1 INTRODUCTION

At present, three main sources of secondary hard radiation from laser-accelerated electrons are actively discussed: betatron oscillations of electrons during their acceleration, nonlinear Compton (Thomson) scattering of electrons in a counterpropagating laser beam, and bremsstrahlung radiation in an additional converter target [2, 3]. It has already been demonstrated that the bremsstrahlung of laser-accelerated electrons is an efficient source of gamma rays, which can be used both for photonuclear reactions with the production of neutrons, positrons, and even muons, and for radiography of dense hidden objects [4, 5] (see also paper [6], where a betatron gamma-ray source was used for radiography). However, for its practical application and increasing the ability to radiograph through shielded objects (a maximum shielding thickness of an object being radiographed currently corresponds to a linear density of ~100 g/cm2 [5]), it is necessary to significantly increase the number of generated gamma quanta, and, consequently, the number of accelerated electrons. On this path, the recently proposed regime of electron acceleration under conditions of relativistic self-trapping of a laser pulse seems to be very promising, which makes it possible to accelerate a significant number of electrons to energies of hundreds of MeV [7, 8].

With the commissioning of a multipetawatt XCELS laser, a unique opportunity arises to achieve this regime of laser generation of high-energy electrons, which would provide a flux of gamma-ray quanta with an energy of tens of MeV, sufficient to effectively excite a record-high number of photonuclear reactions near giant resonance for most elements, as well as would ensure a necessary flux for radiography of a test sample in deep layers of a surrounding solid-density material in a single laser shot. The energy of the resulting electron beams can be efficiently (with a conversion coefficient of 50–70%) converted into gamma quanta energy due to electron bremsstrahlung in a converter target placed immediately after the laser target. This was previously demonstrated when considering an electron beam accelerated by a 130 TW laser pulse (with a beam charge of 7 nC and an energy above 30 MeV) in the relativistic light self-trapping regime, where a total gamma yield of ~1 MeV reaches 3 × 1011 photons with a total energy of ~0.35 J, which gives a laser-to-gamma energy conversion efficiency at a level of 8% [8]. A simple extrapolation of these results to the parameters of the XCELS laser system already allows us to hope for a gamma-ray flux at the level of 1013 photons or more per laser shot. We can expect that the use of such high-power fluxes of gamma quanta for radiography will make it possible to clearly detect hidden objects and distinguish materials with a large atomic weight (platinum, uranium, etc.) from materials with an average atomic weight (iron, aluminum), providing sufficiently good image contrast of an object even strongly shielded by a dense substance (for example, a layer of steel) at a depth of up to 0.5 m. Numerical simulation of the generation of a gamma-ray flux by an electron beam accelerated by an XCELS laser, as well as a demonstration of its capabilities for deep gamma radiography of dense hidden objects with a currently record-breaking shielding thickness is the goal of this work.

2 SETTING UP (SCHEME OF) THE EXPERIMENT

The proposed method is based on electron acceleration in the optimal regime of relativistic self-trapping by a 25-fs XCELS laser pulse with a power of 10–20 PW, which provides a maximum electron beam charge with an energy of several hundred megaelectronvolts. The target could be a dense gas jet (hydrogen/helium) or a gas cell with an electron density n of the critical order, nc, or a target formed upon preliminary homogenization of a low-density target (foam) by a low-intensity laser prepulse. Behind the laser target is a dense (tantalum/platinum) target for converting the energy of bombarding electrons into gamma rays. The multi-MeV gamma-rays obtained by irradiating the converter target with an electron beam are directed to a shielded dense sample (for example, made of tungsten) for its radiographic examination. The sample is placed inside a steel container, which can be located at a distance of one meter from the source. To detect transmitted radiation, use can be made of a set of detectors similar to those used in positron emission tomography. The scheme of the simulated and real experiment is shown in Fig. 1a. Note that the use of several XCELS beams for deep gamma radiography of an object irradiated from different sides will make it possible to restore the three-dimensional structure of the shielded dense object under study.

Fig. 1.
figure 1

(a) Scheme for the implementation of a gamma-ray source and deep gamma radiography based on laser electron acceleration, and (b) radiographically studied structured sample; Fe are the shielding layers of iron.

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3 SIMULATION OF THE EXPERIMENT

For the XCELS laser parameters (the laser pulse energy of one channel, 400 J and the power, 16 PW), we performed end-to-end numerical calculations of the effect of laser radiation on a plasma target with a density on the order of nc to generate a beam of high-energy electrons, decelerate electrons in the converter target, and generate gamma-quantum fluxes, as well as of their passage through dense shielded objects. At the first stage, we performed particle-in-cell simulations by the commercial code VSim (Vorpal) to study the acceleration of electrons from targets with a density on the order of nc. The calculations were carried out using the moving window method in the region x × y × z = 58λ × 58λ × 58λ with a resolution of 0.02λ × 0.07λ × 0.07λ. We used 2 particles per cell for electrons and ions. Various conditions for focusing a 25-fs laser pulse with a wavelength λ = 0.91 μm were considered. In the case of focusing a laser pulse into a spot with a diameter D = 10 μm, the dimensionless laser field amplitude a0 = 89 was achieved, and when it was focused into a spot with a diameter of about 6 μm (D = 5.93 μm), a0 was equal to 150.

The electron beam characteristics obtained in calculations simulating the action of a laser pulse on a low-density plasma target were used as input data for Monte Carlo calculations (GEANT4 code) of the interaction of these electrons with metal converters for generating gamma-rays. The calculation results are presented for the case when a tantalum layer was used as a converter. The converter target was located at a distance of 1 cm from the electron source. The number and energy of gamma quanta behind the target were calculated for different target thicknesses.

The GEANT4 code was also used to describe the propagation of the generated gamma-ray beam through a shielded dense object to demonstrate the capabilities of deep gamma radiography. To do this, in the simulation, a complex tungsten object was placed at a distance of one meter from the laser electron source; this object was composed of two sets of parallel strips of increasing thickness (from 0.5 to 25.5 mm), forming two triangles rotated by 90° relative to each other, with a characteristic transverse size of about 20 cm (Fig. 1b). The object in question was shielded on both sides by a layer of 0.2-m thick iron. Behind this object, at a distance of 2 m from it, there was a detector that recorded the transmitted gamma-ray signal. The transverse size of the detector was chosen to be 3 × 3 m with a resolution of 1000 × 1000 pixels, which provided a single-pixel size of ~3 × 3 mm.

4 SIMULATION RESULTS

As a result of the simulation, it was found that the interaction of an XCELS laser pulse with a field amplitude a0 = 150 with a plasma target with a density of 0.55nc and a thickness of 240 μm leads to the generation of a beam of high-energy electrons (only electrons with energies above 30 MeV were taken into account) with a total charge of about 150 nC and a maximum energy over 2 GeV (2.1 GeV). With increasing focusing spot size D to 10 μm and decreasing field amplitude to a0 = 89, the optimal target density will be about 10% of the critical density (0.115nc), and the target thickness will increase to 480 μm. In this case, the charge of accelerated energy electrons will be 112 nC, and the maximum energy will reach 2.4 GeV. The spectra of accelerated electrons are shown in Fig. 2. Note that in both cases of focusing, almost all the energy of the electron beam is carried away by electrons with energies above 300 MeV, for which the spectrum has a plateau-like character.

Fig. 2.
figure 2

Spectra of electrons accelerated from a target with a density of 0.55nc by a laser pulse with a0 = 150 (red curve) and from a target with a density of 0.115nc by a pulse with a0 = 89 (black curve).

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These electron beams were used to produce gamma-rays from a tantalum converter target, whose thickness varied from 4 to 20 mm. Calculations showed that the maximum energy of gamma rays is achieved for a target with a thickness of 12–14 mm (Fig. 3). Since this value is smaller than the characteristic electron deceleration length in a dense converter material, one would expect an increase in the number of produced photons with increasing target thickness. However, the use of thicker targets leads to the fact that the generated gamma quanta begin to enter into photonuclear reactions inside the converter target, producing secondary products and losing energy at the target output.

Fig. 3.
figure 3

Dependences of (shown in black) the total number of generated gamma quanta, Nγ, and (shown in red) the total energy of gamma-rays, εγ, on the thickness l of a converter target irradiated by an electron beam generated by laser pulses with a0 = (dashed curves) 150 and (solid curves) 89.

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This is well illustrated by the gamma-ray spectrum behind the target (Fig. 4), which has a descending character: It is inversely proportional to the photon energy for low energies [9] and decreases exponentially in the high-energy region. In this case, the number of the highest-energy gamma quanta decreases with increasing target thickness. An electron beam accelerated by a more intense laser pulse and having a somewhat higher charge (albeit a lower maximum energy)—a beam with a0 = 150—creates a more efficient gamma-ray source, but the difference between the cases under consideration (with a0 = 150 and 89) is very insignificant (see Figs. 3 and 4). The maximum laser-to-gamma energy conversion coefficient turns out to be slightly higher than 8% (the energy of the latter is about 35 J). In this case, the electron beam spends about half of its energy on gamma-rays. The maximum number of gamma rays is approximately 3 × 1013 per shot. The average photon energy in a gamma-ray pulse varies from 20 MeV for thin (6–10 mm) to 7 MeV for thick (~18 mm) converter targets.

Fig. 4.
figure 4

Gamma-ray spectra for converter target thicknesses D = (red curves) 6, (blue curves) 12, and (black curves) 18 mm, upon irradiation by an electron beam generated by laser pulses with a0 = (dashed curves) 150 and (solid curves) 89. The inset in the corner shows the spectra on a linear scale.

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The characteristic divergence of the gamma-ray beam is about 6°–8°. The gamma-ray source brilliance is largely determined by the converter target thickness and increases with decreasing thickness, even though the total number of quanta decreases. This is due to a decrease in the size of the source (its characteristic radius Rγ) and the gamma-ray pulse duration τγ, which for a converter with a thickness of 0.5 mm are as follows: Rγ ~ 40 μm and τγ ~ 100 fs. As a result, the brilliance of a 10 MeV gamma-ray source is ~1019 photon s–1 mm–2 mrad–2 0.1%BW. Note that for the considered spectrum of accelerated electrons and the converter targets with a thickness of 1–2 cm, electrons with an energy on the order of GeV or higher make a significant contribution to bremsstrahlung gamm-rays, including the energy range of gamma rays most interesting for nuclear applications, 7–20 MeV. This is due to the fact that the instantaneous loss of an electron with an energy of 1 GeV in tantalum by bremsstrahlung is 2.4 × 103 MeV/cm, while the characteristic path length to an almost complete arrest is about 2 cm, while the loss of an electron with an energy of 100 MeV is only 2.2 × 102 MeV/cm, and the path length is about 1 cm. Taking into account that the energy of ultrarelativistic electrons is distributed almost equally probably between high and low energy gamma-ray quanta, yielding a greater number of the latter, we can expect that electrons with energies at a GeV level will be an order of magnitude more efficient for generating gamma-rays than electrons with an energy of 100 MeV. At the same time, if we obtain an electron beam with the same total energy, but with a lower cutoff energy (for eaxample, ~500 MeV), then it will probably be able to provide the same efficiency of generating gamma-rays with photon energies up to 20 MeV at the correctly selected thickness of the converter target.

The simulation also demonstrated the high efficiency of using a laser source of gamma-rays for deep radiography of hidden dense objects. The structure of an object screened with iron even 0.4 m in thickness (linear density of ~320 g/cm2) is quite clearly visible on the detector (Fig. 5a). In this case, the highest image contrast, reaching approximately 0.5 (the ratio of signals inside and outside the object), was obtained in the areas of the strongest absorption in tungsten, i.e., on two mutually perpendicular sets of plates with a total thickness of 5.1 cm (linear density of ~100 g/cm2). When the thickness of the tungsten object is less than 1.5 cm (linear density is less than 30 g/cm2, the region of the lower right corner of the object), any noticeable image contrast cannot be achieved. Note that the presented image was obtained using an electron beam with a charge of 3.2 nC (2% of the total number of electrons). Using the total charge of the accelerated electrons will further increase the image contrast. For comparison, Fig. 5b also shows an image of an object shielded on both sides with 10-cm thick iron, obtained using an electron beam with a charge of 0.2 nC (0.13°% of the total number of accelerated electrons).

Fig. 5.
figure 5

Detector images of a radiographically studied structured sample shielded with two layers (at the front and the back, see Fig. 1) of steel (a) 20 and (b) 10 cm thick; Eγabs is the energy of gamma rays absorbed at the detector.

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If the total number of gamma rays flying into an open angle of ~0.03 mrad is 3 × 1013 photons, then the radiation flux at a distance of 3 m from the source will be at a level of 1010 photons/cm2. Let the characteristic value of attenuation of gamma rays with an energy of 7–10 MeV in iron be ~30 g/cm2; then, according to the estimates, the linear density of the material, in which though-propagating gamma rays can be still measured with a detector (in this case, a flux of ~105–106 photons/cm2 [6] is needed), will be at a level of 270–320 g/cm2, which corresponds to an iron layer thickness of about 35–40 cm. Note that the maximum depth of penetration of gamma rays through dense targets is achieved precisely at their energies in the range of 5–10 MeV, which corresponds to the average energy of the source obtained here.

5 REQUIREMENTS FOR THE EXPERIMENT

The possibility of using XCELS laser pulses to generate gamma-ray fluxes and their use for radiography of dense objects has been demonstrated above. Numerical calculations have shown that an optimal target for electron acceleration is a target with a density slightly lower than the critical density and a thickness on the order of tens of mm. Implementation of such targets in practice is a separate task. The use of gas targets assumes the presence of a preplasma gradient at the laser pulse input. As was recently shown, the correct focusing of the pulse on the preplasma profile does not impair the self-trapping of the laser pulse [10], but this should also be taken into account when planning experiments (see also the discussion in [11]).

Lead tungstate crystals (PbWO4) can be used as a detector [12]. If the detector is located at a distance of about 10 m, then the size of one pixel should be about 2 cm for more efficient local absorption of gamma rays with an energy of 10 MeV [12]. When obtaining an image on a detector for radiography of dense objects, one should take into account the possibility of additional blurring of the image of the object of study due to the ingress of secondary photonuclear-reaction products onto the detector.

6 CONCLUSIONS

Summarizing the results of the studies, we emphasize once again that a laser pulse of the XCELS facility can be used to produce a source of gamma rays with a photon energy noticeably higher than 1 MeV and record-high values of total energy (~35 J), power (~50 TW), and total number of quanta per pulse, i.e., with characteristics exceeding all known ones for petawatt lasers. This is achieved due to efficient acceleration of an electron beam from a near-critical density plasma in the regime of relativistic laser pulse trapping, which leads to the generation of electron beams with a charge of higher than 0.1 μC and a maximum energy of higher than 2 GeV. Such electron beams are capable of converting more than half of their energy in a classical way into the energy of gamma bremsstrahlung, for example, in a tantalum converter target. A possibility has been shown of using the proposed pulsed gamma-ray source for high-spatial-resolution deep radiography of dense objects in a single laser shot, which makes it possible to determine the shape of an object, even shielded by iron layers up to 0.4 m thick (this corresponds to a linear density of 320 g/cm2, which is more than three times the shielding thickness obtained to date [5]).

It should be noted that the development of deep gamma radiography technology with a high temporal resolution (determined by the time-of-flight scale) is promising. This is due to the pulsed nature of the generated radiation and the possibility of using additional synchronized (with a controlled delay) XCELS channels. This technique is important for studying fast processes occurring deep in the surrounding matter.