Polarized positron beams via intense two-color laser pulses

TL;DR

This paper presents a theoretical study demonstrating that intense two-color laser pulses can generate highly polarized ultrarelativistic positron beams with significant polarization, low divergence, and high density, within femtosecond timescales.

Contribution

It introduces a novel method using two-color laser pulses to produce polarized positrons, leveraging spin asymmetries in pair production processes in strong fields.

Findings

Positron beams with approximately 60% polarization can be generated.

The produced positrons have a small angular divergence of about 74 mrad.

The density of the positron beam can reach approximately 10^14 cm^-3.

Abstract

Generation of ultrarelativistic polarized positrons during interaction of an ultrarelativistic electron beam with a counterpropagating two-color petawatt laser pulse is investigated theoretically. Our Monte Carlo simulation based on a semi-classical model, incorporates photon emissions and pair productions, using spin-resolved quantum probabilities in the local constant field approximation, and describes the polarization of electrons and positrons for the pair production and photon emission processes, as well as the classical spin precession in-between. The main reason of the polarization is shown to be the spin-asymmetry of the pair production process in strong external fields, combined with the asymmetry of the two-color laser field. Employing a feasible scenario, we show that highly polarized positron beams, with a polarization degree of $\zeta\approx 60\%$, can be produced in a femtosecond time scale, with a small angular divergence, $\sim 74$ mrad, and high density $\sim 10^{14}$ cm$^{-3}$. The laser-driven positron source, along with laser wakefield acceleration, may pave the way to small scale facilities for high energy physics studies.

Full text

Accelerated beams of polarized positrons have important applications in high-energy physics, and solid-state physics. Polarized electrons and positrons are powerful probes for precise measurement of the nucleon spin structure by deep inelastic lepton scattering Subashiev et al. (1998); Voutier (2014), for measurement of the electroweak mixing angle in Møller scattering Anthony et al. (2005), as well as for study of magnetic properties and inner structural defects of materials Gidley et al. (1982); Krause-Rehberg and Leipner (1999). The future International Linear Collider (ILC) is designed to bring revolutionary new insight into our understanding of the fundamental interactions, to test the Standard Model with unprecedented precision, and to search for new physics beyond it. A key element for maximizing the physics capability of ILC is the ability to provide intense (3$\times 10^{10}$/bunch) highly polarized electron ( $>80\%$ polarization) and positron ($30\%\sim 60\%$ polarization) sources Moortgat-Pick et al. (2008); Vauth and List (2016); Scott et al. (2011).

While there are several methods for electron polarization, for instance, illuminating a photocathode by circularly polarized light Pierce and Meier (1976), or with radiative polarization in a storage ring via the Sokolov-Ternov effect Sokolov and Ternov (1964, 1968); Baier and Katkov (1967); Baier (1972), however, it is much more demanding to obtain polarized positron beams. For the latter a two step method has been commonly applied. Firstly, circularly polarized $\gamma$-photons are produced, which are then converted to polarized positrons via pair production in a thin high-$Z$ target. Polarized $\gamma$-photons can be generated by Compton backscattering of circularly polarized laser light off ultrarelativistic electrons Sakai et al. (2003); Omori et al. (2006). With the same scheme, in the Stanford Linear Accelerator Center (SLAC) polarized positrons have been successfully produced in an undulator-based experiment (E166), where multi-MeV circularly polarized photons are produced by a 46.6-GeV electron beam passing through a helical undulator Alexander et al. (2008, 2009). However, the high cost of providing suitable helical undulator and techniques to avoid destruction of target may limit the application of these schemes to a wide community. Moreover, the present technique available for ILC, is based on a 100 m long helical undulator, and allows positron sources with only up to $30\%$ polarization degree Barish (2006), and challenging technical upgrades are required to reach the ILC target parameters Scott et al. (2011).

Recent development of the strong laser technique, see e.g. Yanovsky et al. (2008); Kessel et al. (2018); AST , raised hopes to polarize electrons and positrons with laser fields. At first sight, the strong magnetic field of a laser pulse could induce a significant radiative polarization of electrons (positrons) interacting with it. However, unfortunately the laser field has an oscillating character, changing the field direction in subsequent field cycles, as a consequence in a monochromatic laser field the polarization of a particle due to nonlinear Compton scattering is vanishing Kotkin et al. (2003); Ivanov et al. (2004); Karlovets (2011) and is small in a case of a short laser pulse Seipt et al. (2018). Recent progress in the theory shows that significant polarization for electrons can be acquired in a rotating electric field Del Sorbo et al. (2017, 2018), which models anti-nodes of a circularly polarized standing laser wave. However the electrons cannot be trapped in anti-nodes of a circularly polarized standing wave Bashinov et al. (2017), in contrast to the anomalous radiative trapping in the case of linear polarization Gonoskov et al. (2014). In another development, it has been shown recently Li et al. (2018) that with a fine tuning of the ellipticity of the symmetric laser field, the splitting of the particle beam with respect to polarization can be achieved due to spin-dependent radiation reaction. The same scheme is employed in the pair production regime to split the created positrons with respect to polarization Wan et al. .

The petawatt laser technology Danson et al. (2015); Vul ; ELI ; XCE enables another potential method to produce polarized positrons via the multiphoton Breit-Wheeler process Ritus (1985), when $e^{-}e^{+}$ pairs are produced due to a high-energy $\gamma$-photon interacting with a strong laser field, accompanied with multiple photon absorption from a strong laser field (firstly demonstrated in the famous SLAC experiment E-144 Burke et al. (1997)). Note that recently generation of unpolarized electron-positron jets for laboratory astrophysics has been demonstrated experimentally in laser-solid interaction Chen et al. (2009, 2010); Liang et al. (2015), and in laser-electron beam interaction Sarri et al. (2015).

Generally, the radiative polarization of electrons (positrons) requires asymmetric laser fields, but what is remarkable, with a given asymmetric field the spin-dependent asymmetry is stronger for the pair production process than for a photon emission. Consequently, the polarization of the electrons (positrons) during pair production process in that field generally will outstrip the radiative polarization. In previous studies Tsai (1993); Ivanov et al. (2005); Jansen et al. (2016), the polarization effects in the multiphoton Breit-Wheeler process have been considered in plane wave laser fields mostly of moderate intensity. It remained unclear if the sizable polarization of positrons in realistic strong laser fields is feasible.

In this Letter, we investigate theoretically the feasibility of production of collimated and highly polarized ultrarelativistic positron beams during interaction of an ultrarelativistic electron beam with a counterpropagating two-color intense laser pulse in quantum radiation dominated regime, based on the setup in Fig. 1. During the interaction $\gamma$-photons via nonlinear Compton scattering are generated, which subsequently decay into electron-positron pairs in multiphoton Breit-Wheeler process. With Monte Carlo simulations we study the spin-resolved dynamics of electrons and positrons during pair production and photon emission processes, as well as during propagation in the laser field. In our scheme, positrons are mostly polarized due to the intrinsic asymmetry of spin-resolved pair production probability in strong fields, combined with the asymmetry of the two-color laser field configuration. As a result, an ultrarelativistic positron beam with $60\%$ polarization, with uniformly distributed polarization within the divergence angle can be generated with realistic laser fields.

We employ a semi-classical method to describe the electron (positron) spin-resolved dynamics in nonlinear Compton scattering Ridgers et al. (2014); Elkina et al. (2011); Green and Harvey (2015). The photon emissions and pair productions are simulated via spin-resolved quantum probabilities and the Monte Carlo algorithm, similar to Li et al. (2018) (see also the more recent work Geng et al. (2019)). The employed spin resolved photon emission and pair production probabilities are derived with the QED operator method under the local constant field approximation Shaisultanov ; Baier et al. (1998); sup . The spin precession in the external field is described by Bargmann-Michel-Telegdi (BMT) equation Bargmann et al. (1959); Walser et al. (2002). The accuracy of our Monte-Carlo code is confirmed by reproducing the results on the radiative polarization Baĭer (1972); Jackson (1976); Del Sorbo et al. (2018); Seipt et al. (2018); Li et al. (2018) and pair production Gonoskov et al. (2015); Sokolov (1986), see sup .

We consider interaction of an intense two-color linearly polarized laser pulse with a counterpropagating ultrarelativistic electron beam, as shown in Fig. 1. The two-color field consists of two laser pulses of $\lambda_{1}=1\,\mu$m and $\lambda_{2}=0.5\,\mu$m wavelengths, and $\tau_{p1}=10T_{1}$ and $\tau_{p2}=20T_{2}$ pulse durations, respectively. Their peak intensities ($I_{0i}$, $i=1,2$) fulfill the ratio $R\equiv\xi_{1}/\xi_{2}=2$, with the dimensionless field parameter $\xi_{i}=|e|E_{0i}/(m\omega_{i})=85.5\sqrt{\lambda_{i}\,[\mu\text{m}]^{2}I_{0i}\,[10^{22}\text{W/cm}^{2}]}$, the laser field amplitude $E_{0i}$, and frequency $\omega_{i}$, the electron charge $e$, and mass $m$; the relativistic units with $\hbar=c=1$ are used throughout. The phase difference between the two color fields is chosen as $\Delta\phi=0$ to obtain the maximum field asymmetry. The beam waist size is $5\lambda_{1}$ for both laser pulses. The cylinder electron beam has a longitudinal uniform distribution and transverse Gaussian distribution, with a standard deviation $\sigma=0.4\lambda_{1}$, beam length $L_{e}=10\lambda_{1}$, the number of electrons in the bunch is $N_{e}=10^{6}$. The initial kinetic energy spread of electron bunch is $\Delta\varepsilon/\varepsilon_{0}=0.02$, and the angle divergence is $1$ mrad.

When choosing the laser intensity and the electron energy, we should take into account that the pair production is substantial when the quantum field parameter $\chi_{\gamma}\gtrsim 1$, where $\chi_{\gamma,e}=|e|\hbar\sqrt{(F_{\mu\nu}p_{\gamma,e}^{\nu})^{2}}/m^{3}$, with $p_{\gamma,e}$ being the 4-momentum of the $\gamma$-photon, and electron, respectively, and $F_{\mu\nu}$ the field tensor. One may assume that during nonlinear Compton scattering photon and electron energies are of the same order, and estimate $\chi_{\gamma}\sim\chi_{e}$. In the counterpropagating setup $\chi_{e}\approx 2(\omega_{i}/m)\xi_{i}\varepsilon_{0}/m\approx 0.59\times\varepsilon_{0}\,[\text{GeV}]\sqrt{I[10^{22}\,\text{W/cm}^{2}]}$, with the electron initial energy $\varepsilon_{0}$.

As the presently available laser intensities do not exceed $10^{22}\,\text{W/cm}^{2}$ Yanovsky et al. (2008), and for the electron energies via laser wakefield acceleration the electron energy is less than 10 GeV Leemans et al. (2014), we choose as typical parameters: the initial electron energy $\varepsilon_{0}=2$ GeV, and the laser full intensity parameter $\xi_{0}=\xi_{1}+\xi_{2}=100$. The produced positron beam parameters are summarized in Fig. 2. The total number of produced positrons is $N_{+}\sim 2\times 10^{4}$, which travel in forward direction, with the full width at half maximum (FWHM) of the angular distribution $\theta_{+}\approx 74$ mrad, see Fig. 2 (c), and (i). The averaged spin component of the produced positrons along magnetic field direction ($y$-axis) has a nearly uniform angular distribution ($\overline{\zeta_{y}}=0.58$) within FWHM, see Fig. 2 (f) and (i). The angle-independence of the positron beam polarization renders further collimation feasible without polarization damage. The produced electrons have similar properties as positrons except the opposite sign for polarization, see Fig. 2 (b), (e), and (h). The seed electrons have narrower angular distribution, as shown in Fig. 2 (a) and (g), but the polarization degree is significantly lower, $\overline{\zeta}_{y}=-0.077$, than that of the produced $e^{-}e^{+}$ pairs. The latter indicates that the polarization mechanisms for the seed electrons and created particles are different.

To elucidate the reason for the significant polarization of positrons in the two-color laser field, we compare the spin dynamics in one- and two-color laser fields with $\xi_{0}=100$ in Fig. 3 (a). It can be seen that the polarization of seed electrons oscillates in the laser fields for both cases, but only in the two-color field seed electrons acquire a small $\overline{\zeta}_{y}$. The reason is the almost complete symmetry in the laser magnetic field direction in the case of a single color field, and its asymmetry in the two color field. After each photon emission the electrons (positrons) are more likely to flip opposite (along) the magnetic field direction in the particle rest frame, which is approximately parallel (anti-parallel) to the magnetic field direction $B_{y}$ for electrons (positrons) in the Lab-frame. This is because the spin resolved emission probability is in favor of spin down for electrons. As shown in Fig. 3 (d), $W_{r\downarrow}/W_{r}>50\%$, where $W_{r}$ is the radiation total probability, and $W_{r\downarrow}$ is the probability with finial spin anti-parallel to the magnetic field. Therefore, $\overline{\zeta}_{y}$ of seed electrons increases during $B_{y}<0$ and decreases during $B_{y}>0$, see Fig. 3 (a). In the one-color laser pulse, $\overline{\zeta_{y}}$ oscillates symmetrically in consecutive laser cycles. While two-color field breaks this symmetric pattern in $\overline{\zeta}_{y}$ oscillation, more electrons emit photons and acquires $\zeta_{y}<0$ during $B_{y}>0$, which results in a -7.7$\%$ polarization at the end of the interaction, see Fig. 3 (a).

Unlike the seed electrons that are slightly polarized due to radiative polarization, the produced positrons (electrons) are highly polarized $\overline{\zeta}_{y}\sim 60\%$, see Fig. 2 (i). Although, the polarization of seed electrons and created pairs both benefit from the asymmetry of the two-color field configuration, however, the asymmetry has more significant impact on the polarization of the pairs than on the seed electrons. This is because seed electrons are polarized by radiative polarization due to photon emissions, while the pair polarization mainly comes from the creation process. There are two reasons for spin-asymmetry in the pair production process in an asymmetric field. First of all, the spin related terms in the probabilities play a more important role in the case of pair production than in radiation, as shown in Fig. 3 (d). It is much more probable to have a positron along magnetic field during the pair production process (around $80\%$), than due to photon emission (around $55\%$). Secondly, the probability of the pair production has a stronger dependence on the laser intensity than the radiation probability. As shown in Fig. 3 (c), the pair production takes place mainly in the dominant half-cycles of the two-color field, and fully suppressed in the weak half-cycle, while photons are emitted in both half-cycles with slightly different probabilities. The second is the main reason for highly polarized positrons in a two-color field.

Since positrons are more probable to be produced along the instantaneous laser magnetic field, in one-color symmetric laser field the averaged polarization is negligible after the interaction, as shown in Fig. 3 (a). While in the two-color asymmetric field a large polarization for positron beam is obtained, because positrons are mostly produced at $B_{y}>0$, see Fig. 3 (b) and (c), and the probability for these positrons to be polarized with $\zeta_{y}>0$ is very large, see Fig. 3 (d). Therefore, the positron density for $\zeta_{y}>0$ is far higher than that for $\zeta_{y}<0$.

We underline that the positron initial polarization degree during the production process further decreases due to photon emissions. This is because the radiative polarization has less spin dependence than the pair production, according to Fig. 3 (d). Positrons produced with $\zeta_{y}>0$ have a chance to flip to $\zeta_{y}<0$ when emitting photons at $B_{y}<0$, which brings down the polarization. Fortunately, the decrease of the polarization degree is not large from, the $\overline{\zeta}_{y}\sim 60\%$ at the production point to the final $\overline{\zeta}_{y}\sim 58\%$, as it is shown in Fig. 2 (i).

We have investigated the optimal conditions for positron polarization and the results are summarized in Fig. 4. Firstly, we varied the ratio ($R$) of laser intensities. Fig. 4 (a) shows that $R=2$ is the optimal choice of relative laser intensities to obtain higher polarization. In fact, in this case the two-color field is most asymmetric, when the $B_{y}<0$ parts of the field reaches to minimum strength. Increasing laser intensity yields more pairs, see Fig. 3 (c), but reduces the averaged polarization and increases angular divergence, see Fig. 3 (a) and (b). This is because higher laser intensity triggers more pair production in negative parts of laser fields, bringing in more positrons with $\zeta_{y}<0$. The similar scaling laws can also be found for electrons’ initial energy, as shown in Fig. 4 (c)-(d). More energetic electrons give rise to more pairs and better emittance but compromise the polarization degree. Therefore, polarized positron beam production is a multidimensional problem with cross-talking parameters. If high polarization has priority over positron density, smaller laser intensity and initial electron energy is preferable to suppress contributions from $B_{y}<0$. If one aims for an intense $e^{+}$ beam with moderate polarization degree, higher laser intensity and more brightness of electrons are more preferable.

The number of initial electrons in our simulation is $10^{6}$, which yields a final electron number in the bunch $10^{6}$, and $10^{4}$ positrons in the bunch, with $8\%$ and $60\%$ polarization degree, respectively. The available laser wakefield acceleration technique can provide approximately $10^{10}$ electrons in the GeV regime Leemans et al. (2014), which will allow for $10^{8}$ polarized positrons in the bunch with $\zeta\approx 60\%$ degree of polarization ($10^{10}$ electrons per bunch with $\zeta\approx 8\%$). The latter parameters are sufficient to permit experiments for future colliders.

In summary, we have put forward a concept of two-color laser-based production of polarized positron beams. It employs an unpolarized electron driver and presently available ultrastrong lasers. In contrast to known radiative polarization, the polarization of positrons during their creation in the laser field is shown to be much more sensitive to the field asymmetry, and allows for a high degree of polarization. This technique is not based on a large scale facility and opens access for polarized positron beams to a wide community.

P.-L.H. acknowledges the support from the China Scholarship Council (CSC).