Nanotechnology and plasmonics for fusion

Eur. Phys. J. Spec. Top. https://doi.org/10.1140/epjs/s11734-025-01562-7 THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS Regular Article Nanotechnology and plasmonics for fusion Tamás Biróa and for the NAPLIFE collaboration NAPLIFE, Wigner Research Centre for Physics, Konkoly Thege Miklós u. 29-33, 1121 Budapest, Hungary Received 6 November 2024 / Accepted 3 March 2025 © The Author(s) 2025 Abstract We use nanotechnology-improved targets for femtosecond laser pulse shots in order to take advantage of plasmonic effects when accelerating electrons and ions. We seek to reach proton energies sufficient for igniting nuclear fusion processes with the surrounding material. In particular, the pB reaction is aimed at, not producing primary neutrons, just alpha particles. This paper reports about the state of our experimental research as presented at the conference on Particles and Plasmas, June 10–12, 2024, Budapest, Hungary. 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 [3–8], 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 × 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 [12–14], 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 +11B → 3α process has a resonant cross-section at 148 keV proton energy on boron eleven isotope nuclei [16–18] 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. The original title at PP2024 was “NAPLIFE: NAnoPlasmonic Laser Ignited Fusion Experiment - nanofusion progress 2023/24”. a e-mail: (corresponding author) 0123456789().: V,-vol 123 Eur. Phys. J. Spec. Top. 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 Np = np V is governed by the equation, NB dNp = −σvrel  Np dt V (1) with Np , NB 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 = 4πr3 /3 ≈ 1.7 × 105 nm3 ≈ 1.7 × 10−22 m3 . Furthermore, the averaging of the rate factor, σvrel , 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, σvrel  ≈ σpeak v, (2) with mv 2 /2 = 148 keV. From this, we obtain v 2 /c2 = 296 keV/938 MeV ≈ 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 ≈ 5 × 106 m/s. The cross-section at the resonance peak we estimate to be σpeak ≈ 100mb ≈ 10−29 m2 . 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 σpeak v ≈ 5 × 10−23 m3 /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 Γ = σv/V ≈ 0.3 s−1 . Now, one needs to estimate the time for the non-equilibrium fusion reactions. Within huge uncertainties, we consider here τ ≈ (1 . . . 100) ns. Using these values, we have Γτ ≈ 3 × 10−8 . . . 3 × 10−10 . The expected number of alpha particles produced in pB reactions per one nanorod becomes ΔNα = 3Γτ Np NB . An estimate for the number of protons and borons available for the fusion reaction is also uncertain. Assuming Np = 3300 and NB = 300, we arrive at the product of the number Np NB ≈ 106 . This leads to an estimated alpha production per single nanorod of about ΔNα ≈ 10−3 . . . 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  = 800 nm = 8 × 10−7 m. We associate a one-nanorod action 3 −21 volume as a sphere with radius /2, and obtain Vrod space ≈ 4π m3 . The (...truncated)