To date, intense research has been carried out on laser plasma acceleration concepts^[1] to achieve high-energy, high-quality electron beams with GeV energies in a cm-scale plasma^[2–6], a 1%-level energy spread^[7], a 1 mm mrad level transverse emittance^[8], and a 1 fs level bunch duration^[9], ensuring that the stability of reproduction is as high as that of present high-power ultra-short-pulse lasers^[10]. Recently, staged laser plasma acceleration^[11–13] has been successfully demonstrated in conjunction with ionization-induced injection^[14–16] and phase-locking acceleration^[17]. Relativistic electron beams from ultraintense laser plasma interactions can be conceived to be compact particle accelerators, inspiring a wide range of applications of unique particle beam and radiation sources, such as THz^{[18, 19]} and X-ray/Gamma-ray radiation^[20–25].

Here we present an extreme ultraviolet (EUV) radiation source for next-generation lithography and a laser Compton Gamma-beam source for nuclear physics research. EUV lithography with wavelengths below 13.5 nm is capable of providing resolution below 30 nm in semiconductor manufacturing. We propose a self-amplified spontaneous emission (SASE) free electron laser (FEL) driven by relativistic electron beams from laser plasma accelerators. For example, this FEL system, capable of generating an average EUV power of 1 kW at 13.5 nm, comprises a fiber-based chirped pulse amplification (CPA) laser delivering a 1 MW average laser power, a 5 cm gas cell-type plasma accelerator producing a 660 MeV electron beam with a 1.6% relative energy spread and a 0.5 nC charge, and a 1 m long undulator with a 15 mm period and a 1.4 T peak magnetic field.

High-quality Gamma beams generated from inverse Compton scattering off relativistic electron beams interacting with an intense laser pulse have aroused interest in photonuclear physics and nuclear astrophysics research, the characterization of nuclear materials or radioactive waste and so on. We present a table-top all-optical laser plasma accelerator-based Gamma-beam source comprising a high-power laser system with synchronous dual outputs, a laser plasma accelerator producing 300–900 MeV electron beams, and scatter optics whereby the laser pulse is focused onto the electron beam to generate a Gamma beam via Compton scattering with photon energies of 2–20 MeV.

Most of the laser plasma acceleration experiments that have successfully demonstrated the production of quasi-monoenergetic electron beams with a narrow energy spread have been elucidated in terms of self-injection and acceleration mechanisms in the bubble regime^{[26, 27]}, where a drive laser pulse with wavelength , peak power , intensity , and focused spot radius is characterized by a normalized vector potential with respect to the electron rest energy , given for the linear polarization as

 (1)

Here we consider the self-guided case, where a drive laser pulse propagates in a homogeneous density plasma. The equations of longitudinal motion of an electron with normalized energy and longitudinal velocity are written approximately as^[28]

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

 (10)

 (11)

 (12)

 (13)

 (14)

In laser wakefield acceleration, an accelerated electron beam induces its own wakefield and cancels the laser-driven wakefield. Assuming the beam loading efficiency defined by the fraction of plasma wave energy absorbed by particles of the bunch with a root mean square (r.m.s.) radius , the beam-loaded field is given by , where is the accelerating field without beam loading, given by for the bubble regime . Thus, a loaded charge is calculated as^[29]

 (15)

 (16)

 (17)

 (18)

Electron beams can be produced and accelerated in the injector stage driven by the same laser pulse as that in the accelerator stage, relying on a self-injection mechanism such as the expanding bubble self-injection mechanism^[30] or an ionization-induced injection scheme with a short mixed gas cell^{[14–16, 31]}, where tunnel ionization leads to electron trapping near the centre of the laser wakefield. Here we consider the ionization-induced injection scheme. According to theoretical considerations in ionization-induced injection^[31], for trapping electrons ionized at the peak of the laser electric field, the minimum laser intensity is given by . At a plasma density in the injector, the required minimum laser field is . The maximum number of trapped electrons saturates at approximately at a gas length for a plasma density with a nitrogen concentration of and laser parameters of and due to the beam loading effects and initially trapped particle loss from the separatrix in the phase space. From the particle-in-cell (PIC)-simulation results^[31], the trapped electron density scales as

 (19)

 (20)

In the SASE FEL process, coupling the electron bunch with a co-propagating undulator radiation field induces an energy modulation of electrons that yields current modulation of the bunch due to the dispersion of the undulator dipole fields, known as microbunching. It means that the electrons are grouped into small bunches separated by a fixed distance that resonantly coincides with the wavelength of the radiation field. Consequently, the radiation field can be amplified coherently. In the absence of an initial resonant radiation field, a seed may build up from spontaneous incoherent emission in the SASE process.

The design of the FEL-based EUV light source is carried out using one-dimensional FEL theory as follows^[32]. The FEL amplification takes place in an undulator with undulator period and peak magnetic field at a resonant wavelength given by

 (21)

 (22)

 (23)

 (24)

 (25)

 (26)

 (27)

For an EUV light source based on a FEL, a planar undulator comprising alternating dipole magnets is used, e.g., a pure permanent magnet (PPM) undulator with (Nd–Fe–B) blocks or a hybrid undulator comprising PPMs and ferromagnetic poles, e.g., a high saturation cobalt steel such as Vanadium Permendur or a simple iron. For a hybrid undulator, the thickness of the pole and magnet is optimized in order to maximize the peak field. The peak field of the gap is estimated in terms of the gap and period according to for a gap range , where , and for the hybrid undulator with Vanadium Permendur. Table 1 summarizes design examples for a fiber laser-driven laser plasma accelerator-based FEL-produced EUV radiation source at 13.5 nm wavelength using undulators with periods 5 mm (Case A), 10 mm (Case B), 15 mm (Case C), 20 mm (Case D), and 25 mm (Case E), all cases of which have the same gap:period ratio 0.2, e.g.,  mm (Case A), 2 mm (Case B), 3 mm (Case C), 4 mm (Case D), and 5 mm (Case E), respectively. The bunch duration of the electron beam in the injector stage at a plasma density of is assumed to be 10 fs full-width at half-maximum (FWHM), based on a measurement of the electron bunch duration in a recent laser wakefield acceleration experiment^[33]. The relative energy spread of the accelerated electron beam with an injection energy of , where is the final beam energy in the accelerator stage, is assumed to be of the order of 10% in the injector stage. After acceleration up to 10 times higher energy in the accelerator stage, the relative energy spread at the final beam energy is reduced to due to adiabatic damping in the longitudinal beam dynamics. The transverse beam size is tuned by employing a beam focusing system. Figure 1 shows a schematic of the EUV light source based on a compact FEL driven by a fiber laser-based plasma accelerator.

The design of a Gamma-beam source based on inverse Compton scattering is carried out by using a result of quantum electrodynamics on photon–electron interactions, namely, the Klein–Nishina formula, which gives the differential cross section of photons scattered from a single electron in the lowest order of quantum electrodynamics. In Compton scattering of a laser photon with energy ( for laser wavelength off a beam electron, the maximum energy of the scattered photon is given by , where is the relativistic factor for an electron beam energy with electron rest mass and the factor . In the laboratory frame, the differential cross section of Compton scattering^[34] is given by

 (28)

 (29)

 (30)

 (31)

 (32)

 (33)

 (34)

Table 2 summarizes design examples for an all-optical laser plasma accelerator-based Gamma-beam source at photon energies 2.5 MeV (Case A), 5 MeV (Case B), 10 MeV (Case C), 15 MeV (Case D), and 20 MeV (Case E), respectively. Figure 2 is a schematic illustration of the Gamma-beam source based on inverse Compton scattering off relativistic electron beams driven by a laser plasma accelerator.

We present methods for producing EUV light at a wavelength of 13.5 nm from a SASE FEL generated by electron beams from a laser plasma accelerator driven by a fiber-based CPA laser and also for producing a Gamma beam with photon energies of 1–20 MeV via inverse Compton scattering off relativistic electron beams from a laser plasma accelerator. For these practical applications of laser plasma accelerators, it is essential to employ high average power, high efficiency drive lasers operating at high repetition pulse rates (of the order of 300 kHz); the corresponding average power of 1 MW means that the EUV FEL is capable of producing an average radiation power of 1 kW at a wavelength of 13.5 nm and the all-optical Gamma beam source can produce a high-quality photon flux of at 10  MeV energy within a 1% bandwidth. One such high average power laser is a coherent combining fiber laser system^[35], comprising a plurality of amplifying fibers wherein an initial laser pulse is distributed and amplified to a 1 mJ level, intended for grouping together the elementary pulses amplified in the fiber in order to form a single amplified global laser pulse with a 1 J level energy.

In both radiation sources, beam transport and imaging from the laser plasma accelerator to the undulator or a focal point of the scatter laser pulse is provided by a beam focusing system that comprises Halbach-type permanent quadrupole magnets made of NdFeB-type rare-earth magnets with a high remanent field^{[36, 37]}. According to simulation results on ionization-induced injection at a plasma density ^[31], the normalized emittance is assumed to be inside the wakefield. The transverse beam size in the beam transport optics is given by , where is the beta function of the beam optics at the undulator or the scattering point. For Case C in Table 1, the beta function should be set to inside the undulator. The electron beam, after passing through the undulator or being scattered by the scatter laser pulse, is bent by the dipole field of a permanent magnet (a beam separator) made of NdFeB material and dumped to a copper beam dump with a water cooling element, while the EUV radiation or the Gamma beam is extracted from a beam separator and directed to an EUV lithography scanner or a photon beam irradiation system.