⁶⁴Cu [T_1/2 = 12.7 h; β⁺ decay with 278 keV mean energy (17.6%); β⁻ decay with 191 keV mean energy (38.5%); low-energy Auger electrons] has decay characteristics that allow for positron emission tomography (PET) imaging and targeted radiotherapy of cancer.^1–364Cu-ATSM is an imaging agent used for measuring hypoxia in human tumors. Hypoxia is an important effect that can influence the resistance of tumor cells to chemo- or radiotherapy.⁴⁶²Cu is a relatively short-lived β⁺ emitter [T_1/2 = 9.67 min; β⁺ decay with 1.32 MeV mean energy (97.6%)] that is very suitable for PET imaging.^1–3 Moreover, ⁶²Cu can form a “matched pair” with ⁶⁴Cu. Note that a β⁻ (or Auger electron) and β⁺ emitting pair of radionuclides of the same element is now termed a theranostic pair¹ and represents a new frontier in the field of nuclear medicine.

At present, ⁶⁴Cu is mainly produced using small cyclotrons with the ⁶⁴Ni(p, n) and ⁶⁴Zn(d, 2p) reactions, as well as in nuclear reactors with the ⁶³Cu(n, γ) reaction.^5–8 On the other hand, ⁶²Cu is commonly produced from ⁶²Zn/⁶²Cu generators, and the parent isotope ⁶²Zn can be obtained by the ⁶³Cu(p, 2n) reaction in a cyclotron.^8–11 Generally, cyclotron-based radioisotope production requires large proton capture cross sections, while radioisotope production by reactor methods needs large fission branching ratios. Furthermore, nuclear reactors lead to large amount of nuclear waste, raising numerous safety and security concerns. Cyclotrons may not pose such risks compared with nuclear reactors, but they produce only a limited range of isotopes for clinical use.¹² In addition to their reasonable half-lives, accelerator-produced neutron-deficient isotopes have relatively high purity and specific activity. Thus, to a certain extent, accelerator production of isotopes represents a favorable option for medical applications.² However, owing to the limited number of production facilities available and the growing global demand for medical isotopes, there is a potential crisis in terms of global under-supply.^13,14 It is therefore vital to explore innovative ways of producing medical isotopes without nuclear reactors.

Recent progress in laser technology, including chirped pulse amplification (CPA) and optical parametric CPA (OPCPA) has stimulated global interest in the development of high-peak-power lasers.¹⁵ Such lasers can be focused to peak intensities of the order of 10²⁰ W/cm².^16,17 Hence, they can be employed to study various nuclear phenomena,^18,19 including the production of key medical isotopes. Fritzler et al.²⁰ have calculated that 13 MBq of ¹¹C can be generated, via (p, n) reaction, using the LOA tabletop laser after 30 min irradiation at 10 Hz. Ledingham et al.²¹ have demonstrated laser-driven ¹¹C and ¹⁸F PET isotope production with the high-power VULCAN laser at the Rutherford Appleton Laboratory (RAL), UK. Photonuclear reactions provide an alternative method for the production of medical isotopes. As an example, for producing ⁶⁴Cu, the ⁶⁵Cu(γ, n) channel does not require a rare and expensive ⁶⁴Ni target or a chemical separation step, which makes it advantageous for medical isotope production. However, an energetic γ-ray beam with sufficient brilliance is still required in order to produce radioisotopes with sufficient activity.

In this paper, an efficient photonuclear scheme is proposed to produce radioisotopes of medical interest by using high-charge relativistic e⁻ beams. Such e⁻ beams are produced from the interaction between an intense laser pulse and a near-critical-density (NCD) plasma. Taking ⁶²Cu as an example, a photonuclear scheme for producing PET isotopes is illustrated schematically in Fig. 1. By focusing the electrons onto a high-Z target such as tantalum, energetic γ-rays are produced through bremsstrahlung radiation. These γ-rays in turn induce photonuclear reactions inside the Cu sample. The (γ, n) reaction is the main reaction that occurs, and the stable isotope ⁶³Cu can be effectively transformed into the short-lived isotope ⁶²Cu. The particle-in-cell (PIC) code EPOCH²² is used to simulate the laser-plasma interaction, and the Monte Carlo (MC) code Geant4-GENBOD^23,24 is then used to model the passage of the particles through matter.

As early as 1995, Modena et al.²⁵ reported relativistic e⁻ beams produced by an intense laser pulse. More recently, Yan et al.²⁶ demonstrated that intense laser interaction with an NCD plasma could generate energetic and dense e⁻ beams. We have previously shown that such e⁻ beams could be used to efficiently transmute long-lived nuclear waste.^27,28 In this section, we first use PIC simulations to investigate the generation of high-current e⁻ beams from an NCD target, and we then use MC calculations to study the subsequent production of bremsstrahlung radiation and the photonuclear isotopes ^62,64Cu.

We first perform full three-dimensional (3D) PIC simulations of ultra-intense laser pulses interacting with gas jets. A sub-petawatt p-polarized laser pulse with Gaussian spatial and temporal profiles, a wavelength of 1 µm, a duration of 33 fs, and a focal spot size of 3.0 µm at FWHM irradiates a gas region from the left. The laser intensity of 3.4 × 10²¹ W/cm² corresponds to a laser peak power of 350 TW. This peak power is far above the critical power of laser self-focusing in an NCD plasma. As a consequence, efficient electron acceleration can be obtained within almost the entire plasma region, which results in the production of dense e⁻ beams with cutoff energy higher than 100 MeV, as discussed below. The simulation box is 80 µm in the longitudinal (x) direction and 30 µm in the transverse (y and z) directions. Eight macro-electrons and two macro-protons are initialized in each cell, the dimensions of which are dx = 80 nm and dy = dz = 125 nm. The plasma region, of thickness 50 µm, is located at 10–60 µm. A wide range of plasma density, n_e = (0.1–2.0)n_c, is used in the simulation, where n_c is the plasma critical density.

The interaction between laser pulse and NCD plasma can be divided into injection and acceleration stages. The injection stage terminates at t = 30T₀, where T₀ is the light period. After the laser pulse hits the target surface, background electrons in the plasma are expelled from the axis of the laser by the transverse pondermotive force. This leads to a symmetric pattern of electron density, and a bubble-like structure appears near the target surface [see Fig. 2(a)]. Meanwhile the ions are hardly affected, and a strong transverse quasistatic electric field is formed because of the effective charge separation. Subsequently, a large number of electrons are captured at the rear of the bubble, forming an over-critical-density e⁻ beam, as shown in Fig. 2(b). Such a dense e⁻ beam can generate a strong radial electric field, which prevents injection of the rest of the electrons. In the following stage of acceleration, the bubble-like structure gradually evolves into a plasma channel, and the injected electrons gain energy from the strong laser field and the longitudinal quasistatic electric field inside the channel ^{[Figs. 2(c) and 2(d)]}.

Figure 3(a) shows the spectral distributions of e⁻ beams accelerated in the NCD plasma. These spectra are broadband and have endpoint energy of the order of 100 MeV. Moreover, the cutoff energy increases with increasing plasma density and reaches a maximum value of 220 MeV at n_e= 0.8n_c. The e⁻ beams produced from the NCD plasma are collimated. Figure 3(b) shows the transverse profile of an e⁻ beam with energy higher than 6 MeV. From the spot size of the e⁻ beam and the transport distance from the accelerator exit to the convertor surface, the divergence angle of the e⁻ beam is found to be ∼15°.

The electric charges of accelerated e⁻ beams for different plasma densities are shown in Fig. 4. Electrons with energy above the giant dipole resonance (GDR) region (≥25 MeV) dominate over those in the GDR region (10–25 MeV). Moreover, the number of electrons above the GDR region first increases and then decreases with increasing plasma density, while the number in the GDR region shows a clear opposite trend. In this study, the plasma density of 0.5n_c is considered to be the optimal density, leading to maximum production of high-energy electrons. At n_e= 0.5n_c, an e⁻ beam with a total charge exceeding 100 nC can be produced, with relativistic electrons (≥10 MeV) carrying an electric charge exceeding 13 nC.

The interactions between the energetic e⁻ beams and the bremsstrahlung convertor, as well as the consequent medical isotope production, are investigated using the Geant4-GENBOD code,^23,24 in which the hadronic interaction module describing the photoneutron reaction process is self-consistently included. Bremsstrahlung radiation is produced by the deceleration of energetic electrons inside the convertor. Neglecting changes in the electron bunch during its propagation in the target, the differential bremsstrahlung cross section is integrated as²⁹dσγdEγ=aZ2(Eγ−1−bEe−1),(1)where Z is atomic number, a = 11 mb, and b = 0.83. The number of bremsstrahlung photons radiated per mega electron volt at photon energy E_γ is evaluated asdNγdEγ≈dcnc∫EγEcutdNedEe⋅dσγdEγdEe,(2)where dN_e/dE_e is the number of energetic electrons [see Fig. 3(a)], d_C and n_C are the thickness of convertor and its atomic number density, respectively, and E_cut is the cutoff energy of the e⁻ beam.

We first consider the convertor material and thickness for efficient production of bremsstrahlung photons. Both Ta and Au plates can realize a high bremsstrahlung conversion efficiency owing to their large atomic numbers. However, Ta is cheaper than Au. With this consideration in mind, we choose a metallic Ta target as the bremsstrahlung convertor. A 2-mm-thick convertor, although not thick enough to give the peak yield of bremsstrahlung radiation, does lead to maximum production of ^62,64Cu. This is attributed to the fact that high-energy electrons penetrating the convertor effectively initiate extra production of the desired isotopes. A similar effect has been observed in the laser transmutation of nuclear ¹²⁶Sn waste.²⁷

We further study the effect of plasma conditions on bremsstrahlung production. The simulation results are shown in Fig. 5. It can be seen that the bremsstrahlung production is most efficient at n_e = 0.5n_c owing to the maximum production of high-energy electrons, as displayed in Fig. 4. When accounting for the photons in the energy region of GDR, we obtain a γ-beam flux of a few 10¹⁰ per laser shot. Since the broadband bremsstrahlung spectrum overlaps a significant part of the cross section on ^63,65Cu(γ, n) reactions, both of which are peaked at around 15 MeV (see Fig. 5), the required isotope production can be initiated efficiently in our scheme.

For a typical photonuclear reaction, the production rate (yield) of the target isotopes depends upon the bremsstrahlung spectrum n_γ(E_γ) and the cross section of the corresponding photonuclear reaction σ_reac(E_γ). Neglecting the attenuation of the photons in the target, the production rate can be written asP0=Nre≈dTnT∫EthEmaxσreac(Eγ)nγ(Eγ)dEγ,(3)where E_th is the threshold energy of the photonuclear reaction, E_max is the endpoint energy of the bremsstrahlung spectrum, and d_T and n_T are the thickness of the activation target and the number of activation target nuclei, respectively. In our simulation, a natural Cu target with an isotopic composition of ⁶³Cu (abundance 69.15%) and ⁶⁵Cu (30.85%) is employed to produce the ^62,64Cu isotopes. As already mentioned, both of these are medically relevant isotopes.

The influence of the target thickness on the production rate of ^62,64Cu isotopes is investigated. The production rate first increases significantly and then decreases slowly with increasing convertor thickness. The maximum production rate appears when the convertor thickness is 2 mm. For different convertor materials, the production rate as a function of the thickness of the activation target is shown in Fig. 6. It can be seen that the production rate is increased significantly when the activation target is thinner than 20 mm. For thicker activation targets, the growth trend is not obvious, owing to the large attenuation of the bremsstrahlung radiation. When the convertor is absent, the collimated e⁻ beam directly irradiates the activation target, in which both the bremsstrahlung radiation and isotope production processes are initiated. However, the production rate of ^62,64Cu isotopes is visibly reduced (see Fig. 6).

To obtain a better understanding of the photonuclear processes induced by the energetic bremsstrahlung radiation, we examine the spatial distributions of the Cu isotopes. It can be seen from Fig. 7 that the intensity of the Cu isotopes decreases along both the radial and longitudinal directions, and the peak intensity is found in the center of the Cu target. The peak is also superposed closely on the incident γ-ray beam. Since, as already mentioned, the γ-ray beam has a small angular divergence, the intensity pattern induced by the photonuclear reactions is dispersed spatially along the direction of γ-beam propagation (see Fig. 7). One can see that the spatial pattern could provide information to help the choice of target geometry. In this case, a Cu target with 2 cm radius and thickness may satisfy the requirement for irradiation.

From target irradiation, a large number of neutrons, electrons, and γ-rays can be generated. Compared with the direct detection of these emitted particles, the activation measurement method can effectively alleviate the disturbance of these online backgrounds. Activity measurements on the radioactive residual nuclei produced by the (γ, n) reaction can be used for many isotopes. By using high-purity germanium (HPGe) detectors, the characteristic energy and decay-time pattern of the nuclear transitions can be measured precisely, allowing determination of the reaction yields³¹ and hence the activity of the reaction products.

We simulate the detection of the characteristic γ-emissions (0.511 MeV) of ^62,64Cu and then analyze quantitatively the activity of the reaction products. An HPGe crystal of radius 29.6 mm, which is close to the front surface of the activation target, is employed in the simulation. Figure 8 shows the production and detection yields of ^62,64Cu as functions of the thickness of the activation target. The detection yield is obviously less than the production yield owing to attenuation of the characteristic γ-lines. When the target thickness exceeds 20 mm, the detection yield becomes saturated (see Fig. 8), which is in good agreement with the theoretical prediction. For the 0.511 MeV γ-rays attenuating inside the Cu target, the linear attenuation coefficient is 0.75 cm⁻¹. This value results in a half-attenuation thickness of 10 mm, indicating that the saturation thickness is of the order of 20 mm. From the simulation results shown in Figs. 7 and 8, we find that the optimal radius and thickness of the activation target are both 20 mm.

The activity of the product isotope can be written as^32,33A0=P0(1−e−λti)(4)where λ = ln 2/τ is the decay constant of the product isotope with a half-life of τ, and t_i is the irradiation time. The activities of ^62,64Cu isotopes for different plasma densities are calculated using the optimal irradiation parameters, and the results are shown in Fig. 9. One can see that the activities of the Cu isotopes are sensitive to the plasma density when this is below 0.3n_c or above 0.8n_c. The activities of the medical isotopes are peaked at n_e = 0.5n_c. The activity level reaches 95% of the maximum (equilibrium) activity after an irradiation time corresponding to three half-lives of the products 3τ_Cu-62 = 0.5 h and 3τ_Cu-64 = 38.1 h. Corresponding activities of 0.18 GBq (4.9 mCi) for ⁶²Cu and 0.06 GBq (1.6 mCi) for ⁶⁴Cu are obtained. When the irradiation stops, the isotopes start to decay with their characteristic half-lives (indicated as cooling), which is also displayed in Fig. 9.

It can be seen that activities of 0.18 GBq for ⁶²Cu and 0.06 GBq for ⁶⁴Cu can be achieved using a sub-petawatt laser pulse (∼350 TW) at 1 Hz repetition rate (see Fig. 9). In recent years, the development of laser technologies has provided the opportunity to produce compact high-repetition-rate systems.^34,35 In particular, the advanced laser at the University of Quebec, Canada³⁶ and the Diocles laser at the University of Nebraska–Lincoln, USA³⁷ have come online at a normal power level of 100 TW and 10 Hz. Furthermore, several laser facilities are being proposed to generate >1 PW power at a repetition rate of 10 Hz, such as the Mercury laser facility at the Lawrence Livermore National Laboratory (LLNL), USA.³⁸ For a sub-petawatt laser at 10 Hz to be used for ^62,64Cu isotope production, the resulting activity needs to be scaled proportionally to the order of gigabecquerels, which is at least one order of magnitude higher than what has previously been achieved (for production of the principal PET isotopes ¹¹C and ¹⁸F).^20,21 Moreover, it is expected to reach the level of the activity required for PET imaging. Figure 10 summarizes our calculations of laser-driven ^62,64Cu isotope production via (γ, n) reactions, together with previous measurements of laser-driven ¹¹C and ¹⁸F isotope production via (p, n) reactions. It can be seen that the potential of PET isotope production scales quantitatively with laser irradiance. It should be possible to generate an amount of activity of ^62,64Cu in 1 s that is equivalent to the required patient dose for PET, but not the greater amount of activity required for targeted radiotherapy. This extrapolation has been made with a great deal of caution, however, because experiments have yet to be performed at laser irradiances higher than 10²¹ W/cm².

The energy that is transferred to the target and the subsequent heating by the e⁻ or γ-ray beam may or not be sufficient to cause melting of the convertor, although this could be evaluated through additional calculations. However, for the specific cases considered in this study, Ta and Cu have melting points of 2996 °C and 1083.4 °C, respectively. Given these low melting points, to prevent excessive heating and avoid melting, it should be possible to use a multiple thin target experimental setup that allows the electrons and positrons produced by Compton scattering and by pair creation to leave the target rapidly, together with a water-cooling blanket.

Synthesis of Cu radiopharmaceuticals is another key issue with regard to clinical applications. It has been demonstrated that the 9.74 min half-life of generator-produced ⁶²Cu is long enough for synthesis of chemically diverse radiopharmaceuticals.³⁹ This should also be the case for laser-produced ⁶²Cu.

We have illustrated by simulations the laser production of ^62,64Cu isotopes through photonuclear reactions. A collimated relativistic e⁻ beam with a high charge of approximately 100 nC, produced by the interaction of a high-intensity laser with an NCD plasma, can generate high-flux (10¹⁰ per laser shot) bremsstrahlung γ-rays in the GDR region. Normally, an argon gas jet is used in experiments to generate NCD plasmas.⁴⁰ The plasma density and target geometry are optimized to enhance the production yields of ^62,64Cu isotopes. The possibility of detecting the activity of ^62,64Cu isotopes has also been presented. This study shows that very intense sources of ^62,64Cu with activity reaching the levels required for PET can be obtained by employing state-of-the-art laser systems. We further expect that laser production will also be suitable for other isotopes of medical interest, such as ⁶⁸Ga, ¹⁸⁶Re, and ²²⁵Ra.