1 Introduction

The first ignition of fusion exceeding the Lawson criterion [1] was achieved at the National Ignition Facility in 2022 [2]. Our nanoplasmonic laser ignited fusion experiment (NAPLIFE) makes use of the so called plasmonic effect [3,4,5,6,7,8], where a collective state of many electrons and photons in motion forms on the surface of certain metals, mostly gold, silver and copper. The metal electron motion alongside nanosize rods (typically 25 nm \(\times\) 85 nm) is resonant to a given laser pulse wavelength [9, 10], following from a careful design and fabrication [11]. Changing the laser wavelength is involved and costly, so we calculate and use nanorods with sizes near to the resonant behavior at the wavelength of 795 nm of our Ti:Sa laser.

The lifetime of plasmons is about 30–40 fs before transferring their energy into heat (atomic motion in a lattice) or ionizing the metal electrons and hence transforming the laser pulse energy into electric current. At the laser intensities, we apply in the NAPLIFE experiments, the latter is the dominant process. We conduct such in-shots in a special, hydrogen-rich environment where further physical processes take place. The hydrogen atoms in the surrounding UDMA-TEGDMA copolymer also get ionized and the protons—two thousand times heavier than the electrons—get accelerated by the plasmon electrons. This extra ionization and proton acceleration is due to a plasmonic phenomenon, called near field enhancement (NFE). We choose this polymer from dentistry research [12,13,14], in order to mix in the gold nanorod particles in fluid phase and then harden it by UV light.

Theoretical simulations predict NFE factors in the range of 10–200, in the case of our special material and nanorod shape NFE factors up to 300 were simulated [9, 10]. The enhanced electric field in the embedding polymer near to the nanometal surface ionizes the hydrogen atoms. After plasmonic co-acceleration, proton kinetic energies up to 200 keV occur. These we also detected in the backward plasma plume during Thomson parabola measurements of ion energy distributions. This is the second type of plasma we produce.

These proton energies are close to or over the near-threshold resonance for some nuclear fusion reactions. E.g., the \(p + ^{11}\!\!B \rightarrow 3 \alpha\) process has a resonant cross-section at 148 keV proton energy on boron eleven isotope nuclei [16,17,18] in the center of mass frame (CMS). Note that this means a proton kinetic energy of 161, 5 keV in the lab frame where the boronized target stands. Also the width of the near threshold resonance in this reaction is narrow, the full width at half maximum is 5.3 keV in the CMS. This resonance is 20 times narrower than could be expected, due to quantum number mismatch in that very reaction which goes through an excited \(C^{12}\) compound.

The products of fusion reactions form the third type of plasma, we encounter in NAPLIFE for a very limited time. These nanofusion processes, based on and triggered by the laser pulses, are far from any thermal equilibrium. Hence, the Lawson criterion [1] (according to which the product of temperature, density and confinement time has to exceed a threshold value) is inappropriate in this case. We have to fall back to non-equilibrium criteria.

2 Alpha yield estimate

A simplified kinetic theory estimate for the produced number of a few MeV alpha particles by this process can be given as follows. The reduction in proton number \(N_p=n_pV\) is governed by the equation,

$$\begin{aligned} \frac{ \textrm{d}{N_p} }{ \textrm{d}{t} } \, = \, - \langle \sigma v_{\textrm{rel}} \rangle \, N_p \frac{N_B}{V} \end{aligned}$$
(1)

with \(N_p, N_B\) being the number of protons and borons, respectively. The reaction volume, V, is estimated from the nanorod metal surface where the field enhancement is active: it consists of two hemispheres with radius \(r=35\) nm at each ends of the cylindrical nanorod [19]. The total volume is \(V=4\pi r^3/3 \approx 1.7 \times 10^5\) nm\(^3\) \(\approx 1.7 \times 10^{-22} \textrm{m}^3\).

Furthermore, the averaging of the rate factor, \(\sigma v_{\textrm{rel}}\), is now over a non-equilibrium distribution. For the sake of the present rough estimate, we consider 148 keV kinetic energy protons and the resonant peak cross-section,

$$\begin{aligned} \langle \sigma v_{\textrm{rel}} \rangle \approx \sigma _{\textrm{peak}} v, \end{aligned}$$
(2)

with \(mv^2/2 = 148\) keV. From this, we obtain \(v^2/c^2 = 296 \, \textrm{keV}/938 \, \textrm{MeV} \approx 0.00031556\). This result justifies the use of the nonrelativistic formula for the proton kinetic energy. The typical velocity of protons able to take part in a pB reaction at the lowest, near-threshold resonance, is, therefore, \(v \approx 5 \times 10^6\) m/s. The cross-section at the resonance peak we estimate to be \(\sigma _{\textrm{peak}} \approx 100 mb \approx 10^{-29} \textrm{m}^2\). This is not what theoretically expected but the experimental average observed at given beam energy resolution. We draw attention to Fig. 1b in Ref. [20] which avoids presenting the peak value used in Eq. 1. There the rate density (fluency) we use is given as \(\sigma _{\textrm{peak}} v \approx 5 \times 10^{-23} \textrm{m}^3/\textrm{s}\). The reaction rate is this quantity divided by the reaction volume (cf. Eq. 1), which is at least as large as the near field enhancement volume, cited above. One obtains \(\Gamma = \sigma v / V \approx 0.3 \, \textrm{s}^{-1}\).

Now, one needs to estimate the time for the non-equilibrium fusion reactions. Within huge uncertainties, we consider here \(\tau \approx (1 \ldots 100)\) ns. Using these values, we have \(\Gamma \tau \approx 3 \times 10^{-8} \ldots 3 \times 10^{-10}\). The expected number of alpha particles produced in pB reactions per one nanorod becomes \(\Delta N_{\alpha } = 3 \Gamma \tau N_p N_B\). An estimate for the number of protons and borons available for the fusion reaction is also uncertain. Assuming \(N_p = 3300\) and \(N_B = 300\), we arrive at the product of the number \(N_pN_B \approx 10^6\). This leads to an estimated alpha production per single nanorod of about \(\Delta N_{\alpha } \approx 10^{-3} \ldots 10^{-1}\).

Furthermore, according to microscopic pictures, the average distance between nanorods is about ten times their length in the Au2 doted setup [12]. That means \(\ell = 800\) nm \(= 8 \times 10^{-7}\) m. We associate a one-nanorod action volume as a sphere with radius \(\ell /2\), and obtain \(V_\mathrm{rod \, space} \approx \frac{4\pi }{3} 4^3 \times 10^{-21} \, \textrm{m}^3\). The volume covered by a laser pulse on the other hand is a cylindrical region with a diameter of \(10 \, \upmu \textrm{m}\) and length of the thickness of the target, in the order of magnitude of \(z \approx 100 \, \upmu \textrm{m}\). This gives \(V_{\mathrm{laser \, pulse}} \approx \frac{\pi }{4} (10 \, \upmu \textrm{m})^2 100 \, \upmu \textrm{m} \approx \frac{\pi }{4} 10^{-14} \, \textrm{m}^3\). These numbers lead to the following estimate for the number of nanorods affected by a single laser pulse: \(N_{\textrm{nanorod}} \approx 3 \times 10^4\). The expected number of alpha particles is the product of this with the above \(\Delta N_{\alpha }\) giving a value between 30 and 3000.

We note here that not all produced alphas can be detected, because of the special arrangement of the detectors covering only a fraction of the total solid angle. A further reduction factor is that not all protons are energetic enough [19]. Therefore, finally the theoretical expectation is a few MeV energy range alpha particles stemming from the pB reaction at one laser shot in the present arrangement. This is a proof of concept experiment.

A further note is due here, namely to consider the possibility of the detection of gammas, produced in the same pB reaction in a ratio of approximately 1/400, compared with the alphas. These energetic gammas would escape the polymer target and then could be detected in principle. The pros and cons of alpha vs. gamma detection is a typical question for nuclear experiments, see, e.g., Ref. [21].

3 Results

Most indications of the effect of the nanotechnological manipulation of the target are indirect. Therefore, the task of the spectroscopy is complex and we are pursuing several methods on various energy levels. These include laser induced breakdown spectroscopy (LIBS) [22, 23] to distinguish between the Balmer alpha line stemming from H and D atoms in the backward plasma plume [24], Raman spectroscopy [25, 26], sensitive to intramolecular vibrations of CH versus CD, and NH versus ND bonds [28], as well as Thomson parabola measurements of ion energies from protons to four times ionized carbons. Beyond these, CR39 nuclear gel detectors were deposited in some of the shootings and serious microscopic investigations were organized offline [29]. Details about the above listed findings were presented in other talks in this session of the PP2024 meeting. Figure 1 presents the scheme of the cooperation among subgroup activities in the NAPLIFE project (courtesy of J. Kámán).

Fig. 1
figure 1

Team relations. Graphics made by Judit Kámán, former member of the NAPLIFE collaboration

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Here, the author would like to focus on some illustrating results of microscopic investigations of the craters, formed upon the femtosecond laser shots in the polymer target. The crater size is an indicator for the liberated energy during and after the shot. By comparing craters with and without resonant nanorod implemented in the target, one concludes that qualitative and quantitative differences occur. For two selected craters, shown in Fig. 2, we found a volume ratio of 3.5, which is promising. The plasmonic effect is evidently at work.

Fig. 2
figure 2

Real size comparison of microscope images of two craters. The small one without Au, the larger one with Au. Picture made by Norbert Kroó

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Collecting crater size data for various shots and targets, the physically most important parameter is likely to be the laser pulse intensity. Figure 3 shows the obtained crater volumes at various laser pulse intensities [30]. Here, an initial rise was observed at threshold intensities of about \(10^{17}\) W/cm\(^2\), achievable at the Hydra laser at the Wigner Research Centre. The characteristic rise at around \(2 \times 10^{17}\) W/cm\(^2\) happened at the best focus and the highest pulse energy (27.5 mJ) we could achieve at the Wigner lab. In the sequel, we have applied for user beam time at the ELI-ALPS, Szeged, for experimenting at higher intensities. A three-week campaign was approved in February 2024, and data from that reached intensities up to \(6 \times 10^{18}\) W/cm\(^2\) due to the better focusing and improved contrast of the Sylos laser available there. In Fig. 3, only some initial findings are depicted. To some dissatisfaction, those did not show the continuation of the rise in crater volume, neither the characteristic difference between resonantly doped and non-resonantly doped or undoped target specimen. The non-resonant sizes also might have been resonant to higher order. The crater volume data seem to saturate at the maximal level, already reached at smaller laser pulse intensities with the resonant nanorods, and the undoped results by higher intensities may come closer to this value.

Fig. 3
figure 3

Crater volumes at various laser intensities, obtained at the Wigner RCP, Budapest and at ELI-ALPS, Szeged. Data collection and visualization by Ágnes Nagyné Szokol

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4 Conclusion

It is too early for a final conclusion, however. We need a more thorough analysis of all the order of 3.000 shots performed so far at ELI-ALPS’ Sylos laser. It is also noted that the quality of the craters differ between the lower intensity Hidra and higher intensity Sylos shots. More work is needed to improve the data analysis. Furthermore, we continue to observe energetic protons in the backward plume on thick targets, when the laser beam did not get through. Here, up to 200 keV protons are already observed in the Sylos experiments, promising a reach of the near-threshold (first) resonance in the p+\(^{11}\)B reaction. We are working on improvements, like enhancing the alpha detection power and implementing a Thomson parabola device also in the Wigner lab. Future thin target experiments and the fabrication of oriented and arranged nanorod arrays shall improve the ion acceleration power.