An analytical expression for focal intensity is derived for arbitrary surface profiles and arbitrary groove patterns of compressor gratings. The expression is valid for different compressor designs: plane and out-of-plane compressors, symmetric and asymmetric compressors (compressors composed by two not-identical pairs of gratings) and a two-grating compressor. It is shown that the quality requirements for the optics used to write a grating are higher than for the grating. The focal intensity can be maximized by rotating each grating around its normal by 180 degrees. Moreover, it may be increased to maximum by interchanging any two gratings in the compressor, because imperfections of an individual grating do not additively affect the focal intensity. The intensity decrease is proportional to the squared pulse spectrum width and the squared total distortions of the second and third gratings of the four-grating compressor and the total distortions of two gratings of the two-grating compressor.

We define the symmetric braid index $b_s(K)$ of a ribbon knot K to be the smallest index of a braid whose closure yields a symmetric union diagram of K, and derive a Khovanov-homological characterisation of knots with $b_s(K)$ at most three. As applications, we show that there exist knots whose symmetric braid index is strictly greater than the braid index, and deduce that every chiral slice knot with determinant one has braid index at least four. We also calculate bounds for $b_s(K)$ for prime ribbon knots with at most 11 crossings.

Fiber-based structured light including cylindrical vector beams (CVBs) and orbital angular momentum (OAM) has gained significant interest for its unique properties. In this work, we propose the concept of a programmable linearly polarized (LP)-mode synthesizer for general structured light generation, in which an LP-mode pool supporting independent and selectable LP-mode output is first established, and then different CVB/OAM modes could be generated in a general way through polarization and phase control. We demonstrate a proof-of-concept LP-mode synthesizer based on a fiber ring laser characterized by a partial five-LP mode weakly coupled few-mode fiber (FMF) cavity and an arbitrary LP-mode switch array. Various CVB/OAM beams including TE01, TM01, OAM±1 and OAM±2 modes are successfully generated. This approach provides new insights into mode manipulation methods, potentially enhancing the performance of optical quantum communications, optical fiber sensing and optical trapping applications.

Let S be a fine and saturated (fs) log scheme, and let F be a group scheme over the underlying scheme of S which is étale locally representable by (1) a finite dimensional $\mathbb{Q}$-vector space, or (2) a finite rank free abelian group, or (3) a finite abelian group. We give a full description of all the higher direct images of F from the Kummer log flat site to the classical flat site. In particular, we show that: in case (1) the higher direct images of F vanish; and in case (2) the first higher direct image of F vanishes and the nth ($n\gt 1$) higher direct image of F is isomorphic to the $(n-1)$-th higher direct image of $F\otimes_{{\mathbb Z}}{\mathbb Q}/{\mathbb Z}$. In the end, we make some computations when the base is a standard henselian log trait or a Dedekind scheme endowed with the log structure associated to a finite set of closed points.

Ion-acoustic waves in a dusty plasma are investigated where it is assumed that the ions follow a Cairns distribution and the electrons are Boltzmann distributed. Two theoretical methods are applied: Sagdeev pseudopotential analysis (SPA) and reductive perturbation theory (RPT). Since SPA incorporates all nonlinearities of the model it is the most accurate but deriving soliton profiles requires numerical integration of Poisson’s equation. By contrast, RPT is a perturbation method which at second order yields the Gardner equation incorporating both the quadratic nonlinearity of the Korteweg–de Vries (KdV) equation and the cubic nonlinearity of the modified KdV equation. For consistency with the perturbation scheme the coefficient of the quadratic term needs to be at least an order of magnitude smaller than the coefficient of the cubic term. Solving the Gardner equation yields an analytic expression of the soliton profile. Selecting an appropriate set of compositional parameters, the soliton solutions obtained from SPA and RPT are analysed and compared.

High-order harmonic generation (HHG) in noble gases driven by femtosecond lasers is currently a feasible solution to obtain ultrafast pulses in the extreme ultraviolet (EUV) wavelength range. Implementation of high-flux EUV sources requires driving HHG using an ultrafast laser source in the visible wavelength range with MHz repetition rate. In this paper, we employ a multi-pass cell followed by chirped mirrors to compress 1-MHz, 200-W, 300-fs pulses at 1.03 μm to a duration of 35 fs. The resulting 186-W compressed pulses are focused onto 0.5-mm thick beta barium borate crystal to drive second-harmonic generation and produce positively chirped pulses at 520 nm. These green pulses are de-chirped to 26 fs in duration with an average power of 64 W, which, to the best of our knowledge, represents the highest average power of green pulses with a duration below 100 fs.

Next-generation X-ray satellite telescopes such as XRISM, NewAthena and Lynx will enable observations of exotic astrophysical sources at unprecedented spectral and spatial resolution. Proper interpretation of these data demands that the accuracy of the models is at least within the uncertainty of the observations. One set of quantities that might not currently meet this requirement is transition energies of various astrophysically relevant ions. Current databases are populated with many untested theoretical calculations. Accurate laboratory benchmarks are required to better understand the coming data. We obtained laboratory spectra of X-ray lines from a silicon plasma at an average spectral resolving power of $\sim$7500 with a spherically bent crystal spectrometer on the Z facility at Sandia National Laboratories. Many of the lines in the data are measured here for the first time. We report measurements of 53 transitions originating from the K-shells of He-like to B-like silicon in the energy range between $\sim$1795 and 1880 eV (6.6–6.9 Å). The lines were identified by qualitative comparison against a full synthetic spectrum calculated with ATOMIC. The average fractional uncertainty (uncertainty/energy) for all reported lines is ${\sim}5.4 \times 10^{-5}$. We compare the measured quantities against transition energies calculated with RATS and FAC as well as those reported in the NIST ASD and XSTAR’s uaDB. Average absolute differences relative to experimentally measured values are 0.20, 0.32, 0.17 and 0.38 eV, respectively. All calculations/databases show good agreement with the experimental values; NIST ASD shows the closest match overall.

The work presented here revisits the Velikhov-ionisation instability, an instability first discovered in the early 1960s (Velikhov, E. P. 1962 1st International Conference on MHD Electrical Power Generation, Newcastle upon Tyne, England, p. 135). This mode strongly deteriorates the performance of magnetohydrodynamic (MHD) energy convertors in which the seed gas must be at a substantially higher temperature than the high density primary gas, the latter gas carrying almost all the energy. Specifically, a finite temperature difference is necessary for the MHD generator to successfully act as a topping cycle for nuclear (fission and fusion) power plants. The ionisation instability has thus been viewed for many years as a show stopper for MHD nuclear topping cycles. Even so, some experimental observations, never fully exploited, show that nearly full ionisation of the seed gas can stabilise this dangerous instability. One goal of the research presented here is to provide a first-principles theoretical explanation for these experimental observations. The stabilisation can theoretically produce high temperature ratios, of the order of 10, by carefully choosing the density of the unionised seed gas. A second goal of the research is to investigate whether or not the recent development of high-field, high-temperature REBCO (rare-earth barium copper oxide) superconductors can lead to substantially improved power plant efficiency. Here, it is shown that the answer is subtle – no clear conclusions can be drawn, a consequence of the fact that the new stability criterion is a local one. What is needed to assess overall plant efficiency is a global analysis. Additional work has recently been completed on a newly developed global model which answers this question and will be reported on in a future paper.

We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterise when the tropical compactification of the moduli space agrees with the theory of geometric tropicalisation. The characterisation statement occurs only when the graph is complete multipartite.

An action of a group G on a set X is said to be quasi-n-transitive if the diagonal action of G on $X^n$ has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act quasi-2-transitively on infinite sets.

The Vlasov–Maxwell equations provide kinetic simulations of collisionless plasmas, but numerically solving them on classical computers is often impractical. This is due to the computational resource constraints imposed by the time evolution in the six-dimensional phase space, which requires broad spatial and temporal scales. The novelty of this study is to implement a quantum–classical hybrid Vlasov–Maxwell solver and the rigorous numerical scheme evaluation by numerical simulations. Specifically, the Vlasov solver implements the Hamiltonian simulation based on quantum singular value transformation, coupled with a classical Maxwell solver. We perform numerical simulation of a one-dimensional advection test and a one-spatial-dimension, one-velocity-dimension two-stream instability test on the Qiskit-Aer-GPU quantum circuit emulator with an A100 GPU. The computational complexity of our quantum algorithm can potentially be reduced from the classical $\mathcal{O}(N^6T^2/\epsilon )$ to $\mathcal{O}\left (\text{poly}(\log {N})\left (NT+T\log \left (T/\epsilon \right )\right )\right )$ for the $N$ grid system, simulation time $T$ and error tolerance $\epsilon$ in the limit where the number of queries is large enough and the error is small enough. Furthermore, the numerical analysis reveals that our quantum algorithm is robust under larger time steps compared with classical algorithms with the constraint of Courant–Friedrichs–Lewy condition.

Two desert cyanobacterial strains, Chroococcidiopsis sp. CCMEE 010 and CCMEE 130, capable far-red light photoacclimation (FaRLiP), were investigated for the stability of biosignatures after six years of desiccation. Biosignature detectability was demonstrated by confocal laser scanning microscopy and Raman spectroscopy thus highlighting that these two FaRLiP cyanobacteria are a novel reservoir of an array of pigments, encompassing canonical chlorophyll a, far-red shifted chlorophylls, phycobilins and carotenoids. The recorded signals were comparable to those of dried cells of Chroococcidiopsis sp. CCMEE 029, CCMEE 057 and CCMEE 064, not capable of FaRLiP acclimation and previously reported for biosignature stability and survivability after exposure to space and Mars-like conditions during the BIOMEX (BIOlogy and Mars EXperiment) and BOSS (Biofilm Organisms Surfing Space) low Earth orbit missions. Since infrared-light driven photosynthesis has implications for the habitability of Mars as well as exoplanets, the stability of far-red shifted chlorophylls in dried Chroococcidiopsis is a prerequisite for future experimentations under simulated planetary conditions in the laboratory or directly into space. It is anticipated that post-flight investigations of FaRLiP cyanobacteria as part of the BioSigN (Bio-Signatures and habitable Niches) space mission will contribute to gather novel insights into biosignature degradation/stability and thus prepare future planetary exploration missions to Mars. In addition, the scored viability of strains CCMEE 010 and CCMEE 130 after prolonged desiccation is relevant to investigate life endurance under deep space conditions, as planned by the BioMoon mission that aims to expose dried and rehydrated extremophiles on the Moon surface after exposure to deep space.

The pulse duration is a critical parameter of picosecond-petawatt laser systems because it directly affects the results of high-energy-density physics experiments. This study systematically investigated the effects of the spectral width, central wavelength and beam-pointing deviations on pulse duration stability at the SG-II facility. A theoretical analysis of the relationship between spectra and pulse duration is conducted to quantify the impact on pulse duration stability, and the results are further validated through experimental measurements. In addition, beam-pointing deviations at the stretcher significantly affect the pulse duration. For example, a 27 μrad deviation can induce a 30% pulse duration variation. In contrast, the compressor exhibits greater robustness. Based on simulation and experimental results, we identify operational tolerance ranges for spectral width and beam-pointing deviation to maintain pulse duration stability within 5% at the SG-II facility. These findings provide critical guidance for optimizing the performance and reliability of chirped-pulse amplification/optical parametric chirped-pulse amplification-based high-power laser systems.