Physical regimes of electrostatic wave-wave nonlinear interactions generated by an electron beam propagating in a background plasma.

Electron-beam plasma interaction has long been a topic of great interest. Despite the success of the quasilinear and weak turbulence theories, their validities are limited by the requirements of a sufficiently dense mode spectrum and a small wave amplitude. In this paper, we extensively study the collective processes of a mono-energetic electron beam emitted from a thermionic cathode propagating through a cold plasma by performing high-resolution two-dimensional particle-in-cell simulations and using analytical theories. We confirm that, during the initial stage of two-stream instability between the beam and background cold electrons, it is saturated due to the well-known wave-trapping mechanism. Further evolution occurs due to strong wave-wave nonlinear processes. We show that the beam-plasma interaction can be classified into four different physical regimes in the parameter space for the plasma and beam parameters. The differences between the regimes are analyzed in detail. We identify a new regime in the strong Langmuir turbulence featured by what we call electron modulational instability (EMI) that could create a local Langmuir wave packet growing faster than the ion plasma frequency. Ions do not have time to respond to EMI in the initial growing stage. On a longer timescale, the action of the ponderomotive force produces very strong ion density perturbations, and eventually, the beam-plasma wave interaction stops being resonant due to the strong ion density perturbations. Consequently, in this EMI regime, electron beam-plasma interaction occurs in a repetitive (intermittent) process. The beam electrons are strongly scattered by waves, and the Langmuir wave spectrum is significantly broadened, which in turn gives rise to strong heating of bulk electrons. Associated energy transfer from the beam to the background plasma electrons has been studied. A resulting kappa (κ) distribution and a wave-energy spectrum E^{2}(k)∼k^{-5} are observed in the strong turbulent regime.

Electron Modulational Instability in the Strong Turbulent Regime for an Electron Beam Propagating in a Background Plasma.

We study collective processes for an electron beam propagating through a background plasma using simulations and analytical theory. A new regime where the instability of a Langmuir wave packet can grow locally much faster than ion frequency is clearly identified. The key feature of this new regime is an electron modulational instability that rapidly creates a local Langmuir wave packet, which in its turn produces local charge separation and strong ion density perturbations because of the action of the ponderomotive force, such that the beam-plasma wave interaction stops being resonant. Three evolution stages of the process and observed periodic burst features are discussed. Different physical regimes in the plasma and beam parameter space are demonstrated for the first time.

Boron nitride nanotube precursor formation during high-temperature synthesis: kinetic and thermodynamic modelling.

We performed integrated modelling of the chemical pathways of formation for boron nitride nanotube (BNNT) precursors during high-temperature synthesis in a B/N2mixture. Integrated modelling includes quantum chemistry, Quantum-classical molecular dynamics, thermodynamic modelling, and kinetic approaches. We demonstrate that BN compounds are formed via the interaction of molecular nitrogen with small boron clusters, rather than through interactions with less reactive liquid boron. (This process can also be described as N2molecule fixation.) Liquid boron evaporates to produce these boron clusters (Bmwithm≤ 5), which are subsequently converted into BmNnchains. The production of such chains is crucial to the growth of BNNTs because these chains form the building blocks of bigger and longer BN chains and rings, which are in turn the building blocks of fullborenes and BNNTs. Additionally, kinetic modelling revealed that B4N4and B5N4species in particular play a major role in the N2molecule fixation process. The formation of these species via reactions with B4and B5clusters is not adequately described under the assumption of thermodynamic equilibrium, as is demonstrated in our kinetic modelling. Thus, the accumulation of both B4N4and B5N4depends on the background gas pressure and the gas cooling rate. Long BN chains and rings, which are precursors of the fullborene and BNNT growth, form via self-assembly of components B4N4and B5N4. Our modelling results-particularly the increased densities of B4N4and B5N4species at higher gas pressures-explain the experimentally observed effect of gas pressure on the yield of high-quality BNNTs. The catalytic role of hydrogen was also studied; it is shown that HBNH molecules can be the main precursor of BNNT synthesis in the presence of hydrogen.

Erratum: Self-Organization, Structures, and Anomalous Transport in Turbulent Partially Magnetized Plasmas with Crossed Electric and Magnetic Fields [Phys. Rev. Lett. 122, 185001 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.122.185001.

Determining the gas composition for the growth of BNNTs using a thermodynamic approach.

High-yield production of high-quality boron-nitride nanotubes (BNNTs) has been reported recently in several publications. A boron-rich material is evaporated using a laser or plasma in a nitrogen-rich atmosphere to supply precursor gaseous species for nucleation and growth of BNNTs. Either hydrogen was added or pressure was increased in the system to achieve high yield and high purity of the synthesized nanotubes. According to the widely-accepted "root grow" mechanism, upon gas cooling, boron droplets form first, then they adsorb nitrogen from the surrounding gas species, and BNNTs grow on their surfaces. However, what are the precursor species that provide nitrogen for the growth is still an open question. To answer this question, we performed thermodynamic calculations for determining the B-N mixture composition considering a broad set of gas species. For the first time, condensation of boron was taken into account and was shown to have a drastic effect on thegas chemical composition. B2N molecules were identified to be a major source of nitrogen for the growth of BNNTs. The presence of B2N molecules in a B-N gas mixture was verified by our spectroscopic measurements during laser ablation of boron-rich targets in nitrogen. It was shown that the increase of pressure has a quantitative effect on the mixture composition yielding an increase of the precursor density. Hydrogen addition might open an additional channel of nitrogen supply to support the growth of BNNTs. The nitrogen atoms react with abundant H2 molecules to form NH2 and then NH3 precursor species, instead of just recombining back to inert N2 molecules, as in the no-hydrogen case. In addition, thermodynamics was applied in conjunction with agglomeration theory to predict the size of the boron droplets upon growth of BNNTs. Analytical relations for the identification of crucial species densities were derived.

Self-Organization, Structures, and Anomalous Transport in Turbulent Partially Magnetized Plasmas with Crossed Electric and Magnetic Fields.

Self-organization and anomalous transport in gradient-drift driven turbulence in partially magnetized plasmas with crossed electric and magnetic fields is demonstrated in two-dimensional fluid simulations. The development of large scale structures and flows is shown to occur as a result of the inverse energy cascade from short wavelength instabilities. The turbulence shows complex interaction of small scale modes with large scale zonal flow modes, vortices, and streamers resulting in strongly intermittent anomalous transport that significantly exceeds the classical collisional values. The turbulence driven secondary instabilities and large scale structures are shown to dominate the anomalous electron current. Such anomalous transport and structures are consistent with a number of experimental observations in laboratory plasmas.

Root-growth of boron nitride nanotubes: experiments and ab initio simulations.

We have synthesized boron nitride nanotubes (BNNTs) in an arc in the presence of boron and nitrogen species. We find that BNNTs are often attached to large nanoparticles, suggesting that root-growth is a likely mechanism for their formation. Moreover, the tube-end nanoparticles are composed of boron, without transition metals, indicating that transition metals are not necessary for the arc synthesis of BNNTs. To gain further insight into this process we have studied key mechanisms for root growth of BNNTs on the surface of a liquid boron droplet by ab initio molecular dynamics simulations. We find that nitrogen atoms reside predominantly on the droplet surface where they organize to form boron nitride islands below 2400 K. To minimize contact with the liquid particle underneath, the islands assume non-planar configurations that are likely precursors for the thermal nucleation of cap structures. Once formed, the caps are stable and can easily incorporate nitrogen and boron atoms at their base, resulting in further growth. Our simulations support the root-growth mechanism of BNNTs and provide comprehensive evidence of the active role played by liquid boron.

Enhanced self-focusing of an ion beam pulse propagating through a background plasma along a solenoidal magnetic field.

It is shown that the application of a weak solenoidal magnetic field along the direction of ion beam propagation through a neutralizing background plasma can significantly enhance the beam self-focusing for the case where the beam radius is small compared to the collisionless electron skin depth. The enhanced focusing is provided by a strong radial self-electric field that is generated due to a local polarization of the magnetized plasma background by the moving ion beam. A positive charge of the ion beam pulse becomes overcompensated by the plasma electrons, which results in the radial focusing of the beam ions. The expression for the self-focusing force is derived analytically and compared with the results of numerical simulations.

Merging of super-Alfvénic current filaments during collisionless Weibel instability of relativistic electron beams.

The theoretical framework predicting the long-term evolution, structure, and coalescence energetics of current filaments during the Weibel instability of an electron beam in a collisionless plasma is developed. We emphasize the nonlinear stage of the instability, during which the beam density of filaments increases to the background ion density, and the ambient plasma electrons are fully expelled from the filaments. Our analytic and numerical results demonstrate that the beam filaments can carry super-Alfvénic currents and develop hollow-current density profiles. This explains why the initially increasing magnetic field energy eventually decreases during the late stage of the instability.

Self-consistent system of equations for a kinetic description of the low-pressure discharges accounting for the nonlocal and collisionless electron dynamics.

In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study, a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the nonuniform plasma density profile on both the current density profile and the EEDF is demonstrated.

Anomalous capacitive sheath with deep radio-frequency electric-field penetration.

A novel nonlinear effect of anomalously deep penetration of an external radio-frequency electric field into a plasma is described. A self-consistent kinetic treatment reveals a transition region between the sheath and the plasma. Because of the electron velocity modulation in the sheath, bunches in the energetic electron density are formed in the transition region adjacent to the sheath. The width of the region is of order V(T)/omega, where V(T) is the electron thermal velocity, and omega is the frequency of the electric field. The presence of the electric field in the transition region results in a collisionless cooling of the energetic electrons and an additional heating of the cold electrons.