All-optical quasi-monoenergetic GeV positron bunch generation by twisted laser ﬁ elds

Generation of energetic electron-positron pairs using multi-petawatt (PW) lasers has recently attracted increasing interest. However, some previous laser-driven positron beams have severe limitations in terms of energy spread, beam duration, density, and collimation. Here we propose a scheme for the generation of dense ultra-short quasi-monoenergetic positron bunches by colliding a twisted laser pulse with a Gaussian laser pulse. In this scheme, abundant γ -photons are ﬁ rst generated via nonlinear Compton scattering and positrons are subsequently generated during the head-on collision of γ -photons with the Gaussian laser pulse. Due to the unique structure of the twisted laser pulse, the positrons are con ﬁ ned by the radial electric ﬁ elds and experience phase-locked-acceleration by the longitudinal electric ﬁ eld. Three-dimensional simulations demonstrate the generation of dense sub-femtosecond quasi-monoenergetic GeV positron bunches with tens of picocoulomb (pC) charge and extremely high brilliance above 10 14 s − 1 mm − 2 mrad − 2 eV − 1 , making them pro-mising for applications in laboratory physics and high energy physics.

ver since the positron was discovered in 1930s by Anderson 1 , extensive theoretical modeling, numerical simulations and experiments have been carried out to investigate the generation and application of positrons in various fields 2,3 , such as material science, particle physics, medical treatments as well as laboratory astrophysics. Spontaneous pair production by a single laser beam in vacuum was predicted by Schwinger 4 when the electric field reaches E S ≈ 1.32 × 10 18 V m −1 . This corresponds to a laser intensity of 10 29 W cm −2 , which is far beyond the current laser technology capability. Although it has been proved theoretically that the threshold could be lowered down to 10 26 W cm −2 by colliding laser beams 5 , the intensity is still at least three orders of magnitude larger than the achievable magnitude in the current laboratories. Several other approaches with seeded particles have been also proposed and extensively investigated in the past decades. For example, the trident process 6,7 relies on the energetic (hot) electrons direct interaction with the Coulomb field of the nuclei, while the Bethe-Heitler (BH) process [8][9][10][11][12][13][14][15] refers to the positron generation by the interaction of bremsstrahlung γ-photons with heavy nucleus. In case of two γ-photons collision, the Breit-Wheeler (BW) process 16 dominates the electron-positron pair production, by which pure light can be transformed into matter. Although the linear BW process has weak probability, researchers have managed to observe this process on the Relativistic Heavy Ion Collider (RHIC) 17 . Different from the pure linear BW process, a significant number of pairs can be generated via the nonlinear BW process, where the energetic γ-photon beams propagate through an electromagnetic field, e.g., a laser pulse. This makes it possible to generate copious positrons in a configuration of laser-laser or laser-electron collisions. The famous SLAC-E144 experiment performed twenty years ago is a typical example 18,19 of the latter choice, where a 46.6 GeV electron beam first created high-energy γ-photons and then underwent multiple collisions with the laser pulses from a Nd:glass laser at 527 nm wavelength. Finally, a signal of 106 ± 14 positrons with a broad energy spectrum in the range of 5-20 GeV was detected. However, such positron beams are not suitable for practical applications due to the trivial positron number produced.
With the advent of multi-petawatt (PW) lasers, significant efforts have been recently dedicated to obtaining high-energydensity electron-positron pairs by use of extremely intense laserplasma interactions in various configurations [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] , such as thin foil target [20][21][22] , laser-electron collision in gas plasma 27 , cone target filled with near critical density (NCD) plasma 29 and plasma channel 34 , some of which have the potential to be prolific positron yield factories and may be tested on the upcoming multi-PW laser systems. Although dramatic progress has been made on the generation of copious numbers or high-energy-density positrons [35][36][37][38][39][40][41][42][43][44] , there are some other restrictions on the practical usage of positrons generated from BH or BW processes, such as the separation of positrons from the plasma background and the preservation of the positron beam quality. Besides, the control of energy spread and duration of the generated positron beam driven by lasers is still extremely challenging and remains to be solved, which is essential for further applications in particle physics, e.g., as positron injection source in electron-positron collider and defect probing in materials. To the best of our knowledge, the methods to achieve dense short monoenergetic positron beams by use of multi-PW lasers in an all-optical way are yet to be explored.
In order to achieve both high yields of positrons and follow-up manipulation on the positron beam properties, here we propose an all-optical scheme for the generation of dense ultra-short quasi-monoenergetic positron bunches by use of a twisted laser pulse. At the first stage of the scheme, a relativistic Laguerre-Gaussian (LG) laser pulse is focused onto a cylindrical NCD plasma with a parabolic transverse density gradient, which can accelerate electrons directly from the background plasma to form sub-femtosecond electron bunches with energy up to several GeV. Then these energetic electrons quiver strongly in the LG laser fields and collide head-on with a high-intensity scattering Gaussian laser field in the second stage, emitting abundant γphotons via the nonlinear Compton scattering (NCS) process. At the final stage, the multi-photon BW process is triggered and copious numbers of positrons are generated. Due to the unique structure of LG laser fields, these positrons are compressed by the radial electric field and suffer phase-locked-acceleration (PLA) by the longitudinal electric field. As a result, dense sub-femtosecond quasi-monoenergetic GeV positron bunches are generated, which can be further accelerated in vacuum.

Results
Motivation of the scheme. Generally, it is difficult to couple the generation, injection, and acceleration of high-energy-density positrons in an all-optical setup. In past decades, thin foils have been extensively employed for dense positron generation [20][21][22] . However, once the ultra-intense laser pulse propagates through the foil plasma, its profile will be modified significantly, making it very difficult to control the positron beam quality without additional laser and beam facilities. Another issue is the fast dispersion of positrons by the drive pulse, whose ponderomotive force pushes the particles off the laser axis. Although ideally suited for electron acceleration, laser wakefields in plasma are not adequate for positron acceleration since positrons are easily expelled away from the bubble in the transverse direction 45 . Therefore, several methods have been proposed to mitigate this problem on positron wakefield acceleration from simulations 46,47 and experiments 48 , but they generally require the pre-injection of monoenergetic positron beams, and these positrons are generally produced via the BH process. It has been shown that appropriate time and spatial waveform of laser fields could potentially manipulate the properties of charged particles. Vortex light 49 is one of the examples, which has been widely used in quantum information 50 , communication 51 , micromanipulation 52 , etc. The LG laser is a typical vortex light characterized by a hollow intensity distribution with a spiral equiphase surface and carrying orbital-angular-momentum (OAM). It has been proved that the LG laser pulse could be used to drive particle acceleration with high OAM 53-55 , generate γ-ray vortex 56,57 as well as harmonics vortex 58 . In our scheme, we propose a configuration composed of a relativistic circularly polarized LG laser pulse with an intensity of order of 10 22 W cm −2 and parabolic NCD plasma channel. This laser pulse has been shown to be achievable by a normal Gaussian pulse incident on optical devices like spiral phase plate 59,60 , by Raman amplification in plasma 61 , or by plasma holograms 62 . With the help of a cone structure 63 , the intensity of LG laser can even be increased to beyond 10 22 W cm −2 . Unlike solid targets, the drive laser can keep its profile almost intact in the NCD plasma, which plays a key role in the manipulation of positron bunches. Figure 1 schematically illustrates the three stages of our scheme, which has been simulated by full threedimensional (3D) particle-in-cell (PIC) simulations (see Methods). It is shown that dense ultra-short quasi-monoenergetic GeV positron bunches can be generated by 10 PW-scale lasers, which may open up potential applications in particle physics.
Dense electron bunches formation. When the LG laser propagates into the NCD plasma, it picks up electrons from the background via the radial electric field, forming a dense electron bunch train as shown in Fig. 2a. This can be attributed to the special structure of the LG laser electric fields. Here, the laser radial electric field can be written as 54,64 , where E 0 is the peak value of the laser electric field, α is the direction angle of electric field in the y−z plane, σ 0 is the focal spot radius, σ is the spot radius related to x coordinates, G(ϕ) is the temporal shape of the laser which is Gaussian in our simulations, f ¼ πσ λ is the Rayleigh length and λ is the wavelength of the laser. The phase , ω 0 is the angular x is the radius of curvature of the wavefront. When ϕ ¼ π=2 þ 2nπ n ¼ 0; 1; 2 Á Á Á ð Þ , E r points outward and has the maximum value that pushes the electrons towards the laser axis; when ϕ ¼ 3π=2 þ 2nπ, E r points inward and has the maximum value that drives electrons off the laser axis. This results in the formation of an electron bunch train with a sub-femtosecond scale duration and 7.8 nC charge per bunch (see Supplementary Note 1).
On the other hand, the longitudinal electric field of the LG laser can be written as 55 where e ≈ 2.718 is the Euler number. It is shown that E x reaches the maximum E x;max ¼ À2 k 0 σ 2 cosψ on the laser axis (r = 0). Thus, the strong longitudinal electric field can accelerate the electrons near the axis most efficiently. This also decreases the dephasing rate 65 R ¼ γ e À p x =m e c, leading to a much longer distance of acceleration, where γ e is the relativistic factor of electron, p x and m e represent the longitudinal momentum and rest mass of electrons, respectively. The laser radiation pressure also plays an important role in the electron bunch acceleration, which can be written as F rad ¼ P Á dS n e dV ¼ 1 Obviously, the force depends on the electron density and position. It reaches the maximum at r ¼ σ= ffiffi ffi 2 p , and is one order of magnitude larger than q e E x;max when n e ¼ 10n c . Here, n c ¼ m e ω 0 =4πq 2 e % 1:1 10 21 cm À3 is the critical density at the laser wavelength of 1 μm, where q e is the charge of an electron. This interprets the fact that the off-axis electrons with lower density are able to be accelerated to much higher energy than the electrons on the laser axis. Figure 2b presents the evolution of electron energy spectrum. It shows that these electrons have a cutoff energy of more than 2 GeV at t = 50T 0 and reach a peak  Dense subfemtosecond electron bunches are formed with a high cutoff energy (~2 GeV), large energy density (~10 5 MeV·n c ) and sub-femtosecond full width at half maximum (FWHM) duration (~825 as). a Energy density distribution of electrons at t = 45T 0 . Here the on-axis electron density distribution is illuminated in the x−z plane. b Evolution of the electron energy spectrum. c Electron angle-energy distribution right before the laser-electron collision (t = 50T 0 ). energy density of 10 5 MeV·n c . Afterwards, the cutoff energy decrease, which is due to the γ-photon emission via the subsequent NCS process at the stage II. The different acceleration mechanisms for the electrons around the axis and off-axis lead to the double-peak structure in the angle-energy distribution of electrons as indicated in Fig. 2c.
Energetic γ-photon emission. The high-energy electrons quiver quickly in the LG laser field so that a large quantity of photons could be emitted in the quantum radiation dominated regime. At this stage, the intensity of photon emission process can be characterized by the quantum invariant , and c is the speed of light in vacuum. Figure 3a illustrates the distribution of χ e along the x axis in the collision zone at t = 50T 0 . It is shown that χ e is between 0.1 and 0.6, exciting the emission of sufficient γ-ray photons when the energetic electron bunches head-on collide with the scattering laser. Due to the short bunch structure, these photons have a similar distribution to the electrons with a peak density of 300n c . Figure 3b presents the photon energy spectrum evolution, which shows a cutoff energy of photons as high as 1 GeV before the collision and 1.5 GeV after the collision. The significant increase of photon energy and number are mainly attributed to the NCS process during the collision. By integrating the energy spectrum, we also see that the radiation power from the quivering electrons in the LG laser field is about 0.27 PW, while the peak radiation power via the NCS process is increased up to 6 PW, an order of magnitude higher than in the former process. Meanwhile, these photons also show a double-peak structure in the angle-energy space as indicated in Fig. 3b. Different from the electron bunches above, the high-energy photons are mainly resided within a smaller divergence angle about 15°. Although the off-axis electrons have larger velocity and energy, the incident scattering laser is Gaussian and has the maximum value on the axis, leading to much larger χ e around the laser axis. Thus, the higher energy photons resulting from the NCS process are generated by the electron bunches near the axis instead of the off-axis electrons. This results in the smaller divergence angle and higher photon energy as indicated in Fig. 3b. This small divergence angle leads to the high peak-brightness of the photon bunch of 8:04 10 25 photons s À1 mm À2 mrad À2 0:1%bandwidth ð Þ À1 with the photon energy centered at 13.13 MeV and the bunch size of 1 μm (see Supplementary Note 2 and 3), the value is comparable to the average-brightness of X-ray free-electron lasers. By use of stronger lasers, one may achieve brighter γ-photon beams (from MeV to GeV) with much higher peak-brightness approaching EuXFEL 66 centered at 25 keV.
Positron bunches generation. The generated γ-photons continue propagating forward and collide with the counter-propagating Gaussian laser field coming from the right side at around t = 55T 0 , hence initiating the multi-photon BW process. At this stage, the quantum invariant determining the electron-positron pair emissivity is χ γ ¼ _ω 0Ẽ? þk cB = 2m e c 2 E S À Á , whereẼ ? is the electric field perpendicular to the velocity of γ-photons, and k ¼ 2πṽ λ ph c is the wave vector of the emitted photon. Here, λ ph is the wavelength of the photon andṽ is the speed vector of the photon. Figure 4a presents the 2D distribution of χ γ in the x−y plane of the collision zone. The result shows that χ γ reaches 0.6, implying the generation of copious electron-positron pairs. Moreover, χ γ is much larger near the laser axis due to higher energy of γ-photons and stronger transverse field of Gaussian laser fields there, leading to the creation of copious electron-positron pairs around the laser axis. Figure 4b demonstrates that most positrons are distributed within a small range in the transverse direction, which shows a similar distribution to the transverse laser electric field. Figure 4c presents the density distribution of positrons at t = 78T 0 . One can see that the positrons are characterized by a train of position bunches each with a duration of about 680 as and a peak density of 8n c (see Supplementary Note 3). The energy spectrum of each positron bunch is presented in Fig. 4d. It is apparent that the positron bunches are quasi-monoenergetic and the cutoff energy of the first bunch is as high as 1 GeV with total charge of about 55 pC. At t = 78T 0 , the absolute FWHM energy spread of the second positron bunch is δE ≈ 60 MeV with the center energy of E ≈ 530 MeV. Thus, the minimum relative energy spread is δE/E ≈ 11.3% (see Supplementary Note 4), which is much less than those obtained in the previous work via the BH process 14,15 . To the best of our knowledge, it is the first time to report such dense quasi-monoenergetic positron bunch generation via the multi-photon BW process. Compared with the BH case 14 at a similar laser intensity, the positron number density is about five orders of magnitude higher. Furthermore, the skin depth of the pair plasma l s % 2:24 μm is smaller than the transverse plasma size of 2.51 μm, inducing weak collective effects of plasmas and making the hot dense pair plasma potential candidate as a test bed for pair plasma physics as well as nonlinear QED physics 2,29 . Acceleration and propagation of positron beams. As the positron bunches co-propagate along with the LG laser pulse, they experience compression and acceleration in the transverse and longitudinal direction, respectively (see Supplementary Note 5). In the transverse direction, the positron bunches are well confined by the negative radial electric field E r , forming collimated energetic positron bunches. For a more intuitive description, we show the 2D distribution of transverse electric and magnetic field forceF ? ¼Ẽ ? q e þ q eṽ B À Á ? experienced by positrons in the y −z plane at t = 65T 0 in Fig. 5a. It is interesting to see that the positrons within the red dashed circle (r ¼ σ= ffiffi ffi 2 p ) are well confined with a very small transverse velocity, while the positrons outside of the circle are scattered off the laser axis by the laser field. This phenomenon can be attributed to the transverse ponderomotive force of the LG laser pulse: where F 0 ¼ ffiffiffiffi ffi 2e p q e E 0 . It is shown that, when r > σ= ffiffi ffi 2 p , the transverse ponderomotive force F tr > 0, so that the positrons beyond the circle are pushed outward. On the contrary, as r < σ= ffiffi ffi 2 p , F tr > 0, positrons are confined within a small range. These are in good agreement with our simulation results as shown in Fig. 4b. Thus, the transverse compression of positrons can be achieved by the special field distribution of LG laser without applying extra magnetic fields as in previous researches 15 . It is in sharp contrast to the case of using normal Gaussian drive laser, where the generated positrons are dispersed quickly in space and there are no obvious positron bunches formed (see Supplementary Note 6). Due to the limited transverse motion, the positrons are well directed with a small divergence angle of 12°, as presented in Fig. 5b. Additionally, the geometric emittance of the positron bunches ϵ s ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi <s 2 ><θ 2 s >À<sθ s > 2 p in y and z direction is ϵ y ¼ 0:036 mm Á mrad and ϵ z ¼ 0:034 mm Á mrad, respectively, which are two orders of magnitude smaller than that recently acquired in experiments 67 . Here, s represents the direction in space (x, y, z), <s> is the average particle position in the s direction, and <θ s > is the average angle between the particle momentum p and the s axis. Correspondingly, the peak beam brilliance is B e þ ¼ N e þ =τ e þ ϵ y ϵ z E e þ ¼ 1:03 10 14 s À1 mm À2 mrad À2 eV À1 with the source size of 1 μm, ten million times brighter than the reactor-based positron source NEPOMUC 68 , where N e þ , τ e þ , E e þ are the total number, duration, and energy of a positron bunch, respectively.
In contrast with electrons, the positrons are accelerated dominantly by the positive longitudinal electric field E x . Here, the positron dephasing rate can be rewritten as R ¼ 1 À q e m e c R E x dt 0 . In our case, E x > 0, the positrons are rapidly accelerated to near the speed of light accompanying with a much longer acceleration length due to the decreasing R, so that they are swiftly phase-locked and accelerated in the NCD plasma. Since the positrons are well confined within a small zone near the laser axis, the positron acceleration is thus dominated by the longitudinal electric field. However, the offaxis positrons are also accelerated by the laser ponderomotive force , which is positive inside the laser spot (r < σ) except on the laser axis (F x = 0).
Here F x is of the same order of magnitude as the longitudinal electric field force q e E x . On the one hand, F x equals zero on the laser axis and increases gradually along the radial direction; on the other hand, the decreased longitudinal electric field force q e E x along with the radial direction compensate the increased F x force, as seen in Fig. 5b, so that the positrons in each bunch can be accelerated as a whole. The unified positron acceleration results in eventually the generation of quasi-monoenergetic positron bunches as shown in Fig. 4d. Figure 5c presents the x−p x phase space distribution of positrons at t = 70T 0 , which indicates a clear sub-femtosecond bunch structure as observed in Fig. 4c. It is shown that the phaselocked positron bunches are well confined by the negative radial electric field E r . Especially, the E x field shows an approximately linear roll-off for a large number of positrons, which plays a crucial role for the positron micro-bunching. Similar to the proton acceleration in the phase-stable-acceleration (PSA) regime [69][70][71] , the phased-locked tail positrons experience larger longitudinal electric field forces and can catch up with the In order to illustrate this, we present the evolution of micro-bunching process of positrons in the x−p x space, as shown in Fig. 5d. It shows that the positron bunch is discrete in the x−p x phase space and is characterized by a typical micro-bunching structure, leading to the generation of quasi-monoenergetic positron bunches.
Moreover, the positron bunches can be accelerated further and sustain their structure for a few tens of laser periods after they propagate into vacuum at t = 88T 0 , as shown in the inset of Fig. 5d. For example, the first positron bunch can be accelerated from 1.2 GeV to 3.8 GeV and maintain its structure after traveling for 40 laser cycles in vacuum (see Supplementary Note 7). Although these bunches show somewhat spatial diffusion in the transverse direction, their energy spread and duration are well maintained. It is interesting to note that the protons from the NCD plasma dephase quickly due to their low energy and large mass, compared with the positrons. Thus, the positron bunches can be well separated from the NCD plasma background, facilitating the further manipulation for potential applications. Figure 6 presents a possible experimental setup. Based on some previous researches 54, 55 , a left-handed circularly polarized LG pulse is chosen as the drive laser to generate short particle bunches. Since the generated electron and positrons are highlycollimated and confined near the laser axis, they may be separated from the laser pulses and γ-ray beams by using magnets, e.g., dipole, quadrupole, and sextupole magnets. However, electronpositron separation with dense beams is still challenging nowadays and should be considered carefully in future experiments. In particular, by use of few-cycle laser pulses, isolated ultra-short electron and X/γ-photon bunches can be generated 72,73 , so that a single positron bunch also can be expected via the BW process.

Discussion
In order to demonstrate the robustness of the scheme, we perform additional simulations to investigate the laser energy and angular momentum conversion efficiency into γ-photons and positrons. Firstly, we vary the drive laser intensity from a d = 180 to 265 while keeping a s = 150. Since the on-axis electrons are accelerated mainly by the longitudinal electric field E x , the energy of electrons depends on a d and the acceleration length. As mentioned before, with such strong drive laser intensity (a d ≧ 180), electrons could be accelerated to near the speed of light within one laser cycle and are phase-locked in the acceleration phase, so that the acceleration length approximates the same. Thus, the energy conversion efficiency from the lasers to electrons scales as ε e ¼ E e =E laser / a d = a 2 d þ a 2 s À Á $ a À1 d . In the near QED regime, the radiation power of energetic electrons can be estimated by P γ % 2 3 N e q e E s cα f χ 2 e g χ e À Á , where N e is the electron number, À Á is the average radiation power factor, and g χ e À Á % 1 þ 12χ e þ 31χ 2 e þ 3:7χ 3 e À Á À4=9 is the quantum weaken factor. The energy of emitted γ-photons is estimated as E γ / E e χ 2 e g χ e À Á , thus we can get the simple approximation of the laser energy conversion efficiency to the γ- d , in accordance with the simulation results in Fig. 7a. The approximate form of the function determining the rate of electron-positron pair production is 28 , where K is the modified Bessel function of the second kind. When χ γ < 8, Since the positron acceleration is dominated by the laser longitudinal electric field, the laser energy conversion efficiency to the positrons is thus , agreeing well with the simulation results shown in Fig. 7a. Especially, when we decrease a d , e.g., to a d = 180, the generated positron bunches are still quasi-monoenergetic. The laser pulse with this intensity will be soon attainable on several laser facilities 74 e.g., ELI-NP, SULF and CoReLS.
Secondly, we keep a d = 265, but vary a s from a s = 100 to a s = 200. The energy conversion efficiency from the laser pulses to the electrons and positrons shows a similar scaling except for photons, as shown in Fig. 7b. Different from the charged particles, the laser energy conversion efficiency to the γ-photons keeps almost unchanged with the increase of a s . Here, the radiated γphotons originate from two parts, the quivering electrons in the drive laser field and the NCS process. Although the NCS process depends on the intensity of both laser pulses, the first part of γphotons is determined only by the drive laser, resulting in different scaling of energy conversion efficiency with a d and a s . Our simulations show that the final laser energy conversion efficiency to photons grows at the same rate as the total laser energy.
It is interesting to see that the OAM of LG laser pulse is also transferred to electrons and positrons efficiently. Here, the angular momentum of laser field is L laser ¼r Ẽ B À Á , while the angular momentum of particles can be calculated by L part ¼r part p part , wherer part andp part are the transverse position and the momentum of particles, respectively. In the case of a d = 265 and a s = 150, the OAM conversion efficiency from laser pulses to positrons can reach 2% which is an order of magnitude higher than previous study 30 . When we increase the scattering laser intensity, the laser angular momentum conversion efficiency to the positrons is also increased efficiently (see Supplementary Note 8). Here, the angular momentum provides the GeV positron bunches an extra degree of freedom so that they may have many potential applications in high energy physics, such as discovering new particles, solving the underlying physics in the collision of e − e + and investigating fundamental QED Fig. 6 Proposal of an experiment set-up to acquire high-quality positron beams. The LG laser pulse can be obtained by irradiating a phase plate with a usual Gaussian laser pulse (see Methods), for example, a 16/32 stair phase plate with the stair-height of tens nanometers employed in previous experiments 60 can be used here. Then, the LG laser pulse interacts with the nanotube foam target and collide with the scattering laser, generating abundant γ-ray and electron-positron pairs. Finally, the collimated electron and positron beams can be separated from the laser pulses and γ-ray beams by use of magnetic fields. processes. Meanwhile, the attosecond-scale positron bunches are not only separated in space, but also in energy, enabling ultrashort time resolution in detecting and accurate injection into accelerators.
In conclusion, we propose an all-optical scheme for the generation, acceleration, and compression of positrons to form dense GeV sub-femtosecond positron bunches with 10 PW-scale lasers. In this scheme, high-energy incoherent γ-photons are efficiently generated via the NCS process. Once the γ-photons collide headon with the scattering laser pulse, abundant positrons are generated via the multi-photon BW process. Owing to the PLA, subfemtosecond quasi-monoenergetic positron bunches are produced. The high-quality positron bunches are sustainable for tens of laser periods when propagating into vacuum along with the drive laser. Besides the short-time duration and narrow energy bandwidth, OAM is also transferred efficiently from the LG laser pulse to the γ-photons and positrons with the efficiency of about 30 and 2%, respectively. In the near future, several laser facilities 75,76 under construction will be capable of delivering ultra-high intensity laser pulses of 10 22 −10 24 W cm −2 with the peak power at 10 PW and above, which is high enough to test our scheme. The bright quasi-monoenergetic sub-femtosecond positron bunches with tunable energy and OAM may find wide applications in science and engineering, such as ultra-fast dynamics, laboratory astrophysics and particle collision experiments.

Methods
Numerical modeling. 3D PIC simulations are carried out using the open-source PIC code EPOCH, with both QED and collective plasma effects included 21,28 . In the simulations, a left-handed circularly polarized LG laser pulse and a linearly polarized Gaussian laser pulse are incident from the left and right boundaries of the simulation box with a time delay of 23T 0 . Except for the parameter scanning, the main results of this manuscript are based on the following laser parameters. The drive laser has an intensity of a d = 265, focal spot radius of r 0 = 3λ 0 , pulse duration ofτ L = 12T 0 (with Gaussian profile), laser period of T 0 = 3.3 fs, and laser wavelength of λ 0 = 1 μm. As for the scattering laser, a s = 150, r 0 = 5λ 0 , and τ L = 10T 0 . While the parameter scanning results in Discussion are acquired with all other parameters unchanged except the laser intensities (details are given in the previous section). From the parameter scanning results, the minimum laser intensity required for quasi-monoenergetic positron bunch generation in our scheme is as low as a 0 = 150 for both drive and scattering lasers. Thus, the corresponding laser power is only 8 PW, smaller than that in several available laser facilities 74,77 , like SULF and ELI-NP. For the sake of maintaining positron bunch quality, the laser fluctuations need to be less than half of the laser spot radius. The simulation box is x × y × z = 80λ 0 × 9λ 0 × 9λ 0 , sampled by cells of 1000 × 225 × 225 with 16 macroparticles per cell. A cylindrical NCD plasma (r = 9λ 0 ) with parabolic density distribution is applied to focus the incident laser and enhance the laser absorption. The plasma exists from 2λ 0 to 78λ 0 with the transverse distribution defined by n 0 = (1 + 0.11r 2 )n c . The intensity of both lasers is tunable in the simulations and the NCD plasma can be manufactured by focusing the laser pulses on gas jets 78 or foams 79 . The electron dynamics and photon emission have been verified by the Virtual Laser Plasma Lab (VLPL) code 80 .
Intense twisted laser pulse generation. It has been already proved that intense twisted laser pulse can be generated through irradiating a spiral-shaped phase plate (light fan) by an intense Gaussian laser pulse 59 . Recently, femtosecond twisted laser pulse with an intensity of 6.3 × 10 19 W cm −2 has been successfully generated in experiments where a 32-stair plate with the step-height of 17.5 nm was used 60 . Here, we investigate numerically the generation of such an ultra-intense twisted laser pulse via the light fan by using the 3D-PIC code EPOCH, as shown in Fig. 8a. The parameters of incoming Gaussian laser (LG 00 ) are: a 0 = 265, r 0 = 3λ 0 , τ L = 12T 0 (with Gaussian profile), and λ 0 = 1 μm. The phase plate is a plastic foil with eight stairs whose height is Δ = λ 0 /16 = 62.5 nm to produce a total phase shift of λ 0 /2, and the minimum thickness of the foil is 2 μm. After the Gaussian pulse is completely reflected by the phase plate, an ultra-intense twisted LG 01 pulse with a 0 ≈ 200 is acquired, as indicated in Fig. 8b, c. In theory, the laser mode of the reflected pulse can be expanded by a series of LG modes and the expansion coefficients can be defined as 81 Here,Δϕ ¼ ∑ 7 n¼0 H ϕ À π=4n À Á H π=4n þ π=4 À ϕ À Á 2π=8n, C st is a normalization constant, R st = (f 2 + x 2 )/x and H(x) is the Heaviside function. Thus, the reflected pulse is composed of several laser modes and the percentage of each mode is given by I st ¼ a st 2 . Because of Δϕ ≈ ϕ in our simulations, the laser modes with the azimuthal mode index l = s − t = 1 contribute the most in the ϕ integral. In our case, the resulting I 10 = 78.5% means that the LG 01 mode dominates the reflected pulse, which agrees well with the PIC simulation results as shown in Fig. 8b, c.
Data availability