SYSTEMS AND METHODS FOR NON-THERMAL FUSION ENHANCEMENT USING NANOSTRUCTURED BORON NITRIDE-BASED TARGETS AND ULTRAFAST, HIGH INTENSITY LASER SYSTEMS

FIELD

[0001] The present disclosure relates generally to nanostructured fusion targets and optical systems for irradiating said targets. More specifically, the present disclosure relates to nanostructured targets comprising multi-walled boron nitride nanotubes and ultrafast, ultraintense laser systems for non-thermal initiation of nuclear fusion reactions and fusion yield enhancement. Provided herein are also methods for using the nanostructured materials and laser systems for achieving laser-driven nuclear fusion burn.

BACKGROUND

[0002] Due to its potential as a limitless, carbon-free source of electricity, fusion energy is widely viewed as the holy grail of energy research. Efforts to expand knowledge and discover pathways to access fusion energy in both thermally- and non-thermally-driven regimes remain ongoing. Classical thermonuclear fusion reactions, as observed in stars and our own sun, have been the primary focus of fusion research since the early 1900s. However, despite the wealth of knowledge around classical thermonuclear fusion reactions, the practical implementation of controlled fusion remains in its infancy.

[0003] The huge energy demands and operational requirements to achieve thermonuclear fusion require maintenance of large facilities and, thus, fusion research is largely restricted to the realm of collaborative research venues. Furthermore, the energetic requirements to initiate and sustain classical thermonuclear fusion reactions remain prohibitively costly and technically demanding. Indeed, although the physical requirements for achieving thermonuclear fusion are well-established, traditional thermally-driven nuclear processes suffer from a number of disadvantages including, for example, regulatory challenges associated with handling materials and fuels (e.g., deuterium-tritium). The factors described above represent a significant barrier to widespread use, scalability and commercialization of thermonuclear fusion. [0004] Thus, there is a need for new materials and systems to achieve reliable, sustainable fusion energy, particularly via non-thermal nuclear fusion, with reduced facilities requirements and lower operational thresholds.

BRIEF SUMMARY

[0005] The present disclosure is directed to systems utilizing the nanostructured targets comprising multi-walled boron nitride nanotubes and ultrafast, high intensity laser pulses to initiate non-thermal laser-driven fusion reactions. The methods and systems described herein take advantage of quantum effects derived from the nanoscale of the targets in combination with ultrashort, ultra-intense visible and near-infrared laser pulses to achieve fusion, and in some instances yield significant enhancement of fusion rates, for energy production.

[0006] In one aspect, provided herein is a method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with a laser pulse to cause the plurality of multi-walled boron nitride nanotubes to responsively generate an x-ray pulse.

[0007] In another aspect, provided herein is a method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with an x-ray pulse to cause the plurality of multi-walled boron nitride nanotubes to responsively generate a gamma-ray pulse.

[0008] In still another aspect, provided herein is a method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with an electron beam to cause the plurality of multi-walled boron nitride nanotubes to responsively generate a gamma-ray pulse.

[0009] In yet another aspect, provided herein is a method for non-thermal fusion ignition, the method comprising: irradiating a first layer of a nanostructured target by a laser pulse, wherein the first layer of the nanostructured target comprises a first plurality of multi-walled boron nitride nanotubes, wherein irradiating the first layer causes the first plurality of multi-walled boron nitride nanotubes to responsively generate an x-ray pulse and a first electron beam; wherein the generated x-ray pulse and first electron beam irradiate a second layer of the nanostructured target comprising a second plurality of multi-walled boron nitride nanotubes; wherein irradiating the second layer causes the second plurality of multi-walled boron nitride nanotubes to responsively generate a gamma-ray pulse and a second electron beam; and wherein the generated gamma ray pulse and second electron beam irradiate a third layer of the nanostructured target comprising a third plurality of multi-walled boron nitride nanotubes.

[0010] In still yet another aspect, provided herein is a system for non-thermal fusion ignition, the system comprising: a nanostructured target comprising a plurality of multi-walled boron nitride nanotubes; and a laser system configured to direct a laser pulse to be incident upon the target, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds.

[0011] In a further aspect, provided herein is a method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a nanostructured target comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the target with a laser pulse, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds, wherein the plurality of multi-walled boron nitride nanotubes generates an x-ray pulse in response to the incident laser pulse.

[0012] In another aspect, provided herein is a method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a target comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the plurality of multi-walled boron nitride nanotubes with one or both of an x-ray beam and a gamma-ray beam, wherein the irradiation induces enhancement of a fusion reaction.

[0013] In still another aspect, provided herein is a method of activating a fuel for non- thermal fusion ignition, the method comprising: providing a nanostructured target comprising a first plurality of multi-walled boron nitride nanotubes and a second plurality of multi-walled boron nitride nanotubes; and irradiating the first plurality of boron nitride nanotubes with an electron beam to cause the first plurality of multi-walled boron nitride nanotubes to responsively generate a gamma radiation pulse, wherein the gamma radiation pulse irradiates the second plurality of multi-walled boron nitride nanotubes to induce enhancement of a fusion reaction and to generate alpha particles and a second electron beam. DESCRIPTION OF THE FIGURES

[0014] The present application can be understood by reference to the following description taken in conjunction with the accompanying figures.

[0015] FIG. 1 shows calculated cross sections for different fusion reactions, including classical inertial confinement fusion (ICF) reactions with deuterium-deuterium (DD), deuteriumtritium (DT) and proton — boron- 11 (p- ⁿ B, p-Bl 1, or pBl 1) fuels, as a function of the center-of- mass energy.

[0016] FIGS. 2A-2C shows illustrations of a boron nitride nanosheet (FIG. 2A), a singlewalled boron nitride nanotube (SW-BNNT) (FIG. 2B), and an exemplary nanostructured target (or portion thereof) comprising a plurality of boron nitride nanotubes with longitudinal axes aligned in parallel (FIG. 2C).

[0017] FIGS. 3A-3B show nanostructured boron nitride. FIG. 3A depicts various exemplary structural motifs of boron nitride, which can be observed in the walls of single- and multi-walled boron nitride nanotubes (MW-BNNT), including armchair, zigzag, and chiral symmetries. FIG. 3B shows defective nanostructured boron nitride material in a structural arrangement known as boron nitride nano “bamboos”.

[0018] FIG. 4 shows an exemplary schematic of the logarithmic intensity of a subpicosecond laser pulse as a function of time, centered at the peak pulse intensity. The temporal contrast ratio, e.g., the intensity before pulse (pre-pulse) relative to the peak of the pulse, shows a non- negligible energy contribution in the nanosecond and picosecond regime prior to the peak intensity.

[0019] FIG. 5A and 5B show illustrations of the nanostructured targets comprising boron nitride nanotubes (BNNTs), and the radiation pathway for the conversion of visible or nearinfrared laser light to x-ray radiation and gamma-radiation (FIG. 5A), and subsequent fusion burn of self-propagating generation of gamma rays and alpha particles (FIG. 5B).

[0020] FIG. 6 shows calculated cross sections for different fusion reactions with DT, DHe ³ and pB ¹¹ under x-ray irradiation of aligned BNNTs. DETAILED DESCRIPTION

[0021] The following description sets forth exemplary methods, parameters and the like. It should be recognized, however, that such description is not intended as a limitation on the scope of the present disclosure but is instead provided as a description of exemplary embodiments.

[0022] The present disclosure provides materials, systems, and methods for initiating and enhancing nuclear fusion reactions, that is, fusion reactions outside of the classical thermal regime. The non-thermal physics regime is predicated on the creation of a relatively cold, degenerate plasma that allows for quantum effects with ignition at much lower temperatures, and which conditions support a fusion burn wave that may be resilient against the problem of turbulence. The methods provided herein are achieved through the use of a combination of nanostructured target material, namely targets comprising multi-walled boron nitride nanotubes with carefully controlled physical properties, and ultrafast, high intensity laser pulses to drive the generation of gamma radiation and subsequent initiation of nuclear fusion reactions, such as the proton — boron- 11 (pBl l) fusion reaction.

[0023] Boron nitride nanotubes (BNNTs) were first predicted in 1994 and experimentally synthesized for the first time in 1995. In the intervening decades, high-quality boron nitride nanotubes have been synthesized with increasingly higher quality and greater control over their properties. Parallel developments at the forefront of laser technology have provided increasingly high-powered, increasingly short laser pulses (with peak powers on the order of petawatts and pulse lengths on the order of tens of femtoseconds). Leveraging and expanding on these advancements in nanotechnology and laser physics may allow, as provided herein, for realizing physics in real-world applications, including the practical implementation of non-thermal, laser- driven nuclear fusion using the nanostructured targets comprising multi-walled boron nitride nanotubes and ultrafast, ultra-intense laser systems described herein.

[0024] The boron nitride nanostructured materials of the present disclosure serve two roles in facilitating the conversion of visible or near-infrared light into x-ray radiation, gamma radiation, and free electrons (as well as conversion of x-ray radiation into gamma radiation and free electrons) and employing the resultant radiation and plasma to initiate and enhance fusion reactions. Photons with energies from 100 eV to 100 keV are typically considered to be x-rays and photons with energies above 100 keV are typically considered to be gamma rays. When nanostructured boron nitride material as disclosed herein is irradiated with ultra-intense ultra- short radiation as disclosed herein, strong quantum-induced screening can enhance the fusion reactivity for pBl 1 at much lower relative energies and temperature thresholds than usual for thermonuclear conditions. The nanostructured targets provided herein may also initiate a fusion burn wave that is resilient against plasma instabilities and produce energy via a low neutronic pBl l nuclear fusion path by generating alpha particles. Quantum induced screening originates from the properties of the boron nitride nanotubes (and the properties and arrangements of the targets in which they are disposed) and from strong fields created by absorbed intense short pulse radiation in the boron nitride target material. Both effects lead to enhanced tunneling via screening and therefore allow pBl 1 to fuse efficiently. The technology for the non-thermal approach to fusion described herein relies upon harvesting quantum effects in a degenerate plasma in order to obtain large enhancement factors and resulting in high fusion rates.

[0025] Experimental results based on carbon nanotubes (CNT) (J. Rocca, C. Bargsten, Volumetric creation of ultra-high-energy-density plasma by irradiation of ordered nanowire arrays, 2016) utilizing vertically aligned nano wire array targets, in combination with ultra-high- contrast several-tens-of-femtoseconds laser pulses focused to relativistic intensity, have already demonstrated the creation of appreciable volumes of Ultra-High-Energy -Density plasma (UHED) under laboratory conditions. In the context of the present disclosure, it is described how boron nitride nanotubes may exhibit analogous propensities and may offer even greater benefits, as explained below. Preliminary experiments with BNNT targets were performed. In these experiments, the BNNTs were unordered. A 45-fs, 7-J, 400-nm laser pulse was focused to an intensity of 1021 W/cm ² at the front surface of the respective target. Over 600 shots were performed on BNNT targets as well as on amorphous BN and CH or Al control targets. Two ion spectrometers, six gamma spectrometers and six CR-39 solid state nuclear track detectors were used to characterize the ion and gamma ray emission. BNNT targets produced a strong gamma ray signal and up to 100 times more ions emitted with MeV energies than amorphous BN or foil targets. The experiments, therefore, provided a clear indication of enhanced absorption of the laser pulse and possibly the onset of enhanced gamma ray conversion. [0026] In general, BNNT is a much more thermo-mechanically stable material than CNT. The walls of the tubes have a very high thermal conductivity which has been shown in experiments to accelerate chemical reactions by up to lO.OOOx. Unlike CNTs, boron nitride nanotubes have a wide bandgap of 5.7 eV and are good electrical insulators.

[0027] Besides the general characteristics of the boron nitride nanotubes, the nanotube wall properties may allow for several degrees of freedom. Referring again, to the carbon counterpart of BNNT, graphene has a viscosity that is defined by the ratio of the shear viscosity to entropy density not far away from the KSS (Kovtun-Son-Starinets) bound:

Y] 1 h s 4n: k _B where:

• r|: Shear viscosity

• s: Entropy density

• kB: Boltzmann constant

• h: Planck constant

[0028] The value of this ratio describes the lower bound to viscosity, yielding a very small figure and is taken as a valid indicator of how strongly coupled a system is. (See M. Bagglio, W - J. Li, Universal bounds on transport in holographic systems with broken translations, 2020.) Because the limit of zero viscosity would be the “perfect” fluid, the bound from the strong KSS conjecture would define “the most perfect” fluid with strong interparticle interactions (correlation). This bound suggests a coupling parameter T in the range of 20 to 25. The behavior of shear viscosity has been analyzed for graphene and has an AdS/CFT description close to a SYK (Sachdev-Ye-Kitaev) model. AdS/CFT is known as the holographic principle, allocating a strongly coupled conformal field theory (CFT) to weakly coupled gravity in the anti-de Sitter (AdS) space in higher dimension. SYK is an exactly solvable quantum mechanical model with strong quantum correlations.

[0029] Accordingly, the pool of strong quantum correlations may be used in a similar way to using a heat reservoir in thermodynamics, and the properties of the tube walls may be utilized to support the wave function overlap needed for enhancement. [0030] In addition to use of the targets described herein, another aspect of the non-thermal physics regime provided herein may be the use of an ultra-short pulse, high intensity laser system in combination with the nanostructured targets. The systems of the present disclosure employ laser pulses having not only petawatt levels of power and subpicosecond pulse lengths, but which achieve very high levels of intensity in femtosecond window relative to those of the picosecond-nanosecond windows (e.g., high temporal contrast ratio). The high temporal contrast ratio contributes significantly to the ability to maintain the nanostructured targets (e.g., avoid destruction) at pre-pulse and - especially - to realize the low temperature requirements of quantum enhancement to achieve non-thermal fusion.

[0031] As provided in the present disclosure, the nanostructured targets comprising multiwalled boron nitride nanotubes may serve dual purposes in enabling fusion. The first layers of the tubes can be viewed as an extension of the laser and support converting the laser light into x- rays and gammas, respectively. The resulting high energy radiation in combination with strong fields within the nanostructured target may drive fusion reactivity in the multi-walled boron nitride nanotubes in the non-thermal regime.

[0032] In some embodiments the irradiation induces enhancement of a fusion reaction rate. In certain embodiments, the irradiation induces enhancement of a fusion reaction rate by a factor of at least 10 ²⁰ as compared to the classical thermonuclear fusion reaction rate at the same temperature.

Background of Non-Thermal Fusion Regime in Astrophysical Context

[0033] In type la supernova explosions (and in Helium flashes on massive stars or in the Deuterium burning in brown dwarfs and supermassive planets), it is known that a burn wave in degenerate plasma can develop detonating or undergo a deflagration-detonation transition.

[0034] A type la supernova explosion starts from a White Dwarf, the remnant of a dead star. The White Dwarf mainly consists of carbon and rapidly cools down after the progenitor star has exhausted its fusion fuel. If the White Dwarf originates from a binary star system, it can draw mass from its companion star by tidal effects, subsequently leading to the White Dwarf reaching a critical mass at which carbon burning sets in, resulting in the supernova explosion. A crucial feature is that the onset of carbon fusion in the White Dwarf is independent of temperature. For example, the progenitor star might have died billions of years ago, in which case the White Dwarf would have thermalized to the temperature of outer space.

[0035] Aspects of carbon burning in a type la supernova explosion are detailed below:

[0036] Ignition: The highly dense core (10 ⁷ - 10 ⁹ g/cc) leads to a degenerate non-thermal contribution to electron pressure in the plasma. It leads at the same time to a strong decrease in screening length. There are different ways to understand the temperature independent ignition. In a microscopic picture, e.g., a description purely in terms of electrons and ions, the strongly increased screening and additional ion wave function overlap leads to strongly increased tunneling rates. Since in this case these quantum effects are density-driven, this leads to a temperature independent ignition. One could also refer to an effective field theory description. Since the high density leads to a diamond like structure of the carbon in the White Dwarf, phonon excitations can be considered in this crystalline structure. Due to the high density, the spectrum of these phonon excitations is relevant for overcoming the Coulomb barrier. Note that overcoming the Coulomb barrier due to vibrational excitations in the plasma is not a try-once-at- a-time process (as in classical ion collisions in thermonuclear fusion) but a continuous process with a Fourier mode description. This is another way to arrive at the conclusion that carbon ignition in a type la supernova explosion is a largely temperature independent process.

[0037] The burn wave: If ignition in a degenerate plasma starts in a phase where degenerate pressure dominates over thermal pressure, we have a short phase with practically no volume expansion. In more detail, the process runs as follows: With the onset of first fusion reactions, energy is set free and temperature rises. Since degenerate pressure is independent of temperature, this will not lead to volume expansion. Consequently, temperature rises steeply which in turn leads to an explosive increase in fusion rates. The reason behind this are the so-called temperature power laws of fusion reactivities. The latter are defined as the integral: f o(v) v fr(v) dv

[0038] This is the integral over the cross section G(V) with the ion energy v (e.g. in keV). The weight of the integral is given by the energy weighted Maxwellian distribution v fr(v) where fi(v) is the classical Maxwellian at temperature T. Expanding this integral leads to the power laws with reactivity behaving as:

[0039] The exponent n is determined by the masses and charges Z of the reacting fusion species. The exponent strongly rises with Z. For example, for hydrogen fusion, n is less than 4 while it rises to as much as 42 for carbon burning in a White Dwarf (i.e., that an increase of only 2% in temperature leads to a doubling of fusion rates).

[0040] For this reason, in the phase in which degenerate pressure dominates, the increase in temperature leads to an explosive increase in fusion rates which in turn leads to a further increase in temperature. This feedback loop continues until finally thermal pressure wins over degenerate pressure. At this point, volume expansion sets in. The set in of volume expansion from the overheated fuel either directly leads to a detonating burn wave, or it leads to a burn wave undergoing a DDT (deflagration detonation transition). Since the detonating regime leads to shock ignition at the burn front, a larger area of the burn front becomes favorable. Hence, turbulence at the burn front (which increases the area of the burn front) in this case contributes to the progression of the burn wave.

[0041] The densities of the astrophysics example are far out of reach and possible only by strong gravitational assist. Note, however, that the fact that these high densities lead to quantum effects enhancing fusion rates does not imply that these quantum conditions in the plasma cannot be achieved using other parameters than density as the driver. Indeed, as disclosed herein, other parameters than density may be used to reach enhancement of fusion rates under lab conditions. Note also that pBl 1 fuel is still comparatively easy to burn, compared to the carbon burning in type la supernova explosions.

[0042] Following the classical thermonuclear approach, a PFI (proton fast ignition) scheme with a pBl 1 -based spark plug target may be considered. This target contains a DT (Deuterium Tritium) spark plug which is ignited by the laser and then ignites the surrounding fuel by nuclear burn. All approaches to burning a target with an advanced fuel face two challenges. [0043] A first challenge is the much higher ignition temperature under classical thermonuclear conditions (the cross section for pBl 1 peaks at around 580keV, compared to around 64keV for DT) which is the main obstacle for the ignition of advanced pBl 1 fuels. In the PFI setting, this is addressed by the spark plug structure of the target.

[0044] A second challenge is hydrodynamic turbulence (Rayleigh-Taylor instabilities, “RTI”) which can destroy the burn front. This is a problem which can beset all previously existing approaches to fusion. The PFI approach should lead to a lower risk of turbulence from a lower level of compression (as compared to classical Direct Drive). It still, however, may face the problem of supporting a proper burn wave progression into the pBl 1 fuel which is much more difficult to ignite.

[0045] Controlling hydrodynamic turbulence is discussed below. One point which makes the problem of plasma turbulence difficult to resolve is the progression to ever finer scales (which would have to be controlled to avoid the onset of turbulence). The underlying challenge is called the existence and smoothness problem of the Navier-Stokes equations and, on a side note, is one of the Millennium Prize Problems. Decades of research have shown that this is not a theoretical problem but very concretely makes its appearance in target design of thermal fusion. Any disturbance of the symmetry of the target (e.g., by surface roughness) gives a potential seed for the later occurrence of turbulence. These requirements on target design (e.g., with increasingly fine surface roughness) may pose a major challenge on potential cost reductions and automated production methods.

[0046] Regarding trying to ignite the fuel in a degenerate plasma with strong quantum effects, temperature independence may address the challenge of high ignition temperature.

[0047] Regarding trying to reach resilience against turbulence, reaching a supersonic detonating burn wave may contribute. For example, utilizing the beneficial effects of a larger shock front and a stabilization of the burn wave in a shock compression regime may address the challenge. Fusion Enhancement Rates

[0048] In the simplified non-dynamical model disclosed below, the use of the nanostructured targets comprising multi-walled boron nitride nanotubes leads to record enhancement with resulting fusion rates above thermonuclear deuterium-tritium (DT) rates. Similar models show that the results do not hold for non- nanostructured pBl 1 target fuels, which would likely be even more difficult to ignite non-thermally than in a thermal approach. The nanostructured targets are intimately tied to the quantum effects, which can ignite and sustain non-thermal fusion reactions for the proton — boron- 11 system.

[0049] Plasma conditions may be characterized by the coupling parameter T which is defined as: where:

• Q: Charge of the ions (for a single species plasma)

• so: Di-electric constant

• d: mean free path length

• k: Boltzmann constant

• T: plasma temperature

[0050] The value of T approximates to the quotient of potential Coulomb energy to thermal energy in the plasma. The following cases may be distinguished:

• T < 1. The case of weakly coupled plasma. This is the case of thermonuclear fusion. Thermal energy dominates the system (hence the name). The description of the plasma under these conditions is very close to that of an ideal gas.

• T > 1. All cases of this type are called strongly coupled plasma. This is the regime in which degenerate plasma conditions are realized. It subdivides into different types.

• For T > 170 ... 180, one speaks of crystalline plasma. This is the phase encountered in White Dwarfs with the diamond like structure and the relevance of phonon excitations.

• For T between 1 and 170 ... 180, we have conditions where the plasma is largely described as a liquid. This phase will be most relevant since the very high T values of the Astrophysics regime will not be reached in the lab.

• In the phase of liquid plasma, we have a parameter range where T takes on values between 20 and 25. This is the parameter range where the absolute minimum of viscosity is reached. This will be important in the context of the nanostructured target. [0051] Two different ways of understanding low temperature ignition in White Dwarfs have been described herein above: the microscopic picture of screening and the effective field theory description in terms of the spectrum of phonon vibrations. These are qualitative pictures. To arrive at quantitative data, one may do a true quantum statistical calculation by calculating the fusion enhancement factors.

[0052] The classical cross section is derived from a two-particle calculation: For two ions which might fuse, one basically takes into account overcoming the Coulomb barrier, with a small correction at the top of the barrier by including quantum tunneling into the Gamow factor (using a WKB approximation). In a full quantum statistical calculation, one finds that, in addition to two-particle effects, three- and four-particle effects are also included in the calculation of fusion rates. The three-particle contribution describes the screening mentioned above with two ions and an electron involved in the process. In addition, 4-particle wave function overlaps are taken into account (which are generally not independent of the screening effect themselves). The fundamental work on quantum statistical calculation of enhancement factors was initiated in the 1990s in a series of papers by S. Ichimaru and co-authors (S. Ichimaru, H. Kitamaru, Pycnonuclear reactions in dense astrophysical and fusion plasmas, 1999) and further developed up to 2019 in three books (S. Ichimaru, Statistical Plasma Physics, Vol. I+II, 2004; S. Ichimaru, Statistical Physics of Dense Plasmas, 2018).

[0053] Enhancement rates may be considered rudimentarily as multiplicative factors (respectively) to the cross sections that are depicted in FIG. 1. In a true calculation, one first derives the two particle fusion rate from the cross section and the multiplication with the enhancement factor is done on the level of fusion rates. This explains why largely temperature independent ignition is possible in White Dwarfs. The rates at low energies - where the contribution from the classical cross section gets very small - can become sizable if sufficiently large enhancement factors are multiplied.

[0054] In principle, enhancement factors are applicable in all fusion rate calculations. But under usual thermonuclear conditions, the contribution from three- and four-particle effects are negligible. Under classical ICF conditions with DT fuel, they never get to 0.1% (and can stay much below); thus, the factor one multiplies the cross section with for classical ICF conditions with DT fuel never exceeds 1.009.

[0055] There are basically two cases where enhancement factors make an important contribution. The first case is given by the plasma conditions of the Astrophysics examples. In these cases, the enhancement is driven by the huge densities present and is stable over a rather large temperature range. For example, fusion in a type la supernova explosion is driven by enhancement at temperatures up to 10 ⁸ K. Though a high temperature, this is still far below the regime (several billion K) where carbon burning would become possible under thermonuclear conditions. The enhancement factor for carbon burning in White Dwarfs is around IO ²³ . Note that this does not mean that one gets very large fusion rates, since the classical cross section - and the resulting two-particle fusion rates - becomes minuscule at low temperatures. Indeed, the total fusion rates, including an enhancement, in these cases give sizable fusion rates but stay orders of magnitude below the 10 ¹⁹ W/g fusion rates calculated for ICF DT fusion. The reason that one still gets a violent explosion in a type la supernova results from the following fact: Once burning sets in, mass shells of constant thickness rapidly include ever larger masses in these large astrophysical bodies.

[0056] The second case of high enhancement factors is given by the case of so called highly pressurized metals. These systems involve isotopes of hydrogen; under very high-pressure conditions, these are metallic hydrogen systems. One such case of a highly pressurized metal is given by the p-Li7 system which combines metallic hydrogen with Li as the second metallic component. In this regime, the enhancement is driven by two conditions: First, the use of temperatures which are very low for fusion standards, ranging from a couple of hundred K to around 2000K; and, second, a liquid metal model.

[0057] The p-Li7 (proton — lithium-7) system (Equation 1) is considered below. From the nuclear side, it is very close to the p-Bl 1 reaction (Equation 2).

P-L17 2a (1) p-BI I ^ 3a (2) [0058] If one takes a more detailed look, the two reactions turn out to be even more similar. The main resonance of the p-Li7 cross section arises from an excited state Be8* of Be8 (Equation 3).

P-L17 Be8* 2a (3)

[0059] In a similar way, the main resonance of the p-Bl 1 cross section at 580keV arises from an excited state Cl 2* of Cl 2, as shown in Equation 4:

[0060] But the three alpha particles do not come out monochromatic, but only two of them share the same energy while the energy of the third differs. The reason is that one alpha comes out first and the reaction transitions through an intermediate excited state of Be8 which then decays into the two remaining alphas. So, in even more detail the p-Bl 1 reaction looks like Equation 5 below p-Bl 1 C12* Be8* + a 3a (5) which shows the close analogy to the p-Li7 reaction.

[0061] The quantum statistical model used by Ichimaru for the p-Li7 system is a liquid metal model. For a density of 140g/cc and a temperature of 2000K, the p-Li7 system shows the highest enhancement factor calculated so far with an enhancement of 10 ⁵⁶ (see Table 1). This case (Case 2) proves that record enhancement factors can be realized in lab range conditions. The density of 140g/cc is not only far away from the densities of Astrophysics, but it is even far below the densities of around lOOOg/cc expected for standard ICF approaches and even considerably below the 300-400g/cc densities expected for DT fast ignition schemes. In addition, the temperatures involved are very low for fusion standards. Reaction: p-Li7 Unit Case 1 Case 2 p _m g/cm ³ 16.0 140

T K 700

P _e Mbar 80.9 3375

Ty 514.5 371.1 log ₁₀ Ajj 52.55 56.15

Table 1. Reaction rates and enhancement factors for p-Li7 as example for ultrahigh-pressure liquid metals according to S. Ichimaru ^FMer! Textmarkemchtdefimert. _ass densities (p _m ) and temperatures (T) are assumed parameters; P _e is the total pressure of the conduction electrons. The molar fraction of the BIMis assumed to be 50%.

[0062] If one uses the record enhancement factor to calculate total fusion rates, one finds again sizable fusion rates but as in the Astrophysics case they remain some orders of magnitude below the 10 ¹⁹ W/g of ICF DT fusion. So, highly pressurized metals prove that large enhancement factors can be achieved at lab scale densities and temperatures, but do not lead to fusion rates which are commercially interesting.

[0063] In some embodiments the irradiation induces enhancement of a fusion reaction rate. In certain embodiments, the irradiation induces enhancement of a fusion reaction rate by a factor of at least 10 ²⁰ as compared to the classical thermonuclear fusion reaction rate at the same temperature.

Nanostructured Targets Comprising Multi-Walled Boron Nitride Nanotubes (MWBNNTs)

[0064] As provided herein, laser-driven fusion reactions are made accessible through the use of carefully controlled nanostructured targets. Enhancement factors which are large enough to lead to commercially viable total fusion rates can be achieved with the specialized nanostructured targets, as described herein. The present disclosure provides nanostructured targets, comprising one or more pluralities of multi-walled boron nitride nanotubes. In some embodiments, the nanostructured target comprises one or more layers, wherein each layer comprises at least one plurality of multi-walled boron nitride nanotubes. More specifically, the present disclosure provides nanostructured targets comprising multi-walled boron nitride nanotubes, wherein the multi-walled boron nitride nanotubes are variously configured to be irradiated by visible or near-infrared laser radiation, x-ray radiation, gamma radiation, and/or electron beams and to responsively generate higher energy radiation, subsequent electron beams, and/or ignite fusion burn, depending upon the incident photon or electron radiation. In still further embodiments, the present disclosure provides nanostructured targets comprising multiwalled boron nitride nanotubes for non-thermal fusion ignition, such as for ignition of pBl 1 fuel for aneutronic fusion.

[0065] In one aspect, the present disclosure provides a nanostructured target for non-thermal fusion ignition, the target comprising a plurality of multi-walled boron nitride nanotubes configured to be irradiated by a laser pulse and to responsively generate an x-ray pulse.

[0066] The properties of the incident (e.g., irradiating) laser pulse which the nanostructured target is configured to receive may be characterized by aspects including, but not limited to the wavelength, intensity, pulse length, energy on the target, spot size, fluence, polarization, etc. The laser pulse may be further adjusted with respect to the angle of incidence upon the nanostructured target relative to the longitudinal (long) axis of the multi-walled boron nitride nanotubes. In some embodiments, laser pulse has zero (0°) degree angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes, that is, parallel the long axis of the nanotube. In other embodiments, the laser pulse has ninety degree (90°) angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes, that is, perpendicular to the long axis of the nanotube. In still other embodiments, the laser pulse has angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes between zero (0°) and ninety (90°) degrees.

[0067] In some embodiments, the laser pulse comprises photons in the spectral range between 400 nm and 1400 nm. In certain embodiments, the laser pulse is monochromatic. In some embodiments, the laser pulse may be characterized by its fluence (e.g., joules/cm ² ). In other embodiments, the laser pulse has a subpicosecond pulse length. In some embodiments, the laser pulse has a pulse length of between 1 femtoseconds and 50 femtoseconds. In some embodiments, the laser pulse has a spot size of between 1 microns and 10 microns in diameter. In still other embodiments, the laser pulse has a spot size of between 1 pm ² and 50 pm ² . In certain embodiments, the laser pulse has a spot size of between 10 pm ² and 50 pm ² . In other embodiments, the laser pulse has a pulse energy of at least 200 J. In still other embodiments, the laser pulse has a peak intensity of between 10 ²¹ W/cm ² and IO ²³ W/cm ² .

[0068] Similar to the irradiating laser pulse, the generated x-ray pulse produced by the nanostructured target may be characterized by its spectral energy, intensity, pulse length, energy on the target, spot size, fluence, polarization, distribution angle around the tube axis, etc. In some embodiments, the generated x-ray pulse may be characterized by its spectral energy range. In some embodiments, the generated x-ray pulse may be characterized by its fluence, for example, in J/cm ² . In other embodiments, the generated x-ray pulse may be characterized by its pulse length, for example, in attoseconds.

[0069] In still other embodiments, the x-ray pulse may be characterized by its (degree of) temporal coherence or lack thereof. In some embodiments, the x-ray pulse is coherent. In other embodiments the x-ray pulse is non-coherent. In still other embodiments, at least a portion of the x-ray pulse is coherent, that is, the x-ray is partially coherent.

[0070] In addition to the attributes described above for the laser pulse which the nanostructured target is configured to receive and the x-ray pulse which it responsively generates, the nanostructured target may also be characterized by its efficiency for the conversion of the laser radiation to x-ray radiation. In some embodiments, the nanostructured target has a conversion efficiency for laser photons to x-ray photons which may be characterized, for example, as the percentage of the energy x-ray photons produced over the total energy of the incident laser photons.

[0071] In another aspect, provided herein is a nanostructured target for non-thermal fusion ignition, the target comprising a plurality of boron nitride nanotubes configured to be irradiated by an x-ray pulse and to responsively generate a gamma-ray pulse.

[0072] It should be recognized that, in some embodiments, the incident (e.g., irradiating) x- ray pulse of the present aspect may be derived from the responsively generated x-ray pulse in the preceding aspect. In other embodiments, the x-ray pulse irradiation may be derived from sources such as electron accelerators (such as linear accelerators, pulsed DC accelerators, betatrons, cyclotrons, or synchrotrons), or laboratory sources of electrons generated outside of the nanostructured target.

[0073] As with the responsively generated x-ray pulse of the preceding aspect, it should also be recognized that the x-ray radiation incident on the nanostructured targets of the present aspect may be similarly characterized by its spectrum, intensity, energy on the target, pulse length, polarization, distribution angle around the tube axis, etc. In some embodiments, the x-ray pulse may be characterized by its spectral energy range. In some embodiments, the x-ray pulse may be characterized by its fluence, for example, in J/cm ² . In other embodiments, the x-ray pulse may be characterized by its pulse length, for example, in attoseconds.

[0074] The generated gamma ray pulse produced by the nanostructured target may be characterized by its spectral energy, intensity, pulse length, distribution angle around the tube axis, etc. In some embodiments, the responsively generated gamma ray pulse may be characterized by its spectral energy range. In some embodiments, the generated gamma ray pulse may be characterized by its fluence, for example, in J/cm ² . In other embodiments, the generated gamma ray pulse may be characterized by its pulse length, for example, in zeptoseconds. In still other embodiments, the gamma ray pulse may be characterized by its (degree of) temporal coherence or lack thereof. In some embodiments, the gamma ray pulse is coherent. In other embodiments the gamma ray pulse is non-coherent. In still other embodiments, at least a portion of the gamma ray pulse is coherent, that is, the gamma ray is partially coherent.

[0075] In addition to the attributes described above for the x-ray pulse which the nanostructured target is configured to receive and the gamma ray pulse which it responsively generates, the nanostructured target may also be characterized by its efficiency for the conversion of the x-ray radiation to gamma radiation. In some embodiments, the nanostructured target has a conversion efficiency for x-ray photons to gamma ray photons which may be characterized, for example, as the percentage of the energy gamma ray photons produced over the energy of the incident x-ray photons.

[0076] In another aspect, the present disclosure provides a nanostructured target for nonthermal fusion ignition, the target comprising a plurality of boron nitride nanotubes configured to be irradiated by an electron beam and to responsively generate a gamma-ray pulse. [0077] It should be recognized that, in some embodiments, the incident (e.g., irradiating) electron beams of the present aspect may be derived from the electron beams responsively generated in any of the preceding aspects from radiant laser or x-ray pulses. As with the x-ray pulses, the incident (e.g., irradiating) electron beam may be characterized by its kinetic energy, intensity, and distribution angle around the tube axis, among others. In some embodiments, the incident electron beam may be characterized by the kinetic energies of the electrons. In other embodiments, the electron beam may be characterized by its fluence, for example, in electrons/cm ² .

[0078] In some embodiments, the generated gamma ray pulse may be characterized by its spectral range. In other embodiments, the generated gamma ray may be characterized by its fluence, such as in J/cm ² .

[0079] The nanostructured target of the present aspect may also be characterized by its efficiency for the conversion of the x-ray radiation to gamma radiation. In still other embodiments, the nanostructured target has a conversion efficiency of electrons to gamma ray photons, which may be characterized, for example, as the percentage of the energy of gamma ray photons produced over the energy of incident electrons.

[0080] The nanostructured targets described herein may comprise many very small cylindrical multi-walled boron nitride nanotubes as depicted in FIGS. 2B and 2C. The tubes are made of sheets (FIG. 2A) in which boron and nitrogen atoms are arranged in a hexagonal network, structurally similar to flat graphene. The sheets, e.g., walls, are single-atom thin boron nitride, without accessible space between concentric, non-telescoping walls (e.g., multi -walled nanotubes).

[0081] The nanostructured targets of the present disclosure may comprise single walled, fewwalled boron nitride nanotubes and/or multi-wall boron nitride nanotubes. While the disclosure herein refers predominantly to multi-walled tubes, it should be understood that in some embodiment single-walled tubes (and/or few-walled tubes) may be used in a same or similar manner. In some embodiments, the nanostructured targets comprise multi-walled boron nitride nanotubes. In certain embodiments, single-walled boron nitride nanotubes may also be present in the nanostructured targets comprising multi-walled boron nitride nanotubes. In some embodiments, the nanostructured targets comprises multi-walled boron nitride nanotubes. In other embodiments, the nanostructured targets comprises few-walled boron nitride nanotubes. In yet other embodiments, the nanostructured targets comprises single-walled boron nitride nanotubes.

[0082] The properties of the multi-walled boron nitride nanotubes provided in the nanostructured targets herein may be characterized by various parameters including but not limited to their aspect ratio, diameter, length, number of walls, chiral vector and angle, and relative alignment.

[0083] In some embodiments, the multi-walled boron nitride nanotubes have at least 2 or at least 3 walls. In some embodiments, the multi-walled boron nitride nanotubes typically have 2-3 walls. In certain embodiments, the plurality of multi-walled boron nitride nanotubes have an average of 2-3 walls (peak of Gaussian distribution). In the nanotube literature, multi-walled boron nitride nanotubes are typically subcategorized as few-walled when the number of walls is predominantly in the range of 1-5 walls (usually with peaks in their aggregate distribution near 2 and 3 walls); and nanotubes described as many-walled are considered to have 6-50 or 10-50 walls though these conventions in the literature are not universal. As described herein, multiwalled nanotubes will include all ranges, many-walled (which is sometimes intended elsewhere by MW instead of that acronym referring to multi-walled) and few-walled (FW).

[0084] In some embodiments, the diameters of the outer walls of the multi-walled boron nitride nanotubes are between 2 nm and 7 nm. In some embodiments, the multi-walled boron nitride nanotubes have an average ratio of the outer nanotube diameter to inner nanotube diameter of between 1.5: 1 and 3:1. In some embodiments, the multi- walled boron nitride nanotubes have a length between 1 microns and 200 microns. In still other embodiments, the plurality of boron nitride nanotubes have an aspect ratio aspect ratio (length-to-diameter) of between 200:1 and 5000: 1. In some embodiments, the multi-walled boron nitride nanotubes have an aspect ratio (length-to-diameter) of between 200: 1 and 5000: 1. It should be understood that the above distributions as provided herein are exemplary and not intended to be limiting.

[0085] Similar to carbon nanotubes, boron nitride nanotubes may exhibit various wall symmetries depending upon their manufacturing conditions. FIG. 3A illustrates three common wall symmetries — armchair, zigzag, and chiral. In some embodiments, nanostructured target comprises boron nitride nanotubes having a zigzag, armchair or chiral wall symmetry, or any combinations thereof. In some embodiments, nanostructured target comprises multi-walled boron nitride nanotubes having a zigzag, armchair or chiral wall symmetry, or any combinations thereof. The use of multi-walled boron nitride nanotubes having a zigzag, armchair or chiral wall symmetry, or any combinations thereof, may cause deviation from properties of an SYK model. Due to the multi-walled nature of the nanostructured boron nitride nanotubes, it should be recognized that different combinations of wall symmetries may be observed between different layers of the nanostructured targets or pluralities of the multi-walled boron nitride nanotubes within the larger nanostructured target, within a plurality of multi- walled boron nitride nanotubes, or even among the walls of a single multi-walled boron nitride nanotube. In some embodiments, the nanostructured targets may be characterized by the weight percentage (% w/w) or packing density (g/cc) of the multi-walled boron nitride nanotubes possessing the various wall symmetries (e.g., armchair, zigzag, chiral).

[0086] In still further embodiments, the plurality of boron nitride nanotubes are aligned in parallel, wherein the plurality of boron nitride nanotubes may comprise single-walled, fewwalled, or multi-walled boron nitride nanotubes, or any combinations thereof. In still further embodiments, the plurality of multi-walled boron nitride nanotubes are aligned in parallel. In certain embodiments wherein the nanostructured targets consists essentially of multi-walled boron nitride nanotubes, the plurality of multi-walled boron nitride nanotubes are aligned in parallel.

[0087] In still yet another aspect, provided herein is a nanostructured target for non-thermal fusion ignition, the target comprising: a first layer comprising a first plurality of multi-walled boron nitride nanotubes configured to be irradiated by a laser pulse and to responsively generate an x-ray pulse and a first electron beam; a second layer comprising a second plurality of multiwalled boron nitride nanotubes configured to be irradiated by the x-ray pulse and by the first electron beam and to responsively generate a gamma-ray pulse and a second electron beam; and a third layer comprising a third plurality of multi-walled boron nitride nanotubes configured to be irradiated by the gamma-ray pulse and the second electron beam. [0088] It should be recognized that the nanostructured target of the present aspect may be characterized by the same properties as described above for the preceding nanostructured targets, including, for example, aspect ratio, diameter, length, number of walls, chiral vector and angle, relative alignment, etc., as well as the properties of the radiation by which it is configured to be irradiated in the various layers, including spectral energy, intensity, pulse length, energy on the target, spot size, fluence, polarization, distribution angle around the tube axis, etc.

[0089] The nanostructured target of the present aspect may also be characterized by its efficiency for the conversion between the various layers of the target (including the conversion efficiency of laser radiation to x-ray radiation, the conversion efficiency of laser radiation to electrons, the conversion efficiency of x-ray radiation to gamma radiation, the conversion efficiency of x-ray radiation to electrons, and/or the conversion efficiency of electrons to gamma ray radiation), as well as the overall photonic conversion efficiency of laser radiation to gamma radiation. In some embodiments, the nanostructured target has a conversion efficiency for laser photons to gamma ray photons which may be characterized, for example, as the percentage of energy of the gamma ray photons produced over the total energy of incident laser photons.

[0090] In some embodiments, the plurality of multi-walled boron nitride nanotubes within each layer are aligned in parallel. In some embodiments of the present aspect, the first plurality, the second plurality, and the third plurality of multi-walled boron nitride nanotubes comprise multi-walled boron nitride nanotubes aligned parallel relative to the plurality of multi-walled boron nitride nanotubes in the other pluralities. In some embodiments, the multi-walled boron nitride nanotubes may be characterized by the lateral distance between each wall, or inter-wall spacing, in angstroms.

[0091] In some embodiments, the nanostructured target has a density of between 1.3 g/cc and 2 g/cc multi-walled boron nitride nanotubes.

[0092] Careful control of the physical properties and minimization of defects within the nanotube structure for the boron nitride nanotubes are relevant considerations for preparing the nanostructured targets. For example, FIG. 3B depicts a damaged nanotube structure known as a “nano bamboo”, which may form during manufacture of boron nitride nanotubes and may negatively influence the overall radiation conversion efficiency (e.g., laser light to gamma radiation) or inhibit initiation of fusion reactions. In some embodiments, the nanostructured target may be characterized by an upper limit for the weight percentage (% w/w) over the percentage (% w/w) of the non-nano bamboo nanotubes present, or alternatively by the total weight percentage of boron nitride material present in the nanostructured target. In still other embodiments, the nanostructured target may be characterized by an upper limit for the packing density (g/cc) of bamboo type boron nitride nanotubes present.

[0093] As would be appreciated by a person of skill in the art in light of the disclosure herein, any one or more characteristics of the various embodiments, examples, aspects, disclosures, and claims set forth herein for the nanostructured targets provided herein may share one or more characteristics with one another and/or may be combined with one another, in whole or in part.

Fuels

[0094] As detailed herein, the nanostructured targets of the present disclosure provide a means for both the conversion of visible or near-infrared laser pulses to gamma radiation and for the ignition or initiation of nuclear fusion. With respect to the initiation of non-thermal fusion reactions, the nanostructured targets take advantage of quantum effects at the nanoscale at lower temperature thresholds than required for classical thermonuclear fusion to ignite fusion fuels and support plasma conditions to achieve fusion rate enhancement.

[0095] In marked contrast to carbon nanotubes, it should be recognized that the walls of the boron nitride nanotubes may serve as a fuel and actively participate in the fusion reaction, particularly the pBl 1 fusion reaction. In some embodiments, at least a portion of the multiwalled boron nitride nanotubes are not filled. In certain embodiments, the multi-walled boron nitride nanotubes are not filled with a fuel. However, in other embodiments, the channels of the multi-walled boron nitride nanotubes may be filled with a fuel such that both the added fuel and the boron nitride nanotube walls contribute to the overall efficiency of the fusion process.

[0096] Depending upon the desired primary fusion reaction, the nanostructured target may be filled with a target fuel for the fusion reaction. The nature of the fuel (e.g., chemical composition) as well as the quantity of fuel added (e.g., percentage of nanotubes filled, density of fuel) may be adjusted to optimize the efficiency of the fusion reaction. [0097] In some embodiments of the foregoing nanostructured targets, at least a portion of the multi-walled boron nitride nanotubes are filled with a fuel. In some embodiments, the fuel is selected for the desired fusion reaction, which is to be initiated. For example, in some embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with a fuel suitable for pBl 1 aneutronic fusion. Suitable fuels for driving particular fusion reactions may be selected on the basis of atomic elements (e.g., hydrogen or boron source), molecular volume (e.g., volume relative to inner diameter of the multi-walled nanotubes), and/or other physical properties relevant to handling. For example, ammonia borane may serve as a source of chemically-bound hydrogen and has a melting point at 97.6 °C; relative to typical fusion targets, ammonia borane requires less stringent handling (e.g, non-cryogenic).

[0098] In some embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with a fuel suitable for pBl 1 aneutronic fusion, wherein the fuel is ammonia borane (HeBN). In still other embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with a non-reactant or less-reactive fuel (or gas). For example, whereas ammonia borane serves as a reactant that provides hydrogen for the reaction, xenon gas may minimally participate in the fusion reaction but may be employed to augment electron density and promote plasma generation within the nanotubes (e.g., each xenon atom may set free three times the number of electrons of ammonia borane (HeBN) that are positioned very close to the wall because the xenon filling may stay very close to the wall).

[0099] In some embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with ammonia borane (HeBN), xenon (Xe) gas, or a combination thereof. In some embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with ammonia borane (HsBN). In still other embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with xenon gas. In still other embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with ammonia borane and xenon gas. In some embodiments wherein the multi-walled boron nitride nanotubes are filled with ammonia borane (HeBN), the target may be characterized by the total protonation level of the target, for example, reflecting the degree of filling by ammonia borane. [0100] In still other embodiments wherein at least a portion of the multi-walled boron nitride nanotubes within the nanostructured target are filled with a fuel, particular fuel densities may be desired in order to achieve certain threshold efficiencies for any stage of the conversion from laser light to x-ray radiation to gamma radiation to fusion reaction. In some embodiments, at least a portion of the multi-walled boron nitride nanotubes are filled with a fuel at a density of between 1.3 g/cc and 2 g/cc.

Systems Comprising the Nanostructured Targets and Radiation Source(s)

[0101] As described above, the present disclosure employs a combination of nanostructured targets, comprising multi-walled boron nitride nanotubes, and ultrafast, high intensity visible and near-infrared laser systems to provide an overall system for non-thermal fusion ignition. The combination of the nanostructured boron nitride targets and ultra-short, high intensity pulses as described herein allow for the highly efficient deposition of photonic energy by the laser into the nanostructured target, which generates a cascade of energetic radiation (x-rays, gamma rays) and electrons to initiate and propagate a fusion burn wave.

[0102] In still another aspect, provided herein is a system for non-thermal fusion ignition, the system comprising: a nanostructured target comprising a plurality of multi-walled boron nitride nanotubes; and a laser system configured to direct a laser pulse to be incident upon the target, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds.

[0103] In some embodiments, the laser system generates laser pulses at a repetition rate of between 0.0167 Hz and 20 Hz.

Laser Pulse Properties

[0104] The specifications of the incident laser pulse may be characterized by any number of parameters including but not limited to wavelength, peak intensity, pulse duration, temporal contrast ratio, spot size, energy per pulse, fluence, repetition rate, polarization and/or angle of incidence relative to the long axis of the nanotubes. It should be recognized that any of the laser parameters may be independently or simultaneously adjusted in order to achieve the necessary downstream gamma radiation intensity and/or energy to initiate nuclear fusion. [0105] CPA (chirped pulse amplification) lasers with single beam peak-powers of at least 10 PW and at most 50 femtosecond pulse durations (e.g., as built in the Extreme Light Infrastructure project, based on amplification in the most frequently used broadband laser material Titanium Sapphire (Ti:Sa) at a central wavelength around 800 nanometers (nm)) may be used in some embodiments of the systems described herein. Furthermore, short pulse high-power laser radiation, which can be generated using nonlinear crystals as the amplifying medium via optical parametric chirped pulse amplification (OPCPA), may be used in some embodiments of the systems described herein. Both amplifying materials may require green ns-laser pulses with durations between 3 and 50 nanoseconds (ns) for pumping the corresponding amplifiers. The 10PW systems may use flashlamp-pumped amplifiers providing a repetition rate of 1 shot per minute whereas the ELI 1PW HAPLS laser can fire up to 10Hz due to the advanced diode pumped solid-state pump laser (DPSSL) and its very advanced gas-cooling technology. In some embodiments, the system comprises an advanced diode pumped solid-state pump laser.

[0106] In some embodiments of the systems described herein, the pulse duration for systems described herein may be in the range of or below 50 femtoseconds (fs) to be able to utilize both the strongly quantum coupled properties of the nanotube walls and the high field strength induced quantum effects. Very high intensity contrast is also desirable to keep pre-pulse heating effects below the damage threshold of the nanotubes. With high temporal contrast, the structure of the nanotubes is preserved while the laser pulse hits the target and allows high intensity laser radiation to penetrate the target surface and deposit energy in the fusion target. To be able to ignite as many nanotubes as possible, the spot size needs to be reasonably large while still providing the desired intensities. Combining these requirements with a laser spot size of around 10 pm ² , the peak-power of a single laser beam should be in the range of > 10 Petawatts (PW). This translates to 200 Joules (J) of energy focused on the target for a single beam.

[0107] In some embodiments, the laser pulse comprises photons in the spectral range between 400 nm and 1400 nm. In certain embodiments, the laser pulse is monochromatic. In some embodiments, the laser pulse may be further characterized by its fluence, for example, in J/cm ² . [0108] In some embodiments, the laser pulse has a pulse length of less than or equal to 50 femtoseconds. In some embodiments, the laser pulse has a pulse length of between 1 femtoseconds and 50 femtoseconds.

[0109] In still other embodiments, the laser pulse has a spot size of between 10 pm ² and 50 pm ² . In other embodiments, the laser pulse has a pulse energy of at least 200 J. In still other embodiments, the laser pulse has a pulse energy of at least 250 J.

[0110] In order to achieve efficient energy deposition into the nanostructured target, the focused laser intensity on the nanostructured target is at least 10 ²¹ W/cm ² . In some embodiments, the laser pulse has a peak intensity of between 10 ²¹ W/cm ² and IO ²³ W/cm ² , between 10 ²¹ W/cm ² and 10 ²² W/cm ² , or between 10 ²² W/cm ² and IO ²³ W/cm ² . In still other embodiments, the laser pulse has a peak intensity of between 10 ²² W/cm ² and IO ²³ W/cm ² .

[0111] In some embodiments, the laser pulse has a focused pre-pulse laser intensity of less than or equal to 10 ⁹ W/cm ² , wherein the pre-pulse intensity is measured at greater than or equal to 100 femtoseconds from peak intensity. In still other embodiments, the laser pulse has a temporal contrast ratio of at least 10 ¹³ .

[0112] The laser pulse may be further adjusted with respect to the angle of incidence upon the nanostructured target relative to the longitudinal (long) axis of the multi-walled boron nitride nanotubes. In some embodiments, laser pulse has zero (0°) degree angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes, that is, parallel the long axis of the nanotube. In other embodiments, the laser pulse has ninety degree (90°) angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes, that is, perpendicular to the long axis of the nanotube. In still other embodiments, the laser pulse has angle of incidence relative to the longitudinal axis of the multi-walled boron nitride nanotubes between zero (0°) and ninety (90°) degrees.

[0113] In some embodiments, the requisite laser intensities may be achieved with the assistance of multi-beam configurations and/or various techniques within the system for shortening pulse length and increasing temporal contrast. [0114] For example, a multibeam configuration can enhance the overall peak-power of the system through coherent combining. In some embodiments, the system further comprises one or more additional laser systems configured to generate one or more additional laser pulses, wherein each of one or more additional laser pulses independently has a focused laser intensity of greater than or equal to 10 ²¹ W/cm2 and a pulse duration of less than or equal to 50 femtoseconds, and wherein the one or more additional laser pulses is coherently combined with laser pulse directed to be incident upon the target.

[0115] In some embodiments, the system is configured to perform one or more pulseshortening techniques and/or one or more temporal contrast enhancing techniques. In some embodiments, the system is configured to perform one or more pulse-shortening techniques. In other embodiments, the system is configured to perform one or more temporal contrast enhancing techniques. In still other embodiments, the system is configured to perform one or more pulse-shortening techniques and one or more temporal contrast enhancing techniques. The system may include one or more components configured to perform the techniques described herein, as would be appreciated by a person having ordinary skill in the art in light of the disclosure herein. For example, in some embodiments, the one or more pulse-shortening techniques and/or one or more temporal contrast enhancing techniques may include but are not limited to self-phase modulation, relativistic mirrors, a chirped pulse amplification and compression, a second harmonic generation, plasma mirrors, or any combination thereof.

Pulse-shortening Techniques

[0116] In some embodiments, the system is configured to perform one or more pulseshortening techniques. In some embodiments, the one or more pulse-shortening techniques comprises self-phase modulation. Nonlinear pulse compression schemes based on self-phase modulation (SPM) in thin transparent media allow for further pulse compression.

[0117] In other embodiments, the one or more pulse-shortening techniques comprise relativistic mirrors. Relativistic mirrors may be employed for compression of optical pulses and x-ray generation. Relativistic engineering also provides the opportunity for shorter pulses. It has been shown both experimentally and theoretically that TW and PW laser induced relativistic mirrors in a co- or counterpropagating geometry compress fs-pulses to attoseconds with a strong Doppler effect, such that the optical pulses are at the same time efficiently shifted to the x-ray regime (Kando, Esirkepov, Bulanov Coherent, short pulse X-ray generation via relativistic flying mirrors, Quantum Beam Science, 2018,2,9, Review paper). Relativistic compression of a single cycle optical pulse leads to relativistic generation of scalable isolated attosecond pulses (Naumova, Mourou PRL Vol. 92, No 6, 13 February 2004).

Temporal Contrast Enhancement Techniques

[0118] FIG. 4 illustrates the temporal contrast ratio of an exemplary laser pulse. As illustrated in FIG. 4, an exemplary laser pulse for the systems as described herein may exhibit a subpicosecond temporal profile. In the temporal window preceding and following the most intense temporal window for the main pulse, which may be considered as time zero, appreciable intensity contributions from the laser pulse can also be observed at the picosecond (e.g., 10-100 ps) and nanosecond timescales before and after time zero. The temporal contrast ratio is defined as the intensity at the peak of the pulse to the intensity before the pulse, also known as the prepulse. Although the energy contained in these picosecond and nanosecond pedestals is very low compared to the main pulse, it is certainly not negligible. The interaction point of an ultrahigh intensity laser is typically not with a solid target structure, but rather with the plasma plume created from the target heated by the pulse pedestal. In some embodiments, the laser pulse has a pre-pulse laser intensity of less than or equal to 10 ⁹ W/cm ² , wherein the pre-pulse intensity is measured at greater than or equal to 100 femtoseconds from the peak intensity at time zero.

[0119] For the nanostructured targets of the present disclosure, temporal contrast ratios on the order of 10 ¹³ - 10 ¹⁴ (with respect to the peak intensity of at least 10 ²¹ W/cm ² ) keep the prepulse intensity below 10 ⁹ W/cm ² . which corresponds to typical ablation thresholds of materials.

[0120] There are many causes that contribute to the pre-pulse pedestal. These include amplified noise (ns-level), scattered light from the stretcher or compressor of the chirped pulse amplification (CPA) process, discrete reflected pulses in a multi-pass amplifier, and nonlinear contributions.

[0121] The baseline is limited by amplification of the underlying noise where single photons get amplified and contribute to the pedestal. This is referred to as amplified spontaneous emission (ASE) for laser amplification of parasitic fluorescence (PF) for parametric amplification systems. Petawatt systems require a huge amplification factor (>10 ¹² x) from nanojoule to kilojoule.

[0122] Double chirped pulse amplification (CPA) breaks this amplification up into two back- to-back systems of stretching, amplification, and compression with a nonlinear pulse cleaner in between. The common techniques are cross polarization wave generation (XPW) (A. Julien Opt Lett 30, 920) and OPA (optical parametric amplification)-based pre-pulse elimination (OP APE) (Wang JOSAB 11,1531). Both systems generate a new pulse with a cubic intensity ~I(t) ³ dependent on the injected pulse I(t). For example, a pulse with 5 orders of magnitude contrast would then have up to 15 orders of magnitude and significantly reduce ASE and PF. These processes are typically 10% efficient; the gain may be compensated by the additional CPA stages.

[0123] In the stretcher, the various colors of the laser pulse propagate along different paths to create the frequency chirp for CPA which the compressor later ideally compensates for.

Scattering of imperfect optical components in these dispersive sections leads to contrast degradation in the 1-100 picosecond (ps) range. Super-polishing stretcher components to only 0.1 nm roughness has recently shown a 3 Ox improvement, with an improved contrast near 10 ⁷ -l 0 ⁸ at l-10ps before the pulse. (Ranc, Opt. Lett. 45, 4599)

[0124] The picosecond degradation is reduced in Optical Parametric systems with only a few-ps of stretch and CPA pump lasers, but ultimately this will be a compromise between pulse energy and desired chirp factor.

[0125] Discrete pre-pulses generated by unwanted reflections in the amplifier can be avoided or at least significantly reduced by careful architecture of the system and use of high-quality optics. Post-pulses on the other hand, are extremely difficult to avoid since any pass in any amplification disk or other optics results in such pulses. Post pulses within the duration of the stretched main pulse interfere with the latter. Nonlinear effects then create, in any systems operating with acceptable efficiency, a set of mirrored pre-pulses that influences the laser interactions. [0126] In some embodiments, the system is configured to perform one or more temporal contrast enhancing techniques.

[0127] Two contrast improvement options remain after the pulse is fully amplified and compressed. These are second harmonic generation (SHG) and plasma mirrors (PM). Both come at a significant expense of laser energy and peak power reduction.

Second Harmonic Generation

[0128] In some embodiments, the one or more temporal contrast enhancing techniques comprises second harmonic generation (SHG).

[0129] SHG depends on the square of the intensity ~I(t) ² of the incident light and therefore doubles the contrast of the output on a logarithmic scale. The process is typically 30-40% efficient for ultra-short pulses, requires a thin (0.5-0.8mm) suitable nonlinear crystal, requires some dispersion compensation with chirped mirrors, and results in pulses at half the wavelength (e.g., Ti:Sa systems convert from 800 nm to 400 nm). The cleaned pulse can then be separated by a set of ~6-7 dichroic mirrors from the input at the fundamental wavelength. At this point, no crystal exists that is large enough to handle multi-petawatt pulses, but an array of precisely matched and precisely tuned crystals can be used. It is important to mention that the diffraction limited focus will also reduce for the frequency doubled pulse, so the achievable intensity will at least remain at the same level.

Plasma Mirrors

[0130] In some embodiments, the one or more temporal contrast enhancing techniques comprises plasma mirrors. Plasma mirrors work as a sub-picosecond optical switch, where the laser transmits through an optical element until the intensity and the fluence on the surface is high enough to create a plasma, and the surface switches from transparent to highly reflective. (Dromey Rev.Sci.Inst. 75, 645) This way only the main pulse with high enough power reflects while the pre-pulse pedestal is eliminated. A major drawback is that the reflecting surface may become damaged and, in some configurations, the plasma mirrors may be replaced as frequently as for every shot. A pair of plasma mirrors based on liquid crystal surfaces can achieve 300-400x contrast improvements and 70% transmission. [0131] Electro-optical methods (10 ps-level synchronized Pockels cells) allow, to a large extent, the suppression of ASE, which is typically a major concern in all active laser materials due to the fluorescence of the laser transition before the pulse is amplified at the maximum gain.

[0132] Nonlinear saturable absorbers improve the contrast at low energy levels and can mainly be used in the system’s front-ends.

DYNAMICAL INTERACTION OF LASER RADIATION AND NANO STRUCTURED TARGETS, AND METHODS OF USE

[0133] Provided herein is a step-by-step description of the dynamical processes in the target, starting from the first moment of laser pulse interaction with the nanostructured targets comprising multi-walled boron nitride nanotubes, and proceeding with the fusion burn wave. Two fundamental dynamical stages are illustrated in FIGS. 5A and 5B.

[0134] The first stage looks at the very short time scales at which the tube walls are still intact. FIG. 5A shows the dynamical steps of the processes involved in the radiation path. In FIG. 5A, a visible light femtosecond laser pulse irradiates the first layer of tubes. It should be recognized that although the first, second and third layers are represented as single layers of nanotubes that each layer may, in actual practice, comprise several internal layers of the multiwalled boron nitride nanotubes. For the schematic representation of the process, each layer is schematically illustrated as a single layer of nanotubes as in FIG. 5A. The laser enters the tubes in longitudinal direction to the tube axis and the tubes in the target are aligned in a parallel direction.

[0135] Existing research results show that the irradiation of metallic nano-channels or CNTs by a femtosecond pulse laser leads to the production of x-rays, directed around a distribution angle (S. Bagchi et al., Bright, low debris, ultrashort hard x-ray table top source using carbon nanotubes, 2011). As shown in FIG. 5A, the nanotubes in the first layer work effectively to compress the femtosecond visible laser pulse into an attosecond x-ray beam. With respect to FIG. 5A, the femtosecond pulse generates x-rays, propagating along the longitudinal axis of the nanotube. Due to the very high thermal conductivity of the boron nitride nanotubes, the laser will quickly push the electrons in the direction of the tube axis. Consequently, both the x-rays and the electron beam leaving the tubes will be directed around the tube axis. [0136] These first process steps show that the tubes in the nanostructured target play a double role. The first (and the second, see below) layer of tubes does not only serve as the fusion fuel but may be imagined as an extension of the laser into the target. The first layer leads to the production of an x-ray radiation bath in the target. Because the nanotubes in the target are aligned and directed parallel to the laser beam, the radiation bath is provided as a directed radiation beam.

[0137] The second layer of tubes in FIG. 5A is irradiated by the two radiation beams (x-ray and electrons) generated by the first layer. The second layer may not be irradiated by the laser. It has been shown for the case of CNTs (G. Mourou, P. Chen, et al., Particle-in-cell simulation of x-ray wakefield acceleration and betatron radiation nanotubes, 2016) that irradiation of nanotubes by x-rays leads to wakefield acceleration in the nanotubes where - in addition to the classical wakefield case of normal plasma without a nanostructure - there appears a wakefield acceleration of radiation. In addition to a directed electron beam, a directed gamma beam is generated by and leaves the nanotubes. Analogous to the compression of visible light to x-ray photons in the first layer, the second layer of tubes can be seen as further compressing the beam down to zeptoseconds (zs) and gamma rays. In some embodiments, the compression of radiation may be derived from Thomson and/or Compton scattering effects. In Thomson and Compton scattering, a photon (such as a laser photon, x-ray photon, gamma ray photon) and a charged particle (such as an electron) may interact to exchange and transfer energy between the photon and charged particle, thereby decreasing (Compton scattering) or increasing (Thomson, inverse Compton scattering) the spectral energy of the photon. In some embodiments, nanostructured targets and systems comprising the nanostructured targets may be configured to produce Thomson and/or Compton scattering effects, whereupon laser photons may interact with electrons to increase in energy (blue-shift) to x-ray photons (or gamma ray photons); whereupon x-ray photons may interact with electrons to blue-shift to gamma ray photons or decrease in energy (red-shift) to laser photons; and/or whereupon gamma ray photons may interact with electrons to red-shift to x-ray photons.

[0138] In the other embodiments, the compression of radiation may be described as analogous to betatron, cyclotron or synchrotron effects. In some embodiments, the nanostructured targets and systems comprising the nanostructured targets as described herein may exhibit wakefield acceleration of x-ray radiation, for example, to generate gamma radiation. In other embodiments, nanostructured targets and systems comprising the nanostructured targets may be configured to produce betatron, cyclotron or synchrotron effects, or any combinations thereof.

[0139] In some embodiments, the compression of radiation is observed because the irradiation of the tubes leads to excitations of the nanotube walls in both the first and second layer of tubes. These excitations have a very short characteristic time scale, going down to zs dynamics. These wall excitations lead to the emittance of the compressed radiation. Since electron irradiation of the nanotubes leads to the same wall excitations, e.g. in the second layer of nanotubes, the electron irradiation likewise contributes to the generation of directed gamma radiation.

[0140] As shown in FIGS. 5A and 5B, the gamma rays generated from the second layer of tubes are used to drive ignition in subsequent layers of nanotubes. It should be recognized that the amount of energy needed to be deposited in the gammas to drive ignition and burn may depend upon the target fuel and observed enhancement factors. From the number of kilojoules to be deposited in gamma rays, the efficiency of gamma conversion determines the laser energy needed. Calculations of the applicant show that high levels of nuclear state occupation numbers can be achieved by gamma radiation, depending on the parameters, spectrum, intensity, and other specifications of the gamma radiation.

[0141] As described above, the nanostructured targets of the present disclosure may contain a majority of multi- walled boron nitride nanotubes, although single- walled boron nitride nanotubes may be present. The use of predominantly multi-walled boron nitride nanotubes rather than single-walled boron nitride nanotubes may contribute to both an increased intensity and higher spectral energy of the resulting gamma ray output. Gamma output and a shift from electrons to radiation in the wakefield energy balance are driven by nanostructures. By employing multi-walled nanotubes, the additional nano-channel(s) between the walls may lead to a steeply increased effect for gamma radiation output. The dimension between the nanotubes - as mentioned - is too small to accommodate atoms but laser light and x-ray radiation can propagate within these channels. Due to the presence of the nano-channels provided by the multi-walled boron nitride nanotubes, the intensity of gamma output is expected to increase for these very small channels and the spectral distribution, which varies with nanoscale dimensions, is expected to shift to the higher energy end of the spectrum for the smaller channels between tube walls. In the same way, electrons can enter the channel in between nanotube walls. Gamma output over electron beam energy is consequently also expected to increase for electron irradiated multi-wall boron nitride nanotubes.

[0142] The multi-wall boron nitride nanotubes may also provide further augmentation of the gamma shift to higher spectral energies. As detailed above, laser light (or x-ray radiation or electron beams) may propagate on both sides of a wall within a multi-walled nanotube. As such, wall excitations may arise from both sides where the channels on both sides can have widely varying dimensions (e.g., the tube diameter and the much smaller inter-wall spacing between two walls). In such a setting, resonances (e.g., sympathetic) may occur between such channels leading to an up-conversion in frequency.

[0143] In embodiments wherein the nanostructured targets comprise multi-walled boron nitride nanotubes, the multi-walled boron nitride nanotubes offer many mechanisms to systematically design its specifications for driving intensity of gamma output and shift to a higher gamma frequency spectrum, and thus also to drive the overall conversion efficiency of laser light to gamma radiation. Based on the above, the specific morphological parameters of the multi-walled nanotubes including the number of walls, nanotube diameters, and relative ratios of diameters offer a means of modulating the gamma conversion efficiency and intensity and frequency output, which may not be available to single-walled nanotube structures, by fine- tuning the number of walls and the nano-channel space between nanotube walls. For example, in some embodiments, the multi-walled boron nitride nanotubes have a nano-channel space, or inter-wall spacing, which may be characterized by the distance between nanotube walls, for example, in angstroms.

[0144] Assuming a sufficient gamma conversion efficiency in the second layer of FIG. 5A, the third layer of tubes is irradiated with a strong gamma spectrum. Beyond the gamma intensity, the spectral distribution itself is of interest. A spectrum shifted to the higher spectral energies (e.g., mega-electron volts) means that energy levels well below the peak of the spectrum might already be of interest for fusion. A higher spectral distribution of the resulting gamma radiation greatly enhances the total part of the spectrum which is available for fusion ignition and can, to a certain degree, be traded for or used to offset lower intensity gamma radiation.

[0145] Sufficiently strong gamma irradiation (in intensity and/or spectral energy) would ignite a fusion reaction as shown in FIG. 5A. Gamma induced screening effects are not dependent on the ps time scales of thermonuclear reactions which result from the characteristic time scales of passing the Coulomb barrier. In contrast, inner nuclear reactions have much shorter characteristic time scales which, for many nuclear processes, are in the zs range. So, the photo nuclear regime would scale dynamics favorably for meeting short confinement times.

[0146] In one aspect, provided herein is a method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a nanostructured target, comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the target with a laser pulse, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds, wherein the plurality of multi-walled boron nitride nanotubes generates an x-ray pulse in response to the incident laser pulse.

[0147] In some embodiments of the present aspect, the x-ray pulse generated by the plurality of multi-walled boron nitride nanotubes is directed to irradiate a second plurality of multi-walled boron nitride nanotubes, wherein the second plurality of multi- walled boron nitride nanotubes responsively generates an electron beam and gamma ray pulse.

[0148] In still other embodiments, which may be combined with the preceding embodiment, the electron beam and gamma ray pulse generated by the second plurality of multi-walled boron nitride nanotubes are directed to irradiate a third plurality of multi-walled boron nitride nanotubes, wherein the third plurality of multi-walled boron nitride nanotubes leads to enhanced fusion reactivity, responsively generating alpha particles.

[0149] In another aspect, the present disclosure provides a method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a target comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the plurality of multi-walled boron nitride nanotubes with one or both of an x-ray beam and a gamma-ray beam, wherein the irradiation induces enhancement of a fusion reaction. In some embodiments, the irradiation induces enhancement of a fusion reaction rate by a factor of at least IO ²⁰ as compared to the classical thermonuclear fusion reaction rate at the same temperature.

[0150] If the radiation path contributes strongly enough, for example as described above, ignition of subsequent tubes (e.g., fusion burn wave) may occur as shown in FIG. 5B.

[0151] In still another aspect, provided herein is a method of activating a fuel for nonthermal fusion ignition, the method comprising: providing a nanostructured target comprising a first plurality of multi-walled boron nitride nanotubes and a second plurality of multi-walled boron nitride nanotubes; and irradiating the first plurality of boron nitride nanotubes with an electron beam to cause the first plurality of multi-walled boron nitride nanotubes to responsively generate a radiation pulse, wherein the gamma radiation pulse irradiates the second plurality of multi-walled boron nitride nanotubes to induce enhancement of a fusion reaction and to generate alpha particles and a second electron beam.

[0152] It should be recognized that the multi-walled boron nitride nanotubes in the nanostructured targets may experience physical deformation and/or destruction after irradiation with any of the laser pulse, x-ray pulse, electron beams or gamma ray pulse. In some embodiments, the multi-walled boron nitride tubes have a lifetime under irradiation that is longer than the duration of the irradiation pulse. In some embodiments, the multi-walled boron nitride tubes have a lifetime under laser irradiation that is longer than the duration of the laser pulse. In some embodiments, the multi-walled boron nitride tubes have a lifetime under x-ray irradiation that is longer than the duration of the x-ray pulse. In some embodiments, the multi-walled boron nitride tubes have a lifetime under gamma ray irradiation that is longer than the duration of the gamma ray pulse. In some embodiments, the multi-walled boron nitride tubes have a lifetime under laser irradiation that is at least 100 femtoseconds.

[0153] In FIG. 5B, fast electrons are generated as a consequence of energy transfer from fusion reactions occurring within the target. It should be recognized that the generated electrons may subsequently drive the generation of further gamma radiation in subsequent nanotubes, which in turn may propagate further fusion reactions. Because gamma rays travel at the speed of light, the gamma radiation would be expected to arrive at subsequent nanotubes cold, wherein the nanotubes have not yet been irradiated by any laser, x-ray or gamma radiation and wherein heat transfer from any upstream light-matter interaction or fusion burn has not yet occurred. Furthermore, the gamma radiation would be expected to arrive at subsequent nanotubes prior to propagation of any shock, destruction or target deformation from upstream in the nanostructured target, which may contribute to reaching enhancement conditions for burn propagation.

[0154] In some embodiments of the present aspect, irradiating the first plurality of multiwalled boron nitride nanotubes induces a fusion bum wave in the target in which: the second electron beam irradiates a third plurality of multi-walled boron nitride nanotubes in the target, causing the third plurality of multi-walled boron nitride nanotubes to generate a second gamma radiation pulse, the second gamma radiation pulse irradiates a fourth plurality of multi-walled boron nitride nanotubes in the target, causing the fourth plurality of multi- walled boron nitride nanotubes to generate alpha particles and a third electron beam.

[0155] In some embodiments, the successive generation of gamma radiation, alpha radiation and electron beams may be considered as a cyclical process as illustrated in FIG. 5B, wherein an electron beam generated by an upstream layer irradiates one layer of tubes to produce gamma rays, which further irradiate the subsequent downstream layer, and so on. This repeating process may lead to enhanced fusion reactions, in which the energy transfer from fusion reactions leads to fast electrons, which then irradiate next layer of tubes, starting the process again.

[0156] As would be appreciated by a person of skill in the art in light of the disclosure herein, any one or more characteristics of the various embodiments, examples, aspects, disclosures, and claims set forth herein may share one or more characteristics with one another and/or may be combined with one another, in whole or in part.

ENUMERATED EMBODIMENTS

[0157] The following enumerated embodiments are representative of some aspects of the invention. In some embodiments, any one or more features of any one or more of the following enumerated embodiments may be combined (in whole or in part) with any one or more features (in whole or in part) of any one or more of the other enumerated embodiments and/or with any one or more features (in whole or in part) disclosed elsewhere herein, as would be understood by a person of skill in the art in light of the disclosures made herein. In some embodiments, features of different embodiments may be combined with one another (in whole or in part) even where the enumerated interdependencies of the embodiments do not explicitly so indicate.

1. A method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with a laser pulse to cause the plurality of multiwalled boron nitride nanotubes to responsively generate an x-ray pulse.

2. The method of embodiment 1, wherein the laser pulse comprises photons in a spectral range between 400 nm and 1940 nm, preferably between 400 nm and 1400 nm.

3. The method of embodiment 1 or 2, wherein the laser pulse is nearly monochromatic or spectrally chirped.

4. The method of any one of embodiments 1 to 3, wherein the laser pulse has a pulse length of between 1 femtosecond and 50 femtoseconds.

5. The method of any one of embodiments 1 to 4, wherein the laser pulse has a peak intensity of between 10 ²¹ W/cm ² and IO ²³ W/cm ² .

6. The method of any one of embodiments 1 to 5, wherein the plurality of multi-walled boron nitride nanotubes are aligned in parallel with one another.

7. The method of any one of embodiments 1 to 6, wherein irradiating the plurality of multiwalled boron nitride nanotubes causes fusion burning with enhancement in a target that includes the plurality of multi-walled boron nitride nanotubes.

8. A method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with an x-ray pulse to cause the plurality of multi-walled boron nitride nanotubes to responsively generate a gamma-ray pulse.

9. The method of embodiment 8, wherein the plurality of multi-walled boron nitride nanotubes are aligned in parallel with one another.

10. The method of embodiment 8 or 9, wherein irradiating the plurality of multi- walled boron nitride nanotubes causes fusion burning with enhancement in a target that includes the plurality of multi-walled boron nitride nanotubes.

11. A method for non-thermal fusion ignition, the method comprising irradiating a plurality of multi-walled boron nitride nanotubes with an electron beam to cause the plurality of multi-walled boron nitride nanotubes to responsively generate a gamma-ray pulse.

12. The method of embodiment 11, wherein the plurality of multi-walled boron nitride nanotubes are aligned in parallel with one another.

13. The method of embodiment 11 or 12, wherein irradiating the plurality of multi- walled boron nitride nanotubes causes fusion burning with enhancement in a target that includes the plurality of multi-walled boron nitride nanotubes.

14. A method for non-thermal fusion ignition, the method comprising: irradiating a first layer of a nanostructured target by a laser pulse, wherein the first layer of the nanostructured target comprises a first plurality of multi-walled boron nitride nanotubes, wherein irradiating the first layer causes the first plurality of multi-walled boron nitride nanotubes to responsively generate an x-ray pulse and a first electron beam; wherein the generated x-ray pulse and first electron beam irradiate a second layer of the nanostructured target comprising a second plurality of multi-walled boron nitride nanotubes; wherein irradiating the second layer causes the second plurality of multi- walled boron nitride nanotubes to responsively generate a gamma-ray pulse and a second electron beam; and wherein the generated gamma ray pulse and second electron beam irradiate a third layer of the nanostructured target comprising a third plurality of multi-walled boron nitride nanotubes.

15. The method of embodiment 14, wherein the laser pulse comprises photons in a spectral range between 400 nm and 1940 nm, preferably between 400 nm and 1400 nm.

16. The method of embodiment 14 or 15, wherein the laser pulse is nearly monochromatic or spectrally chirped.

17. The method of any one of embodiments 14 to 16, wherein the laser pulse has a pulse length of between 1 femtosecond and 20 femtoseconds.

18. The method of any one of embodiments 14 to 17, wherein the laser pulse has a peak intensity of between 10 ²¹ W/cm ² and IO ²³ W/cm ² .

19. The method of any one of embodiments 14 to 18, wherein one or more of the first plurality of multi-walled boron nitride nanotubes has a lifetime under laser irradiation that is longer than the duration of the laser pulse.

20. The method of any one of embodiments 14 to 19, wherein the plurality of multi- walled boron nitride nanotubes within each layer are aligned in parallel.

21. The method of any one of embodiments 14 to 20, wherein the first plurality, the second plurality, and third plurality of multi-walled boron nitride nanotubes comprise multiwalled boron nitride nanotubes aligned parallel relative to the plurality of multi-walled boron nitride nanotubes in the other pluralities.

22. The method of any one of embodiments 14 to 21, wherein the nanostructured target has a density of between 1.3 g/cc and 2 g/cc multi-walled boron nitride nanotubes.

23. The method of any one of embodiments 14 to 22, wherein one or more of the multiwalled boron nitride nanotubes are filled with a fuel.

24. The method of any one of embodiments 14 to 23, wherein one or more of the multiwalled boron nitride nanotubes are filled with a fuel at a density of between 1.3 g/cc and 2 g/cc.

25. The method of any one of embodiments 14 to 24, wherein one or more of the multiwalled boron nitride nanotubes are filled with ammonia borane, xenon gas, or a combination thereof.

26. The method of any one of embodiments 14 to 25, wherein one or more of the multiwalled boron nitride nanotubes have 2-3 walls.

27. The method of any one of embodiments 14 to 26, wherein a diameter of an outer walls of one or more of the multi-walled boron nitride nanotubes is between 2 nm and 7 nm.

28. The method of any one of embodiments 14 to 27, wherein a length of one or more of the multi-walled boron nitride nanotubes is between 1 micron and 200 microns.

29. The method of any one of embodiments 14 to 28, wherein an aspect ratio (length-to- diameter) of one or more of the multi-walled boron nitride nanotubes is between 200:1 and 5000:1.

30. The method of any one of embodiments 14 to 29, wherein one or more of multi -walled boron nitride nanotubes comprises a zigzag, armchair or chiral wall configuration, or any combinations thereof.

31. The method of any one of embodiments 14 to 30, wherein one or more of the multiwalled boron nitride nanotubes has an average ratio of the outer nanotube diameter to inner nanotube diameter of between 1.5:1 and 3:1.

32. The method of any one of embodiments 14 to 31, wherein irradiating the third layer of the nanostructured target causes fusion burning with enhancement in the target. 33. A system for non-thermal fusion ignition, the system comprising: a nanostructured target comprising a plurality of multi-walled boron nitride nanotubes; and a laser system configured to direct a laser pulse to be incident upon the target, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds.

34. The system of embodiment 33, wherein the laser pulse has a focused pre-pulse laser intensity of less than or equal to 10 ⁹ W/cm ² , wherein the pre-pulse intensity is measured at greater than or equal to 100 femtoseconds from peak intensity.

35. The system of embodiment 33 or 34, wherein the laser pulse has a spot size of between 10 pm ² and 50 pm ² .

36. The system of any one of embodiments 33 to 35, wherein the laser pulse has a pulse energy of at least 200 J.

37. The system of any one of embodiments 33 to 36, wherein the system is configured to perform one or more pulse-shortening techniques and/or one or more temporal contrast enhancing techniques.

38. The system of embodiment 37, wherein the one or more pulse-shortening techniques and/or one or more temporal contrast enhancing techniques comprise self-phase modulation, relativistic mirrors, chirped pulse amplification and compression, second harmonic generation, plasma mirrors, or any combination thereof.

39. The system of any one of embodiments 33 to 38, wherein the system further comprises one or more additional laser systems configured to generate one or more additional laser pulses, wherein each of one or more additional laser pulses independently has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds, and wherein the one or more additional laser pulses is coherently combined with laser pulse directed to be incident upon the target.

40. The system of any one of embodiments 33 to 39, wherein the laser system generates laser pulses at a repetition rate of between 0.0167 Hz and 20 Hz.

41. The system of any one of embodiments 33 to 40, wherein directing the laser pulse to be incident upon the target causes fusion burning with enhancement in the target.

42. A method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a nanostructured target comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the target with a laser pulse, wherein the laser pulse has a focused laser intensity of greater than or equal to 10 ²¹ W/cm ² and a pulse duration of less than or equal to 50 femtoseconds, wherein the plurality of multi-walled boron nitride nanotubes generates an x-ray pulse in response to the incident laser pulse.

43. The method of embodiment 42, wherein the multi-walled boron nitride tubes have a lifetime under laser irradiation that is longer than the duration of the laser pulse.

44. The method of embodiment 42 or 43, wherein the x-ray pulse generated by the plurality of multi-walled boron nitride nanotubes is directed to irradiate a second plurality of multi-walled boron nitride nanotubes, wherein the second plurality of multi- walled boron nitride nanotubes responsively generates an electron beam and gamma ray pulse. 45. The method of embodiment 44, wherein the electron beam and gamma ray pulse generated by the second plurality of multi-walled boron nitride nanotubes are directed to irradiate a third plurality of multi-walled boron nitride nanotubes, wherein the third plurality of multi-walled boron nitride nanotubes leads to enhanced fusion reactions responsively generating alpha particles.

46. The method of any one of embodiments 42 to 45, wherein irradiating the target with the laser pulse causes fusion burning with enhancement in the target.

47. A method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a target comprising a plurality of multi-walled boron nitride nanotubes; and irradiating the plurality of multi-walled boron nitride nanotubes with one or both of an x- ray beam and a gamma-ray beam, wherein the irradiation induces enhancement of a fusion reaction.

48. The method of embodiment 47, wherein the irradiation induces enhancement of a fusion reaction rate by a factor of at least 10 ²⁰

49. A method of activating a fuel for non-thermal fusion ignition, the method comprising: providing a nanostructured target comprising a first plurality of multi- walled boron nitride nanotubes and a second plurality of multi-walled boron nitride nanotubes; and irradiating the first plurality of boron nitride nanotubes with an electron beam to cause the first plurality of multi-walled boron nitride nanotubes to responsively generate a gamma radiation pulse, wherein the gamma radiation pulse irradiates the second plurality of multiwalled boron nitride nanotubes to induce enhancement of a fusion reaction and to generate alpha particles and a second electron beam.

50. The method of embodiment 49, wherein the first plurality of boron nitride nanotubes are irradiated with an x-ray pulse and an electron beam.

51. The method of embodiment 49 or 50, wherein irradiating the first plurality of multiwalled boron nitride nanotubes induces a fusion bum wave in the target in which: the second electron beam irradiates a third plurality of multi-walled boron nitride nanotubes in the target, causing the third plurality of multi-walled boron nitride nanotubes to generate a second gamma radiation pulse, the second gamma radiation pulse irradiates a fourth plurality of multi-walled boron nitride nanotubes in the target, causing the fourth plurality of multi- walled boron nitride nanotubes to generate alpha particles and a third electron beam.

52. The method of embodiment 51, wherein the fusion burn wave causes a self-sustaining cyclical process in which electron beams irradiate boron nitride nanotubes to generate gamma radiation and the generated gamma radiation then irradiates other boron nitride nanotubes to generate alpha particles and a new electron beam, whereby the cycle is repeated starting with the new electron beam.

EXAMPLES

[0158] The presently disclosed subject matter will be better understood by reference to the following Examples, which are provided as exemplary of the invention, and not by way of limitation.

Example 1

[0159] Experiments with boron nitride nanotube targets at the PALS Laser facility in Prague were performed. The table below details the laser pulse capabilities of the PALS laser facility, used in the present example.

[0160] In these targets, the tubes were not aligned yet. This effort would not have made sense since the facility offers a ns laser system, such that the lifetime of the tubes under strong laser irradiation is orders of magnitude below the pulse duration. The central idea of using the targets in these experiments was that they do offer a very high level of control of the protonation. The protonation is determined by the degree of filling of the tubes with an ammonia borane. [0161] The targets reached densities of up to 1.6g/cc.

[0162] Fourteen shots were performed.

[0163] TOF data showed an unexpected strong line above 400keV, which has never been seen before in amorphous BN targets. This suggests that although these experiments have been performed at a facility which does not offer conditions which are well adapted to nanostructured targets, effects of the highly special targets may nonetheless be evident.

Example 2

[0164] The experimental protocols below describe experimental configurations to be performed at various laser facilities on various multi-walled boron nitride nanotube targets. The parameters for the available laser radiation (peak power, pulse length, energy, intensity, temporal contrast ratio) are detailed for the laser facilities in the table in Example 1 above.

Laser for Fast Ignition Experiment (LFEX) facility (Osaka University)

[0165] Experiments at the Laser for Fast Ignition Experiment (LFEX) facility in Osaka are conducted to evaluate target stability and/or disintegration under irradiation.

[0166] The targets will be similar to the targets described in Example 1 above. With a picosecond pulse length, the pulse duration is far above the expected time for destruction of the targets. Ten to twelve targets will be irradiated in single-shot experiments at LFEX.

Laboratory for Advanced Lasers and Extreme Photonics (L-ALEPH) (Colorado State University)

[0167] The below describes experimental efforts to evaluate the dependence of alpha and neutron yield of nanostructured targets on intensity, contrast and target composition.

[0168] The experiments are performed at the L-ALEPH at Colorado State University, using the 45 femtosecond beam at a wavelength of 400nm. Targets to be evaluated at L-ALEPH include the non-aligned targets described in Example 1 above. Additional targets will have boron nitride nanotubes aligned to one another and are irradiated with the laser beam parallel to the long axis of the tubes. The targets are irradiated with and without xenon filling. For benchmarking, amorphous boron nitride targets and pure ammonia borane targets are also irradiated. Over 600 shots were performed. Two ion spectrometers, six gamma spectrometers and six CR-39 solid state nuclear track detectors were used to characterize the ion and gamma ray emission. BNNT targets produced a strong gamma ray signal and up to 100 times more ions emitted with MeV energies than amorphous BN or foil targets. The experiments provide a clear indication of enhanced absorption of the laser pulse and possibly the onset of enhanced gamma ray conversion.

European X-Ray Free-Electron Laser Facility (XFEL) (Hamburg)

[0169] Experiments at the European X-Ray Free-Electron Laser facility (XFEL) in Hamburg are conducted to observe effects of strong x-ray irradiation of aligned boron nitride nanotubes. Targets containing aligned boron nitride nanotubes are irradiated with x-ray pulses having photon energies in the range of 3 keV to 25 keV, with pulse lengths of less than 100 femtoseconds. Calculations made by the applicant in preparation of an experiment show the enhancement of pB ¹¹ fusion rates under x-ray irradiation. Especially, the results show that x-ray enhancement is stronger for higher Z materials, it increases from DT to DHe ³ and further to pB ¹¹ . The results of these calculations are visualized in FIG. 6.

Extreme Light Infrastructure Facility (ELI-NP) (Maguerele, Romania)

[0170] The below describes experiments to be performed at the ELI-NP facility at Magurele to evaluate the dependence of alpha and neutron yield on intensity and target composition. Targets containing multi-walled boron nitride tubes with and without nanotubes aligned are irradiated with laser pulses at 23 fs with 300-500J.

Example 3

[0171] A simplified non-dynamical model for calculating enhancement was computed to assess potential enhancement factors that could be achieved in nanostructured pBl 1 targets.

[0172] It was expected that the strong nonperturbative quantum correlations of the tube wall (see above) in the target would provide a pool for quantum correlations to start from. Much as a heat reservoir in thermodynamics, the idea is that such a reservoir of quantum correlations might support reaching plasma conditions that can realize sufficient enhancement. The next step then involves checking this expectation first by analytical calculations and then by simulations.

[0173] As a first step to study the pBl 1 reaction in our nanostructured targets, a simplified non-dynamical model was built. The nitrogen in the tube walls was treated as inert on the nuclear level - that is, fusion rates of the corresponding side reactions were neglected - and it was assumed that the boron was completely purified to Bl 1. Thus, on a nuclear level, only the pBl 1 reaction was involved.

[0174] The wall structure of the tubes enters in two ways. First, the very high thermal conductivity of the tube walls was leveraged. This shows that, although the tubes are not metallic conductors, the electrons can move very fast in the tube walls. Since this is an essential ingredient for calculating the screening length, the simplification at this point was made to treat the wall in a metallic model. Note, this step neglects the band gap of around 5.7eV. As mentioned, the justification for this is that the enormous thermal conductivity should be expected to give the essential ingredient for the screening length.

[0175] Second, the fact that the viscosity of the wall is very low and close to the KSS bound was also leveraged. This implies that the coupling parameter T has to be in the range of 20 to 25. So, in plasma conditions, the wall appears as a liquid. The second simplification therefore will be that we treat the wall as a liquid, using a liquid metal model of Ichimaru for the quantum statistical approach to our targets. Considering mechanical conditions - like tensile strength - the wall will not appear as a liquid. The justification for this simplified step is that one does not expect such mechanical properties to dominate a statistical model for fusion, but the range of the coupling parameter T to be the relevant input, here.

[0176] Using a liquid metal model for pBl 1 at densities of 150g/cc and temperatures in the range of 500-1000K, the simplified model obtained (1) enhancement factors far above the previous record of 10 ⁵⁶ obtained for the p-Li7 system and (2) resulting total fusion rates that are considerably higher than the 10 ¹⁹ W/g of ICF DT fusion.

[0177] As mentioned, a quantum statistical mechanics treatment for a liquid metal model was used. The system is precisely constructed in parallel to the liquid metal treatment of p-Li7 according to S. Ichimaru (S. Ichimaru, Statistical Plasma Physics, Vol. II, 2004; S. Ichimaru, Statistical Physics of Dense Plasmas, 2018).

[0178] It is a non-dynamical model, in that it is only a treatment of the target and not of the coupled system laser and target. Especially, it does not include a dynamical treatment of how the target develops over time after being irradiated by the laser. The enhancement factors and fusion rates calculated are very high, and a correction in a full dynamical treatment may be expected. However, there are several orders of magnitude room for this correction without compromising the improvements over prior systems in enhancement factors and total fusion rates calculated.

[0179] Nanostructured targets cannot easily be compressed because they are quickly destroyed under compression. The density was used only as a model parameter which serves to give a feeling for the difficulty to achieve these conditions. In a full dynamical model, density may be replaced by other parameters which may serve to achieve the same effect for enhancement factors. For example, field strength of the very strong fields induced in laser irradiated nanostructured targets may be one such parameter.

[0180] Two different techniques were used to setup the details of the model, one based on Statistical Plasma Physics, Vol. II by S. Ichimaru and the other based on his paper on “Pycnonuclear reactions in dense astrophysical and fusion plasmas” from 1999. Both approaches roughly agreed and we use the more conservative numbers for next steps.

[0181] An input for these calculations was the screening length. There are a number of different ways to calculate the screening length. At this point a different path to the statistical mechanics calculation was used as compared to Ichimaru. For the screening length the result based on the KSS method was used; thus, a much more modern approach than Ichimaru’ s approach was used. One reason for this choice is the fact that the viscosity of the tube walls is close to the KSS bound and, more generally, the tube walls are structurally close to an SYK (Sachdev-Ye-Kitaev) model. So, a screening length based on a holographic model is the appropriate choice for taking the properties of the tube wall into account. In addition, the screening length as calculated by the KSS approach gives the largest value for all possible approaches. In other words, again the most conservative choice for screening was made in this way. [0182] The expectation that the tube wall supplies a reservoir of quantum correlations is based on the KSS approach. In other words, it is based on a string theoretic argument using a holographic argument. On the other hand, the model described herein is a quantum statistical mechanics model along the lines established by Ichimaru. So, the initial expectation was confirmed by a completely different and independent approach.

Example 4

[0183] The below describes a simulation conducted to model enhancement factors for amorphous pBl 1 targets. The calculation of the present Example was similar to the calculation described in Example 3 above but for amorphous pBl 1. In this model, the pBl 1 reaction but not the properties of a nanostructured target were modeled. Metallic conditions were assumed, but in this case this can only be justified after interaction with the laser (see below). Without the very special viscosity properties of the wall, a liquid cannot be assumed. Thus, in this case, we treated pBl l as a solid.

[0184] Enhancement factors on the order of IO ²⁰ were calculated, but multiplied with the very low two particle fusion rates at temperatures of 500-1000K - which are in the range of IO' ⁶⁰ -negligible total fusion rates were calculated. The rates were so low that pBl 1 fuel would be even more difficult to ignite non-thermally than in a thermal approach.

[0185] Igniting pBl 1 non-thermally and getting enhancement and large fusion rates may thus be dependent on using the nanostructured targets described herein.

Example 5

[0186] The model below describes simulations conducted to assess laser interaction with nanostructured targets to generate x-ray radiation, and x-ray interaction with the nanostructured targets.

[0187] The first step was to extend the model to consider the laser going into the target. To reach very short time scales and get radiation wavelengths appropriate for the nanostructured targets, the model used the first layer of tubes to reach a further compression of the laser beam to attosecond x-ray radiation. [0188] X-ray irradiation of the nanotubes has two important consequences for the model for enhancement calculations. First, the x-ray beam sees shallow bound electrons in plasma conditions, e.g., for the x-ray beam the target appears as metallic. This is the reason why we can use a metallic model for the amorphous case, too (in the amorphous case only the relativistic mirror would work to produce the x-ray beam, of course). This also shows that once the x-ray beam is in the target, a fully metallic model may be used. In this way, the simplification of neglecting the band gap is overcome.

[0189] As mentioned, for the x-ray beam, the electrons appear in plasma condition. This also means that with the coupling parameter T in the range of 20 to 25 the tube wall appears as liquid. So, the liquidity assumption of our model was also validated once the x-ray beam is in the tubes.

[0190] The filling of the tubes can be treated as liquid just from chemical properties and the hydrogen in the filling can be treated as metallic once the x-ray beam is in the tube. So, with the laser entering the target and x-ray emission setting in, the model became more stable. Under these conditions, a liquid metal model is provided, dropping two of the simplifications, e.g., the system is now even more close to the p-Li7 system.

Example 6

[0191] The details below describe simulations to be conducted to model compression of laser light to x-rays and gamma rays in the nanostructured targets, including the laser input parameters and x-ray and gamma outputs.

[0192] As illustrated in FIGS. 5A and 5B, if nanotubes remain intact for a sufficiently long time, there can be a path of radiation compression to shorter wavelength. As described above, the first layer of tubes is irradiated by femtosecond red laser light and gives a directed output of x- rays and electrons. Irradiation of the second tube layer gives a gamma (and electron) output, which is likewise directed.

[0193] A simulation is conducted, which in some parts resembles the PIC EPOCH code simulation as cited in a Mourou (G. Mourou, P. Chen, Particle-in-cell simulation of x-ray wakefield acceleration and betatron radiation nanotubes, 2016). Mourou details wakefield acceleration in carbon nanotubes. The simulation by Mourou is used as a benchmark to the BNNT results of the present simulations. The simulations use the following inputs:

• For the first and second layer of tubes: geometry (aspect ratio, diameter, number of walls, chiral vector and angle) and chemical composition (filling, degree of filling, density) which determines the input data from the target side.

• For the first layer of tubes: radiation input data as given by the laser (wavelength, intensity, pulse length, energy on target, polarization).

• For the second layer of tubes: radiation input data as given by the output data of x-rays and electrons of the first layer.

[0194] The goal of the simulation is to get the following data as output:

• For the first layer of tubes: data of x-rays (spectrum, intensity, pulse length, polarization, distribution angle around the tube axis) and electrons (spectrum, intensity, distribution angle around the tube axis).

• For the second layer of tubes: same data with the x-rays replaced by the gamma output of the second tube layer.

[0195] In a first simplified approach to the dynamics of the wall and its destruction, a background field can be added to these simulations. This addition would serve to capture leading effects of the strong fields appearing from destruction of the wall.

[0196] The central goal of these simulations is to determine the conversion efficiency to gammas for a defined laser input.

[0197] For a better understanding of the dynamics of this conversion process, the simulation explores whether energy levels in the dynamics of the wall are blocked to quickly give an occupation of energy levels which are high enough to result in an efficient conversion to x-rays and gammas, respectively.

[0198] If radiation (laser or x-ray) enters the tube in longitudinal direction, it will lead to wall excitations which will satisfy a standing wave condition in the longitudinal direction. If strong fields shift the lattice structure of the walls sufficiently, the laser will slightly miss the longitudinal direction. Together with longitudinal periodic boundary conditions, this will force the excitations of the walls caused by the laser into spiraling around the tubes. This spiraling has to satisfy a periodic boundary condition at the tube ends, too. Projecting this spiraling to the tube diameter, we see that the resulting dipole should lead to a compression of the wavelength - relative to the longitudinal excitation - which is given by the aspect ratio of the tube or a multiple thereof. The simulation assesses the effect of the aspect ratio (e.g., a topological condition from the geometry of the tubes) which results in a topological condition on the excitation spectrum and, in this way, could lead to a shift in occupation numbers of energy levels of the wall excitations.

[0199] In a first approach, the simulations are considered from the effect of background fields on the excitation spectrum.

[0200] Since the x-ray and gamma emission will result from electron movements in or very close to the wall of the tubes, enhancement effects by bringing in or modeling electrons close to the walls are evaluated. Adding material to the filling of the tubes that is sufficiently nuclear inert and deposits additional electrons close to the wall would be one embodiment. One embodiment would be adding xenon to the filling of the tubes which would result in positioning electrons precisely to this location. So, to directly test these effects, simulations are conducted to model the interaction between x-ray and gamma radiation with nanotubes with and without xenon filling.

[0201] The simulation also assesses the role of periodic boundary conditions as influenced by different options for the chiral angle and the chiral vector of the tubes - like zig-zag or armchair. Different options in terms of chiral vector and angle are used as further input data for the simulation.

Example 7

[0202] At a density of 1.3g/cc, an alpha stopping distance of around 15pm is provided by nanotube targets as described herein. A simulation is planned to study the alpha stopping in the additional presence of very strong fields, such as fields resulting from the irradiation of the tubes. To define the strong fields in this simulation, a field strength of about 10 ¹⁶ V/m may be used.