Brilliant petawatt gamma-ray pulse generation in quantum electrodynamic laser-plasma interaction

We show a new resonance acceleration scheme for generating ultradense relativistic electron bunches in helical motions and hence emitting brilliant vortical γ-ray pulses in the quantum electrodynamic (QED) regime of circularly-polarized (CP) laser-plasma interactions. Here the combined effects of the radiation reaction recoil force and the self-generated magnetic fields result in not only trapping of a great amount of electrons in laser-produced plasma channel, but also significant broadening of the resonance bandwidth between laser frequency and that of electron betatron oscillation in the channel, which eventually leads to formation of the ultradense electron bunch under resonant helical motion in CP laser fields. Three-dimensional PIC simulations show that a brilliant γ-ray pulse with unprecedented power of 6.7 PW and peak brightness of 1025 photons/s/mm2/mrad2/0.1% BW (at 15 MeV) is emitted at laser intensity of 1.9 × 1023 W/cm2.

100 s MeV can be generated by irradiating a solid target with an ultraintense laser [26][27][28] . However, for laser interaction with steep solid density targets, where no preplasmas exist, the γ-ray emission occurs only in the small skin-depth region 2,26-28 , therefore, the conversion efficiency from laser to γ-rays is still low, and the peak brightness of γ-rays is also limited. Recently, a self-matching resonance acceleration scheme 32,33 in near-critical plasmas by circularly polarized laser pulses has been explored, which can generate much denser relativistic electron beams than the case of direct laser acceleration with linearly polarized lasers 34,35 . However, the laser intensity used there is comparatively low in the non-QED regime, electron resonance acceleration is dominantly governed by only the self-generated electromagnetic fields in the plasma, which limits both the energy and the density of the electron bunch for synchrotron radiation.
In this paper, by using a near-critical plasma interaction with ultraintense circularly polarized (CP) laser pulses, we report on a new resonance acceleration scheme in the QED regime for generating ultradense ultrarelativistic electron bunches in helical motions [see Fig. 1(a)] and therefore emitting brilliant vortical γ-ray pulses. In this QED scheme, on the one hand, because of the quantum radiation losses, the transverse phase space of electrons is confined 36,31 , and the electrons are easily trapped in the center of laser-produced plasma channel; on the other hand, due to the additional contribution of radiation reaction recoil force, the resonance bandwidth 37 between laser frequency (in the electron rest frame) and that of electron betatron oscillation under quasistatic electromagnetic fields in the channel is significantly broadened, that is, the resonance condition is much relaxed. Both of these effects result in formation of an ultradense electron bunch under resonant helical acceleration in CP laser fields, where both the particle number and energy are much larger than those under only direct laser acceleration (DLA) by linearly polarized lasers 29,31 . Furthermore, the synchrotron radiation efficiency is much enhanced by the resonant electrons' helical motion feature in the self-generated axial and azimuthal magnetic fields due to the use of CP lasers, comparing with that by linearly polarized lasers 29,31 , eventually leading to production of brilliant petawatt vortical γ-ray pulses. Three dimensional (3D) particle-in-cell (PIC) simulations show that brilliant γ-ray pulses with unprecedented peak brightness of 10 25 photons/s/mm/mrad 2 /0.1% BW at 15 MeV and power of 6.7 PW are produced at laser intensity of 1.9 × 10 23 W/cm 2 .

Theoretical Analysis
The properties of γ-ray radiation depend strongly on electron dynamics. Let' s start with the dynamics of a single electron interacting with the laser and self-generated electromagnetic fields in laser-produced plasma channel by taking into account of the QED effects. In the ultrarelativistic limit γ  1 e , the radiation reaction force can be approximately written as [38][39][40]  where F LL is the classical radiation reaction force in the Landau-Lifshitz form 38 . In order to take the quantum effect of radiation reaction force into account, we use a quantum-mechanically corrected factor G e 39,40 , which reduces the amount of electrons' unphysical energy loss due to the overestimation of the emitted photon energy in classical calculations. ε rad = 4πr e /3λ, r e = e 2 /m e c 2 is the electron radius. β = v/c, a S = eE S /m e ωc corresponds to the QED critical field E S ( α = E er / S e 2 ), and α = e c / 2  is the fine-structure constant. e, m e , v are electron charge, mass, and velocity, respectively, ω 0 and λ refer to laser frequency and wavelength, and c is light speed. The probability of γ-photon emission by an electron is characterized by the relativistic gauge-invariant parameter  longitudinally. Considering the quantum radiation reaction force Eq. (1), the electron's transverse motion in channel can be described as , as they are slowly-varying comparing with the fast-varying p y and p z . Further assuming κ δ Here Ω = . ω L = κω 0 refers to laser frequency in the electron rest frame, and a 0 = eE L /m e ω 0 c is the normalized laser amplitude. In Eqs (2) and (3), the third term Ω x is mainly distributed on the laser axis and can be neglected for the ultrarelativistic electrons in the electron bunch. Therefore, the betatron oscillation frequency can be estimated as ω For electrons under resonance acceleration in laser fields, one can assume , where P rad is the momentum amplitude and ϕ is its initial phase. Substituting p y,z into Eqs (2) and (3), one has From Eq. (4), the amplitude of electron transverse oscillation can be obtained as On the one hand, Eqs (4) and (5) show that P rad and R rad decrease when the radiation reaction factor β rad increases, that is, the transverse phase space of the electrons is confined by the radiation reaction force 36 . This helps trapping of a great amount of electrons in the plasma channel center. On the other hand, by taking dP rad /dω L = 0 from Eq. (4), one can get the resonance condition between laser frequency in the electron instantaneous rest frame and that of electron betatron oscillation ω r in the plasma channel as Here, one can treat Eq. (4) as a function of P rad (ω L ), and the resonance curves for different radiation reaction factors β rad are plotted in Fig. 1(b). It shows that the resonance bandwidth Δ ω, i.e., the full-width-at-half-maximum (FWHM) value of the resonance curve 37 , is significantly broadened when the radiation reaction factor β rad increases [See inset figure of Fig. 1(b)]. Results indicate that the resonance condition of the accelerated electrons is much relaxed. Both of these effects eventually result in formation of an ultradense electron bunch under resonant helical acceleration by laser, and hence emission of unprecedented brilliant vortical γ-ray pulses.

Simulation and Results
To verify our scheme, 3D PIC simulations are carried out using the QED-PIC code EPOCH 41 , which takes into account of the QED effects in the synchrotron radiation of γ-rays by using a Monte Carlo algorithm 42 . From Fig. 1(a), we clearly see that an ultradense helical electron bunch is formed in laser-produced plasma channel, which undergoes resonance acceleration by the laser pulses. For comparison, simulations with the QED calculation switched off are also carried out. Figure 2 plots electron density maps in plane z = 0 at different times for the cases with (upper row) and without (lower row) the QED effects taken into account. At early time t = 30T 0 [2(a) and 2(e)], both of the cases show similar characters that a number of electrons are firstly injected into the center of the plasma channel. However, at later time t = 60T 0 , they show completely different physics. For the case without the QED effects, most electrons in the channel do not satisfy the narrow resonance condition, and the focusing force provided by the self-generated electromagnetic fields is not strong enough to offset the laser radial ponderomotive force 31 , so that they are expelled from the plasma channel, as shown in Fig. 2(f). For the case with the QED effects, as predicted by our theory, the radiation reaction force provides not only "trapping" but also"resonant" effects on electrons in the plasma channel, where a great amount of electrons are trapped and undergo direct resonance acceleration by intense lasers, shown in Fig. 2(b). At t = 80T 0 , in the case with QED effects, the transverse phase space of electrons is adequately confined by the radiation reaction recoil force, shown in Fig. 2(d), compared with that in Fig. 2(h). We see from Fig. 2(c) that an ultradense relativistic electron bunch with density above 100n c is formed in the channel under helical resonant motion in CP laser fields. Such an ultradense helical electron bunch leads to generation of strong axial magnetic field B Sx up to 5.0 × 10 5 T and azimuthal B Sz up to 8.0 × 10 5 T [See Fig. 3(a)]. The axial magnetic field helps to trap the background electrons near the laser axis undergoing pre-acceleration to hit the resonance condition 32 . The azimuthal magnetic field in turn Scientific RepoRts | 7:45031 | DOI: 10.1038/srep45031 not only provides additional confined forces to help trapping and achieving resonance acceleration of electrons, but also significantly enhances the probability of γ-photon emission 29 . Figure 3(b) shows the typical electron motion trajectories under resonance acceleration. It can be seen that the electrons are injected from the front interaction surface and the wall of the plasma channel. As the role of quantum radiation losses increases, the transverse phase space of these electrons is confined 36 , and they are easily trapped in the plasma channel. Further with the aid of the radiation reaction force, as expected, a great amount of these electrons undergo resonance acceleration in CP laser fields, whose energies increase dramatically (see the color evolutions of the lines). For electrons undergoing resonance acceleration, their energies are gradually transferred from the transverse component into the longitudinal one by the v × B force, whose ⊥ p p / eventually decreases to a small value of 0.2, shown in Fig. 3(c).    Fig. 3(e) inset and 3(f), we conclude that the QED effects lead to great increase in the particle number and decrease in the divergence angle of high-energy electrons, in consistence with our theoretical expectations. The energy spectrum of electrons by using a LP laser with the same other parameters is shown by the green line in Fig. 3(f), which shows much lower cutoff energy and smaller number of high energy electrons, eventually leading to much weaker γ-ray emission.
When the ultradense electron bunch undergoes resonance acceleration in CP laser fields, high-energy γ photons can be synchronously emitted. Figure 4(a) plots the 3D isosurface distribution of the γ-ray photon energy density at t = 80T 0 . It shows that a brilliant, vortical γ-ray pulse with energy density above 5.0 × 10 3 n c m e c 2 , transverse size of 2 μm and duration of 40 fs is generated. The radiation power can increase to 18 J/T 0 (6.7 PW) and then decrease with the dissipation of the laser pulse [See the inset figure of Fig. 4(c)], more γ photons and higher energy conversion efficiency from laser to γ-ray can be obtained when the laser pulse is fully dissipated. At t = 100T 0 , the total number of γ-ray photons with energy above 2.0 MeV is about 3.08 × 10 14 with a 15.9 MeV mean energy, and the total energy of γ-ray photons is about 780 J, which corresponds to 22.91% from the laser energy, significantly higher than that in the case using LP laser (16.15%). The energy spectrum of the γ photons at 80T 0 is plotted in Fig. 4(c). The maximum photon energy exceeds 1.0 GeV, and the peak brightness of the γ-ray pulse at 15 MeV is 1.4 × 10 25 photons/s/mm 2 /mrad 2 /0.1% BW. At t = 100T 0 , it can arrive at 3.5 × 10 25 photons/s/ mm 2 /mrad 2 /0.1% BW. To the best of our knowledge, this is the γ-ray source with the highest peak brightness in tens-MeV regime ever reported in the literature. From Fig. 4(b), we can also see that the high-energy photons are highly collimated.

Discussion
The scaling properties of the emitted γ-rays by the proposed scheme have also been investigated. For a fixed self-similar parameter S = n e /a 0 n c = 1/30, which strongly determines the electron dynamics in near-critical plasmas as discussed in ref. 43, a series of simulations are carried out with different laser intensities, i.e., a 0 . As shown in Fig. 5(c), our scheme still works at lower a 0 = 150, though the density of the electron bunch drops, which leads to lower energy conversion efficiency of 8.0% from laser pulse to γ photons [ Fig. 5(a)]. When the laser intensity increases, the energy conversion efficiency from laser to electrons drops and that from laser to photons grows up to 27% and then becomes saturate, shown by the blue lines in Fig. 5(a). And due to the enhanced resonance acceleration under stronger radiation reaction recoil force and self-generated electromagnetic fields, both the number and mean energy of the emitted γ-photons increase as well with the laser intensity, shown in Fig. 5(b). Different from the previous theoretical and numerical results 43 , which is based on the betatron radiation properties in the non-QED regime with linearly polarized lasers (a 0 ≤ 80), here the scaling shows to be as linear as N ph ∝ a 0 and ∝ E a ph 0 respectively. To verify that our scheme still works for a more reasonable laser pulse, an additional simulation is performed. The laser pulse has a exact temporal profile of a = 250sin 2 (πt/22T 0 ) with a duration of 11T 0 (29.3 fs) and total energy of 266 J, which can be achieved, for example, with the ELI laser 24 under development and Vulcan 44 (planned updating) in the near future. The electron density map in plane z = 0 is plotted in Fig. 5(d). It can be clearly seen that an ultradense electron bunch is still formed undergoing stable resonance acceleration in the plasma channel and then brilliant γ-ray pulse is generated. As a result, 4.1 × 10 13 γ photons are emitted and the energy conversion efficiency from laser pulse to γ photons can reach as high as 33%. Therefore, this robust electron acceleration and γ-ray emission scheme still works if a more reasonable laser pulse is used.
In this paper, we have reported a novel electron resonance acceleration scheme in the QED regime of CP laser-plasma interactions, where the quantum radiation loss helps trapping of electrons and the radiation reaction recoil force significantly relaxes the resonance condition between electrons and lasers. A great amount of electrons gather around the center of the plasma channel and undergo resonance acceleration, forming an ultradense, vortical relativistic electron bunch. As a result, unprecedentedly brilliant petawatt γ-ray pulses can be obtained.

Methods
The 3D PIC simulations are carried out using the QED-PIC code EPOCH. In the simulations, 900 cells longitudinally along the x axis and 240 2 cells transversely along y and z axes constitute a 75 × 20 × 20λ 3 simulation box. A fully-ionized hydrogen plasma target with an uniform electron density of 1.7 × 10 22 cm −3 (10n c ) is located from x = 5 to 75 λ. Each cell of plasma is filled with 12 pseudoelectrons and 12 pseudoprotons. A CP laser pulse with peak intensity 1.9× 10 23 W/cm 2 and wavelength λ = 0.8 μm propagates from the left boundary into target. The laser pulse has a transverse Gaussian profile of FWHM radius r 0 = 4λ and a square temporal profile of durations τ = 60T 0 (T 0 = 2π/ω 0 ), which is composed of 30 T 0 sinusoidal rising and 30 T 0 constant parts.
The resonance curve of the transverse momentum in Fig. 1(b) is obtained by Eq. (4). The value β rad /ω b = 0.074 is estimated from the parameters gotten in our simulation. For comparison in Fig. 3(f), under the premise of ensuring the same laser intensity, we have also carried out simulations that the incident laser is linearly polarized. The spectrums here are for electrons within a radius of 3 λ and a spreading angle of 0.38 rad. To investigate the scaling properties of the emitted γ-ray in Fig. 5, we fix the self-similar parameter S = 1/30 and the other parameters in the simulations are same. In order to check the accuracy of our simulation results, we have also carried out the simulation at a higher resolution with spatially half of the current grid size, which shows almost the same results as here.