We present a construction of left braces of right nilpotency class at most two based on suitable actions of an abelian group on itself with an invariance condition. This construction allows us to recover the construction of a free right nilpotent one-generated left brace of class two.

We present the first experimental observations of the dust acoustic wave where the wave was observed to propagate in the directions of gravity and magnetic field when these directions were not aligned. The experiments were conducted in the Magnetized Dusty Plasma eXperiment facility using a novel electrode system that allows for the angle between gravity and the magnetic field to be varied in a controlled way. This letter reports on measurements in an rf glow discharge argon plasma environment where the angle between direction of gravity and the magnetic field is 45$^{\circ }$. When there was no applied magnetic field, the wave was observed to propagate in the direction of gravity. However, as the magnetic field increased and the ions transitioned from flowing in the direction of gravity to the direction of the magnetic field, a second wave emerged and two distinct waves were observed to simultaneously propagate, one in the direction of gravity and one in the direction of the magnetic field. As the magnetic field was further increased, the wave that propagated in the direction of gravity was suppressed and the wave was only observed to propagate in the direction of the applied magnetic field. We also observe that the speed and the kinetic temperature of the dust for the mode that propagated in the direction of gravity decreased with increasing magnetic field while the speed and the kinetic temperature of the dust for the mode that propagated in the direction of the magnetic field increased with increasing magnetic field. These measurements suggest that an ion-dust streaming instability is at least partially responsible for the high temperatures that have previously been observed in dusty plasmas when the dust acoustic wave is present.

A quasi-linear reduced transport model is developed from a database of high-$\beta$ electromagnetic nonlinear gyrokinetic simulations performed with spherical tokamak for energy production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid kinetic ballooning mode turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat top of the conceptual design, but do not demonstrate how this state can be accessed.

Using two counter-propagating ultra-intense laser interactions with a solid target, we conducted a study on the generation of electron-positron pairs via the multi-photon Breit–Wheeler (BW) process and trident process. These processes were simulated using the particle-in-cell (PIC) code EPOCH. Our proposed scheme involves irradiating two targets with two counter-propagating lasers. High-energy photons are produced when hot electrons collide with the reflected laser pulse at the target's front, leading to electron and positron pair production. In the single-target scenario, electron bunches are extracted from the target by the p-polarized laser electromagnetic field and accelerated by the laser ponderomotive force before colliding with the counter-propagating laser. However, using two targets enhances pair creation compared with the single-target set-up. We observed that in two-target configurations, the increased number of high-energy gamma-rays contributes to higher-energy electron–positron generation. Additionally, the generation of hot electrons is also more pronounced in this scheme. Consequently, the laser demonstrates higher efficiency in generating gamma photons and positrons in the dual-target set-up, which is beneficial for investigating high-energy pair production and gamma-ray emission. The generated positrons exhibit a density of the order of $10^{27}\,\text {m}^{-3}$ and can be accelerated to energies of 1.5 GeV. The involvement of hot electrons in the target is crucial for generating high-energy photons and positrons. The maximum pair yield reaches $8 \times 10^9$ for the BW process and $10^8$ for the trident process. Notably, the total laser energy conversion efficiencies to electrons, $\gamma$-rays and positrons show improvement in the dual-target configuration. Specifically, the laser energy absorbed by positrons increases from 11.62 % in Case A to 13.12 % in Case B. These enhancements in conversion efficiency and electron/positron density have significant practical implications in experimental set-ups. In both the BW and trident processes, the two-target set-up dominates, highlighting its effectiveness. We also compared the strengths of both approaches, suggesting that these simple models of implementing two targets can be used in experiments as well.

Magnetic reconnection leads to the formation of island-shaped magnetic structure(s). Due to disagreement between theoretical evaluations of the characteristic reconnection time and observations, it is commonly accepted that the collisionality (or resistivity) is too low to explain magnetic reconnection phenomena in fusion plasmas. Thus, magnetic reconnection still raises many open questions. The work presented here aims to improve the fundamental knowledge about ‘the life of a magnetic island’. Here, in the light of the many works of the last 70 years, a new paradigm for understanding magnetic reconnection in fusion plasmas is proposed. The life of a magnetic island (whatever its scale) follows three phases: the origin, the growth and the saturation. The possible physical mechanisms at play in these three phases will be investigated. First, for the island origin, typical time scales in link with magnetic reconnection will be evaluated for three tokamaks of different sizes (TCV, WEST and JET) to verify if magnetic reconnection is such an unexplained phenomenon in fusion plasmas. Second, for the island drive, the richness of possible mechanisms leading to ‘rapid’ magnetic island growth in fusion devices will be presented for small and large scales. Third comes the island saturation step. Results on the prediction of a large island width at saturation are presented and discussed.

In hydrodynamic (HD) turbulence, an exact decomposition of the energy flux across scales has been derived that identifies the contributions associated with vortex stretching and strain self-amplification (Johnson, Phys. Rev. Lett., vol. 124, 2020 104501; J. Fluid Mech., vol. 922, 2021, A3) to the energy flux across scales. Here, we extend this methodology to general coupled advection–diffusion equations and, in particular, to homogeneous magnetohydrodynamic (MHD) turbulence. We show that several MHD subfluxes are related to each other by kinematic constraints akin to the Betchov relation in HD. Applied to data from direct numerical simulations, this decomposition allows for an identification of physical processes and for the quantification of their respective contributions to the energy cascade, as well as a quantitative assessment of their multi-scale nature through a further decomposition into single- and multi-scale terms. We find that vortex stretching is strongly depleted in MHD compared with HD, and the kinetic energy is transferred from large to small scales almost exclusively by the generation of regions of small-scale intense strain induced by the Lorentz force. In regions of large strain, current sheets are stretched by large-scale straining motion into regions of magnetic shear. This magnetic shear in turn drives extensional flows at smaller scales. Magnetic energy is transferred from large to small scales predominantly by the aforementioned current-sheet thinning in regions of high strain. The contributions from current-filament stretching – the analogue to vortex stretching – and from bending of magnetic field-lines into current filaments by vortical motion are both almost negligible, although the latter induces strong backscatter of magnetic energy. Consequences of these results for subgrid-scale turbulence modelling are discussed.

There is growing evidence that the broadband radio spectral energy distributions (SEDs) of star-forming galaxies (SFGs) contain a wealth of complex physics. In this paper we aim to determine the physical emission and loss processes causing radio SED curvature and steepening to see what observed global astrophysical properties, if any, are correlated with radio SED complexity. To do this, we have acquired radio continuum data between 70 MHz and 17 GHz for a sample of 19 southern local ($z \lt 0.04$) SFGs. Of this sample 11 are selected to contain low-frequency ($ \lt $300 MHz) turnovers (LFTOs) in their SEDs and eight are control galaxies with similar global properties. We model the radio SEDs for our sample using a Bayesian framework whereby radio emission (synchrotron and free-free) and absorption or loss processes are included modularly. We find that without the inclusion of higher frequency data ($ \gt $17 GHz) single synchrotron power-law based models are always preferred for our sample; however, additional processes including free-free absorption (FFA) and synchrotron losses are often required to accurately model radio SED complexity in SFGs. The fitted synchrotron spectral indices range from $-0.45$ to $-1.07$ and are strongly anticorrelated with stellar mass suggesting that synchrotron losses are the dominant mechanism acting to steepen the spectral index in larger/more massive nearby SFGs. We find that LFTOs in the radio SED are independent from the inclination of SFGs; however, higher inclination galaxies tend to have steeper fitted spectral indices indicating losses to diffusion of cosmic ray electrons into the galactic halo. Four of five of the merging systems in our SFG sample have elevated specific star formation rates and flatter fitted spectral indices with unconstrained LFTOs. Lastly, we find no significant separation in global properties between SFGs with or without modelled LFTOs. Overall these results suggest that LFTOs are likely caused by a combination of FFA and ionisation losses in individual recent starburst regions with specific orientations and interstellar medium properties that, when averaged over the entire galaxy, do not correlate with global astrophysical properties.

A classical result of Erdős, Lovász and Spencer from the late 1970s asserts that the dimension of the feasible region of densities of graphs with at most k vertices in large graphs is equal to the number of non-trivial connected graphs with at most k vertices. Indecomposable permutations play the role of connected graphs in the realm of permutations, and Glebov et al. showed that pattern densities of indecomposable permutations are independent, i.e., the dimension of the feasible region of densities of permutation patterns of size at most k is at least the number of non-trivial indecomposable permutations of size at most k. However, this lower bound is not tight already for $k=3$. We prove that the dimension of the feasible region of densities of permutation patterns of size at most k is equal to the number of non-trivial Lyndon permutations of size at most k. The proof exploits an interplay between algebra and combinatorics inherent to the study of Lyndon words.

Observations of Galactic supernova remnants (SNRs) are crucial to understanding supernova explosion mechanisms and their impact on our Galaxy’s evolution. SNRs are usually identified by searching for extended, circular structures in all-sky surveys. However, the resolution and sensitivity of any given survey results in selection biases related to the brightness and angular scale of a subset of the total SNR population. As a result, we have only identified 1/3 of the expected number of SNRs in our Galaxy. We used data collected by the Murchison Widefield Array (MWA) to perform a visual search for SNR candidates over $ 285^{\circ} \lt l \lt 70^{\circ}$ and $|b| \lt 16^{\circ}$. We then used the Widefield Infrared Survey Explorer to eliminate likely Hii regions from our SNR candidate sample. By exploiting the resolution and sensitivity of MWA data, we have successfully detected 10 new candidates using our proposed method. In addition, our method has also enabled us to detect and verify 10 previously known but unconfirmed candidates. The 20 SNR candidates described in the paper will increase the known SNR population in the Galaxy by 7%.

Using the ONEDFEL code we perform free electron laser simulations in the astrophysically important guide-field dominated regime. For wigglers’ (Alfvén waves) wavelengths of tens of kilometres and beam Lorentz factor ${\sim }10^3$, the resulting coherently emitted waves are in the centimetre range. Our simulations show a growth of the wave intensity over fourteen orders of magnitude, over the astrophysically relevant scale of approximately a few kilometres. The signal grows from noise (unseeded). The resulting spectrum shows fine spectral substructures, reminiscent of those observed in fast radio bursts.

The regulation of electron heat transport in high-$\beta$, weakly collisional, magnetized plasma is investigated. A temperature gradient oriented along a mean magnetic field can induce a kinetic heat-flux-driven whistler instability (HWI), which back-reacts on the transport by scattering electrons and impeding their flow. Previous analytical and numerical studies have shown that the heat flux for the saturated HWI scales as $\beta _e^{-1}$. These numerical studies, however, had limited scale separation and consequently large fluctuation amplitudes, which calls into question their relevance at astrophysical scales. To this end, we perform a series of particle-in-cell simulations of the HWI across a range of $\beta _e$ and temperature-gradient length scales under two different physical set-ups. The saturated heat flux in all of our simulations follows the expected $\beta _e^{-1}$ scaling, supporting the robustness of the result. We also use our simulation results to develop and implement several methods to construct an effective collision operator for whistler turbulence. The results point to an issue with the standard quasi-linear explanation of HWI saturation, which is analogous to the well-known $90^{\circ }$ scattering problem in the cosmic-ray community. Despite this limitation, the methods developed here can serve as a blueprint for future work seeking to characterize the effective collisionality caused by kinetic instabilities.

Ion cyclotron resonance heating is a versatile heating method that has been demonstrated to be able to efficiently couple power directly to the ions via the fast magnetosonic wave. However, at temperatures relevant for reactor grade devices such as DEMO, electron damping becomes increasingly important. To reduce electron damping, it is possible to use an antenna with a power spectrum dominated by low parallel wavenumbers. Moreover, using an antenna with a unidirectional spectrum, such as a travelling wave array antenna, the parallel wavenumber can be downshifted by mounting the antenna in an elevated position relative to the equatorial plane. This downshift can potentially enhance ion heating as well as fast wave current drive efficiency. Thus, such a system could benefit ion heating during the ramp-up phase and be used for current drive during flat-top operation. To test this principle, both ion heating and current drive have been simulated in a DEMO-like plasma for a few different mounting positions of the antenna using the FEMIC code. We find that moving the antenna off the equatorial plane makes ion heating more efficient for all considered plasma temperatures at the expense of on-axis heating. Moreover, although current drive efficiency is enhanced, electron damping is reduced for lower mode numbers, thus reducing the driven current in this part of the spectrum.