2. Experimental arrangement

A deuterated polyethylene target of 0.2 mm in thickness was exposed to a laser intensity of aapproximately $3\times 10^{16}\ \mathrm{W\ cm}^{-2}$ with the fundamental wavelength of $1.315\ \mu \mathrm{m}$ delivered by the laser system PALS. The laser beam struck the $\mathrm{CD}_{2}$ target parallel to the target surface normal. The accelerated deuterons impacted a 1-mm-thick natural LiF slab with a surface area of $17\ \mathrm{cm}^{2}$, which was positioned 10 cm off the primary $(\mathrm{CD}_{2})_{\mathrm{n}}$ target, as Figure 1 shows. The characteristics of the ions were measured using ion collectors (ICs) and a Thomson parabola spectrometer (TPS) positioned in the far expansion zone, i.e. outside the recombination zone. The emission of neutrons was observed by means of a calibrated temperature-compensated bubble dosimeters (BD-PND) with a sensitivity of ${\sim }4\ \mathrm{b}\ \mu \mathrm{Sv}^{-1}$ (Bubble Technology Industries, Chalk River, Ontario, Canada KOJ 1J0) and five calibrated neutron time-of-flight (N-TOF) scintillation detectors composed of a fast plastic scintillator of BC408 type and of a photomultiplier tube^{[Reference Klir, Kravarik, Kubes, Rezac, Litseva, Tomaszewski, Karpinski, Paduch and Scholz24]}, which were positioned at distances of 1–3 m in various directions, as sketched in Figure 1. The BD-PND detectors were positioned inside and outside the target chamber to observe anisotropy in the neutron emission. To reduce the scintillator response to the gamma rays, the scintillation detectors were mounted inside a protective housing composed of 10-cm- thick interlocking lead bricks. The scintillation detectors were operated in a current mode.

Figure 2. (a) Typical time-resolved ion current density observed using an IC positioned at a distance of 1.5 m from a massive $\mathrm{CD}_{2}$ target in a backward direction at $30^\circ $ with respect to the laser vector. The first peak was induced by XUV radiation. The peak at 70 ns was induced by 2.4 MeV protons. (b) Charge density of ions impacting on a secondary target at a distance of 10 cm for the $\mathrm{CD}_{2}$ primary target, which was derived from the IC signal using the relationship (2). The dashed line shows the energy of deuterons. The laser irradiance on target was ${\sim }3\times 10^{16}\ {\rm W\ cm}^{-2}$.

3. Results and discussion

When a $\mathrm{CD}_{2}$ thick foil target is irradiated with the PALS laser, neutrons are generated via $\mathrm{D(d,n)}{}^{3}\mathrm{He}$ and${}^{12}\mathrm{C(d,n)}{}^{13}\mathrm{N}$ nuclear reactions^{[Reference Krása, Klír, Velyhan, Margarone, Krouský, Jungwirth, Skála, Pfeifer, Kravárik, Kubeš, Řezáč and Ullschmied22]}. The neutron yield per energy reaches a value up to ${\sim } 3.5\times 10^{5}\ \mathrm{neutrons/J}$ for an average laser energy of 550 J. This value equals the highest efficiency values observed at laser–solid interactions driven by high laser intensities ranging from $1\times 10^{18}$ to $5\times 10^{19}\ \mathrm{W\ cm}^{-2}$. Besides the neutrons, the laser-produced $\mathrm{CD}_{2}$ plasma emits fast ions having energies of MeV, as Figure 2(a) shows. The time of flight value of 70 ns at a distance of 1.5 m corresponding to the peak induced by a group of fast protons indicates an energy of 2.4 MeV, while the maximum energy reaches a value of approximately 4 MeV. These protons are followed by deuterons, which impact the LiF catcher target traversing the distance between both the targets. It causes a delay in the emission of the neutrons from the D–Li reaction. The time needed to travel that distance can be determined from the TOF spectrum of ions obtained by transforming the IC signal to the TOF spectrum of the ion charge density:

(1)$$\begin{equation} \rho (L,t)=q n_{\mathrm {IC}} (L,t) \propto j_{\mathrm {IC}} (L,t)/v, \label {eqn1} \end{equation}$$

where $q$ is the ion charge, $n_{\mathrm{IC}}(L,t)$ is the ion density, $j_{\mathrm{IC}}(L,t)$ is the ion current density observed at a distance $L$ from the primary target and $ v$ is the ion velocity. We note that the ion current is commonly a sum of partial currents $j_{i}$ of all the ionized species $j_{\mathrm{IC}}(L,t)=\Sigma j_{i}(L,t)$, including deuterons and carbon ions which are fully ionized as well as partially recombined. One of the partial currents is that of the protons, which originate from impurities on the front target surface. The partial currents can be revealed using a deconvolution of the TOF spectrum, as has been shown for a polyethylene plasma^{[Reference Krása, Klír, Velyhan, Margarone, Krouský, Jungwirth, Skála, Pfeifer, Kravárik, Kubeš, Řezáč and Ullschmied22, Reference Krása, Velyhan, Jungwirth, Krouský, Láska, Rohlena, Pfeifer and Ullschmied25]}.

Figure 3. Scintillation detector signal induced by emission of $\gamma $ radiation and neutrons produced via ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$, $\mathrm{D(d,n)}{}^{3}\mathrm{He}$, and ${}^{12}\mathrm{C(d,n)}{}^{13}\mathrm{N}$ nuclear reactions. The emission was observed in the radial direction N3 (see Figure 1) at a distance of 230 cm from the target (shot #44511).

Using a similarity relationship for $\rho $ detected by identical detectors placed at two different distances $L_{1}$ and $L_{2}$ in the same direction^{[Reference Krása, Parys, Velardi, Velyhan, Ryć, Delle Side and Nassisi26]}

(2)$$\begin{equation} \rho (L_{1},t_{1}) L_{1}^{3}= \rho (L_{2},t_{2}) L_{2}^{3}, \label {eqn2} \end{equation}$$

where $L_{1}/t_{1}=L_{2}/t_{2}$, we can determine a time-resolved ion charge density $\rho (L_{2},t_{2})$ at a chosen distance $L_{2}$ when $\rho (L_{1},t_{1})$ is observed at a distance $L_{1}$. The validity of the relationship (2) is limited for distances beyond some critical distance from the target, $L_{\mathrm{cr}}$, where the three-body recombination becomes insignificant due to the plasma rarefaction, the expanding ions have frozen charge states and their total charge $Q_{0}$ can be regarded as constant^{[Reference Lorusso, Krása, Rohlena, Nassisi, Belloni and Doria27]}. The value of $L_{\mathrm{cr}}$ depends on the laser irradiance on the target and the target material; in this experiment $L_{\mathrm{cr}} < 50\ {\rm cm}$. It is evident that the transformation of $\rho (L,t)$ to a short distance $L_{\mathrm{s}} < L_{\mathrm{cr}}$ gives underestimated values of the ion charge density due to the three-body recombination in this area. Although the ICs can hardly be used at a short distance from the target due to harmful effects caused by both the electrical breakdown of IC initiated by the collected current with a density of ${\sim } 100\ \mathrm{A\ cm}^{-2}$ and the strong electromagnetic pulse (EMP) interference^{[Reference De Marco, Pfeifer, Krousky, Krasa, Cikhardt, Klir and Nassisi28]}, the use of a passive detector, e.g., solid state track detector stacks, may partially solve the problem. Nevertheless, the obtained time-resolved density of charges $\rho (L,t)$ impinging on a catcher target provides an acceptable approximation of the flight times of deuterons to the LiF target, as Figure 2(b) shows. Two dominating peaks corresponding to the deuteron energy of ${\sim }$400 and $\sim $200 keV are characteristic for the time-resolved charge density of ions.

Figure 4. (a) Geometry of a nuclear reaction in the laboratory frame in which an incident deuteron with energy $E_{\mathrm{D}}$ impinges on a Li atom of the stationary LiF target and angular distribution of the neutron energy calculated for a value $Q=15.03\ {\rm MeV}$ of the ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$ reaction. (b) Deuteron energy dependence of the energy of d–Li neutrons detected in chosen directions as calculated using formula (1) in [Reference Petrov, Higginson, Davis, Petrova, McGuffey, Qiao and Beg10] describing the kinematics of neutron production in binary collisions between a projectile and an atom in a stationary target.

A typical signal of the scintillation detector that is induced by $\gamma $ radiation and neutrons coming from nuclear reactions ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$, $\mathrm{D(d,n)}{}^{3}\mathrm{He}$, ${}^{12}\mathrm{C(d,n)}{}^{13}\mathrm{N}$ is shown in Figure 3.

In contrast to the zero time coordinate for neutrons from the $\mathrm{D(d,n)}{}^{3}\mathrm{He}$ and ${}^{12}\mathrm{C(d,n)}{}^{13}\mathrm{N}$ reactions, which is related to the TOF of gamma radiation, the determination of the start time of neutrons produced via the ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$ reaction is encumbered by uncertainty caused by the broadband TOF spectrum of deuterons impinging on the LiF catcher target. A way to minimize this uncertainty consists of calculations of flight times $\mbox{TOF}_{\mathrm{D}}$ of deuterons to the LiF catcher target and flight times $\mbox{N-TOF}_{\mbox{D--Li}}$ of D–Li neutrons to the scintillation detectors. The value of $\mbox{N-TOF}_{\mbox{D--Li}}$ can be determined using formulae describing the kinematics of neutron production in binary collisions between a projectile and an atom in a stationary target, such as those derived and discussed in^{[Reference Petrov, Higginson, Davis, Petrova, McGuffey, Qiao and Beg10, Reference Izumi, Sentoku, Habara, Takahashi, Ohtani, Sonomoto, Kodama, Norimatsu, Fujita, Kitagawa, Mima, Tanaka and Yamanaka29]}. The dependence of neutron energy on the energy of deuterons and on the direction of observation is shown in Figure 4.

Figure 5 shows the arrival time of neutrons, $t_{\mathrm{N}}$, related to the time of the beam–target interaction, which is the sum of the time of flight $\mbox{TOF}_{\mathrm{D}}$ of deuterons to the catcher LiF target and the time of flight $\mbox{N-TOF}_{\mbox{D--Li}}$ of ${}^{7}\mathrm{Li(d,n)}^{8}\mathrm{Be}$ neutrons from the LiF target to the scintillation detectors:

(3)$$\begin{equation} t_{\mathrm {N}} =\mathrm {TOF}_{\mathrm {D}}+\mbox {N-TOF}_{\mbox {D--Li}}. \end{equation}$$

Figure 5. Deuteron energy dependence of the neutron arrival time at detectors N1–N5 (see Figure 4) related to the laser–target interaction. The distances from the catcher LiF target to the scintillation detectors were $L_{\mathrm{N1}}=1.81\ {\rm m}$, $L_{\mbox{N2--4}}=2.28\mbox{--}2.41\ {\rm m}$, and $L_{\mathrm{N5}}= 0.85\ {\rm m}$.

Figure 6. Scintillation detector signals observed in directions N1 to N5 ranging from $50^\circ $ to $110^\circ $ with respect to the mean direction of deuterons impinging on the LiF target and at distances from 0.8 to 2.4 m (see Figures 1 and 5).

Figure 6 shows the scintillation detector signals observed at five different distances and directions N1 to N5 with respect to the mean direction of deuterons impinging on the LiF target (see Figures 1 and 4). Using the dependence of the arrival times of neutrons on the energy of deuterons, $E_{\mathrm{D}}$, we can interpret individual maxima or partial peaks in the scintillation detector signals. The maxima in the signals shown in figure 6 may be sorted into two groups with respect to the energy of deuterons: $E_{\mbox{D-1}}\cong 400\ {\rm keV}$ (N1 – 52 ns, N2 – 64 ns, N4 – 60 ns, N5 – 33 ns) and $E_{\mbox{D-2}}\cong 200\ {\rm keV}$ (N1 – 59 ns, N2 – 64 ns, N3 – 68 ns, N5 – 41 ns). The beginnings of all the signals N1 – N5 correspond to a deuteron energy of ${\sim }$1 MeV. The 400 keV deuterons induce a peak in the time-resolved ion charge density at ${\sim }$16 ns for a distance of 10 cm, and the second group of deuterons with $E_{\mbox{D-2}} \sim 200\ {\rm keV}$ create a peak at ${\sim }$23 ns, which is the second highest one. The occurrence of protons and deuterons with energy $>$1.9 and 2.4 MeV, respectively, was confirmed by the tracks observed on a CR-39 track detector protected with an Al foil of $40\ \mu {\rm m}$ in thickness. The number of these ions was estimated to be ${\sim } 10^{12}$ per shot. The contribution of MeV deuterons to the neutron generation was insignificant.

Sorting of the peaks in the scintillation detector signals indicates that the repetitive bursts observed in the emission of fast ions in sub-nanosecond laser–solid experiments^{[Reference Krása, Klír, Velyhan, Margarone, Krouský, Jungwirth, Skála, Pfeifer, Kravárik, Kubeš, Řezáč and Ullschmied22]} may give rise to bursts in emission of fast neutrons generated via the beam–target ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$ reaction. Clear evidence is given by the observed well-separated maxima, for example at 52 and 59 ns in the N1 signal, and also at 60 and 78 ns in the N4 signal, that correlate well with the peaks of 200 and 400 keV deuterons appearing in the time dependence of the ion charge density (see Figure 2(b)).

The energy of the observed neutrons depends not only on the kinetic energy of fusing deuterons, but also on the direction of observation. Most of the neutrons emitted in the forward direction with respect to the direction of impinging deuterons have energy ${>}14\ {\rm MeV}$. Only a minority of them can reach ${\sim }$16 MeV energy. The maximum neutron yield from both the primary and secondary reactions was $3.5\times 10^{8}$ neutrons per shot. The partial contributions of both the $\mathrm{D(d,n)}^{3}\mathrm{He}$ and ${}^{7}\mathrm{Li(d,n)}{}^{8}\mathrm{Be}$ reactions can be estimated from the scintillation detector signal, by taking into account the dependence of the scintillation intensity on the energy deposited by neutrons. If we consider the solid angle of the expanding plasma plume containing the fast deuterons^{[Reference Krása, Velyhan, Jungwirth, Krouský, Láska, Rohlena, Pfeifer and Ullschmied25]} reduced by the solid angle of the laser beam, because the deuterons are emitted from the front target surface, the possible maximum yield could be as high as $Y_{\mbox{D--Li,max}}\sim 2\times 10^{8}\ \mathrm{neutrons\ sr}^{-1}$. This value is more or less comparable to the value of $Y_{\mbox{D--Li}}=8\times 10^{8}\ \mathrm{neutrons\ sr}^{-1}$ of the ${}^{7}\mathrm{Li(d,xn)}$ nuclear reaction driven by an intensity of$2\times 10^{19}\ \mathrm{W\ cm}^{-2}$^{[Reference Higginson, McNaney, Swift, Petrov, Davis, Frenje, Jarrott, Kodama, Lancaster, Mackinnon, Nakamura, Patel, Tynan and Beg7]}. In that work the deuterons were produced using the Titan laser (energy 360 J and pulse length 9 ps) and accelerated from the rear surface of the foil through the TNSA mechanism. It follows from this comparison that different power-law relations govern both the experiments. Moreover, the similarity parameter $I\lambda ^{2}$ does not also fully scale the generation of DD neutrons driven by high-power lasers with femtosecond to nanosecond pulse durations^{[Reference Krása, Klír, Velyhan, Margarone, Krouský, Jungwirth, Skála, Pfeifer, Kravárik, Kubeš, Řezáč and Ullschmied22]}. Thus, not only the laser intensity, but also the nonlinear phenomena occurring affect the laser energy absorption by the generated plasma and, thus, the ion acceleration.

Both the analysis of the N-TOF spectra and time-resolved ion charge density of the produced ions have shown that deuterons induced the ${}^{7}\mathrm{Li(d,n)}$ nuclear reaction while possessing kinetic energy $E_{\mathrm{d}} < 1\ {\rm MeV}$. Under these conditions the neutron source becomes isotropic^{[Reference Davis, Petrov, Petrova, Willingale, Maksimchuk and Krushelnick6]}. A number of neutron detectors used contemporaneously at various directions and distances allow an evaluation of the anisotropy in the neutron emission. Nevertheless, our previous measurement of fusion neutron spectra outside the plasma focus device PF-1000 demonstrated the significant influence of the plasma vessel on the primary spectrum of generated neutrons^{[Reference Králík, Krása, Velyhan, Scholz, Ivanova-Stanik, Bienkowska, Miklaszewski, Schmidt, Řezáč, Klír, Kravárik and Kubeš30]}. Considering also shot-to-shot fluctuations in the ion emission^{[Reference Krása, Velyhan, Margarone, Krouský, Láska, Jungwirth, Rohlena, Ullschmied, Parys, Ryć and Wołowski31]}, more complex laboratory equipment is needed to measure anisotropy in neutron emission through the beam–target reaction.