The technique for producing polarized beams depends not only on the particle species, but also on their kinetic energies. For stable ones, such as electrons or protons, polarized sources can be employed with subsequent acceleration in a linear accelerator or a synchrotron. For unstable particles, like muons, polarization-dependent particle decays are exploited^[3], while stable secondary beams, like antiprotons, might be polarized in dedicated storage rings by spin-dependent interactions^[13]. Electron or positron beams also spontaneously polarize in the magnetic fields of storage rings due to the emission of spin-flip synchrotron radiation, the so-called Sokolov–Ternov effect^[14–16]. This effect was first experimentally observed with low degrees of polarization^[17,18], and later utilized at several electron rings to generate a highly polarized beam during storage^[19–25].

All of the above scenarios still rely on conventional particle accelerators that are typically very large in scale and budget^[16]. In circular accelerators, depolarizing spin resonances must be compensated by applying complex correction techniques to maintain the beam’s polarization^[26–32]. In linear accelerators, such a reduction of polarization can be neglected due to the very short interaction time between particle bunches and the accelerating fields.

Concepts based on laser-driven acceleration at extreme light intensities have been promoted during recent decades. Ultra-intense and ultra-short laser pulses can generate accelerating fields in plasmas that are at the order of tera-volts per meter, about four orders of magnitude greater compared to conventional accelerators. The goal, therefore, is to build the next generation of highly compact and cost-effective accelerator facilities using a plasma as the accelerating medium; see for example Ref. [33]. Despite many advances in the understanding of the phenomena leading to particle acceleration in laser–plasma interactions, however, a largely unexplored issue is how an accelerator for strongly polarized beams can be realized. In simple words, there are two possible scenarios: either the magnetic laser or plasma fields can influence the spin of the accelerated beam particles, or the spins are too inert, such that a short acceleration has no influence on the spin alignment. In the latter case, the polarization would be maintained throughout the whole acceleration process, but a pre-polarized target would be required.

In this paper, we review the concepts and methods that could lead to the generation of polarized particle beams based on ultra-intense lasers. We focus on two main approaches. The first one is devoted to collision between unpolarized high-energy electron beams and ultra-relativistic laser pulses, introduced in Section 2.1. Section 2.2 focuses on concepts for pre-polarized targets for sequential particle acceleration. Suitable targets are described in Section 7.

Strong-field quantum electrodynamics (QED) processes – like nonlinear Compton scattering and radiation reactions – can strongly modify the dynamics of light charged particles, such as electrons or positrons. Analogous to the Sokolov–Ternov effect in a strong magnetic field, electrons can rapidly spin-polarize in ultra-strong laser fields due to an asymmetry in the rate of spin-flip transitions, i.e., interactions where the spin changes sign during the emission of a γ-ray photon. Several such scenarios have been discussed in the literature; for a more quantitative discussion we refer to Section 4.

It is still an issue for current research how particle spins are affected by the huge electromagnetic fields that are inherently present in laser-induced plasmas or in the laser fields themselves, and what mechanisms may lead to the production of highly polarized beams. Early attempts to describe these processes can be found in Refs. [47,58]. A schematic overview of the interplay between single particle trajectories (blue), spin (red) and radiation (yellow) is shown in Figure 8; details can be found in Ref. [48].

In cgs units the rotational frequency $\overrightarrow{\varOmega}$ is given by^[16]

 (2)

where

 (3)

Spin precession is a deterministic process and can be calulated by treating the spin as an intrinsic electron magnetic moment. In the non-QED regime, only a theory, which contains the T–BMT equation, describes the particle and spin motion in electromagnetic fields in a self-consistent way.

Under classical and semi-classical limits, the acceleration of charged particles is treated within the framework of classical field theory. This theory also describes the reaction of the particle motion due to radiation, if the particle energy and/or laser field strength is sufficiently high. Introducing spin into electron dynamics leads to a spin-dependent radiation reaction. The radiation power of electrons in different spin states varies such that they feel a stronger radiation-reaction force when the spins are anti-parallel to the local magnetic field in the rest frame of the radiating electron, which can lead to a split of electrons with distinctive spin states.

The Stern–Gerlach force primarily influences the trajectory of a particle. In general, the radiation-reaction force exceeds the Stern–Gerlach force by far if the particles are relativistic (kinetic energies well above 1 GeV) or even ultra-relativistic (above 1 TeV) (see also Ref. [36]). There are, however, some field configurations that reverse this situation, so that the radiation-reaction force can be neglected compared to the Stern–Gerlach force (see e.g., Ref. [61]).

A direct coupling between single particle spins and radiation fields is treated in the context of quantum field theory. Within this theory, the mechanism that describes the spontaneous self-polarization of an accelerated particle ensemble is known as the Sokolov–Ternov effect. The stochastic spin diffusion from photon emission is a non-deterministic process resulting in the rotation of the spin vector in the presence of a magnetic field with the emission of a photon.

A discussion of the generalized Stern–Gerlach force shows that the trajectories of individual particles are perturbed by a change of the particle’s motion induced by the T–BMT equation rather than by coupling of the spin to the change of the particles’ energy or velocity rates; while even small field variations must be taken into account^[48]. With regard to a possible polarization build-up through spin-dependent beam split effects, it is found that a tera-electron volt electron beam has the best option to be polarized when the plasma is dense enough and the acceleration distance (time) is large enough. For protons, we do not see any realistic case to build up a polarization by beam separation. In conventional circular accelerators, the Sokolov–Ternov effect restores the alignment of the spins in experimentally proven polarization times in the range of minutes or hours, depending on the energy of the beam and the bending radius of the beam in bending magnets. The scaling laws for laser-plasma fields predict that the spins of electron moving in strong (≈10¹⁷ V/m) fields should be polarized in less than a femtosecond^[48].

Del Sorbo et al.^[37,39] proposed that this analog of the Sokolov–Ternov effect could occur in the strong electromagnetic fields of ultra-high-intensity lasers, which would result in a buildup of spin polarization in femtoseconds for laser intensities exceeding 5 × 10²² W/cm². In a subsequent paper^[38] they develop a local constant crossed-field approximation of the polarization density matrix to investigate numerically the scattering of high-energy electrons from short, intense, laser pulses.

Description of the spin-dependent dynamics and radiation in optical laser fields requires a classical spin vector that precesses during photon emission events following the T–BMT equation. This is accomplished by projecting the spin states after each emission onto a quantization axis. The latter could be the local magnetic field in the rest frame of the radiating electron^[34,42]. Alternatively, Seipt et al.^[40] suggest that the spin orientation either flips or stays the same, depending on the radiation probability. It has recently been pointed out by Geng et al.^[62] that, by generalizing the Sokolov–Ternov effect, the polarization vector consisting of the full spin information can be obtained.

In a follow-up paper, Guo et al.^[35] investigate stochasticity effects in radiative polarization of a relativistic electron beam head-on colliding with an ultra-strong laser pulse in the quantum radiation-reaction regime. These enhance the splitting effect into the two oppositely polarized parts as described by Li et al.^[34]. Consequently, an increase of the achievable electron polarization by roughly a factor of two is predicted at the same required high accuracy for the selection of the electron deflection angles.

Another paper from Li et al.^[63] investigates the impacts of spin polarization of an electron beam head-on colliding with a strong laser pulse on the emitted photon spectra and electron dynamics in the quantum radiation regime. Using a formalism similar to that of Li et al.^[34], they developed an alternative method of electron polarimetry based on nonlinear Compton scattering in the quantum radiation regime. Beam polarization can be measured via the angular asymmetry of the high-energy photon spectrum in a single-shot interaction of the electron beam with a strong laser pulse.

For positrons, rather high degrees of polarization seem to be achievable, even for currently achievable laser parameters. Chen et al.^[42] employ a scenario with an initial electron energy of 2 GeV and laser full intensity a₀ = 83. It has been shown that highly polarized positron beams with 2 × 10⁴ particles and a polarization degree of 60% can be obtained within a small angular divergence of ~ 74 mrad. Wan et al.^[43] find that their optimal parameters include a laser intensity of the order of 10²² W/cm², an ellipticity of the order of 0.03, a laser pulse duration less than about 10 cycles and an initial electron energy of several giga-electron volts (GeV). This leads to 86% polarization of the positron beam, with the number of positrons more than 1% of the initial electrons. As for the electron beams in Ref. [34], however, the emission angles of the two positron beams with opposite polarization differ by only a few milliradians. Li et al. use a peak laser intensity of I = 2.75 × 10²² W/cm² (a₀ = 141), a full width at half maximum (FWHM) pulse duration of five laser periods, laser wavelength 1 μm and focal radius 5 μm. The initial electron kinetic energy is 10 GeV, the energy spread 6% and the angular divergence 0.2 mrad^[44]. In this scenario, a highly polarized (up to 65%), intense (up to 10⁶/bunch) positron beam can be obtained.

Wen et al.^[45] demonstrate that kilo-ampere (kA) polarized electron beams can be produced via laser-wakefield acceleration from a gas target. For this purpose, they implement the electron spin dynamics in a PIC code, which they use to investigate electron beam dynamics in self-consistent three-dimensional particle-in-cell simulations. By appropriately choosing the laser and gas parameters, they show that the depolarization of electrons induced by the laser-wakefield acceleration process can be as low as 10%. In the weakly nonlinear wakefield regime, electron beams carrying currents of the order of 1 kA and retaining the initial electronic polarization of the plasma can be produced. The predicted final electron beam polarization and current amount to (90.6%, 73.9%, 53.5%) and (0.31 kA, 0.59 kA, 0.90 kA) for a₀ = (1, 1.1, 1.2), respectively. Wen et al. point out that compared to currently available conventional sources of polarized electron beams, the flux is increased by four orders of magnitude.

From the literature outlined in Sections 2–5 it becomes clear that a wealth of (mostly theoretical) pathways towards the realization of laser-induced polarized particle acceleration have been put forward in recent years. These concepts strongly differ for the various particle species. In some cases it is necessary to wait for significant progress in laser technology. Our conclusions for a strategy aiming at the speedy realization of laser-induced polarized particle acceleration are given below.

1. (1)For currently realistic laser parameters, pre-polarized targets are needed to achieve electron beams with polarizations well above 10%. Such targets should provide high degrees of electronic polarization (> 50%) and should allow for operation at laser facilities (e.g., robustness against electromagnetic pulses (EMPs) and target heating).
2. (2)Due to their three-orders-smaller magnetic moments, measurable polarization for heavier particles (protons, ions) can only be achieved with nuclear pre-polarized targets.
3. (3)For positrons, no pre-polarized targets can be realized. Here, high degrees of polarization (90%) can be obtained from the scattering of peta-watt laser pulses off an unpolarized relativistic electron beam (which can be laser-generated). Such schemes require precise control of all involved beam pointings (to the few-milliradian level).
4. (4)Gas-jet targets are preferable to foil targets since they allow operation with state-of-the-art kilo-hertz laser systems. Low-density targets are also less challenging in terms of depolarizing effects.

For the experimental realization of polarized beam generation from laser-induced plasmas, the choice of the target is a crucial point. Pre-polarized solid foil targets suitable for laser acceleration via target normal sheath acceleration (TNSA) or radiation-pressure acceleration (RPA) are not yet available, and their realization seems extremely challenging. In previous experiments, hydrogen nuclear polarization has mostly been realized through a static polarization, e.g., in frozen spin targets^[65] or with polarized ³He gas. For proton acceleration alone, polarized atomic beam sources based on the Stern–Gerlach principle are currently available, which, however, offer a too small particle density^[66]. To laser-accelerate polarized electrons and protons, a new approach with dynamically polarized hydrogen gas targets is needed. A statically polarized ³He target, a dynamically polarized hydrogen target for protons, as well as a hyperpolarized cryogenic target for the production and storage of polarized H₂, D₂ and HD foils are being prepared at the Forschungszentrum Jülich within the ATHENA project.

The magnetic holding field consists of an outer Halbach array composed of an upper and lower ring of 48 NdFeB permanent magnets, 1100 mm in diameter, together with an inner Helmholtz coil array consisting of four single Helmholtz coils. In the Halbach array the permanent magnets are stacked at an optimum distance such that its field homogeneity is sufficiently high to maintain nuclear ³He polarization. The Helmholtz coils are oriented so that their magnetic field is aligned parallel to the laser-propagation direction. A single coil consists of a coiled Cu sheet with a width and thickness of 40 mm. The outer and inner diameters of the naked Cu coil are 789 mm and 709 mm, respectively. Both inner coils are separated by 285.75 mm, while the two single front/rear coils are separated by a distance of 218.95 mm. In contrast to electric coils, the permanent magnets used do not need to be cooled in vacuum, and they provide a constant field, even in the presence of huge EMPs^[67].

The second essential component for the layout of a polarized ³He target is the gas-jet source. The pre-polarized ³He gas is delivered at an intrinsic pressure of 3 bar. By using a pressure booster built of non-magnetic materials, the desired final pressure can be reached (up to 30 bar). To synchronize the gas flux with the incoming laser pulse, a home-made non-magnetic valve with piezo actuators has been prepared. In order to generate a broad plateau-like density distribution with sharp density gradients, a supersonic de Laval nozzle is used.

The fifth-harmonic beam is guided by customized optics with the highest possible light reflectance (reflection > 98% at 45° incidence angle provided by Layertec GmbH) having a diameter of one inch for a beam diameter of 12 mm. A quartz quarter-wave plate with two-sided anti-reflection coating from EKSMA Optics converts the initially linearly polarized laser beam to circular polarization. Finally, the UV beam is focused below the HCl or HBr nozzle inside the interaction chamber. The fundamental beam at 1064 nm is guided by standard mirrors with dielectric Nd:YAG coatings and focused to an intensity of about 5 × 10¹³ W·cm⁻² into the HCl or HBr gas. The gas is injected into the interaction chamber by a high-speed short-pulse piezo valve that can be operated at a maximum 5 bar inlet gas pressure to produce a gas density in the range of about 10¹⁹ cm^−3[51^,64^]. The valve is adjustable in height so that sufficient amounts of HCl or HBr molecules, which are spread in a cone-like shape, interact with the laser beams by keeping the backing pressure low, and thus the molecules’ mean free path large enough.

In the next step, a small pipe, to include an independent cooling and power supply, will be installed on one side of the cell having no direct contact with the cell. In this way, molecules can be generated and pre-cooled in the storage cell before they are frozen in the new pipe. Thus, the molecules in the storage cell can still be ionized and accelerated to measure their polarization. After the atomic flow is stopped, the pipe slowly warms up. In this way, the polarization of the molecules that have been frozen can be measured to compare the polarization values of the just-recombined molecules and those that are frozen into ice. The residual gas is pumped by cryogenic panels below 10⁻⁸ mbar without gas load to the cell. Using a superconducting solenoid at a temperature of 4 K, a magnetic field of up to 1 T in the storage cell can be generated. Additionally, it focuses an electron beam, which is produced by an electron gun at energies of a few 100 eV on the left side of the apparatus. The interaction of the polarized atoms and evaporated molecules with the electron beam results in an ionization process. Next, the ionized protons and ${\mathrm{H}}_2^{+}$ ions are accelerated by a positive electric potential across the cell of up to 5 kV to the right-hand side. The nuclear polarization of protons/deuterons or the molecular ions ${\mathrm{H}}_2^{+}$ / ${\mathrm{D}}_2^{+}$ and ${\mathrm{HD}}_2^{+}$ is measured with a Lamb-shift polarimeter connected to the right end of the apparatus.

In order to experimentally determine the degree of polarization of laser-accelerated particle bunches, dedicated polarimeters must be used. Similar devices are widely used in particle physics, for example to determine beam polarizations at classical accelerators. They are typically based on a scattering process with known analyzing power, which converts the information about the beam polarization into a measurable azimuthal angular asymmetry. In the case of laser-accelerated particles, however, a couple of peculiar requirements have to be taken into account.

1. (1)Due to the time structure of the laser pulses, all scattered particles hit the detector within a few tens of femtoseconds. Thus, it must be virtually dead-time free or, more realistically, all particle signals from one laser shot must be integrated up.
2. (2)The detectors must have a high EMP robustness. This is especially challenging for electronic detectors with an on-line readout.
3. (3)A high angular resolution is required in some cases; see Figure 9.
4. (4)Depending on the phase-space densities of the accelerated particles, it may be required to measure small particle numbers (per laser shot); see Ref. [72].

For the polarimetry of protons with higher kinetic energies, CH₂ (polypropylene foils), rather than silicon, is the proper material for the polarimeter. A new proton polarimeter is now being commissioned and calibrated with polarized protons at COSY-Jülich, where beam energies from 45 MeV up to 2.88 GeV are available.

Depending on the electron beam energy, which determines the analyzing power as well as experimental access to the scattering products, one of the following spin-dependent QED processes can be used for electron polarimetry^[73].

1. (1)Mott scattering^[74–76], i.e., scattering off the nuclei in a target, used for beams between 10 keV and 1 MeV, often for polarimetry of electron sources at large accelerators.
2. (2)Bremsstrahlung emission in a target^[77], used from about 10 MeV to a few 100 MeV, relies on measuring the degree of circular polarization of photons generated when passing the beam through a thin target^[78]. Statistical significance of the order of 10% can be achieved.
3. (3)Møller (or for positron beams Bhabha) scattering^[79], i.e., scattering off the electrons in a target, used from a few 100 MeV to GeV energies in fixed target experiments at SLAC^[80–83] and JLab^[84], but also at ELSA^[85] and MAMI^[86]. Precisions down to 0.5% can be reached^[87].
4. (4)Compton scattering^[88], i.e., scattering off a laser, used for GeV and higher energies, offers high analyzing power $\mathcal{O}(1)$ , large and precisely known cross-section^[89] and robust control over experimental systematics. Long-established for measuring longitudinal and transverse polarization, e.g., at SLC^[90], LEP^[91], HERA^[25,92], ELSA^[93], MAMI^[94] and JLab^[95], it is also the method of choice for future colliders^[96–98]. Precisions from a few percent down to a few permil can be reached.

The short bunch length typical for plasma-accelerated beams is not a problem for any of these methods; rather, it is an advantage. All methods apart from Compton scattering are destructive. Due to the typical energies obtained in laser-wakefield experiments, method 2 is the most applicable technique for diagnosing the degree of polarization of such beams. A new polarimeter for measuring polarization of laser-plasma accelerated electrons is being designed and constructed at DESY.

In this review paper we discuss the current status of polarized beam generation, including polarization techniques for conventional accelerators, new ideas for laser-based accelerator facilities at relativistic laser intensities and corresponding concepts for beam polarimetry.

Polarized particle beams are an important tool in nuclear and particle physics for the study of the interaction and structure of matter and to test the Standard Model of particle physics. All techniques to deliver polarized beams for such applications are currently based on conventional particle accelerators. Unfortunately, these are typically very large in size and devour huge financial resources.

Novel concepts based on laser-driven acceleration at extreme intensities have been investigated intensively over recent decades. The advantage of laser-driven accelerators is the capability to provide accelerating fields up to tera-volts per meter, about four orders of magnitude greater than conventional ones. It is therefore a highly desirable objective to build the next generation of compact and cost-effective accelerator facilities making use of laser-plasma techniques.

To get a deeper understanding of the processes leading to polarized beam production, theoretical and experimental work is gaining momentum. First of all, particle spins subject to the huge magnetic fields of laser-plasma accelerators can be monitored in theoretical studies using PIC simulations. More comprehensive tests of QED-based models have also been made to account for the radiative polarization and spin-dependent reaction effects. Much more theoretical and experimental work needs to be done to obtain a complete picture of spin motion in ultra-strong relativistic electromagnetic fields.

Simulations and analytical estimates indicate that light particles like electrons can be either polarized directly by strong laser-plasma fields or preserve polarization from pre-polarized targets. In contrast, heavy particles like protons and ions require the latter. The first such targets, which are tailored to laser applications, are in the commissioning phase. Therefore, the first successful experiments at currently available laser intensities are to be expected within the next few years. In view of this, it seems advisable to foresee options for polarized beams for the planning of next-generation accelerator facilities.