Highly efficient γ-ray generation by 10 PWclass lasers irradiating heavy-ion plasmas

Mi TIAN(田密)and Ziyu CHEN(陳自宇),2,?

1 Key Laboratory of High Energy Density Physics and Technology(MoE),College of Physics,Sichuan University,Chengdu 610064,People's Republic of China

2 National Key Laboratory of Shock Wave and Detonation Physics,Mianyang 621999,People's Republic of China

Abstract 10 PW-class lasers irradiating overcritical plasmas in the quantum electrodynamics regime promise to generate ultrabright γ-ray sources in the laboratory.Here using two-dimensional particle-in-cell simulations,we report highly efficient γ-ray generation in the parameter regime of 10 PW-class lasers at an intensity level of 1023 W cm–2 interaction with heavy-ion plasmas which have large-scale preplasmas.The laser-to-γ-ray(＞1 MeV)energy conversion efficiency reaches close to 60%with an above 1014 γ-photons/pulse.The average γ-photon energy is about 14 MeV with the highest photon energy exceeding 1 GeV.The high-energy γ-photons are mainly directed in the forward direction.We also find that plane target geometry is efficient enough for high power γ-ray radiation,which is beneficial for easing the difficulty of complex target manufacturing and alignment in experiments.

Keywords:laser plasma interactions,γ-ray source,particle-in-cell simulations

1.Introduction

High power γ-rays with photon energy ＞1 MeV are indispensable tools for a wide range of applications.For example,in high-energy-density experiments,γ-ray flash radiography is a critical technique for investigating the inner structure and dynamic response of thick dense materials under extreme impact or explosion conditions[1–3].Conventional powerful γ-ray source facilities,such as the DARHT[4]at Los Alamos National Laboratory,generate an intense beam of electrons through a large linear accelerator.The high-energy electrons then hit a high-Zconverter target to produce γ-rays via Bremsstrahlung radiation.The radiography spatial resolution is mainly limited by the source size at the millimeter or submillimeter scale.

The advent of high-power laser technology leads to novel accelerator schemes and light sources[5].Ultrashort and ultraintense laser-driven sources have the advantages of short duration(～fs scale),small source size(～μm scale),compact,and easy synchronization.Relativistic lasers with an intensity＞1018W cm–2can accelerate electrons to 8 GeV energies in about 20 cm long plasmas based on laser wakefield acceleration(LWFA)[6].The LWFA process can also be utilized to generate a γ-ray pulse.With 100 TW-class lasers,experiments have demonstrated the generation of γ-rays with 107photons/pulse between 1 and 7 MeV by resonant betatron oscillations of accelerated electrons in the rear of the laser pulse[7].Numeric simulations show the possibility of generating 1012γ-ray photons/shot above 1 MeV with energy conversion efficiency ＞10% by multi-PW lasers from a twostage LWFA[8].The method based on the hosing evolution of the LWFA bubble is also proposed[9].To enhance the electron energies in the center-of-mass frame and thus the radiated photon energies,the scheme of relativistic electron bunch from LWFA collision with a counter-propagating laser is employed to produce high-energy γ-rays,i.e.the so-called all-optical inverse Compton scattering γ-ray source[10–16].Photons with energy above 30 MeV have been obtained experimentally[17].Another way to generate γ-rays using electrons from LWFA is via Bremsstrahlung radiation with high-Zconverters[18–21].Due to a low density in the underdense plasmas and a small amount of accelerated highenergy electrons,the above-mentioned LWFA-based γ-ray generation methods suffer from a relatively low energy conversion efficiency.

In recent years,ultra-high-power laser facilities,such as the Shanghai super-intense ultrafast laser facility(i.e.SULF)[22,23],can reach the level of 10 PW,while even higherpower 100 PW laser facilities are proposed and under construction[24,25].The 10–100 PW lasers can deliver a peak intensity above 1023W cm–2,with the corresponding normalized laser amplitudea0=eE0/meω0c～102for laser wavelength λ=1 μm,wherecis the speed of light in vacuum,eandmeare the electron charge and mass,E0and ω0are laser field amplitude and angular frequency,respectively.Since the electron quiver energy in the laser field γe～a0,the characteristic energy of photons emitted by ultrarelativistic electrons via the synchrotron-like nonlinear Thomson scattering mechanism,scaling asis thus in the γ-ray range.Besides,the critical plasma densitybecomes much higher in this case due to the relativistic correction,which means the plasma density and amount of energetic electrons participating in the γ-ray emission under the action of the ultraintense laser are much larger than those in the underdense plasma case of LWFA.In addition,in this intensity regime,effects such as radiation reaction[26,27]and other quantum electrodynamics(QED)processes[28],can further enhance the γ-ray emission by changing the electron dynamics,laser absorption,and energy partition,etc.Therefore,10–100 PW laser interactions with the bulk of overcritical plasmas represent a new regime that has great potential to develop powerful γ-ray sources.

Several groups have numerically studied high power γray flash generation in 10 PW-class laser and solid-plasmas interactions in the QED regime.Most of the results rely on two-dimensional(2D)particle-in-cell(PIC)simulations implemented with relevant QED processes,i.e.discontinuous synchrotron emission,radiation reaction,and Breit–Wheeler pair production[29].Bradyet alreported conversion efficiency～1% with an average γ photon energy of 1 MeV at laser intensity of 1022W cm–2and～14% with 32 MeV at 8×1023W cm–2using uniform CH2plastic targets,while the efficiencies for 30 fs and 500 fs lasers are about the same[30].Ridgerset alobtained a conversion efficiency of～35% with an average photon energy of 16 MeV using Al targets at a laser intensity of 8×1023W cm–2[31].Nakamuraet alfound a conversion efficiency of～32%for a 10 PW laser interacting with D plasmas at an optimal density scale length of 2.5 μm[32].Lezhninet alalso identified preplasma length as a parameter of key importance to γ-ray generation.A conversion efficiency of～37% can be obtained with 10 PW lasers at an optimal corona length approximately equal to the laser pulse length[33].Starket alachieved a conversion efficiency of～15%at a reduced laser intensity of 5×1022W cm–2with the help of a foam and plastic relativistically transparent channel target that produces a high quasistatic magnetic field of 0.4 MT[34].Jiet alalso reported γ-photon enhancement in a micro-tube hollow channel target by boosting the laser intensity from 5×1022to 4.3×1023W cm–2inside the channel[35].Zhuet alfound that the conversion efficiency can be enhanced from 5%to 10%at 4.4×1022W cm–2with H plasmas by using a target configuration of gold cone confinement[36].

In this work,we report highly efficient γ-ray generation from 10 PW-class laser-driven overcritical plasmas with a laser-to-γ-ray(＞1 MeV)conversion efficiency close to 60%from 2D simulations.This is achieved by using heavy-ion plasmas with large-scale preplasmas.The radiation mechanism is nonlinear Thomson or multi-photon Compton scattering.We also study how the ion charge-to-mass ratio,laser power,electron density,and target configuration influence the γ-ray generation efficiency.

2.Simulation setup

We carry out a series of 2D PIC simulations using the fully relativistic PIC code EPOCH[37]including relevant QED effects.Ay-polarized Gaussian pulse is normally incident from the left boundary(atx=0)and propagates along thexaxis.The laser has a wavelength of λ=1 μm,pulse width of τ0=30 fs,and spot radius ofr0=2.5λ.The laser peak power is 20 PW,corresponding to a peak intensity of 1.0×1023W cm–2.The initial plasma is composed of a uniform plasma slab and a preplasma corona localized at the front of the slab.In the parallel direction(x-direction),the preplasma density changes from 0.1ncto the maximum density ofnmaxexponentially with a preplasma length ofL=45λ.The plasma slab has a thickness of 5 μm.According to the results by Lezhninet alin reference[33],this plasma length configuration is optimal for a 30 fs,20 PW laser pulse to produce γrays.The initial plasma density is homogeneous in the transverse direction(ydirection).The initial plasma is located at 5λ ≤x≤55λ and-25λ ≤y≤25λ.The initial ion density

isnmax=10ncfor heavy-ion plasmas whilenmax=40ncfor H plasmas.In the code,we set different charge and mass parameters of the ion particles to distinguish different ion species.The simulation box size isx×y=75λ×60λ and the grid step is Δx×Δy=λ/40×λ/40.Each cell is filled with 10 macro-particles in the region of the initial plasma.The total simulation time is 340 fs.The total energy error is less than 5% in all simulations.This acceptable energy error may be caused by numerical resolution,photon energy cutoff,and particles moving out of the simulation box.In the simulations,the minimum photon energy of 1 MeV is set for the tracked γ photons.Photons emitted with energy below this cutoff still cause electron recoil but are not tracked.This helps to save computational resources and the ignored lower energy photons only account for a small number of the total energy.

3.Results and discussion

We first take a look at the characteristics of the γ-ray emissions from C6+-plasma targets.Figure 1(a)shows the energy spectrum of the γ-photons,exhibiting a synchrotron-like spectral feature.The highest photon energy exceeds 1 GeV and the average photon energy is about 14 MeV.Figures 1(b)shows the spatial distribution of γ-photon number density att=280 fs when most of the γ-photons have left the target.The spot size of the γ-rays is less than 10 μm,one to two orders of magnitude smaller than that of linac-based γ-ray sources.Figures 1(c)–(e)show the angular distribution of γphotons att=280 fs for different photon energy ranges.Most of the γ-photons are directed in the forward direction of laser propagation.The higher-energy γ-photons have better directivity.Such a directed γ-ray beam with a small source size and ultrashort duration is desirable for high spatial-temporal resolution detection of the structure and dynamics of dense materials.

Figure 1.Characteristics of the emitted γ-ray photons from C6+-plasma targets.(a)Energy spectrum of γ-rays.(b)Spatial distribution of γ-ray number density.(c)–(e)Angular distribution of γ-rays with photon energy(c)eγ ＜10 MeV,(d)10 MeV ＜eγ ＜100 MeV,and(e)100 MeV ＜eγ ＜1000 MeV.The time is t=280 fs when most of the γ-photons have left the target.

Figure 2.Energy fraction evolution of particles(electrons,ions,positrons,and γ-photons)and fields in the simulations for different target materials:(a)H+-plasmas,(b)C6+-plasmas,and(c)Al13+-plasmas.

Figure 3.Effects of target materials on γ-ray emission.Spatial distribution of(a)–(d)γ-photon number density,(e)–(h)electron number density,and(i)–(l)self-generated magnetic field at t=240 fs when the maximum photon conversion fraction is reached.The columns from left to right correspond to H+,C6+,Al13+,and Fe6+ plasmas,respectively.

Figures 2(a)–(b)show the energy evolution of fields and particles throughout the simulations for the H+and C6+plasmas,respectively.For both cases,the laser field energy is almost absorbed completely by the plasmas and converted to other particles,leaving less than 10%in the plasmas mainly in the form of quasistatic magnetic and electric fields.For the case of 20 PW laser irradiating H+plasmas(figure 2(a)),the maximum energy fraction to γ-photons(＞1 MeV)is close to 40%,which reproduces the results reported by Lezhninet al[33]and shows the reliability of our simulations.This high efficiency is mainly attributed to the large-scale preplasma configuration as identified in reference[33].At the same time,ions(i.e.protons)are efficiently accelerated and acquire the largest fraction of energy.The energy fraction to positrons is nearly zero,showing this parameter regime(a0much less than 1000)is not suitable for pair production,in agreement with previous results[27,33].

Figure 4.The γ-ray conversion efficiency for C6+-plasma target as a function of(a)driving laser power and(b)initial electron density.The electron density ranges from 60nc to 240nc,corresponding to the initial ion density ranging from 10nc to 40nc.

In comparison,for the case of heavy-ion C6+-plasmas,the maximum energy fraction to ions is greatly reduced.While,remarkably,the energy fraction to γ-photons further boosts to about 55%,making up the largest fraction of energy.This would produce γ-ray energy as high as 330 J for a 30 fs,20 PW laser,while the energy of 3.3 kJ and power of 11 PW for a 300 fs,20 PW laser.With an average photon energy of about 14 MeV,the corresponding photon number per pulse reaches 1014and 1015,respectively,demonstrating the great potential of 10 PW-class laser-driven heavy-ion plasmas as an extremely efficient way to generate ultrabright γ-rays.Aside from that,when the target is changed from C6+-plasmas to Al13+-plasmas,the γ-ray efficiency and energy partition are almost the same,as shown in figure 2(c).

To understand the effects of heavy ions on γ-ray generation,we plot the spatial distribution of γ-photon density,electron density,and self-generated magnetic field for different plasma targets att=240 fs when the maximum photon conversion fraction is reached.We first compare the cases of H+-,C6+-,and Al13+-plasmas.From figures 3(a)–(c),we see that the regions of high number density of emergent γ-photons increase for heavy-ion plasmas,which is in accordance with the areas of high electron density and strong selfgenerated magnetic field shown in figures 3(e)–(g)and figures 3(i)–(k),respectively.At such high laser intensities,the ponderomotive effect on ions is significant.The ponderomotive force of particles with chargeqand massmcan be expressed as

the ponderomotive force induced accelerationThen the ions with a smaller charge-to-mass ratio are more difficult to be scattered and vacated.As the electrons would follow the positions of the ions and move around them,we see that the plasma channels for C6+- and Al13+-plasmas get smaller.At the same time,more electrons are confined in the channels compared to the case of H+-plasmas,where they are in the region around the ions as well as the laser fields(figures 3(e)–(g)).Aside from that,strong self-generated magnetic field are formed in the channels(figures 3(i)–(k)).Therefore,heavy-ion plasmas lead to denser electron bunches confined around the laser electromagnetic field which simultaneously experience strong acceleration by the self-generated magnetic field in the channel.As a result,γ-ray emission via the nonlinear Thomson or multi-photon Compton scattering mechanism is enhanced for heavier-ion plasmas.In addition,the effects of radiation reaction trapping of electrons which emit highenergy γ-photons intensively would further increase the electron density inside the channel and enhance the γ-emission process in return.This explains the enhancement in conversion efficiency of γ-emission for heavy-ion C6+- and Al13+-plasmas compared to H+-plasmas.Since C6+- and Al13+-ions have nearly the same charge-to-mass ratio,they lead to similar energy partition and evolution.We also consider Fe6+-plasmas with fixed ionization states.This is unphysical,but only for the purpose of checking the case of a smaller charge-to-mass ratio of ions.The results are shown in the fourth column of figure 3.We can observe the smaller channel,denser electron bunches,and stronger self-generated magnetic field more clearly.In this case,the γ-ray conversion efficiency is enhanced to about 65%.This result further confirms the aforementioned physical picture that a smaller ion charge-to-mass ratio is preferred for a higher γ-ray conversion rate.For targets with heavier ions,such as tungsten and gold,the charge-to-mass ratio of ions may be smaller than 0.5 due to the increased proportion of neutrons and potentially un-ionized inner shells because of the extremely strong atomic potential.The resultant γ-ray conversion efficiency may be expected to increase.Figure 4(a)shows the γ-ray conversion efficiency as a function of laser peak power,which grows steeply with laser power increasing from 10 to 20 PW and then saturates(close to 60%)gradually with further increasing laser power up to 50 PW.The trend is in good agreement with previous studies[33].10 PW laser is not optimal because of the relatively low laser intensity of 5.0×1022W cm-2.This is consistent with most of the previous studies[30,32,34]which show that an appreciable fraction of laser energy converting to γ photons through synchrotron emission occurs at laser intensity above 1023W cm-2.For even higher-power lasers,more charged particles would be pushed aside by the light pressure which would limit the γ-ray conversion.To balance laser cost and γ-ray efficiency,20 PW peak power would be a better option.Nevertheless,higher-power lasers can produce more powerful γ-rays with respect to photon numbers per shot.Figure 4(b)shows the conversion efficiency for C6+plasmas with different initial ion densities(ranging from 10ncto 40nc)and electron densities(ranging from 60ncto 240nc).It is seen that higher plasma density does not lead to enhanced performance of γ-ray conversion.Instead,as demonstrated before,it is the ion charge-to-mass ratio that is of key importance for improving the γ-ray generation efficiency.Here the ion charge-to-mass ratio has a greater impact on the γ-emission enhancement compared with laser peak power and particle density because these laser power and plasma density parameters are still around the optimal conditions for bright γemission.Under these conditions,the lasers form a channel and penetrate the high-density region of the target and deplete most of their energy.So the conversion rate of γ-emission is largely affected by the number of electrons confined around the ions in the channel experiencing the laser fields and selfgenerated fields.

Previous studies show that a novel target design with a high-density confinement geometry is beneficial for enhancing γ-ray conversion efficiency from H+plasmas at a relatively low laser intensity of about 1022W cm-2[36].Here we compare the conversion efficiency in our parameter regime,i.e.10 PW-class lasers at 1023W cm–2and heavy-ion plasmas with large-scale preplasmas,for a plane C6+-plasma target and a gold-cone confined C6+-plasma target.The Au ion density iscorresponding to a mass density of 19.32 g cm-3.The Au electron density is about 260nc.The cone with a half-angle of θ=14° is located between 5λ ≤x≤45λ with a thickness of 2λ.The right inner opening radius of the cone isR=2.5λ.The other parameters are the same as those in figure 1.We find that the γ-photon energy evolution and conversion efficiency are almost the same as using the plane and gold-cone-confined targets.Figure 5 compares the spatial distribution of γ-photon density,electron density,and magnetic field for both target configurations.The corresponding results look quite similar.The laser field develops a plasma density channel in the plane-plasma target with a shape much like the cone,as a result of relativistic selffocusing effects.As a consequence,the localized region and density of the trapped electrons around the laser field which give the γ-ray emission are quite close for both target cases.Besides,the region and strength of the magnetic field are also similar.Thus the generated γ-rays are nearly the same.This result shows that in our case a simple plane target is efficient enough for γ-ray emission,which is beneficial for easing the difficulty of target manufacturing and alignment in experiments.

Figure 5.Comparison between target configurations of(a)–(c)a gold-cone confined C6+-plasma target and(d)–(f)plane C6+-plasma target.Columns from left to right correspond to the spatial distribution of γ-photon number density,electron number density,and magnetic field,respectively.

Previous work by Lezhninet al[33]has compared the difference in γ-ray generation between 2D and 3D PIC simulations with similar laser–plasma parameters as ours.It is found that,for 10 PW laser interaction with H+plasmas,the γ-ray conversion efficiency is close to 40%in 2D simulations,while it only drops to no less than 20% in the 3D case.Here we obtain an efficiency reaching about 60%in 2D simulations.Considering heavy-ion plasmas are more efficient than H+plasmas in γ-ray generation,an efficiency of more than 30% may be estimated in the 3D case.

4.Conclusions

In summary,through 2D PIC simulations,we present highly efficient γ-ray generation from 20 PW laser-irradiated overcritical plasmas in the QED regime via the nonlinear Thomson or multi-photon Compton scattering mechanism,achieved by using heavy-ion plasmas with large-scale preplasmas.The ion charge-to-mass ratio is of great importance to the γ-emission enhancement,while the laser peak power and particle density have less influence in the considered parameter regime around the optimal conditions for efficient γ-emission.Besides,we also find that a simple plane target gives similar γ-ray emission with that of a gold-cone-confined plasma target,which is beneficial for easing the difficulty of complex target manufacturing and alignment in experiments.Such ultrabright γ-ray sources with photon numbers reaching 1014–1015photons/pulse and pulse energy at～100 J–kJ level in the MeV–GeV photon energy region open up new opportunities for a broad range of applications.

Acknowledgments

This work was supported in part by the National Key Laboratory of Shock Wave and Detonation Physics(No.JCKYS2020212015),National Natural Science Foundation of China(No.12175157),and the Fundamental Research Funds for the Central Universities(No.YJ202025).

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