1. INTRODUCTION
To create large numbers of MeV positrons in the laboratory is of considerable research and application interest. Novel positron sources are needed for the electron-positron linear collider (Hirose et al., Reference Hirose, Dobashi, Kurihara, Muto, Omori, Okugi, Sakai, Urakawa and Washio2000), nuclear medicine (Raichle et al., Reference Raichle1985), and as diagnostic tools. For example, positron annihilation spectroscopy (PAS) is a valuable tool in materials research, atomic physics, as well as condensed matter physics (Mills et al., Reference Mills1982; Schultz et al., Reference Schultz and Lynn1988; Hunt et al., Reference Hunt, Cassidy, Selim, Haakenaasen, Cowan, Howell, Lynn and Golovchenko1999; Gidley et al., Reference Gidley, Peng and Vallery2006). PAS makes use of slow positrons from radioactive sources or from pair production through energetic beam-target interaction. Shortening the positron pulses can increase the accuracy of PAS (Jean et al., Reference Jean, Mallon and Schrader2003), and can open a door for pump-probe type PAS applications for investigating ultrafast dynamics in material and biological structures.
Several schemes for generating positron beams have been proposed (Surko et al., Reference Surko, Leventhal and Passner1989; Liang et al., Reference Liang, Wilks and Tabak1998; Cowan et al., Reference Cowan, Perry, Key, Ditmire, Hatchett, Henry, Moody, Moran, Pennington, Phillips, Sangster, Sefcik, Singh, Snavely, Stoyer, Wilks, Young, Takahashi, Dong, Fountain, Parnell, Johnson, Hunt and Kühl1999; Andreev et al., Reference Andreev and Platonov2000; Kurihara et al., Reference Kurihara, Yagishita, Enomoto, Kobayashi, Shidara, Shirakawa, Nakahara, Saitou, Inoue, Nagashima, Hyodo, Nagai, Hasegawa, Inoue, Kogure and Doyama2000; Shen et al., Reference Shen and Yu2002). Positrons can be obtained from β+ emitters (Surko et al., Reference Surko, Leventhal and Passner1989) and large-scale facilities such as linear electron accelerators (linacs) (Kurihara et al., Reference Kurihara, Yagishita, Enomoto, Kobayashi, Shidara, Shirakawa, Nakahara, Saitou, Inoue, Nagashima, Hyodo, Nagai, Hasegawa, Inoue, Kogure and Doyama2000), as well as nuclear reactors (Hugenschmidt et al., Reference Hugenschmidt, Lowe, Mayer, Piochacz, Pikart, Repper, Stadlbauer and Schreckenbach2008). Continuous positron sources from beta decay have limitations such as low intensity and relatively wide angular distribution. Positron beams from linacs can have intensities up to 108/s, but they are of long duration, namely on the order of tens picoseconds. Intense relativistic picosecond positron beams at ≥2 × 1010 positrons/s can be obtained from laser-solid interactions with lasers capable of 102–103 J/shot (Chen et al., Reference Chen, Meyerhofer, Wilks, Cauble, Dollar, Falk, Gregori, Hazi, Moses, Murphy, Myatt, Seely, Shepherd, Spitkovsky, Stoeckl, Szabo, Tommasini, Zulick and Beiersdorfer2011), which is at present still rare. In addition, Taira et al. (Reference Taira, Adachi, Zen, Katoh, Yamamoto, Hosaka, Takashima, Soda and Tanikawa2010) proposed picoseconds positron beam generation from laser-Compton γ rays at 90° collision geometry.
Since the development of high-power tabletop lasers (Perry et al., Reference Perry and Mourou1994), particle accelerators based on the interaction of ultrashort ultraintense (USUI) laser pulses with plasmas, in particular, laser wakefield acceleration (LWFA) (Tajima et al., Reference Tajima and Dawson1979), can be realized. LWFA can generate several hundred GeV/m electric fields and deliver high-quality relativistic (≥100 MeV), up to 0.5 nC, electron beams. The latter also have low (few percent) energy spread, small (few mrad) spatial divergence, and short (few femtosecond) pulse duration (Mangles et al., Reference Mangles, Murphy, Najmudin, Thomas, Collier, Dangor, Divall, Foster, Gallacher, Hooker, Jaroszynski, Langley, Mori, Norreys, Tsung, Viskup, Walton and Krushelnick2004; Geddes et al., Reference Geddes, Toth, Tilbory, Esarey, Schroeder, Bruhwiler, Nieter, Cary and Leemans2004; Faure et al., Reference Faure, Glinec, Pukhov, Kiselev, Gordienko, Lefebvre, Rousseau, Burgy and Malka2004; Reference Faure, Rechatin, Norlin, Lifschitz, Glinec and Malka2006; Leemans et al., Reference Leemans, Nagler, Gonsalves, Toth, Nakamura, Geddes, Esarey, Schroeder and Hooker2006; Lundh et al., Reference Lundh, Lim, Rechatin, Ammoura, Ben-Ismail, Davoine, Gallot, Goddet, Lefebvre, Malka and Faure2011). They are therefore useful to some tunable sources of ultrashort radiation, such as the laser-Compton light source (Catravas et al., Reference Catravas, Esarey and Leemans2001; Schwoerer et al., Reference Schwoerer, Liesfeld, Schlenvoit, Amthor and Sauerbrey2006; Phuoc et al., Reference Phuoc, Corde, Thaury, Malka, Tafzi, Goddet, Shah, Sebban and Rousse2012).
In this paper, we propose a scheme for generating ultrashort positron beams by irradiating femtosecond γ-ray pulses (GRPs) obtained from Compton scattering off a thin metal target. The scheme is illustrated schematically in Figure 1. Since the head-on collision geometry is used for the Compton scattering, the GRP duration only depends on the (very short) length of the LWFA electron bunch, thereby eliminating the need (a key issue in current linacs or storage rings) for shortening the electron bunches. It is found that GRPs with average flux of 108/s can be obtained, and MeV positrons at over 107/s can be produced on a sub-100 fs time scale. In practice, such a positron source would be much compacter than the current linac or reactor based sources.
Fig. 1. Schematic illustration of positron generation via Compton scattering of laser light off LWFA electron beams (e− beams) and the resulting pair creation. An USUI pump laser is focused onto a gas-filled capillary-discharge waveguide or gas jet to generate an LWFA electron bunch. The X/γ rays are then generated by colliding the USUI electron bunch from LWFA with the light from a TW laser that drives the Compton scattering. After passing through the off-axis parabola, the Compton backscattered γ rays impinge on a thin high-Z target to generate an ultrashort positron pulse.
2. LWFA-DRIVEN FEMTOSECOND GRP
2.1 Principle
Compton scattering has been proposed as a means of generating tunable, short pulses of X/γ rays with narrow bandwidth (Hartemann et al., Reference Hartemann, Tremaine, Anderson, Barty, Betts, Booth, Brown, Crane, Cross, Gibson, Fittinghoff, Kuba, Sage, Slaughter, Wootton, Hartouni, Springer, Rosenzweig and Kerman2004; Chouffani et al., Reference Chouffani, Harmon, Wells, Jones and Lancaster2006; Luo et al., Reference Luo, Xu, Pan, Cai, Chen, Fan, Fan, Li, Liu, Lin, Ma, Shen, Shi, Xu, Xu, Xu, Zhang, Yan, Yang and Zhao2010). The most intense Compton scattered photons are produced when the laser light is backscattered off the electrons. For such head-on interaction geometry, the energy of the scattered photon is given by
$$E_P \approx \displaystyle{{4{\rm \gamma} ^2 E_L \over 1 + {\rm \gamma}^2 {\rm \theta}^2 + 4 {\rm \gamma}^2 E_L E_e}}\comma \;$$where E L and E e are the energies of incident photon and electron, respectively, γ is relativistic factor of the electron, and θ is the scattering angle relative to the electron trajectory. Accordingly, scattering of 800 nm (Ti:Sa) laser light off a 1 GeV LWFA produced electron bunch can generate a ≥20 MeV GRP. Considering the small divergence and narrow energy spread of the LWFA driven electron bunch, the on-axis spectral broadening of GRP for sufficiently small laser bandwidth and divergence can be roughly given by
$${\Delta E_P \over E_p} \sim \sqrt{\matrix{\displaystyle{{\rm \gamma}^4 \lpar \Delta {\rm \xi}_{xe}^2 + \Delta {\rm \xi}_{ye}^2\rpar ^2 \over 4} + {4\Delta {\rm \gamma}^2 \over {\rm \gamma}^2} \cr \displaystyle+ {\lpar \Delta {\rm \xi}_{xL}^2 + \Delta {\rm \xi}_{yL}^2\rpar ^2 \over 4} + {\Delta E_{_L}^2 \over E_{_L}^2}}}\comma \;$$where Δγ/γ and ΔE L /E L are the energy spreads of the electron beam and laser pulse, ξxe and ξye are the transverse (in the x and y directions, respectively) emittance of the electron beam, ξxL and ξyL are the effective (1/e 2) transverse emittance of the focused laser beam, using the analogy of the Rayleigh range to the beta function of a particle beam focus (Brown et al., Reference Brown and Hartemann2004), Δξxe,ye and ΔξxL,yL are the 1/e 2 divergence of the electron beam and laser pulse. The latter are both assumed to be Gaussian and narrow. It should however be emphasized that the GRP distribution is usually non-Gaussian, so that its spectral bandwidth should better be determined from the final energy spectrum after convolution with the distributions of the laser and electron beam parameters causing the broadening. On the other hand, the estimates in Eq. (2) should be applicable to the on-axis (or very small solid angle) γ rays.
The duration τp of the Compton-scattering GRP is determined by the interaction time of the electron and laser beams. For head-on collision, it is (Pogoelsky et al., Reference Pogoelsky, Ben-Zvi, Hirose, Kashiwagi, Yakimenko, Kusche, Siddons, Skaritka, Kumita, Tsunemi, Omori, Urakawa, Washio, Yokoya, Okugi, Liu, He and Cline2000)
$${\rm \tau}_p = {\rm \tau}_e + {\rm \tau}_L / 4{\rm \gamma}^2\comma \;$$where τL and τe are the durations of the laser pulse and the electron beam, respectively. Thus, LWFA electron bunches of sufficiently short duration can be used to generate fs GRPs.
For spatially overlapped and synchronized Gaussian laser pulse and electron beam of sufficiently small energy spread and emittance, the scattered photon flux can be approximately given by
$$N_p = {\,f\,{\rm \sigma} N_e N_L \over 2{\rm \pi} \sqrt{{\rm \sigma}_{ye}^2 + {\rm \sigma}_{yp}^2}} {1 \over \sqrt{\matrix{\lpar {\rm \sigma}_{xe}^2 + {\rm \sigma}_{xp}^2\rpar \lpar 1 - \cos {\rm \theta} _L\rpar ^2 \cr + \lpar {\rm \tau}_e^2 + {\rm \tau}_L^2\rpar c^2 \sin^2 {\rm \theta}_L}}}\comma \;$$where f is the laser and electron collision repetition rate, σ is the Compton scattering cross section, N e is the number of electrons in the bunch, N L is the total number of photons in the laser pulse, θL is the laser incident angle with respect to the electron beam, the subscripts e and p denote electrons and laser photons, respectively, and σx,y are the transverse beam sizes of the laser pulse.
2.2 Characterization of fs GRP from the LWFA
To investigate the spatial, temporal, and spectral characteristics of Compton scattering X/γ-ray sources, a 4D (three dimensional time and frequency domain) Monte Carlo laser-Compton scattering simulation (MCLCSS) code (Luo et al., Reference Luo, Xu, Pan, An, Cai, Fan, Fan, Li, Xu, Yan and Yang2011) has been developed with the Geant4 toolkit (Agostinelli et al., Reference Agostinelli2003). The code is used to investigate the properties of the USUI GRPs from the LWFA. The electron-bunch parameters given in Table 1 correspond to the LWFA experiments at the Lawrence Berkeley National Laboratory (Leemans et al., Reference Leemans, Nagler, Gonsalves, Toth, Nakamura, Geddes, Esarey, Schroeder and Hooker2006). For comparison, the parameters of current synchrotron radiation facilities are also given. Electron energies up to 1.0 GeV are of particular interest, since they can yield MeV to tens MeV γ rays, which are needed for pair production on the femtosecond time scale, as well as for other applications such as nondestructive assay of nuclear fuel, waste, and specific nuclide using nuclear resonance fluorescence.
Table 1. LWFA driven electron beam parameters (Leemans et al., Reference Leemans, Nagler, Gonsalves, Toth, Nakamura, Geddes, Esarey, Schroeder and Hooker2006) and Ti:Sa laser-pulse parameters used in the simulation. For comparison, the key parameters of typical linac-based storage rings are also shown
Figure 2a shows the total γ-ray energy spectrum obtained from the Monte Carlo simulations. For the LWFA driven electron beam with energies of 1.0 (0.5) GeV, the average on-axis γ-ray energies equal to about 23.2 (5.9) MeV. Since an infinitely small collimation angle is employed, the γ-ray spectral broadening is calculated to be about 6.0% at 23.2 MeV based on Eq. (3). The total (at all frequencies and angles) γ-ray dose is about 1.06 × 107 photons. From Eq. (4), one see that for a 10 Hz laser-electron collision repetition rate the flux of the resulting GRP is 1.06 × 108 photons/s, with the peak flux exceeding 4 × 1020 photons/s. When the 1.0 GeV LWFA driven electron beam is used, the corresponding peak γ-ray brilliance can be up to 1020 photons/s/mm2/mrad2/0.1%bandwidth.
Fig. 2. (a) Total energy spectrum obtained from the MCLCSS code. (b) Temporal profile of the GRP obtained from a Gaussian LWFA electron bunch. The LWFA driven electron beam parameters are: 50 pC charge, 5 nm-mrad emittance, 3 µm (rms) spot sizes, and 2.5% energy spread.
Figure 2b shows that a 10-fs LWFA electron bunch can produce a similarly short GRP. Although at present the experimental measurement of ultrashort GRP remains an issue, besides useful for pair production on the femtosecond time scale, such short-pulse GRPs are of interest to applications such as pulse radiolysis since the properties of the scattered GRP is fully determined by the temporal profile of LWFA electron bunch and the GRP can yield fast time resolved information on the latter.
3. ULTRA-SHORT MeV POSITRON BEAM GENERATION
To produce positron-electron pairs, the energy of the scattered photons must be larger than the threshold E 0 = 1.022 MeV. For m ec 2 ≪E p < 137m ec 2Z −1/3, the cross section for pair production is (Rossi, Reference Rossi1952)
$${\rm \sigma}_{\rm pair} = {\rm \sigma}_0 Z^2 \left[{28 \over 9} \ln \left({2E_p \over m_e c^2} \right)- {218 \over 27} \right]\comma \;$$where σ0 = 5.8 × 10−28 cm2, Z is the atomic number, and m ec 2 is the electron rest energy. Since the cross section of the pair production is proportional to Z 2, high-Z material should be used.
We use the Monte Carlo code Geant4 to determine the electron-positron pair production (emission) rate for several high-Z materials including Pt, W, and Pb. It is found that the Pb target results in maximum pair yield. Figure 3 shows that the optimum target thickness for pair production is about 4 mm, corresponding to a maximum generation rate of about 0.10 per γ-ray photon. For the γ-ray flux of 108/s mentioned earlier, one can expect an emission flux of 107 positrons/s in the form of a relativistic positron beam with about 20° divergence angle. Thus, about 3 × 107 positrons per unit solid angle may be achieved.
Fig. 3. Total positron flux and the corresponding bunch length as a function of the target thickness, from Monte Carlo simulation with the Geant4 toolkit. The calculation is for the spectrum (dotted curve) in Figure 2a.
The duration of the positron pulse depends mainly on the target thickness and the duration of the GRP. As shown in Figure 3, a thinner target will result in shorter positron pulse duration. When a 4-mm-thick Pb plate is irradiated, the root mean square bunch length of the positrons can be as short as 166 fs. If one decreases the thickness of Pb plate to less than 2 mm, a sub-100 fs ultrashort positron bunch of considerable charge can be obtained. In practice, the bunch duration can be longer because of its interaction with the nuclei or the outer electrons via multiple scattering, ionization, and bremsstrahlung, but it is still shorter than that from the existing position sources by at least one order of magnitude.
Figure 4 shows the evolution of the energy spectrum of the emitted positrons. It has a peak at around 7 MeV. The energy spectrum of the electrons has a similar peak. However, the total electron flux (the green-circle curve in Fig. 3) is always higher than the positron flux (the blue-square curve in Fig. 3). This is to be expected, since the electrons are from both Compton scattering and pair creation, but the positrons are only from the latter.
Fig. 4. Evolution of the positron spectrum, obtained from Monte Carlo simulation. The calculation corresponds to the spectrum given by the dotted curve shown in Figure 2a, for a 4 mm lead target.
4. SUMMARY
In this paper, a scheme for generating ultrashort positron bunches using moderate-flux short-pulse γ-ray radiation is proposed. The GRP is generated by Compton scattering of laser light off an USUI LWFA driven electron beam. The GRP is then impinged on a thin metal target to realize pair production and the energetic positron bunch. It is shown that from a 1 GeV, 50 pC, and 10 fs LWFA electron bunch, femtosecond GRP with a flux of 108/s can be obtained. By optimizing the thickness of the Pb target, more than 107 positrons/s in 100 fs pulses at peak energies of about 7 MeV can be obtained. Energetic positrons with even higher fluxes can be expected if a higher charged, such as the ≥160 pC pulse from the electron bow-wave injection Scheme (Ma et al., Reference Ma, Kawata, Yu, Gu, Sheng, Yu, Zhuo, Liu, Yin, Takahashi, Xie, Liu, Tian and Shao2012), electron bunch is used to generate the GRP.
ACKNOWLEDGMENTS
This work was supported by the National 863 High-Tech Committee and the National Natural Science Foundation of China (projects 11247215, 11175253, 10976031, and 10835003). We would like to thank the National Supercomputing Center in Tianjin for providing their computational facilities.
