Collimated GeV attosecond electron-positron bunches from a plasma channel driven by 10 PW lasers

High-energy positrons and bright {\gamma}-ray sources are unique both for fundamental research and practical applications. However, GeV electron-positron pair jets and {\gamma}-ray flashes are still hardly produced in laboratories. Here we demonstrate that, by irradiating two 10 PW-scale laser pulses onto a near-critical density plasma channel, highly-directional GeV electron-positron pairs and bright {\gamma}-ray beams can be efficiently generated. Three-dimensional particle-in-cell simulations show that GeV positron jets show high density (8*10^21/cm^3), attosecond duration (400 as) and a divergence angle of 14{\deg}. Additionally, ultrabright (2*10^25 photons/s/mm2/mrad2/0.1%BW) collimated attosecond (370 as) {\gamma}-ray flashes with a laser energy conversion efficiency of 5.6% are emitted. Once realized in experiment, it may open up new possibilities for a wide variety of applications.


Introduction
Since Anderson observed positrons [1], researches on positrons have excited great interest and play an important role in various domains [2,3], including fundamental science, medicine, and industry. Compared with the conventional positron sources, laser-driven positron sources have many potential advantages, such as having a high energy, yield and density, ultrashort beam size, etc. Currently, by use of high power intense lasers, multi-MeV positrons can be easily produced in laboratories [4][5][6][7]. However, giant highly-energetic (i.e., GeV and TeV energies) positron jets with extremely high-density are still out of reach, which occur only in energetic astrophysical environments [2,8,9], such as γ-ray bursts, pulsars and black holes. It is very difficult to achieve such positron sources on earth with the current laser technologies or traditional methods.
On the other hand, the atto-beams of relativistic electrons and X/γ-rays [10][11][12][13] show powerful tools for diverse scientific research and technical applications, enabling the time-space imaging with sub-atomic resolution in attosecond regime, however, the atto-beam property of laser-driven positrons has been scarcely investigated.
Several ongoing and arranged laser facilities [14-17] will deliver ultrahigh intensity laser pulses of interactions in the radiation and quantum-dominated regime [18,19]. The proposed schemes show that when the laser intensity is above 10 23 W/cm 2 , high-energy dense positron sources can be produced significantly via the multiphoton Breit-Wheeler (BW) process [20] from various media such as plasmas [21][22][23][24][25][26][27] or relativistic electron beams [28][29][30]. However, so far, the production of dense positron jets and bright γ-ray flashes with both atto-scale beam duration and GeV energies at currently available laser systems has not yet been achieved.
In this paper, we present a practical approach to generate collimated GeV positron beams and bright γ-ray flashes with attosecond duration at an achievable laser intensity of ~10 22 W/cm 2 . Figure 1 multi-GeV energies, so that energetic attosecond γ-rays are efficiently emitted via nonlinear Compton scattering (NCS) [13,31]. The dense GeV atto-beams of electrons and γ-rays then collide with the second probe pulse from the right side, and the multiphoton BW process is triggered, resulting in abundant dense GeV positrons with atto-scale beam duration. As a comparison, we also consider the plasma with a uniform density distribution, as shown in Fig. 1(c).

Results
Three-dimensional (3D) particle-in-cell (PIC) simulations were performed using the code EPOCH [32] with both QED and collective plasma effects incorporated [33,34]. In the simulations, two 10 PW-scale high-power linearly-polarized Gaussian laser pulses (drive laser and probe laser) are incident with a time delay of 55 0 from the left side and right side of the box, respectively. The temporal profile of both laser pulses are trapezoidal with a duration of 12 0 (1 − 10 − 1 0 ) for the drive pulse and 5 0 (1 − 3 − 1 0 ) for the probe pulse. The normalized amplitude of both lasers is 0 = 0 / 0 = 150, corresponding to a currently approachable intensity of 3 × 10 22 W/cm 2 in laboratory [35], with a focus spot of 0 = 4 0 .
Here is the unit charge, is the electron mass, 0 is the laser oscillation frequency, 1 is the laser wavelength, and is the speed of light in vacuum. The NCD plasma has a transverse density profile of = 0 + ∆ ( 2 / 0 2 ) in the plasma channel located between 3 and 53 0 , where = ω 0 2 /4 2 is the critical density, 0 = 1 , ∆ = 0.1 0 0 / 0 2 ( 2 ), and = 2 + 2 is the radial distance from the channel axis. For the case with the uniform plasma, the density is = 3.9 to keep the total number of plasma electrons unchanged. The simulation box is × y × z = 60 × 20 × 20 0 3 with a cell of ∆ × ∆y × ∆z = 0 /30 × 0 /12 × 0 /12 and 16 macro-particles in each cell. In order to save the computing sources, a moving window is employed in all simulations below.  that the electrons in the plasma channel can be accelerated to much higher energy than that in uniform plasma case. This can be attributed to the coupling effects of high-intensity laser interaction with NCD plasmas [36,37], where the plasma channel works as a optical lens to enhance the intensity of laser pulse significantly, as presented in Fig. 2(b). Since a large number of electrons are confined in the high intensity area of the laser pulse, they consume the most laser energy by emitting high-energy γ-rays during the rapid acceleration. It is interesting to note that the laser intensity is still enhanced by four times within the plasma channel. The beam energy density of the accelerated electrons is as high as 3 × 10 19 J/m 3 with a high energy of 2.5 GeV and a ultrashort beam duration of several hundreds of attoseconds, which is more than eight-fold higher than the threshold of high-energy-density physics (HEDP) [38].  Since the critical parameter in the case with plasma channel is much larger than that with the uniform plasma, GeV γ-rays are efficiently emitted with a high photon energy density, as shown in Fig. 3(a).
Here, the attosecond γ-rays radiated have a smaller divergence angle with high photon energies than that with the uniform plasma, as presented in Figs. 3(b) and 3(c). With the plasma channel, the γ-ray beam has a total photon yield of 2.5 × 10 11 at 25 MeV, a full width at half maximum (FWHM) cross-section of ~1.5µm 2 , a FWHM divergence of 0.1 × 0.1rad 2 , and a total pulse duration of ~900as at FWHM. The results indicate that the GeV γ-ray with a peak brightness of ~2 × 10 25 photons/s/mm 2 /mrad 2 /0.1%BW is obtained, which is several orders of magnitude higher than the presented in current laboratories [40][41][42][43] and is also much brighter than the level in other simulations [26,[44][45][46]. Meanwhile, the γ-ray beam is characterized with a desirable ultrashort duration of <370as per pulse, which may open the door to a new realm of ultrafast-science research in a wide range of scientific fields.

Discussion and conclusion
The present simulations demonstrate a promising and efficient approach for generating well-collimated, energetic, dense positron jets with attosecond-scale beam duration from a NCD plasma channel, which is driven by 10 PW-scale intense lasers. In order to further explore the parametric effects and robustness of this scheme, a series of 3D PIC simulations are carried out by employing different NCD plasma channels and laser intensities. First, the effect of laser intensity on the jet generation is investigated, where all other parameters are kept the same as before except for the laser amplitude of 0 and the corresponding plasma density of . Figure 5(a) shows the simulation results. One can see that as the laser intensity increases, the efficiency of laser-produced positrons is enhanced significantly. This is due to the fact that, with the increase of laser intensity, the multiphoton BW process can be easily triggered. Note that the critical quantum parameter ~ℏ | ⊥ |/ 2 ∝ ℏ 0 . With the forthcoming multi-PW laser facilities, our scheme potentially gives rise to highly-efficient dense GeV positron jets and bright γ-ray flashes with desirable attosecond-scale beam property. which can obtain a higher energy with a longer acceleration distance and efficiently radiate giant energetic γ-rays in NCD plasmas [36,37]. However, further increase of the channel length is not always better. For example, the generation of positrons saturates for > 60 0 , because the drive laser pulse is rapidly depleted in such a long plasma channel, so that the electron acceleration and γ-ray emission become limited and the electron-positron pair production does not enhance any more. This could be used for tuning and enhancing the positron jet generation in future experiments.
In summary, we have investigated the generation of collimated GeV attosecond positron beams from 10 PW laser interaction with the NCD plasma at a currently achievable laser intensity of ~10 22 W/cm 2 . It is shown that high-yield, well-collimated, dense GeV attosecond positron beams are efficiently produced within a plasma channel. Compared with the uniform plasma case, the positron production is greatly enhanced due to the strong focusing and enhancement of the incident laser pulse in the plasma channel. The yield, energy conversion efficiency, and cutoff energy of the positrons obtained increase with the incident laser intensity, which can be further enhanced by using a long plasma channel. With the upcoming next-generation laser facilities (e.g., ELI [14], XCELS [15], Apollon [16], and SULF [17]), such collimated 9 / 11 dense GeV positron jets and bright γ-ray flashes both with desirable atto-beam capability may open new avenues for ultrafast studies in physics, chemistry, biology, etc.