Generation of GeV positron and {\gamma}-photon beams with controllable angular momentum by intense lasers

Although several laser-plasma-based methods have been proposed for generating energetic electrons, positrons and {\gamma}-photons, manipulation of their microstructures is still challenging, and their angular momentum control has not yet been achieved. Here, we present and numerically demonstrate an all-optical scheme to generate bright GeV {\gamma}-photon and positron beams with controllable angular momentum by use of two counter-propagating circularly-polarized lasers in a near-critical-density plasma. The plasma acts as a"switching medium", where the trapped electrons first obtain angular momentum from the drive laser pulse and then transfer it to the {\gamma}-photons via nonlinear Compton scattering. Further through the multiphoton Breit-Wheeler process, dense energetic positron beams are efficiently generated, whose angular momentum can be well controlled by laser-plasma interactions. This opens up a promising and feasible way to produce ultra-bright GeV {\gamma}-photons and positron beams with desirable angular momentum for a wide range of scientific research and applications.


INTRODUCTION
/ 21 yet been reported so far on how to obtain high-energy dense positron and γ-photon beams with a highly controllable angular momentum at currently affordable laser intensities.
In this paper, by use of ultra-intense CP lasers interacting with a near-critical-density (NCD) plasma, we show that ultra-bright GeV γ-photon and dense positron beams with controllable angular momentum can be efficiently produced via nonlinear Compton scattering (NCS) 35,36 and the multiphoton BW process.
It involves the effective transfer of the SAM of laser photons to the BAM of high-energy γ-photons and dense positrons, and offers a promising approach to manipulate such ultra-relativistic particle beams with special structure. This γ-photon and positron beams would provide a new degree of freedom to enhance the physics capability for applications, such as discovering new particles and unraveling the underlying physics via the collision of + − /γγ. This scheme may provide possibilities for interdisciplinary studies 1,2,13 , such as revealing the situations of rotating energetic systems, exploring fundamental QED processes, modelling astrophysical phenomena, and so on.

RESULTS AND DISCUSSION
Overview of the scheme Figure 1a illustrates schematically our scheme and some key features of produced γ-photons and positron beams obtained based upon full three-dimensional particle-in-cell (3D-PIC) simulations with QED and collective plasma effects incorporated. In the first stage, electrons are accelerated by the drive laser and emit abundant γ-photons via the NCS. This results in strong radiation reaction (RR) forces [37][38][39][40][41][42] , which act on the electrons so that a large number of electrons are trapped in the laser fields under the combined effect of the laser ponderomotive force and self-generated electromagnetic field. Dense helical beams of the trapped electrons and γ-photons are formed synchronously, as shown in Fig. 1b. As the trapped electrons collide with the opposite-propagating scattering laser in the second stage, the γ-photon emission is boosted significantly in number and energy. Finally, such bright γ-photons collide with the scattering laser fields to trigger the nonlinear BW process in the third stage. A plenty of GeV positrons with high density and controllable angular momentum are produced (Figs. 1c and 1d).
When the trapped electrons collide head-on with the opposite-propagating scattering laser pulse, the electrons undergo a strong longitudinal ponderomotive force and are reversely pushed away by such scattering laser, inducing a strong longitudinal positive current > 0. Finally, the created pairs can be effectively separated from the background plasmas, so that quasi-neutral pair plasma is generated, as shown in Fig. 2. Since the ratio / ≈ 1.8 here, it is likely to induce collective effects of the pair plasma 9, 10 , where and = /√8 2 + / ̅ + are respectively the transverse size and the skin depth of the pair plasma, ̅ is the average Lorentz factor of the pair, is the elementary charge, + and + are the positron density and mass. Such dense GeV pair flows would offer new possibilities for future experimental study of the pair plasma physics in a straightforward and efficient all-optical way. This scheme could be thus used as a test bed for pair plasma physics and nonlinear QED effects, and may serve as compact efficient GeV positron and γ-ray sources for diverse applications. (1) A right-handed CP drive laser (DL) pulse incident from the left irradiates a NCD plasma slab to generate and trap a helical electron beam; (2) By colliding of the electron beam with a scattering laser (SL) pulse, dense energetic γ-photons are emitted via NCS; (3) The γ-photons further collide with the SL fields, which triggers the multiphoton BW process to produce numerous electron-positron pairs. The red-and blue-arrows indicate respectively the propagating directions of the DL and SL pulses. The black-dashed lines mark the dividing line between the step (1) and steps (2,3).  to 50 0 with an initial electron density of 0 = 1.5 ( = 0 2 /4π 2 , where is the electron mass, and 0 is the laser angular frequency) is employed, which can be obtained from foam, gas or cluster jets 47,48 . Such plasma density is transparent to the incident laser pulse due to the relativistic transparency effect ,~0 ≫ 0 , so that the drive laser pulse can propagate and accelerate electrons over a longer distance in the plasma. The parameters of lasers and plasmas are tunable in simulations.

The QED emission model
The stochastic emission model is employed and implemented in the EPOCH code using a probabilistic Monte Carlo algorithm 49,50 . The QED emission rates are determined by the Lorentz-invariant parameter 51 : On the contrary, if the particles counter-propagate with the pulse, one can obtain ~2 | ⊥ |/ and ~(ℏ / 2 )| ⊥ |/ , where ⊥ is the electric field perpendicular to the motion direction of the particles. The energy of most emitted photons can be predicted as 15 ℏ ≈ 0.44 2 . The parameter is thus rewritten as ~0.22 2 at the collision stage, implying that ∝ 2 | ⊥ | 2 / 2 increases significantly with the laser intensity and the positron production becomes more efficient accordingly.
The radiating electrons experience a strong discontinuous radiation recoil (called the quantum-corrected RR force) due to the stochastic photon emission in the QED regime 49,50 . The stochastic nature of such radiation allows electrons to attain higher energies and emit higher energy photons than those undergoing a continuous recoil in the classical regime. The resulting photon energies are comparable to the electron energies, as illustrated in Figs. 3a and 3d. is a function accounting for the correction in the radiation power excited by QED effects 51 . The transverse motion of the electron can be thus described as where = 1 − / ℎ and = 2 2 g( )/3 . For a highly relativistic electron, one can reasonably assume that ̇≈ 0, ̇≈ 0, and ̇≈ 0, because they are slowly-varying compared with the fast-varying term of ̇ and ̇. Under these assumptions, one can obtain the time derivative of the equations of electron motion as follow Here = = − , 0 = / 0 , and = 0 is the laser frequency in the moving frame of the electron. The resulting self-generated annular magnetic field is approximately proportional to the distance from the laser axis, so that can be assumed as a constant in this case. The solutions of electron transverse momentum with time can be thus expressed as , ( ) = ⊥ cos ( + 0 ), where 9 / 21 0 is the initial phase and ⊥ is the transverse momentum amplitude. By substituting , ( ) into Eqs. (3) and (4) Figure 4b shows the self-generated annular magnetic field ~2 . This plays a significant role in electron trapping by the centripetal pinching force × ( ) and in the γ-photon emission by the quantum radiation | × |/ →~(1) 53, 54 . Thus, the electron trapping is attributed to the RR effect together with the self-generated magnetic field around the channel dug by the CP laser in the NCD plasma. Here the NCD plasma is employed for providing more background electrons being trapped and accelerated, and for forming an intense self-generated magnetic field, which is very beneficial for the high-energy γ-photon emission. When an ultra-intense Gaussian laser pulse propagates in the NCD plasma 53, 55 , electrons can be accelerated directly by the laser fields, which induces intense electric currents and forms plasma lens. This enhances the laser intensity greatly (see Figs. 4c and 4d) due to the strong relativistic self-focusing and self-compression of the pulse in plasmas, the resulting laser amplitude is significantly boosted with the dimensionless parameter ~250. In the stochastic photon emission, electrons can be accelerated directly by the laser to a high energy without radiation loss or radiation recoil before they radiate high-energy photons. The maximum energy of electrons is thus approximately proportional to the focused laser amplitude 2 , which energy can be as high as 10 GeV. For most energetic electrons, their energies are significantly decreased due to the high-energy γ-photon emission when the RR effect comes into play.
Finally, a substantial energy of the radiating electrons is converted into high-energy γ-photons, providing an efficient and bright GeV γ-ray source.
For effective γ-photon emission, here we only consider the trapped electrons with energy >100MeV from the region within the off-axis radius < 4 , whose total number can be estimated as ~2 .
Here ~( 0 / )√ 0 / is the electron beam radius, ~0 is the beam length (matching with the laser pulse duration), 0 is the formation time of the electron beam dependent on the laser-plasma interaction. Thus the total electron number is ~0 0 2

Efficient generation and control of high angular momentum of electron, γ-photon and positron beams
In our scenario, the NCS at the collision stage of energetic electrons with the scattering laser pulse dominates the radiation emission over that at the first stage, resulting in greatly boosted γ-photon emission, as seen in Fig. 5a. In the regime of quantum-dominated radiation production, the total radiation power of the trapped electrons can be estimated by This suggests that the NCS in NCD plasma provides an efficient way to generate GeV γ-rays in the multi-PW level with extremely high intensity of ~10 23 W cm −2 . In addition to the extreme high peak power of γ-rays, the twist formation of the γ-photon beam is particularly interesting, which is found to be strongly dependent upon the polarization of the laser pulse or the SAM of laser photons. For a drive laser pulse propagating along the x direction, generally its electric field can be described as where ~0 0 2 0 / is the number of the trapped electrons before entering the collision stage. This implies that the electron angular momentum can be optically controlled by tuning the laser parameters, e.g., Although the γ-photons emitted at the first stage have a large number and high energies, these γ-photons almost co-move with the drive laser pulse so that the key quantum parameter determining the positron generation becomes much smaller, i.e., ≲ (0.1). This results in very limited positron production. At the subsequent stage when the γ-photons collide with the scattering laser pulse, is greatly increased (~4, as seen in Fig. 3f), leading to highly efficient positron production via the multiphoton BW process. Finally, a high-yield (2.5 × 10 10 ) dense (~) GeV positron beam with the same helicity of right-handedness as the γ-photon beam is produced, as shown in Fig. 1c.
In our configuration, the drive laser pulse acts as micro-motors to seed angular momentum in laser-NCD plasma interactions, while the scattering laser pulse triggers the multiphoton BW process and plays the role of a torque regulator. The positron angular momentum is mainly controlled by tuning the polarization of the drive laser pulse. To illustrate this, we consider two drive laser pulses with different polarization: δ = 0 for LP; and δ = √2/2 for EP, while the scattering laser is always left-handed CP.
According to Eq. (6), the electron angular momentum is determined by δ, implying that it can reach the maximum when δ = 1 , while → 0 for δ = 0 and → √3 /2 for δ = √2/2 . The simulation results show a good agreement with the theoretical predictions: ≈ 0 by a LP laser, and ≈ 0.82 by the given EP laser. Meanwhile, the angular momentum of the γ-photons changes similarly, because their angular momentum originates from the parent electrons, as plotted in Fig. 6b. We also see that the positrons can get less angular momenta from the scattering laser pulse (≲ 0.17 + , as plotted in Fig. 6c) when the LP drive laser is used. This is reasonable because the parent electrons and γ-photons obtain almost no angular momentum from the LP drive laser pulse. This offers an efficient and straightforward approach to explore the angular momentum transfer between the laser and particles, and to optically control the angular momentum and helicity of such energetic beams for future studies.
One can also tune the angular momentum of positrons by simply changing the chirality of the scattering laser pulse. This can be attributed to the torsional effect of the CP laser (like a wrench). The electric fields of both drive laser and scattering laser pulses rotate in the same azimuthal direction when using a left-handed CP scattering laser pulse, whereas their electric fields rotate in the opposite direction when using a right-handed CP scattering laser pulse, so that they can tune the rotation of the positron beam in the same direction or in the opposite direction, respectively. As a result, the positron angular momentum tuned by the left-handed CP scattering laser pulse is higher than that tuned by the right-handed CP scattering laser pulse, as seen in Fig. 6a.

Robustness of the regime and discussion
Further simulations have been performed to explore the scaling of the angular momentum of energetic particle beams as a function of the laser amplitude, as shown in Fig. 7a. Here, we keep the parameter 0 / 0 = constant for ultra-relativistic laser-plasma interactions 56 . The efficiency of positron production increases with the laser intensity, which is valid for all considered laser intensities. In our configuration, the key quantum parameter ~(1), so that the multiphoton BW process can be efficiently triggered to create copious numbers of high-energy electron-positron pairs. However, is greatly suppressed at a much lower laser intensity, e.g, ≪ 1 at 0 < 100, which leads to very limited positron creation. This indicates that there exsits a threshold laser amplitude (i.e., ℎ~1 20 in our scenario), for highly-efficient prolific positrons production. For lasers with a fixed polarization, we all obtain ∝ 0 2 from Eq. (6). The ratio scaling of the electron angular momentum is then expressed as = / ,0~( 0 / ℎ ) 2 for different laser intensities.
This is in accordance with the simulation results, as seen in Fig. 7a. The instantaneous radiation power emitted by the electron scales as 2 g( ) and the photon angular momentum can be then approximately written as ∝ 2 g( ) ∝ 0 10/3 . The positron angular momentum originates mainly from the γ-photons so that its scaling shows a similar trend. Finally, we obtain that ~( 0 / ℎ ) 11/3 and +~( 0 / ℎ ) 10/3 from the PIC simulations, which is reasonably close to the analytical estimation above.
Here, the total SAM of the CP drive laser pulse approximates = δℏ , where = /ℏ 0 ∝ 0 2 is the total laser photon number. Thus the conversion efficiency from the laser SAM to the angular momentum of electrons, γ-photons, and positrons scales: →~0 0 , →~0 5/3 , and → +~0 4/3 , respectively. The scaling is well validated by the simulation results as shown in Fig. 7b. Taking the forthcoming lasers like ELI for example, we estimate the positron angular momentum up to 6.5 × 10 −15 kg • 2 • −1 with a high angular momentum conversion efficiency of ~0.15%. Since the γ-photons are emitted by electrons in helical motion and via the NCS of a CP pulse, the resulting high angular momentum γ-rays may carry away well-defined orbital angular momentum along the propagation direction, which has been verified theoretically in recent several studies 27,28 . By manipulating the electron motion in plasmas, it is a potential way for generating γ-ray beams with coherent angular momentum. Such γ-ray beams may find potential applications, such as providing additional effects in the interaction with nucleus, controlling nuclear processes, probing the structure of particles, etc.

CONCLUSION
In conclusion, we have proposed and numerically demonstrated an efficient scheme to produce high angular momentum γ-photon and positron beams in NCD plasma irradiated by two counter-propagating high power lasers with circular polarization under currently affordable laser intensity ~10 22 W cm −2 . It is shown that ultra-intense multi-PW γ-rays and dense (10 21 cm −3 ) GeV positrons with a high charge number of ~4 nano-Coulombs can be efficiently achieved. In addition, the angular momentum and helicity of such energetic beams are well controlled by the drive laser pulse and are tunable by the scattering laser pulse.
With the upcoming laser facilities like ELI, this all-optical scheme not only provides a promising and practical avenue to generate ultra-bright PW γ-rays and dense positron beams with GeV energies and high angular mometum for various applications, but also enables future experimental tests of nonlinear QED theory in a new domain.