NCD hydrogen plasmas, which has an initial density of ne 3nc. These parameters are tunable in simulations. For reference, we also

compared the simulation results to the case with a Gaussian temporal pulse prole, which shows a comparable positron yield and density (Supplementary Fig. 4;

Supplementary Fig. 5; Supplementary Note 3). Note that we only count the photons with energy 41 MeV in above simulations.

Data availability. The data that support the ndings of this study are available from the corresponding authors on request.

References

1. Di Piazza, A., Mller, C., Hatsagortsyan, K. Z. & Keitel, C. H. Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 11771288 (2012).

2. Danielson, J. R., Dubin, D. H. E., Greaves, R. G. & Surko, C. M. Plasma and trap-based techniques for science with positrons. Rev. Mod. Phys. 87, 247306 (2015).

3. Abramowicz, H. & Caldwell, A. C. HERA collider physics. Rev. Mod. Phys. 71, 12751409 (1999).

4. Mourou, G. A., Tajima, T. & Bulanov, S. V. Optics in the relativistic regime. Rev. Mod. Phys. 78, 309371 (2006).

5. Schwinger, J. On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951).

6. Bethe, H. & Heitler, W. On the stopping of fast particles and on the creation of positive electrons. Proc. R. Soc. Lond. A 146, 83112 (1934).

7. Nakashima, K. & Takabe, H. Numerical study of pair creation by ultraintense lasers. Phys. Plasmas 9, 1505 (2002).

8. Cowan, T. E. et al. High energy electrons, nuclear phenomena and heating in petawatt laser-solid experiments. Laser Part. Beams 17, 773783 (1999).

9. Chen, H. et al. Relativistic positron creation using ultraintense short pulse lasers. Phys. Rev. Lett. 102, 105001 (2009).

10. Liang, E. et al. High e /e ratio dense pair creation with 1021W cm 2 laser

irradiating solid targets. Sci. Rep. 5, 13968 (2015).11. Gahn, C. et al. Generating positrons with femtosecond-laser pulses. Appl. Phys. Lett. 77, 2662 (2000).

12. Sarri, G. et al. Table-Top Laser-Based Source of Femtosecond, Collimated, Ultrarelativistic Positron Beams. Phys. Rev. Lett. 110, 255002 (2013).

13. Sarri, G. et al. Generation of neutral and high-density electron-positron pair plasmas in the laboratory. Nat. Commun. 6, 6747 (2015).

14. Xu, T. et al. Ultrashort megaelectronvolt positron beam generation based on laser-accelerated electrons. Phys. Plasmas 23, 033109 (2016).

15. Chen, H. et al. Relativistic Quasimonoenergetic Positron Jets from Intense Laser-Solid Interactions. Phys. Rev. Lett. 105, 015003 (2010).

16. Mller, C. & Keitel, C. H. Antimatter: Abundant positron production. Nat. Photon. 3, 245246 (2009).

17. Di Piazza, A., Hatsagortsyan, K. Z. & Keitel, C. H. Quantum radiation reaction effects in multiphoton Compton scattering. Phys. Rev. Lett. 105, 220403 (2010).

18. Breit, G. & Wheeler, J. A. Collision of Two Light Quanta. Phys. Rev 46, 1087 (1934).

19. Burke, D. L. et al. Positron Production in Multiphoton Light-by-Light Scattering. Phys. Rev. Lett. 79, 1626 (1997).

20. Yanovsky, V. et al. Ultra-high intensity-300-TW laser at 0.1 Hz repetition rate. Opt. Express 16, 2109 (2008).

21. Marklund, M. & Shukla, P. K. Nonlinear collective effects in photon-photon and photon-plasma interactions. Rev. Mod. Phys. 78, 591640 (2006).

22. Ritus, V. I. Quantum effects of the interaction of elementary particles with an intense electromagnetic eld. J. Russ. Laser Res. 6, 497617 (1985).

23. Turcu, I. C. E. et al. HPLS-TDR2: high eld physics and QED experiments at ELINP: technical design report. Rom. Rep. Phys. 68, supplement, S145S231 (2016).

24. Sokolov, I. V., Naumova, N. M., Nees, J. A. & Mourou, G. A. Pair Creation in QED-Strong Pulsed Laser Fields Interacting with Electron Beams. Phys. Rev. Lett. 105, 195005 (2010).

25. Bulanov, S. S. et al. Multiple Colliding electromagnetic pulses: a way to lower the threshold of e e pair production from vacuum. Phys. Rev. Lett. 104, 220404 (2010).

26. Bell, A. R. & Kirk, J. G. Possibility of Prolic Pair Production with High-Power Lasers. Phys. Rev. Lett. 101, 200403 (2008).

27. Ridgers, C. P. et al. Dense electron-positron plasmas and ultraintense g rays from laser-irradiated solids. Phys. Rev. Lett. 108, 165006 (2012).

28. Pike, O. J., Mackenroth, F., Hill, E. G. & Rose, S. J. A photon-photon collider in a vacuum hohlraum. Nat. Photon. 8, 434436 (2014).

29. Blackburn, T. G., Ridgers, C. P., Kirk, J. G. & Bell, A. R. Quantum radiation reaction in laserelectron-beam collisions. Phys. Rev. Lett. 112, 015001 (2014).

30. Lobet, M., Davoine, X., dHumires, E. & Gremillet, L. Generation of high-energy electron-positron beams in the collision of a laser-accelerated electron beam and a multi-petawatt laser. Preprint at http://arxiv.org/abs/1510.02301

Web End =http://arxiv.org/abs/1510.02301 (2015).

31. Chang, H. X. et al. Generation of overdense and high-energy electron-positron-pair plasmas by irradiation of a thin foil with two ultraintense lasers. Phys. Rev. E 92, 053107 (2015).

the terms b cB and

^

NATURE COMMUNICATIONS | 7:13686 | DOI: 10.1038/ncomms13686 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 7

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13686

32. Pukhov, A. & Meyer-ter-Vehn, J. Laser wake eld acceleration: the highly nonlinear broken-wave regime. Appl. Phys. B 74, 355 (2002).

33. Thomas, A. G. R. et al. Strong radiation-damping effects in a gamma-ray source generated by the interaction of a high-intensity laser with a wakeeld-accelerated electron beam. Phys. Rev. X 2, 041004 (2012).

34. Bulanov, S. S., Schroeder, C. B., Esarey, E. & Leemans, W. P. Electromagnetic cascade in high-energy electron, positron, and photon interactions with intense laser pulses. Phys. Rev. A 87, 062110 (2013).

35. Erber, T. High-energy electromagnetic conversion processes in intense magnetic elds. Rev. Mod. Phys. 38, 626659 (1966).

36. Landau, L. D. & Lifshitz, E. M. The Classical Theory Of Fields vol. 2 (Butterworth-Heinemann, 1980).

37. Yu, T. P. et al. Dynamics of laser mass-limited foil interaction at ultra-high laser intensities. Phys. Plasmas 21, 053105 (2014).

38. Chen, M., Pukhov, A., Yu, T. P. & Sheng, Z. M. Radiation reaction effects on ion acceleration in laser foil interaction. Plasma Phys. Contr. Fus. 53, 014004 (2011).

39. Ji, L. L. et al. Radiation-reaction trapping of electrons in extreme laser elds. Phys. Rev. Lett. 112, 145003 (2014).

40. Zhu, X. L. et al. Enhanced electron trapping and g ray emission by ultra-intense laser irradiating a near-critical-density plasma lled gold cone. New J. Phys. 17, 053039 (2015).

41. Pukhov, A. Three-dimensional electromagnetic relativistic particle-in-cell code VLPL (Virtual Laser Plasma Lab). J. Plasma Phys. 61, 425 (1999).

42. Kodama, R. et al. Plasma devices to guide and collimate a high density of MeV electrons. Nature 432, 10051008 (2004).

43. Zhu, X. L. et al. Ultra-bright, high-energy-density g-ray emission from a gas-lled gold cone-capillary. Phys. Plasmas 22, 093109 (2015).

44. Yu, T. P. et al. High-energy-density electron jet generation from an opening gold cone lled with near-critical-density plasma. J. Appl. Phys. 117, 023105 (2015).

45. Davidson, R. C. et al. Frontiers in High Energy Density Physics: The X-Games of Contemporary Science (National Academies Press, 2003).

46. Lobet, M. et al. Ultrafast Synchrotron-Enhanced Thermalization of Laser-Driven Colliding Pair Plasmas. Phys. Rev. Lett. 115, 215003 (2015).

47. Nerush, E. N. et al. Laser eld absorption in self-generated electron-positron pair plasma. Phys. Rev. Lett. 106, 035001 (2011).

48. Zhang, P., Ridgers, C. P. & Thomas, A. G. R. The effect of nonlinear quantum electrodynamics on relativistic transparency and laser absorption in ultra-relativistic plasmas. New J. Phys. 17, 043051 (2015).

49. Cipiccia, S. et al. Gamma-rays from harmonically resonant betatron oscillations in a plasma wake. Nat. Phys 7, 867871 (2011).

50. Yu, T. P. et al. Bright Betatronlike X Rays from Radiation Pressure Acceleration of a Mass-Limited Foil Target. Phys. Rev. Lett. 110, 045001 (2013).

51. Telnov, V. Principles of photon colliders. Nucl. Instr. and Meth. in Phys. Res. A 355, 318 (1995).

52. Ridgers, C. P. et al. Modelling gamma-ray photon emission and pair production in high-intensity laser-matter interactions. J. Comput. Phys. 260, 273 (2014).

53. Fedotov, A. M., Narozhny, N. B., Mourou, G. & Korn, G. Limitations on the Attainable Intensity of High Power Lasers. Phys. Rev. Lett. 105, 080402 (2010).

54. Fukuda, Y. et al. Energy increase in multi-MeV ion acceleration in the interaction of a short pulse laser with a cluster-gas target. Phys. Rev. Lett. 103, 165002 (2009).

55. Chen, S. N. et al. Density and temperature characterization of lonf-scale length, near-critical density controlled plasma produced from ultra-low density plastic foam. Sci. Rep 6, 21495 (2016).

56. Ma, W. et al. Directly synthesized strong, highly conducting, transparent single-walled carbon nanotube lms. Nano Lett. 7, 23072311 (2007).

57. Corvan, D. J. et al. Femtosecond-scale synchronization of ultra-intense focused laser beams. Preprint at http://arxiv.org/abs/1409.4243

Web End =http://arxiv.org/abs/1409.4243 (2014).

58. Schroeder, C. B. et al. Physics considerations for laser-plasma linear colliders. Phys. Rev. ST Accel. Beams 13, 101301 (2010).

59. Arber, T. D. et al. Contemporary particle-in-cell approach to laser-plasma modelling. Plasma Phys. Contr. Fus. 57, 113001 (2015).

Acknowledgements

We acknowledge the fruitful discussions with M.Y. Yu, F. Pegoraro, C. Plostinar, andM. Zhong. The work was supported by the National Natural Science Foundation of China (Project Nos. 11622547, 11474360, 11175255, 91230205 and 11374210), the National Basic Research Program of China (Grant No. 2013CBA01504), a Leverhulme Trust Research Project Grant, the U.K. EPSRC (Grant No. EP/N028694/1), Plasma HEC Consortium EPSRC Grant (No. EP/L000237/1), the Science Challenge Program (Grant No. JCKY2016212A505), and the Research Project of NUDT (JQ14-02-02). The EPOCH code was developed as part of the UK EPSRC grants EP/G056803/1 and EP/G055165/1. All simulations were performed on TianHe High Performance Computers.

Author contributions

X.-L.Z. and T.-P.Y. conceived the scheme and X.-L.Z carried out all simulations. T.-P.Y. and X.-L.Z. performed the data analysis and wrote the manuscript. Z.-M.S., Y.Y. and A.P. claried details of the physics and contributed to the writing of the manuscript. I.C.E.T. proposed the schematics of the experiment and evaluated its feasibility with ELI-NP facilities. All authors discussed the results, commented on the manuscript, and agreed on the contents.

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How to cite this article: Zhu, X.-L. et al. Dense GeV electronpositron pairs generated by lasers in near-critical-density plasmas. Nat. Commun. 7, 13686 doi: 10.1038/ ncomms13686 (2016).

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