Photon and positron production by ultrahigh-intensity laser interaction with various plasma foils

School of Physics Science and Technology,Xinjiang University,Urumqi 830046,People’s Republic of China

Abstract The generation of γ photons and positrons using an ultrahigh-intensity laser pulse interacting with various plasma solid foils is investigated with a series of quantum electrodynamic particlein-cell(PIC)simulations.When ultrahigh-intensity lasers interact with plasma foils,a large amount of the laser energy is converted into γ photon energy.The simulation results indicate that for a fixed laser intensity with different foil densities,the conversion efficiency of the laser to γ photons and the number of produced photons are highly related to the foil density.We determine the optimal foil density by PIC simulations for high conversion efficiencies as approximately 250 times the critical plasma density,and this result agrees very well with our theoretical assumptions.Four different foil thicknesses are simulated and the effects of foil thickness on γ photon emission and positron production are discussed.The results indicate that optimal foil thickness plays an important role in obtaining the desired γ photon and positron production according to the foil density and laser intensity.Further,a relation between the laser intensity and conversion efficiency is present for the optimal foil density and thickness.

Keywords:laser-plasma interaction,positron generation,γ ray emission,nonlinear Compton scattering,particle-in-cell(PIC)simulation

1.Introduction

The rapid progress of ultraintense laser technology has opened some promising areas in strong field physics.Some new laser facilities[1],such as the Extreme Light Infrastructure(ELI)[2],iCAN[3],and Apollon laser[4]projects,promise to provide a 10-100 PW class laser,with a corresponding laser intensity of over 1023W/cm2.For such ultrahigh-intensity lasers,the quantum electrodynamic(QED)effects are dominated in most laser-plasma interactions,such as γ photon emission and positron production[5-11].

In recent years,γ photon emission and positron production by ultrahigh-intensity lasers have been intensely studied because of the variety of important applications in various areas,such as nuclear and particle physics research[12],laboratory astrophysics[13,14],and medical imaging and radiography[15,16],as well as for the development of materials science and to motivate novel industrial applications[17].

Recently,several studies have indicated that ultrahighintensity laser-plasma interaction could trigger the processes of γ photon emission and electron-positron pair production[10,11,18-23].Various mechanisms have been proposed[24-28]and,simultaneously,considerable theoretical and numerical studies have been undertaken to provide detailed physical explanations for these QED processes[5-11,18-31].If the generation process of the γ photon can be triggered,it will produce a dense beam of positrons in the laboratory,which will facilitate several new fields of research[12,14,18-21].

In the study of ultrahigh-intensity laser-plasma interactions,the three most commonly investigated QED processes include the Bethe-Heitler(BH)[24],Breit-Wheeler(BW)[25],and trident[26-28]processes.In the trident process,the electron-positron pairs are produced by energetic electrons interacting with the Coulomb field or the strong laser field[27,28].Under relatively moderate laser intensities(I～1022W/cm2),electrons are accelerated into high-Z nuclei,which results in the generation of positrons.In the BH process,electron-positron pairs are produced by nuclei interacting with γ photons radiating from decelerated electrons[24].Some studies have indicated that electron-positron pairs could be produced by direct laser-plasma foil interactions through the trident and BH processes.However,the positron yields obtained from experiments are too low to be used in applications,so it is necessary to enhance the energy conversion efficiency,positron yield,and energy.In the BW process,under a super-intense laser condition,the electrons are accelerated by the laser field and radiate γ photons through nonlinear Compton scattering.Consequently,electron-positron pairs are produced by the multiphoton BW process(γ+nγlaser→e?+e+)[25],which produces additional γ photons and electron-positron pairs,resulting in QED cascades[11,20].Recently,some particle-in-cell(PIC)simulation studies have predicted that in ultrahigh-intensity laser-plasma interaction,high-energy electron-positron pai rs can be generated through the BW process.

In this paper,we research ultrahigh-intensity laser and plasma foil interactions to produce high-energy photons and positrons using numerical simulations.We perform twodimensional(2D)QED-PIC simulations using EPOCH code[32].We present the simulation results for foils of various densities,thicknesses,and materials,as well as with different laser intensities.We show that there exists an optimal foil density and thickness,which play key roles in enhancing the energy conversion efficiency,number of produced photons,and positron number.We also investigate the interactions of laser pulses with different intensities and the optimized plasma foil.The simulation results show that a suitable laser intensity is also crucial to enhance the photon emission and trigger the QED cascade.

2.Model and simulation parameters

PIC simulation is an effective tool for studying certain fields in laser-plasma interaction physics,such as in laser-based particle acceleration,high-energy-density physics,fast ignition in inertial confinement fusion,etc.[33-37].Since the coupling between the QED processes and plasma dynamics is very complicated,numerical simulations have recently been shown to be an effective way to clearly explore such interactions.Therefore,a series of QED-PIC simulation investigations have been performed on QED processes in laserplasma interactions[9-11,20,38].

In our 2D PIC simulations,linearly polarized ultrahighintensity laser pulses enter the simulation area from the right side at t=0,propagate along the positive x direction,and are incident normally onto the thin plasma foil.The laser has a Gaussian intensity profilewith wavelength λ=1 μm,focal spot y0=1 μm and duration TL=15 fs.The peak intensity of the laser is I=4×1023W/cm2,which corresponds to a normalized laser amplitude of a0=eA/mec2=540,where e and meare the electron charge and mass,respectively,A is the vector potential,and c is the speed of light in a vacuum.In the simulations,we used carbon,aluminum,and gold flat foils to compare the effect of the target material on the photon emission.The foil height in the y direction was 6 μm,the foil front surface was located at x=2 μm,and four different foil thicknesses were considered in the simulation.The simulation box size was 6 μm(x)×6 μm(y)with a grid of 600×600 cells.For the number of particles in each cell,we chose 100 electrons and 50 ions.The longitudinal and transverse initial temperatures of the electrons and ions were so small that their effects could be ignored.The boundary conditions were periodic in the transverse direction and simple-outflow longitudinally.

In our simulations,we consider the radiation reaction regime and the γ photon emission is characterized by QED parameterwhich requires χe≥1 for efficient photon emission.A multiphoton BW process is considered for positron production,which is characterized by another QED parameterand Kγare the 4-momenta of the electron and photon,respectively,and Fμνis the field tensor.These processes are enabled in EPOCH code with a QED block via Monte Carlo algorithm.

3.Simulation results

In order to show the effect of the target density on photon emission and positron generation,we compared the 2D QEDPIC simulation results for plasma foils with different densities.Figure 1(a)shows the relations between foil densities and conversion efficiencies of the laser energy to electrons,photons,and positrons for various foil densities with a fixed foil thickness and laser parameters at 16.7 fs.From this figure,we observe that the conversion efficiencies(defined as the fraction of total laser energy carried by each species)to electrons,photons,and positrons increased rapidly with foil density until ne=250nc,then decreased with foil density to approximately ne=500nc,and then decreased very slowly with a further increase in the foil density.Figure 1(b)shows a plot of the spatial evolution of the photon number for various foil densities with the same foil thickness and laser parameters as those in figure 1(a)at 16.7 fs.More photons were produced with an increase in the foil densities until ne=250nc;then,for the photon number as well as its distributions,no obvious differences were observed between the ne=400nc,500nc,and 700nccases.It is worth noting that the peak of the photon number spatial distributions moved to the left with increasing foil density,as shown in figure 1(b).This was attributed to the different laser penetration depths for the various foil densities,as discussed in figure 2.

Figure 1.(a)Laser energy to electrons,photons,and positrons conversion efficiencies as well as the total conversion efficiency,and(b)spatial evaluation of the photon number in the x direction for different foil densities at 16.7 fs.The foil density ne varies from ne=50nc to ne=700nc while the foil thickness is fixed at l=1 μm.

Figure 1 shows that the conversion efficiencies and produced photon numbers were highly dependent on the foil density,which plays a key role in laser plasma interaction QED problems for given laser parameters.The results indicate that there exists an optimal foil density,which results in an enhancement of the energy conversion efficiency and the produced photon number.When the chosen foil density is optimal,more photons and positrons are obtained under the proper laser conditions.The optimal foil density in our studied case,which was determined by 2D QED-PIC simulations,was ne=250ncfor a0=540 and l=1 μm,as shown in figure 1.The optimal foil density for different foil thicknesses and laser intensities is discussed in the following parts of this paper.

Figures 2(a)-(f)present the spatial distributions of the electron density in the(x,y)plane at 16.7 fs for foil densities of ne=100nc,250nc,400nc,500nc,600nc,and 700nc,respectively.Figure 2(a)shows that,for the low-density foil(ne=100nc),the foil was transparent to the ultrahigh-intensity laser,owing to relativistic transparency.Moreover,the strong ponderomotive force of the laser expels target electrons from the high-field region very easily.Consequently,there was no reflected laser field and the standing wave could not develop inside the foil.This resulted in a lower conversion efficiency of the laser energy to electrons and lower photon emission.However,for the foil density of ne=250nc,a highdensity electron layer was produced in the right half of the foil with a thickness of approximately 0.5 μm and a density of ne=400nc,as shown in figure 2(b).With a further increase in the foil density,the thickness and density of the electron layer decreased and increased,respectively.More importantly,unlike in the ne=250nccase,the electron layer was produced in the left half of the foil for the higher-density foil cases,as shown in figures 2(c)-(f).This meant that for the foils with density higher than the optimal density(ne=250nc),the penetration depth of the laser into the foil was shortened and the laser was reflected from the front surfaces of the foils.This resulted in a lower energy conversion of the laser energy to electrons,which finally led to small amounts of photon and positron generation.

The spatial distributions of the transverse electric field Eyin the(x,y)plane and phase space distribution of electrons at t=16.7 fs for different foil densities(ne=100nc,250nc,400nc,and 700nc)are given in figure 3.Figure 3(a)shows that for the foil with density ne=100nc,almost all of the laser fields were transmitted to the back of the foil without any disruption of the foil and some energetic electrons appeared at the back of the foil,as shown in figure 3(a1).However,for the ne=250ncfoil,the laser field penetrated deep into the foil and was reflected from the high-density electron layer at the right side of the foil,as shown in figure 3(b).More importantly,more energetic electrons stayed in the laser reflection region,as shown in the phase space portrait of figure 3(b1).For the foils with densities of ne=400ncand ne=700nc,almost all of the laser fields were reflected from the foil front surface without penetration and there were few energetic electrons in the laser reflection region,as shown in figures 3(c),(d),(c1),and(d1).All these results indicated that for the lower foil density,the laser was easily transmitted to the back of the foil and there was no reflected field.This resulted in lower correlation and conversion efficiencies between the laser and electrons,as shown in figures 1 and 2.For the ne=400ncand ne=700nccases,there were highdensity electron layers at the front side of the foil(see figure 2),which acted like a plasma mirror and instantly reflected almost all of the laser fields.Consequently,the incident and reflected lasers had less chance to interact with electrons,which resulted in a lower conversion efficiency.However,for the case of ne=250nc,the laser could penetrate deep into the foil,and the dense electron layer produced at the rear of the foil could reflect the laser field like a plasma mirror(see figure 2(b)).Accordingly,more energetic target electrons remained in the high-field region,as shown in figures 3(b)and(b1).This resulted in enhancements of the conversion efficiencies and the chance of photon emission as well as positron production.

We can estimate the optimal target density by theoretical analysis for our simulated case,where the laser field is fully reflected by the high-density electron layer.The laser radiation pressure for this case can be expressed as Prad=2I(1+R+T)/c,and we assume that the laser field is fully reflected by the high-density electron layer,which acts as a plasma mirror,so we have T=0 and R=1.Let us assume that when the target density is equal to the optimal density,an electron-ion double layer is developed and the laser radiation pressure is compensated by the pressure of the electrostatic fieldwhereis the charge separation electrostatic field and y0is the laser focal spot radius.The distance is chosen as y0/2 since at this point the radiation pressure is maximal[39].We obtain an estimate of the optimal target density.It gives the valuefor a laser pulse with an intensity of I=4×1023W/cm2and a focal spot radius of y0=1 μm.This result agrees very well with our PIC simulation results.

Figure 2.Spatial distribution of the electron densities in the(x,y)plane at 16.7 fs for foils with densities of ne=100nc(a),ne=250nc(b),ne=400nc(c),ne=500nc(d),ne=600nc(e),and ne=700nc(f).

Figure 3.Spatial distribution of the transverse electric field Ey in the(x,y)plane(top row)and phase space distribution of electrons(x,px)at t=16.7 fs for foils with densities of ne=100nc[(a)and(a1)],ne=250nc[(b)and(b1)],ne=400nc[(c)and(c1)],ne=700nc[(d)and(d1)].The electric field is normalized by mecω0/c.

Figure 4 plots the spatial distributions of the photon and positron densities in the(x,y)plane at 16.7 fs,with the foil thickness l=1 μm and densities of ne=100nc,250nc,400nc,500nc,600nc,and 700ncfor a0=540.Both the photon and positron densities were shown to be closely related to the foil density.For the foil with a density of approximately ne=250nc,as mentioned above(figure 3),the laser fields were reflected by the high-density electron compressed layer at the rear of the foil and an electromagnetic standing wave was produced by the incident and reflected laser fields.Accordingly,the electron motion in the standing wave led to more efficient photon emission and positron production than in the other density cases.These results also confirmed that ne=250ncwas the optimal density for an l=1 μm plasma foil interacting with ultrahigh-intensity laser pulses with a0=540.

Figure 4.Spatial distribution of the photon(top row)and positron(bottom)row densities in the(x,y)plane at 16.7 fs for foils with densities of ne=100nc[(a)and(a1)],ne=250nc[(b)and(b1)],ne=400nc[(c)and(c1)],ne=500nc[(d)and(d1)],ne=600nc[(e)and(e1)],and ne=700nc[(f)and(f1)].

Figure 5.Electron phase space distribution(x,px)for the(a)l=0.5 μm,(b)l=1 μm,(c)l=2 μm,and(d)3=1 μm cases.Laser energy to(e)electrons,photons and total,and(f)positron conversion efficiencies for different foil thicknesses at 16.7 fs.The foil density ne is fixed to the optimal density of ne=250nc,while the foil thickness is varied.

Next,we investigated the effect of the foil thickness on the efficiency of photon emission and positron production.According to the results from figures 1-4,we chose the optimal foil density ne=250ncand normalized laser intensity a0=540 for this section.Therefore,we studied the phase space distribution of electrons and the evolution of the conversion efficiencies with foil thickness,as shown in figure 5.Figures 5(a)-(d)show that for the l=0.5 μm case,electrons have broad phase space distribution at the front and back of the target.However,for the l=1,2 and 3 μm cases,the electrons have similar phase space distribution and the energetic electrons are confined in the laser reflection zone.Figures 5(e)and(f)show that all the conversion efficiencies increased rapidly with the foil thickness until l=1 μm,and then remained unchanged with a further increase in the foil thickness.This indicated that for a given laser intensity and foil density of ne=250nc,l=1 μm was a favorable foil thickness to enhance the energy conversion efficiencies and photon emission.

Figure 6.Spatial distribution of the electron densities(top row)and the transverse electric field Ey(bottom row)in the(x,y)plane at 16.7 fs.The foil density ne is fixed at the optimal density of ne=250nc,while the foil thickness varies.

To validate our above statements,we determined the spatial distributions of the electron density and the transverse electric field Eyin the(x,y)plane at t=16.7 fs for different foil thicknesses,as shown in figure 6.We observed that when the foil thickness l was too small,that is,l=0.5 μm,it could not satisfy the condition of electron-ion double layer formation(which isμmin our case),the foil was transparent to the incident laser,and the laser pulse continued to travel and push some electrons in front of the laser pulse like a light sail,as shown in figures 6(a)and(a1).This normally results in suppression of the energy conversion efficiencies,as mentioned in the previous paragraph.However,for the foil thicknesses of l=2 and 3 μm,the highdensity-electron compressed layers were observed(hole-boring process)at the same place with the same density as in the case of l=1 μm,as shown in figures 6(b)-(d).Furthermore,the spatial distribution of the transverse electric field Eyin the(x,y)plane was similar for all three cases,as shown in figures 6(b1),(c1),and(d1).Thus,there were similar conversion efficiencies for the l=1,2,and 3 μm cases,as shown in figure 5.

We investigated the relation between the laser intensity and conversion efficiencies,which included the total conversion efficiency as well as the conversion efficiencies to electrons,photons,and positrons.We undertook PIC simulations for two kinds of plasma foils with densities of ne=250ncand ne=500nc,while the foil thickness was fixed as 1 μm and the dimensionless laser amplitude was varied 11 times as a0=50,100,200,300,400,500,600,700,800,900,and 1000.The conversion efficiencies as a function of the laser amplitude a0for the ne=250ncdensity case are shown in figure 7(a).The total energy conversion efficiency increased,reached a maximum of approximately 70%,and then decreased almost linearly with the laser amplitude a0.The fraction of the energy coupled to electrons steadily decreased from 60% to approximately 20% with increasing laser amplitude.The conversion efficiency to photons increased rapidly from a few percent,reached a maximum of approximately 25%,and then became saturated with the increase in laser intensity.It is worth noting that the laser energy coupled to electrons was comparable to that of the photons at approximately a0=650.As the laser intensity increased,the photons absorbed more energy than the electrons.

Figure 7.Energy conversion efficiencies for(a)a low-density plasma foil(ne=250nc)and(b)a high-density plasma foil(ne=500nc)with different laser amplitudes.The foil thickness is fixed at l=1 μm.

Figure 8.Energy spectra of the electrons,photons and positrons for different target materials at t=16.7 fs with/without ion mobility:(a)for carbon,(b)for aluminum,and(c)for gold.Here,the optimal target density and thickness are used.

Figure 9.Distributions of QED parameter χe for different target(a)densities,(b)thicknesses,and(c)materials at t=16.7 fs with mobile ions.

Table 1.Energy conversion efficiencies for different target materials with/without ion mobility.

The conversion efficiencies as a function of the laser amplitude a0for the ne=500ncdensity case are shown in figure 7(b).In this case,the total conversion efficiency decreased with a0,and the general trend for the electron,photon,and positron conversion efficiencies was similar to the ne=250nccase.Moreover,the conversion efficiencies to the electrons and photons were the same at the laser intensity of approximately a0=650,which was the same as the ne=250nccase.However,the energy absorbed by both electrons and photons decreased to approximately 12%at this critical intensity,which was less by approximately 10% than the ne=250nccase.This,generally,could be attributed to the fact that for the lower-density case(ne=250nc),the laser penetration distance was larger than that in the higher-density case(see figure 2),which directly resulted in higher energy conversion efficiencies to each species and enhancement of the photon emission and positron generation.

4.Discussion

In this section,we discuss the effects of the target materials and ion mobility on the conversion efficiency and photon emission.Figure 8 shows the electron energy spectra for different target materials with and without ion mobility.For the lower Z target,the cut-off energies and conversion efficiencies of the species were smaller than those for higher Z targets both with and without ion mobility,as shown in figure 8(a)and table 1.For the aluminum target,the cut-off energies for all species were almost the same and there was no significant change in the energy conversion efficiencies with and without ion mobility,as shown in figure 8(b)and table 1.However,for the gold target with immobile ions,the cut-off energies and number of the species were higher than those in the immobile ion case,as shown in figure 8(c),and the conversion efficiencies decreased remarkably for the mobile ion case,as shown in table 1.

Finally,we discussed the distribution of the QED parameter χefor different target densities,thicknesses,and materials.The photon emission is governed by an invariant QED parameter χeand it is required that χe≥1 for efficient photon emission,where.For the low-density and thin aluminum target,the double-layer formation condition is not satisfied and electrons experience light sail acceleration in front of laser pulse,the electrons have high energy(see phase space distribution in figures 3 and 5),and χe≥1,as shown in figures 9(a)and(b).However,electrons cannot stay in the high-field region,which results in reducing the efficiency of photon emission.For the optimal target density,more electrons with higher χestay in the highfield region,increasing the efficiency of photon emission.For the targets of density higher than the optimal density,the value of χedecreases to half of that for the optimal density case,while for thicker targets,the distributions of χeare unchanged,as shown in figure 9(b).Figure 9(c)shows the distributions of χefor different target materials with ion mobility.It is found that the value of the χeis higher for the aluminum target than for the other two target cases.

5.Conclusion

In this paper,we have numerically studied the interactions of ultrahigh-intensity femtosecond laser pulses and various plasma foils.The effects of the foil density and thickness on energy conversion efficiencies were studied,and laser pulses with different peak intensities were used to generate more γ photons and pairs.

First,we have numerically investigated the effect of foil density on the energy conversion efficiencies and the positron number.The PIC simulation results reveal that for the same laser intensity,the energy conversion efficiency of the laser to γ photons and the produced photon number are highly related to the foil density.We found an optimal foil density of approximately 250ncby PIC simulations and theoretical analysis,which plays a key role during laser-plasma interaction QED processes.Second,using the optimal foil density,we performed simulations for foils with different thicknesses and observed an optimal foil thickness,which resulted in higher energy conversions and pair production.Finally,we investigated the relation between the laser intensity and conversion efficiencies.By comparatively evaluating the energy conversion efficiencies of two density cases(250ncand 500nc)with the optimal thickness,we found that the laser energy to photon conversion efficiency is enhanced by approximately 10%when the foil density is optimized.All of these findings indicate that foil design optimization is essential for a high-efficiency QED process.

Acknowledgments

This work was financially supported by National Natural Science Foundation of China(No.11 664 039).The authors are particularly grateful to CFSA at the University of Warwick for allowing us to use the EPOCH code(developed under UK EPSRC Grants(Nos.EP/G054940/1,EP/G055165/1,and EP/G056803/1)).