Dissipative Collisions Research Articles

Relaxation of weakly collisional plasma: Continuous spectra, discrete eigenmodes, and the decay of echoes.

The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment. We find that the linear response is a temporal convolution of two types of contribution: a continuum that depends on the continuous velocities of particles (crucial for the plasma echo), and another, consisting of discrete modes that are coherent modes of oscillation of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping), as well as collisional dissipation. The continuum is also damped by collisions but somewhat differently than the discrete modes. Up to a collision time, which is the inverse of the collision frequency ν_{c}, the continuum decay is driven by the diffusion of particle velocities and is cubic exponential, occurring over a timescale ∼ν_{c}^{-1/3}. After a collision time, however, the continuum decay is driven by the collisional damping of particle velocities and diffusion of their positions and occurs exponentially over a timescale ∼ν_{c}. This slow exponential decay causes perturbations to damp the most on scales comparable to the mean free path but very slowly on larger scales. This establishes the local thermal equilibrium, which is the essence of the fluid limit. The long-term decay of the linear response is driven by the discrete modes on scales smaller than the mean free path but, on larger scales, is governed by a combination of the slowly decaying continuum and the least damped discrete mode. This slow exponential decay implies that the echo, which results from the interference of the continuum response to two subsequent pulses, is detectable even on scales comparable to the mean free path, as long as the second pulse is introduced within a few phase-mixing timescales after the first.

First Thomson scattering results from AWAKE’s helicon plasma source

Abstract We present the first results of electron density and temperature measurements obtained from Thomson scattering at the helicon plasma source (HPS) for the AWAKE project. These measurements are compared to simulation results from a 1D power and particle balance model (PPM), confirming that the plasma can be fully sustained by collisional power dissipation. The variations in plasma parameters under different experimental conditions are evaluated in the PPM framework. We discuss current limitations of the model and propose possible improvements. Additionally, we suggest modifications to the existing HPS setup to enhance axial plasma homogeneity.

Unveiling Nonsecular Collisional Dissipation of Molecular Alignment.

We conducted a joint theoretical and experimental study to investigate the collisional dissipation of molecular alignment. By comparing experimental measurements to the quantum simulations, the nonsecular effect in the collision dissipation of molecular alignment was unveiled from the gas-density-dependent decay rates of the molecular alignment revival signals. Different from the conventional perspective that the nonsecular collisional effect rapidly fades within the initial few picoseconds following laser excitation, our simulations of the time-dependent decoherence process demonstrated that this effect can last for tens of picoseconds in the low-pressure regime. This extended timescale allows for the distinct identification of the nonsecular effect from molecular alignment signals. Our findings present the pioneering evidence that nonsecular molecular collisional dissipation can endure over an extended temporal span, challenging established concepts and strengthening our understanding of molecular dynamics within dissipative environments.

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

Study on multi-state of meshing-impacting dynamic characteristics of spur gear systems considering friction under localized tooth breakage

Localized tooth breakage is one of the common failures of spur gears, which affects the smooth and safe operation of spur gear transmission systems. The tooth collision cannot be neglected, and it is especially important to reveal the meshing-impacting dynamic characteristics of the gear system under localized tooth breakage to improve the safe and stable operation of the gear system. Based on the gear meshing principle and the dissipative collision contact force model, the drive-side tooth meshing model and back-side tooth impacting model are established with considering the transient nature of tooth back-side contact. The tooth surface meshing model and tooth back collision model under partial breakage are established. According to the contact state and force environment of the gear pair, the multi-state meshing-impacting behaviour under local breakage is classified, and the discrete meshing-impact dynamics model of an involute spur gear system under local breakage is established to explore the influence of local breakage on the meshing stiffness and load distribution. The mechanism of contact force under partial tooth breakage is revealed, and the influence of load coefficient and meshing frequency on the nonlinear dynamics is studied by defining two Poincaré maps. It is found that local tooth breakage affects the contact force of single-and double-tooth meshes and reduces gear load carrying capacity. Larger loads inhibit back-side impact, and smaller loads induce the coexistence behaviour and back-side impact. Larger or smaller meshing frequency induce back-side impact behaviour. The coexistence of chaotic and periodic motions induces back-side impact behaviour, and localized tooth breakage affects the coexistence phenomenon and aggravates the complexity of the dynamic behaviour. The dynamic model of gear system considering energy dissipation and nonlinear vibration under the presence of local tooth breakage of the pinion is explored, and the conditions of back-side impact are studied. This research provides new methods and ideas for nonlinear dynamic modelling and analysis of faulty gear systems.

Femtosecond Collisional Dissipation of Vibrating D_{2}^{+} in Helium Nanodroplets.

We explored the collision-induced vibrational decoherence of singly ionized D_{2} molecules inside a helium nanodroplet. By using the pump-probe reaction microscopy with few-cycle laser pulses, we captured in real time the collision-induced ultrafast dissipation of vibrational nuclear wave packet dynamics of D_{2}^{+} ion embedded in the droplet. Because of the strong coupling of excited molecular cations with the surrounding solvent, the vibrational coherence of D_{2}^{+} in the droplet interior only lasts for a few vibrational periods and completely collapses within 140fs. The observed ultrafast coherence loss is distinct from that of isolated D_{2}^{+} in the gas phase, where the vibrational coherence persists for a long time with periodic quantum revivals. Our findings underscore the crucial role of ultrafast collisional dissipation in shaping the molecular decoherence and solvation dynamics during solution chemical reactions, particularly when the solute molecules are predominantly in ionic states.

Extended kinetic theory applied to pressure-controlled shear flows of frictionless spheres between rigid, bumpy planes.

We numerically investigate, through discrete element simulations, the steady flow of identical, frictionless spheres sheared between two parallel, bumpy planes in the absence of gravity and under a fixed normal load. We measure the spatial distributions of solid volume fraction, mean velocity, intensity of agitation and stresses, and confirm previous results on the validity of the equation of state and the viscosity predicted by the kinetic theory of inelastic granular gases. We also directly measure the spatial distributions of the diffusivity and the rate of collisional dissipation of the fluctuation kinetic energy, and successfully test the associated constitutive relations of the extended kinetic theory, i.e., a kinetic theory which includes the role of velocity correlations. We then phrase and numerically integrate a system of differential equations governing the flow, with suitably modified boundary conditions. We show a remarkable qualitative and quantitative agreement with the results of the discrete simulations. In particular, we study the effect of (i) the coefficient of collisional restitution, (ii) the imposed load and (iii) the bumpiness of the planes on the profiles of the hydrodynamic fields, the ratio of shear stress-to-pressure and the gap between the bumpy planes. Finally, we predict the critical value of the imposed load above which crystallization occurs, based on the value of the solid volume fraction near the boundaries obtained from the numerical solution of the kinetic theory. This notably reproduces what we observe in the discrete simulations.

Viscous overstability in dense planetary rings – effect of vertical motions and dense packing

ABSTRACT We investigate the linear axisymmetric viscous overstability in dense planetary rings with typical values of the dynamical optical depth τ ≳ 0.5. We develop a granular flow model which accounts for the particulate nature of a planetary ring subjected to dissipative particle collisions. The model captures the dynamical evolution of the disc’s vertical thickness, temperature, and effects related to a finite volume filling factor of the ring fluid. We compute equilibrium states of self-gravitating and non-self-gravitating rings, which compare well with existing results from kinetic models and N-body simulations. Subsequently, we conduct a linear stability analysis of our model. We briefly discuss the different linear eigenmodes of the system and compare with existing literature by applying corresponding limiting approximations. We then focus on the viscous overstability, analysing the effect of temperature variations, radial and vertical self-gravity, and for the first time the effects of vertical motions on the instability. In addition, we perform local N-body simulations incorporating radial and vertical self-gravity. Critical values for the optical depth and the filling factor for the onset of instability resulting from our N-body simulations compare well with our model predictions under the neglect of radial self-gravity. When radial self-gravity is included, agreement with N-body simulations can be achieved by adopting enhanced values of the bulk viscous stress.

The magnetised plasma Richtmyer–Meshkov instability: elastic collisions in an ion–electron multifluid plasma

The influence of an applied magnetic field on the collisional plasma Richtmyer–Meshkov instability (RMI) is investigated through numerical simulation. The instability is studied within the five-moment multifluid plasma model without any simplifying assumptions such as infinite speed of light, negligible electron inertia or quasineutrality. The plasma is composed of ion and electron fluids, and elastic collisions are modelled with the Braginskii transport coefficients. A collisional regime is investigated and the magnetic field is applied in the direction of shock propagation, which is perpendicular to the density interface. The primary instability is influenced by several terms affecting the evolution of circulation, the most significant of which are the baroclinic, magnetic field torque and intraspecies collisional terms. The applied magnetic field results in a reduction of interface perturbation growth, agreeing qualitatively with previous numerical simulations for the case of an ideal multifluid plasma RMI. The only major difference in the present case's instability mitigation by applied magnetic field, relative to the ideal case with applied magnetic field, is that the elastic collisions replace and obstruct the secondary vorticity suppression mechanism through collisional dissipation of vorticity. Additionally the collisions, influenced by the combination of self-generated and the applied magnetic field, introduce anisotropy to the problem. The primary suppression mechanism for the RMI is unchanged relative to the ideal case, i.e. the magnetic field torque resisting baroclinic deposition of vorticity in the ion fluid.

Numerical and Experimental Investigations of Particle Dampers Attached to a Pipeline System

The structure of pipeline systems is complex, and the working environment is harsh. Under the excitation of the engine equipment foundation and pump fluid, it is easy to generate excessive vibration, which seriously affects the safe operation of the equipment. Particle damping achieves structural vibration suppression through the principle of particle collision dissipation. Due to the drawbacks of traditional pipeline vibration reduction methods, this article introduces a particle damping technology for pipeline system vibration suppression and designs particle dampers based on the structural characteristics of pipelines. We analyzed the energy dissipation mechanism of particle damping, revealed the influence of the materials, structure, external excitation, and other parameters of the pipeline particle dampers on the energy dissipation characteristics of the particle damping, established a pipeline vibration reduction test system with particle damping, and verified its effectiveness in pipeline system vibration reduction. This study can provide a technical reference for vibration reduction in pipeline systems.

Drift kinetic theory of neoclassical tearing modes in tokamak plasmas: polarisation current and its effect on magnetic island threshold physics

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

Phase space dynamics of unmagnetized plasmas: Collisionless and collisional regimes

Eulerian electrostatic kinetic simulations of unmagnetized plasmas (kinetic electrons and motionless protons) with high-frequency equilibrium perturbations have been employed to investigate the phase space free energy transfer across spatial and velocity scales, associated with the resonant interaction of electrons with the self-induced electric field. Numerical runs cover a wide range of collisionless and weakly collisional plasma regimes. An analysis technique based on the Fourier–Hermite transform of the particle distribution function allows to point out how kinetic processes trigger the free energy cascade, which is instead inhibited at finer scales when collisions are turned on. Numerical results are presented and discussed for the cases of linear wave Landau damping, nonlinear electron trapping, and bump-on-tail and two-stream instabilities. A more realistic situation of turbulent Langmuir fluctuations is also discussed in detail. Fourier–Hermite transform shows a free energy spread, highly conditioned by collisions, which involves velocity scales more quickly than the spatial scales, even when nonlinear effects are dominant. This results in anisotropic spectra whose slopes are compatible with theoretical expectations. Finally, an exact conservation law has been derived, which describes the time evolution of the free energy of the system, taking into account the collisional dissipation.

Prediction of fluidization behaviors of rough sphere with a TFM-DEM hybrid model

Some industrial processes like biomass combustion and gasification involve multi-component fluidization systems with a clear discrepancy of particle size, which restricts the utilization of some traditional simulation methods. In this work, a TFM-DEM hybrid model is employed to evaluate flow behaviors of binary mixture in a fluidized bed reactor with a great discrepancy of particle size, where the rotational effect of bed material is described by the kinetic theory of rough sphere (KTRS) and the fluctuating energy transfer between discrete particles and continuous solid phase is considered. The model prediction is validated by the experimental result. The results reveal that considering the collisional effect on solid-solid interaction, bed material fluctuating energy is weakened and more energy is transferred to fuel particles. Meanwhile, the ratio of collisional dissipation to total energy consumption with particle roughness is also analyzed.

Dynamics of soliton explosions in a polarization-multiplexed ultrafast fiber laser

Soliton explosions are among the most striking soliton phenomena in nonlinear dissipative systems. In this regime, quasi-stable solitons suffer abrupt structural collapses and then recover to their original state. Here, we report on the first experimental observation of soliton explosions triggered by vector dissipative soliton collisions in a polarization-multiplexed ultrafast fiber laser. The fiber laser simultaneously generates two orthogonally polarized pulse trains with different repetition rates, which enables periodic soliton collisions in the cavity. Based on the dispersive Fourier transform technique, the spectral dynamics of collision-induced soliton explosions are identified in real time. The corresponding time-domain measurements demonstrate opposite temporal shifts in the two output pulse trains. Numerical simulations validate the experimental observations and give more insights into the physical mechanism for soliton explosions. Our findings can shed new light on the dynamics of soliton explosions.

Quantum modeling, beyond secularity, of the collisional dissipation of molecular alignment using the energy-corrected sudden approximation.

We propose a Markovian quantum model for the time dependence of the pressure-induced decoherence of rotational wave packets of gas-phase molecules beyond the secular approximation. It is based on a collisional relaxation matrix constructed using the energy-corrected sudden approximation, which improves the previously proposed infinite order sudden one by taking the molecule rotation during collisions into account. The model is tested by comparisons with time-domain measurements of the pressure-induced decays of molecular-axis alignment features (revivals and echoes) for HCl and CO2 gases, pure and diluted in He. For the Markovian systems HCl-He and CO2-He, the comparisons between computed and measured data demonstrate the robustness of our approach, even when the secular approximation largely breaks down. In contrast, significant differences are obtained in the cases of pure HCl and CO2, for which the model underestimates the decay rate of the alignment at short times. This result is attributed to the non-Markovianity of HCl-HCl and CO2-CO2 interactions and the important contribution of those collisions that are ongoing at the time when the system is excited by the aligning laser pulse.

Characterization of the breakup channel in the asymmetric systems Ca40,48+C12 at 25 and 40 MeV/nucleon

An analysis of the asymmetric reactions $^{40,48}$Ca+$^{12}$C at 25 and 40 MeV/nucleon is presented. Data have been collected with six modules of the FAZIA array. The analysis is focused on the breakup channel of sources produced in dissipative collisions, partially corresponding to incomplete fusion processes. The study has been performed both on detected fragments and on some resonances reconstructed by means of particle-fragment correlations, with a focus on the evolution of the breakup channel with the beam energy and the neutron content of the system, looking in particular at the relative velocity between the breakup fragments. Results show that also Carbon fragments reconstructed by means of particle correlations can be in large part interpreted as the light partner of a scission.

Micromechanical analysis of granular dynamics and energy dissipation during hopper discharging of polydisperse particles

This paper presents a numerical study on the hopper discharging of widely polydisperse particles. It focuses on the effects of particle size distributions (PSDs) in the form of the log-normal distribution of the number (nPSD) and volume (vPSD) of particle constituents. In doing so, a recent GPU-DEM model suitable for large-scale simulations is adopted. The numerical results show that the mass discharge rate reduces with increasing nPSD spread but becomes larger at a wider vPSD spread. The discharging process is analyzed in terms of packing density, coordination number, velocities, and force network. It is observed that the packing density equally increases for both PSDs as the spread grows, whereas the coordination of the mixture reduces. Thus, a negative correlation between coordination and packing density is consistently observed. With increasing nPSD spread, the particle vertical velocities drop significantly, which are nearly unchanged for wider vPSDs. The particle-scale analysis is also extended to energy dissipation. The analysis reveals that the effect of PSD on the mass discharge rate is mainly attributed to the relative importance of different energy dissipation mechanisms. Irrespective of PSD type, the friction energy dissipation decreases with widening PSD, which becomes more pronounced near the outlet. In contrast, as the spread becomes wider, the collision dissipation near the outlet turns more important for nPSD but decreases for vPSD. These results account for different trends of discharge rates with respect to PSD type.

Plasma heating by electron cyclotron wave and the temperature effects on lower hybrid current drive on EAST

This paper presents the progress in the long—pulse operation of the electron cyclotron (EC) system and the achievements in high—electron temperature plasmas by the combined EC and lower hybrid (LH) waves heating since the EC system was built in 2015. An electron temperature of up to 12 keV with a duration over 100 s was realized by the simultaneous heating of EC and LH waves at the line-averaged density ∼ 1.8 × 1019 m−3. The plasma heating effect strongly depends on the location of EC power deposition. H-mode plasmas with solely EC wave auxiliary heating have been obtained on EAST for the first time. These H-mode discharges show an enhanced confinement factor H 98(y,2) around 1.0, which is higher than the previous H-mode using LH power alone (Xu et al 2011 Nucl. Fusion 51 072001). The total heating power is very close to the threshold value for L–H transition according to the international tokamak scaling. In addition to the temperature effects inside the separatrix, higher electron temperature produced by EC wave is found to reduce the LH power loss in the scrape-off layer due to collisional absorption, which is beneficial to further increase the LH current drive efficiency. Ray-tracing/Fokker–Planck modeling results indicate that higher electron temperature can shorten the LH wave propagation on EAST in a multiple-pass regime, thus decreasing the collisional dissipation.

Non-Markovian collisional dynamics probed with laser-aligned molecules

The Markov, as well as the secular, approximations are key assumptions that have been widely used to model decoherence in a large variety of open quantum systems, but, as far as intermolecular collisions are considered, very little has been done in the time domain. In order to probe the limits of both approximations, we here study the influence of pressure on the alignment revivals (echoes) created in properly chosen gas mixtures (HCl and ${\mathrm{CO}}_{2}$, pure and diluted in He) by one (two) intense and short laser pulse(s). Experiments and direct predictions using molecular-dynamics simulations consistently demonstrate, through analyses at very short times $(<15 \mathrm{ps})$ after the laser kick(s), the breakdown of these approximations in some of the selected systems. We show that the nonadiabatic laser-induced molecular alignment technique and model used in this paper directly provide detailed information on the physical mechanisms involved in the collisional dissipation. Besides this ``fundamental'' interest, our findings also have potential practical applications for radiative heat transfer in planetary atmospheres and climate studies. Indeed, short time delays in the dipole autocorrelation function monitoring the light absorption spectrum correspond to large detunings from the optical resonances in the frequency domain, thus influencing the atmospheric transparency windows. Furthermore, the fact that the approach tested here for linear rotors can potentially be applied to almost any gas mixture (including, for instance, nonlinear and/or reacting molecules) further strengthens and broadens the perspectives that it opens.

Experimental validation of impact energy scattering as concept for mitigating resonant vibrations.

The Vibro-Impact Nonlinear Energy Sink (or impact damper) is well-known for its ability to engage into transient resonance captures with arbitrary frequencies and thus has inherent broad-band effectiveness. Its working principle relies on (recurrent) energy localization and local dissipation within the contact region. Dissipative (inelastic) collisions are inevitably associated with damage and challenging to predict. Recently, it has been shown theoretically that the device is effective even for purely elastic collisions when the energy is (almost) irreversibly transferred from the critical low-frequency modes to high frequencies.In that case, the device is more properly termed Impact Energy Scatterer (IES). In the present work, we experimentally validate, for the first time, the working principle of the IES. To this end, we design a test rig consisting of a cantilevered beam, hosting a spherical impactor inside a cavity at its tip. The resonant vibrations of the lowest-frequency bending mode are reduced by a factor of 10-20. Given that the IES weighs less than 1% of the host structure, this corresponds to a paramount vibration mitigation capability. We achieve excellent agreement between the measurements and the numerical predictions obtained by modeling the impacts as perfectly elastic. We also demonstrate that the dissipation in the contact region is negligible, while a substantial amount of energy is scattered to higher frequencies, validating the theoretically proposed working principle.