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p + ¹¹B reaction - why is it interesting?

Is a neutron-less fusion reaction!

ultraclean fusion reactor (despite the low reactivity of H¹¹B fuel compared to conventional DT fuel)^[1]
cancer treatments in human bodies^[2]
α particles generated by the ¹¹B(p,α)2α reaction could also be used for neutron-less nuclear fusion based propulsion in space^[3]

[1] H. Hora, S. Eliezer, G. J. Kirchhoff, N. Nissim, J.X. Wang, P. Lalousis, Y. X. Xu, G.H. Miley, J. M. Martinez-Val, W. McKenzie and J. Kirchhoff, Road map to clean energy using laser beam ignition of boron-hydrogen fusion, Laser Part. Beams 35, 730 (2017).

[2] G. A. P. Cirrone, L. Manti, D. Margarone, G. Petringa, L. Giuffrida, A. Minopoli, A. Picciotto, G. Russo, F. Cammarata, P. Pisciotta et al., First experimental proof of Proton Boron Capture Therapy (PBCT) to enhance protontherapy effectiveness, Scientific Reports, 8, 1141 (2018).

[3] C. Ohlandt, T. Kammash, and K. G. Powell, A Design Study of a p - 11B Gasdynamic Mirror Fusion Propulsion System, AIP Conference Proceedings, 654, 490 (2003).

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Cross section and resonances

The 11B(p,3α) reaction has three main resonances:

the first at 163 keV (Γ=0.2 keV and σ=0.2 mb)^[4],
the second and the broad one at 675 keV (Γ=0.2 MeV and σ=1.2 b)^[5],
the third at 2.64 MeV (Γ=400 keV and σ⋍700 keV)^[5].

M. H. Sikora, H. R. Weller, A New Evaluation of the ¹¹B(p,α)αα Reaction Rates, J Fusion Energy (2016) 35:538–543.

[4] J. Liu, X. Lu, X. Wang, W.K. Chu, Cross-sections of ¹¹B(p,α)⁸Be reaction for boron analysis, Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 107–111.

[5] V.F. Dmitriev, α-particle spectrum in the reaction p + 11B → α + 8Be* → 3α, Phys. Atom. Nuclei 72, 1165–1167 (2009).

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Cross section and resonances

Each of these resonances corresponds to a different state of a carbon nucleus. Depending on this state, the ¹²C can break down into three alpha particles (near the resonance at 163 keV) or into an alpha particle plus a ⁸Be. If the energy of impinging protons is E_p=675 keV, the carbon nucleus has an energy of 16.57 MeV and the produced beryllium nucleus is at its first excited state ⁸Be* (3.06 MeV). If E_p=2.64 MeV it is possible to have ⁸Be both at its first excited level and at ground state.

H.W. Becker, C. Rolfs, and H.P. Trautvetter, Low-Energy Cross section for ¹¹B(p,3α), Z. Phys. A 327 (1987) 341

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3-body decay assumption

Focusing on the E_p=675 keV case in which the beryllium is in its first excited level, the ⁸Be* resonance has a width of Γ=1.513 MeV which in turn corresponds to a lifetime of 4.35×10^-22s. This value, typical for strong interactions, means that it is possible to consider the total reaction like a 3-body decay of ¹²C into three α-particles; because of this, the total Q-value is:

Q=M_C+16.57-3m_α=9.295 MeV

IT’S NOT EASY to RECONSTRUCT THE ENERGY DISTRIBUTION!

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Energy spectra

The main peak of the spectra is centered at around 4 MeV, due to primary α₁-particles, and it is superimposed on a continuum due to secondary α-particles. At higher energies there is another little peak due to primary α-particles because the ⁸Be(0) channel gives a tiny contribution to the process.

Ion recoil

J. Liu, X. Lu, X. Wang, W.K. Chu, Cross-sections of ¹¹B(p,α)⁸Be reaction for boron analysis, Nucl. Instr. and Meth. in Phys. Res. B 190 (2002) 107–111

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Comparison between experimental and simulated data

S. Stave, M.W. Ahmeda et al., Understanding the ¹¹B(p,α)αα reaction at the 0.675 MeV resonance, Phys. Lett. B. 696, 26 (2011)

M. H. Sikora, H. R. Weller, A New Evaluation of the ¹¹B(p,α)αα Reaction Rates, J Fusion Energy (2016) 35:538–543

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Outline

p-B fusion reaction
p-B reaction in plasma
PALS2020, recent results

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Why the plasma environment?

The analysis of neutronless fusion reactions for systems with magnetic confinement requires very difficult conditions upon plasma parameters because of high values of ionic temperature, which are needed for initiation of these nuclear reactions. Oppositely, high kinetic energies of atomic ions can simply be obtained in plasmas produced by intense ultrashort laser pulses^[6].

However, the use of p¹¹B with a spherical laser compression scheme would require excessively high laser energies to reach the temperatures and densities needed to achieve a fusion burn in thermal equilibrium. Moreover, energy losses to Bremsstrahlung radiation under such conditions would prevent this reaction from being self-sustaining.

Such problems could be overcome by driving the p¹¹B reaction under conditions far from equilibrium, over shorter timescales than those involved in conventional inertial confinement fusion schemes, using short-pulsed high-intensity lasers^[7].

[6] V. S. Belyaev, A. P. Matafonov, V. I. Vinogradov, V. Krainov, P. Lisitsa, V. S. Roussetski, A. S. Ignatyev, G. N. Andrianov, Observation of Neutronless Fusion Reactions in Picosecond Laser Plasmas, Phys. Rev. E 72, 026406 (2005).

[7] C. Labaune, S. Depierreux, C. Goyon, G. Loisel, V. Yahia, and J. Rafelski, Fusion Reactions Initiated by Laser-Accelerated Particle Beams in a Laser-Produced Plasma, Nat. Commun. 4, 2506 (2013).

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The first experimental evidence

In 2005 Belyaev et al. experimentally demonstrated, for the first time, the possibility to trigger the pB fusion reaction by using an intense ps laser beam (2×10¹⁸ W/cm²) interacting with a boron-rich polymeric target. An α-particle yield of about 10³ α/sr/shot was estimated in this experiment, later corrected by Kimura et al. to a final yield of 10⁵ α/sr/shot.

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Other experimental results

In 2013 Labaune et al. published results of an experiment performed using the LULI laser system in France. In this experiment they used two laser beams: the first, having ns pulse duration, to ionize a solid B target, the second, having shorter duration (ps regime) but very high intensity (6×10¹⁸ W/cm²), to accelerate the proton beam via a second target. They demonstrated a maximum α-particle yield of about 9×10⁶ α/sr/shot, much higher than previously reported.

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Other experimental results

In 2014 Picciotto et al., using a sub-ns laser with modest intensity (10¹⁶ W/cm²) at the Prague Asterix Laser System (PALS) in the Czech Republic, obtained a much higher number of α particles (around 10⁹ α/sr/shot). In particular, they used a hydrogenated silicon target, doped by boron through ion implantation and enriched with hydrogen by an annealing process.

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Other experimental results

In 2020 Giuffrida et al., using a sub-ns laser with modest intensity (10¹⁶ W/cm²) at the Prague Asterix Laser System (PALS) in the Czech Republic, reported an even higher yield of α particles, well above 10¹⁰ α/sr/shot, obtained on boron nitride (BN) thick target.

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Trend of measured α particle yield

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Laser pulse^[9]

[9] L. Giuffrida, F. Belloni et al., High-current stream of energetic α particles from laser-driven proton-boron fusion, Phys. Rev. E 101, 013204 (2020).

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Laser-target interaction^[8]

2 ns before maximum intensity, the laser pulse begins to interact with the Si-H layer causing ablation and ionization of the target material, thus sweeping away the Si-H layer on the target surface.

[8] A. Picciotto, D. Margarone, et al., Boron-Proton Nuclear-Fusion Enhancement Induced in Boron-Doped Silicon Targets by Low-Contrast Pulsed Laser, Phys. Rev. X 4, 031030 (2014).

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Laser-target interaction^[8]

The target ablation reaches the boron layer. Then, the boron plasma is added to the initial plasma.

[8] A. Picciotto, D. Margarone, et al., Boron-Proton Nuclear-Fusion Enhancement Induced in Boron-Doped Silicon Targets by Low-Contrast Pulsed Laser, Phys. Rev. X 4, 031030 (2014).

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Laser-target interaction^[8]

The protons accelerated backward catch the B ions and the nuclear reaction occurs. In fact, the B ions can be assumed to be at rest since the proton velocity is about 1×10⁷m/s and the boron-plasma one is about 2×10⁶m/s.

[8] A. Picciotto, D. Margarone, et al., Boron-Proton Nuclear-Fusion Enhancement Induced in Boron-Doped Silicon Targets by Low-Contrast Pulsed Laser, Phys. Rev. X 4, 031030 (2014).

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Energy spectra^[9]

At the highest proton energies recorded in Giuffrida et al.^[9], around 1.5 MeV, the endpoint is expected to reach 7.3 MeV. Moreover, they observe also that the two maxima in the theoretical spectra (at about 1 and 4 MeV, respectively) are rightward-shifted by 3–4 MeV, depending on the detection angle. This is probably due to the action of the same electric field, generated in the proximity of the critical-density surface, which accelerates plasma ions in the backward direction.

[9] L. Giuffrida, F. Belloni et al., High-current stream of energetic α particles from laser-driven proton-boron fusion, Phys. Rev. E 101, 013204 (2020).

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Outline

p-B fusion reaction
p-B reaction in plasma
PALS2020, recent results

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Aim of the experiment

Study the pB reaction with different kind of target, as respect to those used in previous campaigns, in order to enhance the fusion rate of the reaction and maximize the alpha particle yield.

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Laser

The experimental campaign was performed at the PALS laser facility in Prague (Czech Republic) using an iodine laser working at the fundamental wavelength of 1315 nm, 600 J pulse energy, and sub-ns duration (0.3 ns FWHM).

The laser beam was focused onto the target inside a vacuum chamber (with a pressure lower than 10⁻⁵ mbar) with an incidence angle of 30° with respect to the target normal and a spot diameter of about 80 μm allowing one to reach an optimal intensity on target of about 3×10¹⁶W/cm².

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Target

Three types of targets, different from previous experiments, were used in order to optimize α-particle production.

new FBK

A thickness of silicon of 10 μm with above 10 μm of photoresist. Treated with Boron (by high dose ion implantation) and hydrogenated by annealing in H₂ atmosphere.

old FBK

A thickness of silicon of 10 μm with above 5 μm of photoresist. Treated with Boron (by high dose ion implantation) and hydrogenated by annealing in H₂ atmosphere.

LNS

10 μm of Formvar on which pure ¹¹B is deposited. The Formvar, poly (vinyl formal), is a thermoplastic polymer with a density of 1.23 g/cm³ used to give mechanical resistance to thin or fragile targets.

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Set-up

0°:

TOF

CR39

30°:

TOF

CR39

45°:

TOF

CR39

60°:

TOF

CR39

111°:

150° (not on plane):

TOF

CR39

180°:

TOF (on plane)

TOF (52° up)

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TOF detector - preliminary analysis

For each signal, the following procedure was performed in order to select good shots to analyze

set the zero of the time axis in correspondence with the rise of the photo peak
knowing the distance between the target and the detector and the mass of the particle, convert the TOF value in relativistic kinetic energy
select the cut-off energy

A shot has been selected for each type of target:

#55864 (new FBK)
#55871 (old FBK)
#56006 (LNS)

photo peak

signal

time

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TP detector - 0° - #55864 (new FBK)

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TP detector - 0° - #55871 (old FBK)

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TP detector - 0° - #56006 (LNS)

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TP & TOF detector

	Maximum proton energy [MeV]
n. shot	TP - 0°	TOF - 0°	TP - 180°	TOF - 180°	TP - 111°
#55864	1.63	1.602	2.34	1.968	1.4
#55871	2.06	1.544	1.48	0.809	1
#56006	1.12	0.917	2.33	0.892	<0.3

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CR39 detectors

Several CR39 detectors are placed at the same angles of TOF detectors in order to measure the absolute amount of α particles and protons from the laser-plasma interaction.

A mask, having four Al filters of different thickness, was placed in front of each

to filter the low-energy ion component out (not relevant for the goal of the experiment)
to avoid overlap of neighbouring ion tracks.
to study the energy distribution of α particles reaching the nuclear track detector.

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CR39 detectors - calibration

unfiltered

3 um Al

7 um Al

10 um Al

5485 keV

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Support for irradiation to be inserted inside the vacuum chamber

The support of the CR39s is fixed by means of double-sided adhesive tape to a bracket screwed to the “y-axis” (vertical) motor, which is in turn fixed to the “x-axis” (horizontal) motor. The source support, made of plastic, is fixed on a separate rod. The source is placed inside a cylindrical container on which a hole is made (approx. 1 mm in diameter) to collimate the beam of particles resulting from the decay of the source inside the support.

back

front

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CR39 detectors - calibration

Irradiation occurs in vacuum (approx. 2.4 x 10^-4 mbar) for a time interval of 20 minutes for each area.

It was chosen to irradiate for 20 minutes after making sure that after 2h of etching there was no saturation.

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CR39 detectors - etching

Procedure:

1 CR39 is irradiated for each source
each CR39 undergoes an etching in NaOH, 6.25 M, at 70 ° C in steps of 30 min for a total of 4 steps (therefore from 30 to 120 min)
at each etching step, the CR39 is, in order, immersed in acetic acid for 30 min, immersed in distilled water for 60 min and finally washed with distilled water

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CR39 detectors - calibration

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