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We provide a fundamentally new perspective on subcritical turbulence in plasmas, based on coherent structures, which are obtained and characterised via direct numerical solution. The domains where these coherent states exist appear to be closely connected to the those where related turbulent states can exist, so there may be a deep connection between the stability of these coherent structures and the domain where sustained turbulence is possible. In contrast to previous descriptions of turbulence in terms of a stochastic collection of linear waves, we present a fundamentally nonlinear representation based on more general classes of translating oscillatory nonlinear solutions. In turbulent tokamak plasmas, the transport can often be completely suppressed by introducing a background shear flow, whose amplitude is an important control parameter. As this parameter is decreased below a critical value, radially localised structures appear, becoming larger and more complex, in both gyrokinetic simulations and a simpler fluid model of the plasma. For the fluid model, we directly solve for a particular class of nonlinear solutions, relative periodic orbits, and determine their stability, thus explaining why these isolated structures appear in initial-value simulations. The increase of complexity as the flow shear is reduced is explained by a series of Hopf bifurcations of these nonlinear solutions, which we quantify via stability analysis. In gyrokinetic simulations, we are able to indirectly determine the underlying relative periodic orbits by imposing symmetry conditions on the simulations.
Landau damping is one of the cornerstones of plasma physics. Based on the initial-value approach adopted by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov–Poisson system for different equilibrium distribution functions $f_0(v)$, going beyond the traditional focus on the root with largest imaginary part and investigating the full set of roots that the dispersion relation of the system generally admits. Specifically, we provide analytical insights into the number and the structure of the roots for entire and meromorphic functions $f_0(v)$, such as Maxwellian and $\kappa$ distributions, we discuss the potential issues related to the redefinition of $\partial{f}_0/\partial{v}$ as a complex variable function and we show how different sigmoids affect the root structure associated with non-meromorphic cut-off distribution functions. Finally, based on the comparison of the several root structures considered, we wonder if the multiple roots might hint at a deeper understanding of the Landau damping phenomenon.
The change in direction of the wavevector and group velocity experienced by a wave refracted at the interface of an anisotropic medium in uniform linear motion are determined analytically. These transmission conditions, which are shown to be consistent with the generalised Snell’s law written in the laboratory frame, are then used to examine the effect of motion on waves incident on a magnetised plasma. For an incident wave in the plane perpendicular to the magnetic field the motion is observed to lead to non-negligible deviation of the low-frequency X-mode, as well as to non-symmetrical total reflection angles. These effects are shown to be further complicated when the magnetic field is in the plane formed by the incident wavevector and the medium’s velocity, as the anisotropy now competes with the motion-induced drag. Although obtained in simplified configurations, these results suggest that accounting for motion when modelling plasma wave trajectories could be important under certain conditions, calling for a more detailed quantification of the effect of motion in actual diagnostics and plasma control schemes.
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a dynamical system to a Hamiltonian form, where the Hamiltonian matrix is a function of dynamical variables. To advance in time, we measure expectation values from the previous time step and evaluate the Hamiltonian function classically, which introduces stochasticity into the dynamics. We then perform standard quantum Hamiltonian simulation over a short time, using the evaluated constant Hamiltonian matrix. This approach requires evolving an ensemble of quantum states, which are consumed each step to measure the required observables. We apply this approach to the classic logistic and Lorenz systems, in both integrable and chaotic regimes. Our analysis shows that the solutions’ accuracy is influenced by both the stochastic sampling rate and the nature of the dynamical system.
Dusty plasmas typically contain various species of dust particles, though most studies have focused on homogeneous systems. This paper investigates the propagation of dust acoustic waves in an inhomogeneous dusty plasma with an interface, analysing how plasma inhomogeneity influences wave behaviour. Using scattering and reductive perturbation methods, we show that both transmitted and reflected waves depend strongly on the mass ratio between regions. Dust acoustic waves cannot propagate through a dust lattice when the wavelength is smaller than the lattice constant. At a discontinuous interface, at least one transmitted solitary wave is generated, with its amplitude determined by the mass ratio, while at most one reflected solitary wave can exist. These results underscore the critical role of the mass ratio in wave propagation and suggest a method for estimating dust particle masses and properties by analysing the incident, transmitted and reflected waves.
We study the onset of spontaneous dynamics in the follower force model of an active filament, wherein a slender elastic filament in a viscous liquid is clamped normal to a wall at one end and subjected to a tangential compressive force at the other. Clarke et al. (Phys. Rev. Fluids, vol. 9, 2024, 073101) recently conducted a thorough investigation of this model using methods of computational dynamical systems; inter alia, they showed that the filament first loses stability via a supercritical double-Hopf bifurcation, with periodic ‘planar-beating’ states (unstable) and ‘whirling’ states (stable) simultaneously emerging at the critical follower-force value. We complement their numerical study by carrying out a weakly nonlinear analysis close to this unconventional bifurcation, using the method of multiple scales. The main outcome is an ‘amplitude equation’ governing the slow modulation of small-magnitude oscillations of the filament in that regime. Analysis of this reduced-order model provides insights into the onset of spontaneous dynamics, including the creation of the nonlinear whirling states from particular superpositions of linear planar-beating modes as well as the selection of whirling over planar beating in three-dimensional scenarios.
This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the computational grid, but defines the basis functions in piecewise field-aligned coordinates to avoid grid deformation while naturally representing the field-aligned mode structures. This scheme is formulated and implemented numerically. It also applies to the unstructured triangular meshes in principle. We have conducted linear benchmark tests, which agree well with previous results and traditional schemes. Furthermore, multiple-$n$ simulations are also carried out as a proof of principle, demonstrating the efficiency of this scheme in nonlinear turbulence simulations within the framework of the finite element method.
We analyse distributions of the spatial scales of coherent intermittent structures – current sheets – obtained from fully kinetic, two-dimensional simulations of relativistic turbulence in a collisionless pair plasma using unsupervised machine-learning data dissection. We find that the distribution functions of sheet length $\ell$ (longest scale of the analysed structure in the direction perpendicular to the dominant guide field) and curvature $r_c$ (radius of a circle fitted to the structures) can be well-approximated by power-law distributions, indicating self-similarity of the structures. The distribution for the sheet width $w$ (shortest scale of the structure) peaks at the kinetic scales and decays exponentially at larger values. The data shows little or no correlation between $w$ and $\ell$, as expected from theoretical considerations. The typical $r_c$ depends linearly on $\ell$, which indicates that the sheets all have a similar curvature relative to their sizes. We find a weak correlation between $r_c$ and $w$. Our results can be used to inform realistic magnetohydrodynamic subgrid models for plasma turbulence in high-energy astrophysics.
A point force acting on a Brinkman fluid in confinement is always counterbalanced by the force on the porous medium, the force on the walls and the stress at open boundaries. We discuss the distribution of those forces in different geometries: a long pipe, a medium with a single no-slip planar boundary, a porous sphere with an open boundary and a porous sphere with a no-slip wall. We determine the forces using the Lorentz reciprocal theorem and additionally validate the results with explicit analytical flow solutions. We discuss the relevance of our findings for cellular processes such as cytoplasmic streaming and centrosome positioning.
Particle-laden horizontal turbulent pipe flow is studied experimentally in the two-way coupling regime with a focus on delineating the effects of particle-to-fluid density ratio $\rho _{p}/\rho _{f}=1$ and 1.05 on the fluid and particle statistics. Particle volume fraction $\phi _{v}$ up to $1\,\%$ and viscous Stokes numbers ranging from $St^+ \approx 1.2$ to $St^+ \approx 3.8$ are investigated at friction Reynolds number $Re_\tau \approx 195$ using time-resolved two-dimensional particle image and tracking velocimetry. Substantial differences are observed between the statistics of neutrally buoyant (i.e. $\rho _{p}/\rho _{f}=1$) and denser (i.e. $\rho _{p}/\rho _{f}=1.05$) settling particles (with settling velocities 0.12–0.32 times the friction velocity), which, at most instances, show opposing trends compared to unladen pipe flow statistics. Neutrally buoyant particles show a slightly increased overall drag and suppressed turbulent stresses, but elevated particle–fluid interaction drag and results in elongated turbulent structures compared to the unladen flow, whereas $\rho _{p}/\rho _{f}=1.05$ particles exhibit a slight overall drag reduction even with increased radial turbulent stresses, and shorter streamwise structures compared to the unladen flow. These differences are enhanced with increasing $St^+$ and $\phi _v$, and can be attributed to the small but non-negligible settling velocity of denser particles, which also leads to differing statistics in the upper and lower pipe halves.
We perform simulations of a two-fluid–structure interaction problem involving liquid–gas flow past a fully submerged stationary circular cylinder. Interactions between the liquid–gas interface with finite surface tension and flow disturbances arising from the cylinder induce a variety of interfacial phenomena and wake structures. We map different interface regimes in a parameter space defined by the Bond number $Bo \in [100, 5000]$ and the submergence depth $h/D \in [1, 2.5]$ of the cylinder while keeping the Reynolds (Re) and Weber (We) numbers fixed at 150 and 1000, respectively. The emerging interface features are classified into three distinct regimes: interfacial waves generated by Strouhal vortices, the entrainment of multi-scale gas bubbles and the reduced deformation state. In the interfacial wave regime, we demonstrate that the frequency of transverse interface fluctuations at a specific streamwise location is identical to the vortex shedding frequency. Additionally, the wavelength of interfacial waves is determined by the size of vortex pairs consisting of alternating Strouhal vortices. In the gas entrainment regime at $ Bo = 1000$, our bubble-size distributions reveal that the entrained bubbles have sizes ranging from one to two orders of magnitude smaller than the cylinder. These multi-scale bubbles are formed primarily through plunging and surfing breakers at $h/D = 2.5$. In contrast, at $h/D = 1$, smaller bubbles initially emerge from the breakup of a gas finger. Over time, some of these bubbles grow in size through coalescence cascades. The influence of $ Re \in [50, 150]$ and $ We \in [700, 1100]$ on gas entrainment is quantified in terms of mean bubble size and count. Lastly, we demonstrate how the deformability of the liquid–gas interface drives the hydrodynamic lift force acting on the cylinder. The net downward lift materializes only in the gas entrainment and reduced deformation regimes due to the broken symmetry of the front stagnation point. While our study focuses on two-dimensional simulations, we also provide insights into the three-dimensional gas entrainment mechanism for one of the extreme cases at $h/D = 1$.
Raman fiber lasers, known for their capacity to provide both high-power and precise wavelength emissions, are gaining attraction across a spectrum of applications, including fiber optic communications, sensing, spectroscopy and imaging. However, the scalability of Raman laser power is impeded by the constraints of pump brightness and the deleterious effects of second-order Raman scattering. In this research, we have undertaken a comprehensive experimental and simulation-based investigation into the impact of pump brightness on the output characteristics within an amplifier framework. Our innovative approach integrates high-brightness pumping with multi-mode graded-index fibers. Notably, we have pioneered the introduction of multi-wavelength seed light to facilitate four-wave mixing, thereby effectively mitigating higher-order Raman scattering. This novel strategy has culminated in the achievement of a 4 kW Raman laser output in an all-fiber configuration, representing the highest output power reported so far.
This work reports high-fidelity shock-tube experiments on the convergent Richtmyer–Meshkov (RM) instability at a heavy gas layer. The convergent shock tube is designed based on shock dynamics theory, significantly mitigating interface deceleration and reflected shock. As a result, long-term observation of instability growth up to nonlinear stage, free of interface deceleration and reshock, is achieved. Various types of SF$_6$ layers surrounded by air with controllable thicknesses and shapes, created using a soap film technique, are examined. For thick layers, the evolutions of the outer and inner interfaces are nearly decoupled regardless of the layer shape. The weakly nonlinear model of Wang (Phys. Plasmas,vol. 22, 2015, p. 082702), designed for cylindrical RM instability at a single interface, provides a reasonable prediction of perturbation growth at the inner interface, while slightly underestimating instability growth at the outer interface, as it neglects the effects of rarefaction wave. For thin layers, perturbation growth is fastest at either interface when both interfaces initially possess in-phase perturbations, moderate when only one interface is initially perturbed and slowest when the two interfaces have anti-phase perturbations. This variation in growth rates is due to the fact that the evolution of a thin layer is influenced by both reverberating waves and interface coupling, with each factor being highly sensitive to the layer shape. The original vortex method is extended to address the convergent RM instability by incorporating the influences of unsteady background flow, interface coupling and reverberating waves into the transport of a vortex sheet. This extended vortex method enables accurate prediction of convergent RM instability at a gas layer, covering the full range from early linear to late nonlinear stages.
Turbulent flows over porous substrates are studied via a systematic exploration of the dependence of the flow properties on the substrate parameters, including permeability $K$, grain pitch $L$ and depth $h$. The study uses direct numerical simulations mainly for staggered-cube substrates with $L^+\approx 10$–$50$, $\sqrt {K}/L\approx 0.01$–$0.25$ and depths from $h=O(L)$ to $h\gg L$, ranging from typical impermeable rough surfaces to deep porous substrates. The results indicate that the permeability has significantly greater relevance than the grain size and microscale topology for the properties of the overlying flow, including the mean-flow slip and the shear across the interface, the drag increase relative to smooth-wall flow and the statistics and spectra of the overlying turbulence, whereas the direct effect of grain size is only noticeable near the interface as grain-coherent flow fluctuations. The substrate depth also has a significant effect, with shallower substrates suppressing the effective transpiration at the interface. Based on the direct-simulation results, we propose an empirical ‘equivalent permeability’ $K_{eq}^t$ that incorporates this effect and scales well the overlying turbulence for substrates with different depths, permeabilities, etc. This result suggests that wall normal transpiration driven by pressure fluctuations is the leading contributor to the changes in the drag and the overlying turbulence. Based on this, we propose a conceptual $h^+$–$\sqrt {K^+}$ regime diagram where, for any given substrate topology, turbulence transitions smoothly from that over impermeable rough surfaces with $h=O(L)$ to that over deep porous substrates with $h^+\gtrsim 50$, with the latter limit determined by the typical lengthscale of the overlying pressure fluctuations.
Rogue waves (RWs) can form on the ocean surface due to the well-known quasi-four-wave resonant interaction or superposition principle. The first is known as the nonlinear focusing mechanism and leads to an increased probability of RWs when unidirectionality and narrowband energy of the wave field are satisfied. This work delves into the dynamics of extreme wave focusing in crossing seas, revealing a distinct type of nonlinear RWs, characterised by a decisive longevity compared with those generated by the dispersive focusing (superposition) mechanism. In fact, through fully nonlinear hydrodynamic numerical simulations, we show that the interactions between two crossing unidirectional wave beams can trigger fully localised and robust development of RWs. These coherent structures, characterised by a typical spectral broadening then spreading in the form of dual bimodality and recurrent wave group focusing, not only defy the weakening expectation of quasi-four-wave resonant interaction in directionally spreading wave fields, but also differ from classical focusing mechanisms already mentioned. This has been determined following a rigorous lifespan-based statistical analysis of extreme wave events in our fully nonlinear simulations. Utilising the coupled nonlinear Schrödinger framework, we also show that such intrinsic focusing dynamics can be captured by weakly nonlinear wave evolution equations. This opens new research avenues for further explorations of these complex and intriguing wave phenomena in hydrodynamics as well as other nonlinear and dispersive multi-wave systems.
We provide an assessment of the Infinity Two fusion pilot plant (FPP) baseline plasma physics design. Infinity Two is a four-field period, aspect ratio $A = 10$, quasi-isodynamic stellarator with improved confinement appealing to a max-$J$ approach, elevated plasma density and high magnetic fields ($ \langle B\rangle = 9$ T). Here $J$ denotes the second adiabatic invariant. At the envisioned operating point ($800$ MW deuterium-tritium (DT) fusion), the configuration has robust magnetic surfaces based on magnetohydrodynamic (MHD) equilibrium calculations and is stable to both local and global MHD instabilities. The configuration has excellent confinement properties with small neoclassical transport and low bootstrap current ($|I_{bootstrap}| \sim 2$ kA). Calculations of collisional alpha-particle confinement in a DT FPP scenario show small energy losses to the first wall (${\lt}1.5 \,\%$) and stable energetic particle/Alfvén eigenmodes at high ion density. Low turbulent transport is produced using a combination of density profile control consistent with pellet fueling and reduced stiffness to turbulent transport via three-dimensional shaping. Transport simulations with the T3D-GX-SFINCS code suite with self-consistent turbulent and neoclassical transport predict that the DT fusion power$P_{{fus}}=800$ MW operating point is attainable with high fusion gain ($Q=40$) at volume-averaged electron densities $n_e\approx 2 \times 10^{20}$ m$^{-3}$, below the Sudo density limit. Additional transport calculations show that an ignited ($Q=\infty$) solution is available at slightly higher density ($2.2 \times 10^{20}$ m$^{-3}$) with $P_{{fus}}=1.5$ GW. The magnetic configuration is defined by a magnetic coil set with sufficient room for an island divertor, shielding and blanket solutions with tritium breeding ratios (TBR) above unity. An optimistic estimate for the gas-cooled solid breeder designed helium-cooled pebble bed is TBR $\sim 1.3$. Infinity Two satisfies the physics requirements of a stellarator fusion pilot plant.
AstroSat observed transient neutron star low-mass X-ray binary XTE J1701-462 for a total duration of $\sim$ 135 ks during its 2022 outburst. We report the results of a detailed spectral and timing analysis carried out using this data. The source traced a complete ‘Z’ shaped structure in the hardness intensity diagram (HID). The source exhibited an extended horizontal branch and a short-dipping flaring branch in the HID. The spectra of the source were fitted with different approaches. We find that most suitable spectral model comprises emission from a standard multi-color accretion disk (diskbb in XSPEC) and Comptonised radiation from a hot central corona, described by Comptb model of XSPEC. The observed disk component is cool, having a temperature in the range of $\sim 0.28-0.42$ keV and truncated far ($\sim$ 250 - 1600 km) from the compact object. The Compton corona has an optical depth in the range of $\sim 3.4- 5.1 $ and a temperature in the range of $3.3-4.5$ keV. The disk and corona flux as well as truncation radius vary significantly along the HID. The temperature $kT_{in}$ depends on both luminosity and inner disk radius and hence shows marginal variation as compared to the truncation radius. We discuss possible scenarios to explain the relationship between the spectral evolution and motion of the source along the HID. The timing analysis revealed horizontal branch oscillations (HBOs) in the frequency range $\sim 34-40$ Hz. The frequency and rms strength of HBO vary systematically as the source moves along the horizontal branch (HB). The observed correlation of the HBO properties with the position on the HB is similar to that previously reported in this source using RXTE data during the 2006 outburst of the source. The source also showed normal branch oscillations (NBOs) with frequency $\sim$ 6.7 Hz in the middle and the lower normal branch. The energy-dependent study of the HBO properties suggests that the HBO is stronger in the higher energy band. We also observed very-low frequency noise and band-limited noise (BLN) components in the power density spectra. The break frequency of BLN component was found to be tightly correlated with the HBO frequency. We discuss possible models to explain the origin and nature of the observed features in the PDS.
As new concepts to protect marine structures from ocean waves, we propose the use of a floating elastic annulus. In this paper, two types of annuli are demonstrated. The first is a ‘wave shield’, which creates a calm free surface within an inner domain of the annulus by preventing wave penetration. The second is a ‘cloak’, which not only creates a calm space within the inner domain but also prevents wave scattering outside the annulus. To evaluate the calmness of the inner domain of the annulus, an inlet wave energy factor is newly defined. The wave shield is designed to minimise the inlet wave energy factor to nearly zero. However, the cloak is designed to minimise both the inlet wave energy factor and scattered-wave energy which evaluates the amount of wave scattering at far-field. Each annulus consists of several horizontal concentric annular plates, and the flexural rigidities of the plates are optimised to minimise objective functions at a target frequency. Numerical simulations demonstrate that both the wave shield and the cloak can create calm free surfaces within their inner domains. In addition, the cloak effectively suppresses the outgoing scattering waves and reduces the resultant wave drift force.
We conduct direct numerical simulations (DNS) to investigate the attenuation of turbulence in a periodic cube due to the addition of prolate spheroidal solid particles. Even with a dilute volume fraction of $O(10^{-2})$, particles can drastically attenuate the turbulence. Our DNS show that the turbulent kinetic energy reduces more significantly when the particles’ Stokes number is larger, size is smaller or aspect ratio is larger. We can explain these results based on the formula proposed by Oka and Goto (2022 J. Fluid Mech.949, A45), which relates the turbulence attenuation rate to the energy dissipation rate $\epsilon _p$ around particles. More precisely, under the condition that the volume fraction of particles is fixed, $\epsilon _p$ is larger when the Stokes number and, therefore, the relative velocity between fluid and particles are larger, the particle size is smaller or the aspect ratio is larger. These results also imply that the rotation of the anisotropic particles plays only a limited role in the attenuation of turbulence when the Stokes number of particles is sufficiently large, because the main cause of the attenuation is the relative translational velocity between fluid and particles.
The cosmic 21 cm signal serves as a crucial probe for studying the evolutionary history of the Universe. However, detecting the 21 cm signal poses significant challenges due to its extremely faint nature. To mitigate the interference from the Earth’s radio frequency interference (RFI), the ground and the ionospheric effects, the Discovering the Sky at the Longest Wavelength (DSL) project will deploy a constellation of satellites in lunar orbit, with its high-frequency daughter satellite tasked with detecting the global 21 cm signal from cosmic dawn and reionization era (CD/EoR). We intend to employ the vari-zeroth-order polynomial (VZOP) for foreground fitting and subtracting. We have studied the effect of thermal noise, thermal radiation from the Moon, the lunar reflection, anisotropic frequency-dependent beam, inaccurate antenna beam pattern, and RFI contamination. We discovered that the RFI contamination can significantly affect the fitting process and thus prevent us from detecting the signal. Therefore, experimenting on the far side of the moon is crucial. We also discovered that using VZOP together with DSL, after 1080 orbits around the Moon, which takes about 103 days, we can successfully detect the CD/EoR 21 cm signal.