Collimation, compression and acceleration of isotropic hot positrons by an intense vortex laser

Laser-driven positron sources, characterized by short pulse width, small focal spot and high energy, are promising for potential applications, e.g. electron–positron collider and positron annihilation spectroscopy. However, the broad divergence angle and wide pulse width during the laser-driven positron transport are extremely unfavorable for achieving high spatiotemporal resolution. In this paper, we propose a novel method to manipulate the positrons by using a left-hand circularly-polarized Laguerre–Gaussian (LG) laser pulse. Using the LG laser with a intensity of 1.2×1021Wcm−2 and a duration of a few cycles, three-dimensional particle-in-cell simulations reveal that isotropic hot positrons can be effectively captured, collimated, compressed, and accelerated due to the unique field structure of the LG laser. A high-quality positron bunch is obtained with a peak divergence angle of 1∘, an average pulse duration of 0.5 fs, a maximum energy of 450 MeV, and a density of 70 times that of the initial electron source. A damping vibration model is also formulated to explain qualitatively the quality improvement of the positrons.


Introduction
Laser-driven positron sources have attracted widespread attention for their diverse applications in various areas, such as electron-positron collider [1,2], positron annihilation spectroscopy (PAS) [3,4], laboratory astrophysics [5,6], and injection into plasma-based positron accelerators [7,8].In these applications, high-quality positron pulses with high energy, high density, short duration and low divergence angle are highly desired.For example, in PAS, positron pulses with higher energy can penetrate large-volume targets and increase the detection depth; positron pulses with larger flux can reduce the detection time; and positron pulses with shorter duration can improve temporal resolution [9,10].If positrons are used as injectors for plasma accelerators, small beam size and short pulse duration are also demanded to match millimeter-scale acceleration length in the wakefield [7].Moreover, to enable stable wakefield acceleration, the positron properties such as energy, emittance, and charge also should be carefully optimized [7,8,11,12].
Currently, the generation of positron beams from laser-plasma interaction has achieved significant progress via direct or indirect manners [10,13,14].The indirect manner uses high-quality electrons of wakefield acceleration that collide with a solid target to produce positrons via the Bethe-Heitler/Trident process [15][16][17][18], while the direct approach is to generate positrons by directly irradiating solid targets with ultraintense lasers [19].The indirect manner can produce high-quality positron beams, but with very low yield.In contrast, positrons obtained via the direct manner have a typically much higher yield and a narrower energy spectrum.Therefore, many experimental studies were focused on the direct method in the past decade.Chen et al [20,21] observed an extremely large number of positrons (10 10 -10 12 per shot) with a duration of tens of ps for the first time by irradiating ps laser pulses with ∼10 20 W cm −2 intensity on gold targets of mm thickness.They estimated the positron density to be 10 16 cm −3 , the highest ever achieved in experiments.It was measured that the generated positron beams are quasi-monoenergetic with temperatures around 1 MeV, and divergence angles of about 20 • [22].Subsequent studies explored the scaling of the positron yield with the laser and target parameters.It was shown that the positron yield is proportional to the square of both the laser energy [23] and the atomic number of the target material (Z) [24,25].To increase the laser-to-positron conversion efficiency and the average energy of emitted positrons, micro-structure targets with large-scale Si microwire arrays on the surface are utilized [26].Despite significant progress, positron beams from direct method usually have large divergence angles (typically > 20 • ), which results in broadening pulse width and deteriorating divergence angle during energetic positron transport.
In order to improve the quality of positron beams, external magnetic fields or self-generated target sheath fields are utilized.For example, Chen et al [27] set a pulsed Helmholtz-type coil placed 18 mm from the target to form a peak axial magnetic field of 8 T. They observed for the first time that relativistic positron beams generated by laser-solid interactions were effectively collimated by externally axial magnetic fields.The full width at half maximum (FWHM) of the positron beam divergence angle was reduced from 20 • to 4 • .The positron density was increased by two orders of magnitude, from 5 × 10 7 cm −3 to 1.9 × 10 9 cm −3 at 0.6 m from the target.Due to broad energy spectrum of positron beams, temporal lengthening and density decreasing occur, since positrons of different energy have different focal lengths in axial magnetic fields and different flight times after leaving the external fields.Peebles et al [28] used magnetic mirror fields along the normal direction of the target axes to choose and collimate positrons of roughly 13 MeV over a long distance (>50 cm), while positrons with higher or lower energy were significantly deflected and defocused.Audet et al [10] placed a compact beam-line, consisting of two Hallbach quadrupole magnets, two collimators and two dipole magnets, after targets for energy-collection and collimation of laser-driven positron beams.They experimentally and numerically demonstrated the suitability of laser-driven positron beams as probes for volumetric and high-resolution scanning of materials by generating high-flux positron beams in a 50 keV energy slice with a duration of tens of picoseconds and a kinetic energy tunable from 0.5 to 2 MeV.Xie et al [29] proposed a collection and transmission system composed of a collimator, a solenoid, quadrupoles and a slit to intensity and narrow the divergence of positron beams.It was demonstrated that the designed system can work in the center energy range from 15 to 40 MeV within 10% energy spread and greatly decrease beam divergence to 50 mrad.However, only a small amount of expanding positrons within a narrow band of energies can be focused and collimated when applying external magnetic fields.Kim et al [8] experimentally demonstrated that laser-driven relativistic positron beams could be focused and accelerated by self-generated target sheath electric fields from curved target rear sides.Further simulations showed that the beam density and peak energy were effectively manipulated by the radius of target curvature.However, it is inferred that the beam divergence is still above 10 • after focusing in this scheme.
In this paper, an enhanced capture mechanism for laser-driven positrons is proposed by using a left-hand circularly-polarized Laguerre-Gaussian (LG) laser pulse.In comparison with the magnetic fields capture mechanism mentioned above, positrons can not only be captured and collimated, but also be simultaneously compressed and accelerated in our scheme.With the help of three-dimensional (3D) particle-in-cell (PIC) simulations, it is shown that the pre-generated hot positrons with full divergence angle can be converted into high-quality positron bunches with a peak divergence angle of about 1 • , an average pulse duration of 0.5 fs and an energy of 100 s MeV.About 25% of the positrons are effectively captured and compressed to a density of about 70 times of the initial density.The capture and collimation of the isotropic hot positrons are demonstrated by using a damping vibration model.Furthermore, the dynamics of positron acceleration and angular momentum transfer are also discussed in detail.

Methods
We carry out simulations using fully 3D parallel PIC code EPOCH [30].The size of the simulation box is x × y × z = 12λ 0 × 24λ 0 × 24λ 0 with the spatial resolution ∆x × ∆y × ∆z = 0.025λ 0 × 0.05λ 0 × 0.05λ 0 , where λ 0 = 1 µm is the laser wavelength.There are two macro-positrons in each grid.A moving window is employed which starts moving at t = 11T 0 , where T 0 = λ 0 /c is the laser cycle.A typical simulation lasts 150T 0 and needs 11.5 hours with 240 processors.Considering the fact that the laser-generated positrons from the direct manner usually have a large divergence and ∼MeV energies in experiments, we employ the pre-generated hot positrons with isotropic angular distribution in the simulations.The positron energy spectrum follows a quasi-Maxwellian distribution with 1 MeV temperature.The initial density of positrons is set to n 0 = 10 −5 n c according to recent experimental results by Chen et al [20], where n c = 1.1 × 10 21 cm −3 is the critical density for 1 µm laser wavelength.To save computational resources, the longitudinal length of the positron beam is 15λ 0 .At the start of the simulation, the positron beam is located in the region of 3λ 0 < x < 18λ 0 , −12λ 0 < y < 12λ 0 , −12λ 0 < z < 12λ 0 .

The novel capture scheme for isotropic hot positrons
Figure 1 shows the diagram of the configuration in our simulations.When a left-hand circularly-polarized LG laser pulse irradiates the pre-generated positron beam, a great deal of positrons can be captured and comove with the laser pulse.The positrons are well collimated and focused near the optical axis, as evidenced by their trajectories.The density distribution of positrons in the yz plane at t = 50T 0 , 100T 0 , and 150T 0 in figure 1(a) also shows that the transversal size of positrons gradually decreases.Additionally, the velocity distribution of the positrons at t = 0 and t = 150T 0 are also presented in figures 1(b) and (c).It can be seen that the isotropic hot positrons are turned into collimated positron bunches after they are trapped by the laser fields.
In our scheme, the fields capturing the pre-generated positrons originates from the left-hand circularly-polarized LG laser pulse.With the mode (ℓ, p), the transverse electric field components of the LG laser pulse can be written as where ) 1/2 are the radial position and the laser focal spot radius, respectively, with σ 0 = 5λ 0 being the beam waist radius, x R = π σ 2 0 /λ 0 being the Rayleigh length, and x the longitudinal coordinate relative to the laser focus plane.L ℓ p represents the generalized Laguerre polynomial and g(x − ct) = cos 2 [π (x − ct) / (2cτ )] denotes the temporal profile with c the speed of light in vacuum and τ = 4T 0 .E L0 = a 0 m e0 cω/q e is the peak amplitude of the laser electric field, with a 0 = 30 being the laser dimensionless parameter.The phase is defined by ψ = ωt − kx − kr 2 /(2R c ) + (ℓ + 2p + 1) arctan(x/x R ) + ℓφ with ω = 2π c/λ 0 the laser angular frequency, k = 2π /λ 0 the laser wave number, and the curvature radius of the wave-front.In our scheme, a LG 1 0 mode laser pulse is employed, whose electric field is characterized by the cylindrically-symmetric radial and azimuthal components.In order to exhibit the unique field structure, the field components are rewritten in the cylindrical coordinate system using E r = E y cos φ + E z sin φ and E φ = −E y sin φ + E z cos φ.Thus we get where also be derived and simplified as follows: The detailed derivation is provided in the supplementary materials.One can see that all of the electromagnetic field components of the LG laser pulse are circularly-symmetric and independent of the azimuthal angle φ.In the cylindrical coordinate system, these field components are only determined by the longitudinal and radial coordinates, i.e. x and r.The positron dynamics will be significantly affected by the above unique field structure.
According to equation ( 1), the transverse electric field E ⊥ is proportional to r exp(−r 2 /σ 2 ), and peaks at the critical position r crit = σ 0 / √ 2 ≈ 3.5λ 0 along the radial direction.In the region of r > r crit , with the increase of the radial coordinate r, E ⊥ gradually decreases.Thus the transverse ponderomotive force is in the radial outwards direction.Positrons will spread out under the action of the transverse pondermotive force and leave the laser field quickly.When r < r crit , the transverse ponderomotive force is in the inward radial direction.The positron beam will be effectively trapped near the optics axis and collimated by the transverse ponderomotive force.In order to be stably accelerated, positrons should thus be trapped in the capture region r < r crit .

Collimation, compression and acceleration of positrons
Figures 2(a)-(c) illustrate the evolution of the positron beam density at t = 5T 0 , 50T 0 and 150T 0 .It is shown that positrons are compressed in the longitudinal direction and form a dense positron bunch train.Finally, the thicknesses of the bunches at 150T 0 are 0.10λ 0 , 0.15λ 0 , 0.14λ 0 and 0.2λ 0 (from right to the left), corresponding to 0.34 fs, 0.50 fs, 0.46 fs and 0.66 fs, respectively.At the same time, it can be seen from figures 2(b) and (c) that the positron beam is confined to a small transverse size with the root mean square (RMS) of 3.3λ 0 at t = 150T 0 , which is just in the capture region of r < r crit .In addition, the positron density is also greatly increased, with a maximum density of about 70 times of the initial density at t = 50T 0 .Figure 2(d) illustrates that the positron energy increases significantly as time goes and the maximum energy at t = 150T 0 is up to 450 MeV, which is two orders of magnitude higher than the initial positron energy.It is  noted that the energy spectra here include all positrons within the simulated box.Our simulations also show that each bunch is quasi-monoenergetic, which is shown in the supplementary materials.
According to equations ( 1) and ( 4), the transverse electric field E ⊥ ∝ r exp(−r 2 /σ 2 ), while the longitudinal electric field E x ∝ (r 2 /σ 2 − 1) exp(−r 2 /σ 2 ).Since E ⊥ ≈ 0 and E x is maximal near the optical axis, the positron acceleration process is dominated by the longitudinal electric field E x .As r gradually increases, E ⊥ increases, but E x decreases.The role of E ⊥ in the positron acceleration cannot be ignored.It is important to figure out whether the longitudinal or the transverse electric field is dominant in the acceleration process for the captured positrons.Figure 2(e) shows the distribution of the captured positrons within r < σ/ √ 2 in (η x , η ⊥ ) at t = 100T 0 , where η x (t) = −q 0 ´t 0 v x E x dt/ ( m e c 2 ) represents the energy gain from longitudinal electric fields and η ⊥ denotes that from the transverse electric fields.It can be seen that the energy gain from the transverse electric fields is small for most captured positrons.About 75% of the tracked positrons are located in the region (−50 < η ⊥ < 50, −100 < η x < 450), which indicates that E x is dominant in the acceleration process for most of the captured positrons.Therefore, when studying the capture mechanism of positrons, we can mainly consider the contribution of the E x .By integrating E x over x, the maximum energy that the positron beam can reach can be obtained [31] where x 0 is the position at which the positron begins to be phase-locked and accelerated by E x , with g 0 being the laser temporal profile at x 0 , ψ ′ 0 and ψ ′ x being the transformed phase term at x 0 and x. Figure 3(a) presents the influence of initial radial coordinate r 0 on positron capture according to the 3D PIC simulation results.It is found that the positrons initially located in the region r 0 < r crit will be captured with remarkably high probabilities f norm ≥ 0.85.It is noted that some positrons initially outside the region can also be captured since they can enter the capture region if their inward radial momentums are large sufficiently.Outside the capture region, the probability density f norm quickly decreases and equals zero at r 0 ∼ 13λ 0 , as is shown in figure 3(a).However, the positron beams will be effectively collimated once they are captured by the laser fields.We can see from figure 3(b) that the divergence angle decreases sharply as time goes.The peak divergence angle and its FWHM are about 1 • and 3 • , respectively, at t = 150T 0 .Furthermore, since the laser fields become weak enough outside the beam waist radius σ 0 , only the positrons initially located in the focal spot radius are considered when calculating the capture efficiency.
Table 1 illustrates the capture efficiency of positrons with different laser dimensionless parameter a 0 .Here, the capture efficiency is defined as the percentage of captured positrons located within r (t) < r crit to the number of positrons initially located within the laser focal spot (r 0 < σ).For the laser with a 0 = 10, although the capture efficiency is initially up to ∼35%, it decreases rapidly over time, only ∼17% at t = 50T 0 .When the laser intensity is increased to a 0 = 30, approximately 40% of positrons are initially captured and the capture efficiency can be maintained at over 25% when t = 150T 0 .When the laser intensity is further increased to a 0 = 50, the initial capture efficiency is comparable to that of a 0 = 30.However, the capture efficiency can be maintained at 32% when t = 150T 0 .This suggests that more than 30% of hot positrons are captured initially in the three cases.As the laser intensity increases, positrons are less likely to escape from the capture field.

Capture mechanism of positrons
In order to investigate the relationship between the positron capture and their initial beam divergence angle θ 0 , the positron trajectories at initial divergence angles of 0 • , 45 • and 90 • are presented in figure 4. It can be seen that the positrons in all cases can be effectively captured.Even if the initial divergence angle is θ 0 = 90 • , i.e. the initial momentum of positrons is perpendicular to the optics axis, these positrons can also be well captured and efficiently accelerated by the left-hand circularly-polarized LG laser pulse.Furthermore, the trajectories of positrons with the same divergence are circularly-symmetric, since the electromagnetic fields of the laser pulse are circularly-symmetric.Figures 4(d)-(f) show the evolutions of the average final radial position r f , divergence angle θ f , and energy (represented by the Lorentz factor γ f here) of positrons at t = 150T 0 over initial divergence angles θ 0 .It is shown that all the three parameters vary little with θ 0 , indicating that our novel capture mechanism for collimation, compression and acceleration of positrons is efficient for all the initial divergence angles.
In order to figure out the capture mechanisms of isotropic hot positrons, it is essential to discuss the radial motion equation of positrons.In the cylindrical coordinate, the motion equation can be written as , where m 0 is the positron rest mass and q 0 is the elementary charge, with v φ and v x being the azimuthal and longitudinal velocity.We can see three radial field components on the right side of the equation.In order to analyze which components determine the radial motion of positrons, we first compare the amplitudes of the three components.Figure 5(a) shows the evolution of the three components experienced by a typical positron in the single particle simulations.It is shown that E r and −v x B φ are comparable in magnitude but in opposite directions.E r will be partly canceled out by v x B φ .Another radial component v φ B x is much smaller than the sum of these two components and thus can be ignored.We can also obtain the same conclusion according to theoretical analysis.From equations ( 2)-( 7), one sees that Thus we can get −v x B φ ≈ −β x E r .By substituting it into the radial motion equation, we get It can be seen from equations ( 2) and ( 5) that the maximum value of cB x is about an order of magnitude smaller than that of E r .Since v φ is relatively small for most cases, i.e. v φ < 0.1c, v φ B x can be two orders of magnitude smaller than E r , so it can be ignored, as shown in figure 5(a).Furthermore, it is easy to see that the amplitude of −β x E r is always smaller than E r , although positrons can be accelerated to the relativistic velocities.Thus the net field can be written as (1 − β x ) E r , which indicates that both the direction and magnitude of net radial force mainly depend on the radial electric field E r .The positron motion in the radial direction is just like the damping vibration.The radial electric field force q 0 E r and magnetic field force q 0 v x B φ act as restoring force and damping force, respectively.It is noted that the total Lorentz force does not do work here.However, its transverse component acts as the damping force and does negative work.The radial momentum p r and radial coordinate r will decrease.Furthermore, the duration of the process with outward net radial force is much less than that with inward radial force, which also arises a successive decline of the amplitude of p r and r.
When the positrons with large transverse momentum just enter the laser fields, they cannot be accelerated adequately along the x-axis at the beginning since the laser fields at the rising edge are weak.These positrons will slide to areas with stronger laser fields along the envelope rising edge.If positrons first slip into a deceleration zone (DZ, where E x < 0), they will be decelerated and quickly enter the next acceleration zone (AZ, where E x > 0).If the positrons first enter the AZ, they will also be accelerated.If the acceleration fields are not strong adequately, they will also slip into the next DZ.In this way, these positrons will be accelerated and decelerated along the x-axis again and again until the dephasing time is long enough.For example, it is shown in figures 5(b) and (c) that the positron quickly slides from x − ct = 8 to −1.5 within 10T 0 with a small longitudinal momentum of p x ≈ 0. Meanwhile, these positrons will periodically experience outward and inward radial force when they are accelerated.
Figure 5(d) shows the distributions of radial and longitudinal electric fields of the left-hand circularly-polarized LG laser pulse.It is shown that the phase of E r shifts by π/2 compared with that of E x .In the first half (from right to left) of each AZ, E r > 0 and positrons are subjected to outward net radial force.In the second half of each AZ, E r < 0 and the net radial force is inward.Positrons will undergo half radial constraint and half radial diffuse during each AZ.Especially, when the positrons are in the second half of the AZ, they will have much higher longitudinal velocities than in the first half, since they have been accelerated in half of the AZ.As a result, the positrons slide more slowly in the second half of each AZ, resulting in a longer duration for which they are subjected to inward radial force.By the same token, the duration of radial constraint is also longer for each DZ.For example, in figure 5(a), the net radial force keeps inward for more than 90T 0 , which is much longer than the duration of less than 10T 0 with the outward radial force.Correspondingly, in figure 5(b), the radial momentum decreases from ∼33T 0 to 125T 0 .At last, the positrons are confined in the capture region with sufficiently small radial coordinate and momentum, which is the reason why the positron beam in figures 2 and 3 is characterized with a small transverse size and divergence angle.

Transfer of the OAM from laser to positrons
As we all know, the LG laser pulse carries orbital-angular-momentum (OAM) and may transfer it to charged particles.In our scheme, the initial random distribution of positron transverse momentum is changed to regular distribution after positrons are captured.As shown in figure 6(a), almost all positrons rotate counterclockwise, indicating that positrons have positive OAM.To investigate the transfer of OAM between laser and positrons, a typical positron is selected.The projection of trajectory for the typical positron in the yz plane is shown in figure 6(b).It is found that the positron trajectory can be divided into four sections, i.e. a linear section, two counterclockwise sections and a transition section.Before the interaction between the laser and the positron, the positron keeps a linear trajectory.In each counterclockwise section, the positron rotates counterclockwise, which means it possesses positive OAM.In the transition section, the direction of the transverse velocity changes.Figure 6(c) shows the evolution of the corresponding OAM L x and the relativistic factor γ. Interestingly, L x and γ show the same trend.The zones of γ ≈ 0 with L x < 0 corresponds to the transition sections in figure 6(a).Here, zones with large enough γ and L x > 0 correspond to the counterclockwise sections in figure 6(b).To investigate the OAM variation of positrons, the change rate equation of the OAM is given, namely The right side of equation ( 12) can be separated into the torque of the electric and magnetic field forces along the x-axis, M E,x = q 0 rE φ and M B,x = −q 0 r(v x B r − v r B x ).Substituting equation ( 9) into equation ( 12), M B,x is simplified to −q 0 r (β x E φ + β r cB x ).Since β x ≈ 1 and β r ≈ 0 after positrons are effectively captured, we can obtain M B,x ≈ q 0 rβ x E φ .Figure 6(d) shows the three components of the torque along the x-axis M x .It is also found that −q 0 rv r B x ≈ 0. The net torque along the x-axis is Obviously, both the direction and magnitude of the net torque M n,x mainly depend on the azimuthal electric field E φ .Figure 6(d) also shows that the magnitude of q 0 rE φ is comparable with that of q 0 rv x B r but they are in opposite directions.The net torque M n,x shows the same trend with M E,x , which is consistent with the above analysis.Furthermore, according to equations ( 3) and ( 4), the evolution of E φ and E x are synchronous.The direction of the net torque M n,x is also synchronous with E x .Therefore, we can see from figures 4(a)-(c) that the captured positrons rotate counterclockwise when they are accelerated.

Influence of laser parameters on the quality of the obtained positron beams
In order to evaluate the influence of laser parameters on the quality of the positron beams, additional 3D PIC simulations have been performed.The influence of the carrier envelope phase (CEP), pulse duration τ and the laser dimensionless parameter a 0 on the cut-off energy E c , the peak divergence angle θ p , and the maximum density n m of the positron beam have been investigated and summarized in figure 7. Here, E c , θ p and n m are measured at t = 150T 0 .In each case, we varied one parameter while keeping the others constant.Figure 7(a) demonstrates that the cut-off energy E c , peak divergence angle θ p , and maximum density n m of the positron beams are not sensitive to the variation of CEP, confirming the robustness of the proposed scheme.Figure 7(b) illustrated the effect of laser pulse duration τ on E c , θ p , and n m of the positron beams.It is shown that θ p changes little with the increases of τ , while E c and n m gradually decrease with the increase of τ .This is attributed to the flattening of the laser rising edge due to the increase of τ , which leads to a decrease of E x and E r experienced by the positrons.We can see from figure 7(c) that θ p varies little with the increases of a 0 , while E c and n m increase significantly.This results from the stronger longitudinal electric field E x and radial electric field E r generated by the rise of a 0 .As E r increases, more positrons can be collimated and captured, thus enhancing the maximum density n m .Nevertheless, the final transverse momentum of positrons also increase when the radial field E r increase, thus preventing θ p from decreasing over a 0 .It is noted that E c increases linearly with a 0 .It is found from equation ( 8) that ε m (x) is proportional to a 0 , which is consistent with the linear increase in figure 7(c).In conclusion, the influence of CEP on the quality of positron beams is negligible.Moreover, in order to obtain positron beams with higher energy and density, laser pulses with shorter duration and higher intensity are required.

Conclusion
In summary, a laser-driven novel mechanism of capture, collimation, compression and acceleration for laser-driven positrons by a left-hand circularly-polarized LG laser pulse is proposed and investigated through 3D PIC simulations.It is shown that the pre-generated hot positrons with isotropic angular distribution can be converted into high-quality subfemtosecond positron bunches with an average pulse duration of 0.5 fs and a energy of 450 MeV (at t = 150T 0 ).The peak divergence angle and the FWHM of the divergence angle are only 1 • and 3 • , respectively.It is shown that positrons can be effectively captured and compressed to high density, whatever the initial divergence angle or the CEP is.The feasibility of this capture mechanism is demonstrated by a damping vibration model.In the whole process, the positron motion in the radial direction is just like the damping vibration.The q 0 E r and magnetic field force q 0 v x B φ act as a restoring force and damping force, respectively.The radial momentum p r and radial coordinate r periodically decrease.Furthermore, the captured positrons will rotate counterclockwise when accelerated since the net torque and the acceleration force are synchronous.At last, high-energy collimated positron bunches with large OAM and short pulse duration can be obtained via our scheme.

Figure 1 .
Figure 1.(a) Schematic of novel capture mechanisms for collimation, compression and acceleration of laser-driven positrons.When a vortex laser pulse irradiates a pre-generated positron beam, a great deal of positrons can be captured and comove with the laser pulse.The positrons are well collimated and captured near the optical axis, as evidenced by the colored lines.Here each line represents the trajectory of a tracked positron and three pseudo-color slices show the positron density distribution in the yz plane at t = 50T0, 100T0, and 150T0.(b) The velocity distribution of positrons located at the region of 0 < x < 10 µm, −10 µm < y < 10 µm, −10 µm < z < 10 µm at t = 0. (c) The velocity distribution of these positrons at t = 150T0.

Figure 2 .
Figure 2. PIC simulation results of a pre-generated positron beam captured and accelerated by a left-hand circularly-polarized LG laser pulse.The density distribution of positrons at t = 5T0 (a), 50T0 (b) and 150T0 (c), respectively.(d) The corresponding evolution of energy spectrum of the positron beam.(e) The distribution of tracked positrons in (ηx, η ⊥ ) space at t = 100T0.

Figure 4 .
Figure 4. Trajectories of positrons at the initial divergence angles of (a) 0 • , (b) 45 • and (c) 90 • , respectively, where the initial divergence angle is defined as θ0 = arccos(px0/p0), i.e. the angle between the initial momentum and the x-axis.The evolution of the average final radial position (d), divergence angle (e) and γ factor (f) at t = 150T0 over the initial divergence angle.We divide the range of θ0 ∈ (−90 • , 90 • ) into ten equal parts.The triangle data points in (d)-(f) are obtained by averaging the θ f , r f or γ f values of the positrons that fall in each part.The curves shown in (d)-(f) are obtained via a quartic polynomial fitting method.

Figure 5 .
Figure 5.The collimation of positrons in the LG laser fields.(a) The radial field components (Er, vφBx and −vxBφ, blue curves) and the net radial field (brown curve) experienced by a typical positron with θ0 = 90 • .(b) The evolution of the radial (blue curve) and longitudinal (red curve) momentum of the positron.(c) The evolution of the radial coordinate r (red curve) and comoving coordinate x − ct (blue curve) of the positron.(d) The relative distributions of the radial and longitudinal electric fields along the comoving coordinate x − ct.The pink regions indicate the acceleration zone.

Figure 6 .
Figure 6.(a) The distribution of positron transverse momentum at t = 50T0.(b) The projection of a positron trajectory on the yz plane.(c) The evolution of the orbital-angular-momentum Lx and γ over time.(d) The evolution of the three components of the torque along the x-axis Mx and the net longitudinal torque Mn,x over time.

Figure 7 .
Figure 7. Parametric effects of the laser parameters on the positron beam parameters.That is, the influence of the carrier envelope phase (a), laser pulse duration τ (b), laser dimensionless parameter a0 (c) on the cut-off energy Ec, the peak divergence angle θp and the maximum density nm of the positron beam.The blue squares, red dots and black triangles indicate θp, Ec and nm, respectively.The curves here are generated via cubic spline interpolation.