Abstract
We show a new resonance acceleration scheme for generating ultradense relativistic electron bunches in helical motions and hence emitting brilliant vortical γray pulses in the quantum electrodynamic (QED) regime of circularlypolarized (CP) laserplasma interactions. Here the combined effects of the radiation reaction recoil force and the selfgenerated magnetic fields result in not only trapping of a great amount of electrons in laserproduced 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. Threedimensional PIC simulations show that a brilliant γray pulse with unprecedented power of 6.7 PW and peak brightness of 10^{25} photons/s/mm^{2}/mrad^{2}/0.1% BW (at 15 MeV) is emitted at laser intensity of 1.9 × 10^{23} W/cm^{2}.
Introduction
γray is an electromagnetic radiation with extremely high frequency and high photon energy. As a promising radiation source, it has a broad range of applications in material science, nuclear physics, antimatter physics^{1,2,3}, logistics for providing shipment security, medicine^{4} for sterilizing medical equipment and for treating some forms of cancer, e.g. gammaknife surgery^{5}. γray from distant space can also provide insights into many astrophysical^{6,7} phenomena, including γray bursts, cosmic ray acceleration at shock wave front, and emission from pulsar.
Generating intense bursts of highenergy radiation usually requires the construction of large and expensive particle accelerators^{8,9}. Laserdriven accelerators offer a cheaper and smaller alternative, and they are now capable of generating bursts of γrays^{10}. γray generation has been demonstrated in a number of experiments on laser interactions with solid and gas targets, where the main mechanism is the Bremsstrahlung radiation of fast electrons interacting with highZ material targets^{11,12,13,14,15,16,17}. However, due to the small bremsstrahlung crosssection, the conversion efficiency of this scheme is rather low. Further, the broad divergence and large size of fast electron source also limit the achievable brightness of the generated γrays. γray can also be produced by the nonlinear Compton backscattering, in which an electron beam accelerated by laser wakefields interacts with a counterpropagating laser pulse^{18,19,20,21,22}. However, the number of electrons accelerated by laser wakefields in underdense plasmas is small, which also leads to rather low peak brightness of the produced γrays. Recent experiment^{17} demonstrates that the peak brightness of the γray pulse at 15 MeV can reach only the order of 10^{20} photons/s/mm^{2}/mrad^{2}/0.1% BW.
With the progress of laser technology, laser intensities of 5 × 10^{22} W/cm^{2} are now available^{23} and are expected to reach the order of 10^{23}–10^{24} W/cm^{2} in the next few years^{24}, where the quantum electrodynamic (QED) effects play role in their interaction with plasmas. In the QED laserplasma interaction regime, a promising mechanism for production of γray photons is the nonlinear synchrotron radiation^{25,26,27,28,29,31} of ultrarelativistic electrons in the laser fields, i.e., ^{30}. It is shown that γray photons with the maximum energy extending to 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 γray emission occurs only in the small skindepth region^{2,26,27,28}, therefore, the conversion efficiency from laser to γrays is still low, and the peak brightness of γrays is also limited. Recently, a selfmatching resonance acceleration scheme^{32,33} in nearcritical 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 nonQED regime, electron resonance acceleration is dominantly governed by only the selfgenerated 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 nearcritical 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 γray 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 laserproduced 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 selfgenerated 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 γray pulses. Three dimensional (3D) particleincell (PIC) simulations show that brilliant γray 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 γray radiation depend strongly on electron dynamics. Let’ s start with the dynamics of a single electron interacting with the laser and selfgenerated electromagnetic fields in laserproduced plasma channel by taking into account of the QED effects. In the ultrarelativistic limit , the radiation reaction force can be approximately written as^{38,39,40}
where F_{LL} is the classical radiation reaction force in the LandauLifshitz form^{38}. In order to take the quantum effect of radiation reaction force into account, we use a quantummechanically 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} (), and is the finestructure 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 γphoton emission by an electron is characterized by the relativistic gaugeinvariant parameter , where γ_{e} is the Lorentz factor. The QED effects are negligible for but play an important role for .
Assuming a CP plane laser propagating along xdirection, the laser fields are E_{Ly} = E_{L} cos ϕ, E_{Lz} = E_{L} sin ϕ, B_{Ly} = −E_{Lz}/ν_{ph}, B_{Lz} = E_{Ly}/ν_{ph}, where E_{L} refers to their amplitude. The phase is ϕ = kx − ω_{0}t and the phase velocity is ν_{ph} = ω_{0}/k, where ω_{0} and k are laser frequency and wave number. The selfgenerated electromagnetic fields in the plasma channel are assumed to be E_{Sy}, E_{Sz}, B_{Sy}, B_{Sz} transversely and B_{Sx} longitudinally. Considering the quantum radiation reaction force Eq. (1), the electron’s transverse motion in channel can be described as , and , where κ = 1 − ν_{x}/ν_{ph} and . For highenergy electrons, it is reasonable to assume that , and , as they are slowlyvarying comparing with the fastvarying p_{y} and p_{z}. Further assuming , , we obtain that
Here , and . 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 . 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 Δω, i.e., the fullwidthathalfmaximum (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 γray pulses.
Simulation and Results
To verify our scheme, 3D PIC simulations are carried out using the QEDPIC code EPOCH^{41}, which takes into account of the QED effects in the synchrotron radiation of γrays by using a Monte Carlo algorithm^{42}. From Fig. 1(a), we clearly see that an ultradense helical electron bunch is formed in laserproduced 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 selfgenerated 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 preacceleration to hit the resonance condition^{32}. The azimuthal magnetic field in turn not only provides additional confined forces to help trapping and achieving resonance acceleration of electrons, but also significantly enhances the probability of γphoton 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 eventually decreases to a small value of 0.2, shown in Fig. 3(c). Figure 3(d) plots the energy density distribution of electrons at an isosurface value of 1.2 × 10^{4}n_{c}m_{e}c^{2}. It can be seen that an ultradense, helical relativistic electron bunch is formed, in which the electron maximum energy can reach 2 GeV [see 3(e) and 3(f)] and the total charge of electrons with energy above 500 MeV is about 200 nanoCoulomb [see the red line in 3(f)]. By comparing these high qualities of the beam with those without the QED effects, shown by the blue lines in 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 highenergy 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 γray emission.
When the ultradense electron bunch undergoes resonance acceleration in CP laser fields, highenergy γ photons can be synchronously emitted. Figure 4(a) plots the 3D isosurface distribution of the γray photon energy density at t = 80T_{0}. It shows that a brilliant, vortical γray 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 γray can be obtained when the laser pulse is fully dissipated. At t = 100T_{0}, the total number of γray 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 γray 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 γray 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 γray source with the highest peak brightness in tensMeV regime ever reported in the literature. From Fig. 4(b), we can also see that the highenergy photons are highly collimated.
Discussion
The scaling properties of the emitted γrays by the proposed scheme have also been investigated. For a fixed selfsimilar parameter S = n_{e}/a_{0}n_{c} = 1/30, which strongly determines the electron dynamics in nearcritical 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 selfgenerated electromagnetic fields, both the number and mean energy of the emitted γphotons 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 nonQED regime with linearly polarized lasers (a_{0} ≤ 80), here the scaling shows to be as linear as N_{ph} ∝ a_{0} and 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 γray 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 γray 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 laserplasma 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 γray pulses can be obtained.
Methods
The 3D PIC simulations are carried out using the QEDPIC 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 fullyionized 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 γray in Fig. 5, we fix the selfsimilar 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.
Additional Information
How to cite this article: Chang, H. X. et al. Brilliant petawatt gammaray pulse generation in quantum electrodynamic laserplasma interaction. Sci. Rep. 7, 45031; doi: 10.1038/srep45031 (2017).
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Acknowledgements
This work is supported by the National Natural Science Foundation of China, Grants No. 11575298, No. 91230205, No. 11575031, and No. 11175026; the NSAF, Grant No. U1630246; the National key research and development program No. 2016YFA0401100; the National Science Challenging Program; the National Basic Research 973 Projects No. 2013CBA01500 and No. 2013CB834100, and the National HighTech 863 Project. B.Q. acknowledges the support from the Thousand Young Talents Program of China. M.Z. acknowledge support from the Engineering and Physical Sciences Research Council (EPSRC), Grant No. EP/1029206/1. The computational resources are supported by the Special Program for Applied Research on Super Computation of the NSFCGuangdong Joint Fund (the second phase). H.X.C. acknowledges the comments and suggestions from the anonymous referees.
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Affiliations
Center for Applied Physics and Technology, HEDPS, State Key Laboratory of Nuclear Physics and Technology, and School of Physics, Peking University, Beijing, 100871, China
 H. X. Chang
 , B. Qiao
 , T. W. Huang
 , Z. Xu
 , C. T. Zhou
 , X. Q. Yan
 & X. T. He
Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240, China
 B. Qiao
 & X. T. He
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
 C. T. Zhou
 & X. T. He
Science and Technology on Plasma Physics Laboratory, Mianyang 621900, China
 Y. Q. Gu
Department of Physics and Astronomy, Queen’s University Belfast, Belfast BT7 1NN, United Kingdom
 M. Zepf
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Contributions
B.Q., C.T.Z. and X.T.H. conducted the work. B.Q., H.X.C.,T.W.H. and Z.X. developed the basic theory. H.X.C. carried out all simulations. Some detail of the physics are clarified by Y.Q.G., X.Q.Y. and M.Z. The manuscript is written by H.X.C. and B.Q. All authors reviewed the manuscript.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to B. Qiao.
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