Collisional Damping Research Articles

Collisional Growth within the Solar System’s Primordial Planetesimal Disk and the Timing of the Giant Planet Instability

Abstract The large-scale structure of the solar system has been shaped by a transient dynamical instability that may have been triggered by the interaction of the giants planets with a massive primordial disk of icy debris. In this work, we investigate the conditions under which this primordial disk could have coalesced into planets using analytic and numerical calculations. In particular, we perform numerical simulations of the solar system’s early dynamical evolution that account for the viscous stirring and collisional damping within the disk. We demonstrate that if collisional damping would have been sufficient to maintain a temperate velocity dispersion, Earth-mass trans-Neptunian planets could have emerged within a timescale of 10 Myr. Therefore, our results favor a scenario wherein the dynamical instability of the outer solar system began immediately upon the dissipation of the gaseous nebula to avoid the overproduction of Earth-mass planets in the outer solar system.

Damped dust‐ion‐acoustic solitons in collisional magnetized nonthermal plasmas

AbstractA multispecies magnetized collisional nonthermal plasma system, containing inertial ion species, noninertial electron species following nonthermal ‐distribution, and immobile dust particles, is considered to examine the characteristics of the dissipative dust‐ion‐acoustic soliton modes, theoretically and parametrically. The electrostatic solitary modes are found to be associated with the low‐frequency dissipative dust‐ion‐acoustic solitary waves (DIASWs). The ion‐neutral collision is taken into account, and the influence of ion‐neutral collisional effects on the dynamics of dissipative DIASWs is investigated. It is reported that most of the plasma medium in space and laboratory are far from thermal equilibrium, and the particles in such plasma system are well fitted via the ‐nonthermal distribution than via the thermal Maxwellian distribution. The reductive perturbation approach is adopted to derive the damped KdV (dKdV) equation, and the solitary wave solution of the dKdV equation is derived via the tangent hyperbolic method to analyse the basic features (amplitude, width, speed, time evolution, etc.) of dissipative DIASWs. The propagation nature and also the basic features of dissipative DIASWs are seen to influence significantly due to the variation of the plasma configuration parameters and also due to the variation of the supethermality index in the considered plasma system. The implication of the results of this study could be useful for better understanding the electrostatic localized disturbances, in the ion length and time scale, in space and experimental dusty plasmas, where the presence of excess energetic electrons and ion‐neutral collisional damping are accountable.

Dynamical Models of Chemical Exchange in Nuclear Magnetic Resonance Spectroscopy.

Chemical exchange line-broadening is an important phenomenon in nuclear magnetic resonance (NMR) spectroscopy, in which a nuclear spin experiences more than one magnetic environment as a result of chemical or conformational changes of a molecule. The dynamic process of chemical exchange strongly affects the sensitivity and resolution of NMR experiments, and increasingly provides a powerful probe of the inter-conversion between chemical and conformational states of proteins, nucleic acids, and other biological macromolecules. A simple and often used theoretical description of chemical exchange in NMR spectroscopy is based on an idealized two-state jump model (the random-phase or telegraph signal). However, chemical exchange can also be represented as a barrier-crossing event that can be modeled using chemical reaction rate theory. The time scale of crossing is determined by the barrier height, the temperature, and the dissipation modeled as collisional or frictional damping. This tutorial explores the connection between the NMR theory of chemical exchange line-broadening and strong-collision models for chemical kinetics in statistical mechanics. Theoretical modeling and numerical simulation are used to map the rate of barrier-crossing dynamics of a particle on a potential energy surface to the chemical exchange relaxation rate constant. By developing explicit models for the exchange dynamics, the tutorial aims to elucidate the underlying dynamical processes that give rise to the rich phenomenology of chemical exchange observed in NMR spectroscopy. Software for generating and analyzing the numerical simulations is provided in the form of Python and Fortran source codes.

Small-scale turbulent dynamo in astrophysical environments: nonlinear dynamo and dynamo in a partially ionized plasma

Small-scale turbulent dynamo is responsible for the amplification of magnetic fields on scales smaller than the driving scale of turbulence in diverse astrophysical media. Most earlier dynamo theories concern the kinematic regime and small-scale magnetic field amplification. Here we review our recent progress in developing the theories for the nonlinear dynamo and the dynamo regime in a partially ionized plasma. The importance of reconnection diffusion of magnetic fields is identified for both the nonlinear dynamo and magnetic field amplification during gravitational contraction. For the dynamo in a partially ionized plasma, the coupling state between neutrals and ions and the ion-neutral collisional damping can significantly affect the dynamo behavior and the resulting magnetic field structure. We present both our analytical predictions and numerical tests with a two-fluid dynamo simulation on the dynamo features in this regime. In addition, to illustrate the astrophysical implications, we discuss several examples for the applications of the dynamo theory to studying magnetic field evolution in both preshock and postshock regions of supernova remnants, in weakly magnetized molecular clouds, during the (primordial) star formation, and during the first galaxy formation.

A Pluto–Charon Concerto. II. Formation of a Circumbinary Disk of Debris after the Giant Impact

Abstract Using a suite of numerical calculations, we consider the long-term evolution of circumbinary debris from the Pluto–Charon giant impact. Initially, these solids have large eccentricity and pericenters near Charon’s orbit. On timescales of 100–1000 yr, dynamical interactions with Pluto and Charon lead to the ejection of most solids from the system. As the dynamics moves particles away from the barycenter, collisional damping reduces the orbital eccentricity of many particles. These solids populate a circumbinary disk in the Pluto–Charon orbital plane; a large fraction of this material lies within a “satellite zone” that encompasses the orbits of Styx, Nix, Kerberos, and Hydra. Compared to the narrow rings generated from the debris of a collision between a trans-Neptunian object and Charon, disks produced after the giant impact are much more extended and may be a less promising option for producing small circumbinary satellites.

Collisional damping of spherical ice particles

This paper presents experimental values for the coefficient of restitution (en) for millimeter-sized ice particles colliding with massive walls at different temperatures. Three different wall materials are tested: hardened glass, ice and Acrylonitrile butadiene styrene (ABS) polymer. The results show a high sensitivity to impact velocity Vi, where en decreases rapidly with increasing Vi. The results also show a decrease in en with increasing temperature T. A novel model that predicts en based on the assumption of collisional melting and viscous damping caused by an increased premelted liquid-layer, is proposed. The model predicts both the velocity and the temperature trends seen in the experiments. The difference obtained in experiments between wall materials is also captured by the new model. A generalized regime map for ice particle collisions is proposed to combine the new model with previous work.

Ring dynamics around an oblate body with an inclined satellite: the case of Haumea

Context. The recent discovery of rings and massive satellites around minor bodies and dwarf planets suggests that they may often coexist, as for example around Haumea. Aims. A ring perturbed by an oblate central body and by an inclined satellite may disperse on a short timescale. The conditions under which a ring may survive are explored both analytically and numerically. Methods. The trajectories of ring particles are integrated under the influence of the gravitational field of a triaxial ellipsoid and (a) massive satellite(s), including the effects of collisions. Results. A ring initially formed in the equatorial plane of the central body will be disrupted if the satellite has an inclination in the Kozai–Lidov regime (39.2° < i < 144.8). For lower inclinations, the ring may relax to the satellite orbital plane thanks to an intense collisional damping. On the other hand, a significant J2 term easily suppresses the perturbations of an inclined satellite within a critical semi-major axis, even in the case of Kozai–Lidov cycles. However, if the ring is initially inclined with respect to the equatorial plane, the same J2 perturbations are not a protective factor but instead disrupt the ring on a short timescale. The ring found around Haumea is stable despite the rise in the impact velocities that is due to the asymmetric shape of the body and the presence of a 3:1 resonance with the rotation of the central body. Conclusions. A ring close to an oblate central body should be searched for in the proximity of the equatorial plane, where the J2 perturbations protect it against the perturbations of an external inclined satellites. In an inclined configuration, the J2 term is itself disruptive.

Spatially dependent modeling and simulation of runaway electron mitigation in DIII-D

New simulations with the Kinetic Orbit Runaway electron (RE) Code KORC show RE deconfinement losses to the wall during plasma scrape off are the primary current dissipation mechanism in DIII-D experiments with high-Z impurity injection, and not collisional slowing down. The majority of simulations also exhibit an increase in the RE beam energy due to acceleration by the induced toroidal electric field, even while the RE beam current is decreasing. In this study, KORC integrates RE orbits using the relativistic guiding center equations of motion, and incorporates time-sequenced, experimental reconstructions of the magnetic and electric fields and line integrated electron density to construct spatiotemporal models of electron and partially-ionized impurity transport in the companion plasma. Comparisons of experimental current evolution and KORC results demonstrate the importance of including Coulomb collisions with partially-ionized impurity physics, initial RE energy, pitch angle, and spatial distributions, and spatiotemporal electron and partially-ionized impurity transport. This research provides an initial quantification of the efficacy of RE mitigation via injected impurities, and identification of the critical role played by loss of confinement due to plasma scrape off on the inner wall as compared to the relatively slow collisional damping.

Landau and collisional damping induced power deposition for the m = 0 mode of helicon and Trivelpiece–Gould waves in high density helicon plasmas

By considering the thermal and collisional effects in the analysis of power deposition properties of the helicon and Trivelpiece–Gould (TG) waves in radially uniform and high density (1 × 1013 cm−3) helicon plasmas, theoretical calculations indicate that both the electron temperature and the applied magnetic field have great effects on the wave power deposition. Detailed investigations show that for a typical helicon plasma electron temperature range, 3 eV–5 eV, power deposition due to the TG wave has a dominant role compared to that of the helicon wave for moderate to large (B0 ≥ 100 G) applied magnetic fields. Specifically, collisional damping induced TG wave power deposition dominates for the most of the electron temperature range.

Stimulated effect of SMBI on low-to-high confinement transition of tokamak plasmas

The impact of supersonic molecular beam injection (SMBI) fuelling on the plasma turbulence and shear flows, which form a self-consistent state, has been studied in the HL-2A tokamak. The SMBI flattens the shear layer by the collisional flow damping and increases the turbulence intensity. It is found that the SMBI can enhance the non-linear regulation dynamics and acts as an external tool for turbulence quench via stimulating two dynamic processes. The SMBI-stimulated non-linear interactions facilitate the L-H transition at the marginal heating power for accessing the H-mode. The effective reduction of the H-mode power threshold by SMBI is demonstrated. The result suggests that the SMBI could be a general tool for realization of controllable L-H transition via reducing the H-mode power threshold in future devices.

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

We present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker–Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In particular, we focus on an operator often known as the ‘Lenard–Bernstein’ or ‘Dougherty’ operator. Several novel algorithmic innovations, based on the concept of weak equality, are reported. These weak equalities are used to define weak operators that compute primitive moments, and are also used to determine a reconstruction procedure that allows an efficient and accurate discretization of the diffusion term. We show that when two integrations by parts are used to construct the discrete weak form, and finite velocity-space extents are accounted for, a scheme that conserves density, momentum and energy exactly is obtained. One novel feature is that the requirements of momentum and energy conservation lead to unique formulas to compute primitive moments. Careful definition of discretized moments also ensure that energy is conserved in the piecewise linear case, even though the kinetic-energy term, $v^{2}$ is not included in the basis set used in the discretization. A series of benchmark problems is presented and shows that the scheme conserves momentum and energy to machine precision. Empirical evidence also indicates that entropy is a non-decreasing function. The collision terms are combined with the Vlasov equation to study collisional Landau damping and plasma heating via magnetic pumping.

Equilibrium radiation in a plasma medium with spatial and frequency dispersion

Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation differs from that of Planck equilibrium radiation. Using the quantum electrodynamic approach, the general relation for the spectral energy density of equilibrium radiation in a system of charged particles is found. The obtained result takes into account the influence of plasma on equilibrium radiation through the explicit transverse dielectric permittivity which includes spatial and frequency dispersion, as well as the finite collision damping. For the limiting case of infinitesimal damping the result is identical with the known expression.

Millstone Hill ISR Measurements of Small Aspect Angle Spectra

AbstractThe Millstone Hill incoherent scatter (IS) radar is used to measure spectra close to perpendicular to the Earth's magnetic field, and the data are fit to three different forward models to estimate ionospheric temperatures. IS spectra measured close to perpendicular to the magnetic field are heavily influenced by Coulomb collisions, and the temperature estimates are sensitive to the collision operator used in the forward model. The standard theoretical model for IS radar spectra treats Coulomb collisions as a velocity independent Brownian motion process. This gives estimates of Te/Ti < 1 when fitting the measured spectra for aspect angles up to 3.6°, which is a physically unrealistic result. The numerical forward model from Milla and Kudeki (2011, https://doi.org/10.1109/TGRS.2010.2057253) incorporates single‐particle simulations of velocity‐dependent Coulomb collisions into a linear framework, and when applied to the Millstone data, it predicts the same Te/Ti ratios as the Brownian theory. The new approach is a nonlinear particle‐in‐cell (PIC) code that includes velocity‐dependent Coulomb collisions which produce significantly more collisional and nonlinear Landau damping of the measured ion‐acoustic wave than the other forward models. When applied to the radar data, the increased damping in the PIC simulations will result in more physically realistic estimates of Te/Ti. This new approach has the greatest impact for the largest measured ionospheric densities and the lowest radar frequencies. The new approach should enable IS radars to obtain accurate measurements of plasma temperatures at times and locations where they currently cannot.

Discrete unified gas kinetic scheme for electrostatic plasma and its comparison with the particle-in-cell method.

In this paper, we present a finite-volume direct kinetic method, the so-called discrete unified gas kinetic scheme (DUGKS), for electrostatic plasma. One key feature of this method is the semi-implicit unsplitting treatment of particle transport and collision, and thus the time step in current DUGKS is not limited by the particle collision time. In addition, a fourth-order compact MUSCL scheme with a positivity preserving limiter is implemented in the interface reconstruction, which enables present DUGKS to preserve the favorable conservative property and positivity of distribution function. Combined with this MUSCL method, the semi-Lagrangian scheme is used for the particle transport in velocity space to remove Courant-Friedricks-Lewy restriction induced by the large electric force. As a result, the proposed DUGKS becomes an efficient and stable multiscale scheme. Several numerical experiments, including plasma sheath, linear Landau damping, collisional nonlinear Landau damping, and plasma ion acceleration, are performed to validate current DUGKS. A comparative study of current DUGKS with a general particle in cell (PIC) method which could handle particle collision in a conservative way is also presented. Theory and numerical experiments demonstrate that DUGKS is preferred for plasma flows involving small electrostatic perturbation and high collision regimes, while the PIC method is desired for the field- dominated plasma flows involving a wide range of velocities.

Simulating Damped Ion Acoustic Solitary Waves from Orbital Debris

Nontrackable orbital debris has become a great risk to Earth-orbiting spacecraft. Subcentimeter debris is currently undetectable using ground-based radar and optical methods. Recent analytical, computational, and experimental work has shown that plasma density solitary waves, or solitons, will be produced by orbital debris due to their electrical charge, and propagate along the debris velocity vector. The amplitude and velocity of solitons that may be produced by millimeter–centimeter-scale orbital debris, as well as the orbital altitudes, latitudes, and velocities where solitons can be produced as a function of debris size, have been previously described. The Chan–Kerkhoven pseudospectral method is used now to apply the damped forced Korteweg–de Vries equation, calculate the damping rate of the solitons, and estimate the resulting soliton propagation distance. It is demonstrated that Landau damping dominates over collisional damping for these solitons. Pinned solitons, which travel with the debris, do not experience significant damping due to the presence of the persistent debris force at the soliton location, and will continue to propagate until the debris enters a region where pinned solitons cannot be created. The median propagation distance for precursor solitons, which advance ahead of the debris, is 10 km for 0.5-mm-radius debris and 6 km for 0.5-cm-radius debris. With the current absence of a dedicated, calibrated, on-orbit debris detection sensor, plasma soliton detection would be the first collision-free method of mapping the small debris population. It is necessary to understand the damping of solitons in order to assess the feasibility of on-orbit debris detection.

Lax pair, conservation laws, Darboux transformation, breathers and rogue waves for the coupled nonautonomous nonlinear Schrödinger system in an inhomogeneous plasma

Abstract Plasmas are believed to be possibly “the most abundant form of ordinary matter in the Universe”. In this paper, a coupled nonautonomous nonlinear Schrodinger system is investigated, which describes the propagation of two envelope solitons in a weakly inhomogeneous plasma with the t-dependent linear and parabolic density profiles and nonconstant collisional damping. Lax pair with the nonisospectral parameter and infinitely-many conservation laws are derived. Based on the Lax pair, the Nth-step Darboux transformation is constructed. Utilizing the Nth-step Darboux transformation, we obtain the breather and rogue wave solutions, and find that the amplitude of the nonzero background is nonconstant and dependent on the inhomogeneous coefficients in the system under investigation. Characteristics of the breathers and rogue waves are discussed, and effects of the inhomogeneous coefficients on the breathers and rogue waves are analyzed. Breathers and rogue waves with the dark or bright soliton together are also constructed and their characteristics are discussed. We find that the dark and bright solitons can coexist and generate the breather-like waves.

Effects of electron temperature on energy deposition properties of electromagnetic modes propagating in helicon plasma

Understanding the power deposition characteristic of high density helicon wave plasma source is critical for further investigating into the discharge mechanism of helicon wave discharge. Based on the warm plasma dielectric tensor model which contains both the particle thermal effect and temperature anisotropy and using the insulting boundary condition, the eigenmode dispersion relation of helicon wave and Trivelpiece-Gould (TG) wave propagating in radially uniform plasma column are numerically obtained. Then based on the eigenmode dispersion relation and exact field distribution in the plasma column, the mode coupling properties between the helicon wave and TG wave, the parametric dependence of the cyclotron damping properties of the electron cyclotron wave (TG wave) and power deposition properties of the <i>m</i> = –1, 0, +1 modes under moderate plasma density and low magnetic fields conditions are theoretically investigated in typical helicon plasma parameter range. The detailed investigations are shown below. Under typical helicon plasma parameter conditions, i.e. wave frequency <i>ω</i>/2π = 13.56 MHz and the ion temperature is one-tenth of the electron temperature, there exist a critical magnetic field value <i>B</i><sub>0,c</sub> and a critical electron temperature value <i>T</i><sub>e,c</sub> for which under the conditions of <i>B</i><sub>0</sub> < <i>B</i><sub>0,c</sub> the helicon wave becomes an evanescent wave and the TG wave becomes an evanescent wave when <i>T</i><sub>e</sub> < <i>T</i><sub>e,c</sub>. The cyclotron damping of the TG wave dramatically increases as the wave frequency approaches to the electron cyclotron frequency. The TG wave becomes a growth wave when the ratio of perpendicular electron temperature to parallel electron temperature is above a certain value. For the high magnetic field, i.e. <i>ω</i>/<i>ω</i><sub>ce</sub> = 0.1, most of the power deposition is deposited in the central core region, while for the low magnetic field, i.e. <i>ω</i>/<i>ω</i><sub>ce</sub> = 0.9, the power is deposited mainly in the outer region of plasma column. For typical helicon plasma electron temperature range, <i>T</i><sub>e </sub>∈ (3 eV, 5 eV), the energy depositions induced by the collisional damping and Landau damping of the TG wave are dominant for different electron temperature ranges, which implies that different damping mechanisms have different heating intensities for electrons. Under current parameter condition, compared with the <i>m</i> = +1 mode, the <i>m</i> = –1 and <i>m</i> = 0 mode of the TG wave play major role in the power deposition process, although the cyclotron damping of the TG wave dominates the power deposition in this typical electron temperature range. All these conclusions provide some useful clues for us to better understand the high ionization mechanism of helicon wave discharge.

On the Theory of the Mandelstam–Brillouin Scattering in a Plasma Layer

The evolution of a perturbation from a local source upon the Mandelstam–Brillouin scattering in a plasma layer of a finite thickness and infinite length is examined analytically. It is shown that, in the course of time, the perturbation can either leave the scattering region through one of the two layer boundaries or propagate along the layer with a velocity that is lower than the velocity of propagation of the sound wave and with the amplitude that either exponentially increases or decreases. In the particular case of strictly backward scattering (the scattering angle is π), this propagation velocity is zero. The instability threshold fields and instability increments are calculated taking into account both convective losses and collisional damping of waves. It is shown that the instability threshold for scattering at an arbitrary angle can be lower than that for strictly backward scattering, and, if the intensity threshold of the pump wave is exceeded little, the scattering increment at an angle can also be higher than the increment for backward scattering. If the threshold is exceeded greatly, so that convective losses can be neglected, the greatest increment is observed for backward scattering.

Nonlinear diffusion of cosmic rays escaping from supernova remnants: Cold partially neutral atomic and molecular phases

Aims. We aim to elucidate cosmic ray (CR) propagation in the weakly ionized environments of supernova remnants (SNRs) basing our analysis on the cosmic ray cloud (CRC) model. Methods. We solved two transport equations simultaneously: one for the CR pressure and one for the Alfvén wave energy density where CRs are initially confined in the SNR shock. Cosmic rays trigger a streaming instability and produce slab-type resonant Alfvén modes. The self-generated turbulence is damped by ion-neutral collisions and by noncorrelated interaction with Alfvén modes generated at large scales. Results. We show that CRs leaking in cold dense phases such as those found in cold neutral medium (CNM) and diffuse molecular medium (DiM) can still be confined over distances of a few tens of parsecs from the CRC center for a few thousand years. At 10 TeV, CR diffusion can be suppressed by two or three orders of magnitude. This effect results from a reduced ion-neutral collision damping in the decoupled regime. We calculate the grammage of CRs in these environments. We find that in both single and multi-phase setups at 10 GeV, CNM and DiM media can produce grammage in the range 10–20 g cm−2 in the CNM and DiM phases. At 10 TeV, because of nonlinear propagation the grammage increases to values in the range 0.5–20 g cm−2 in these two phases. We also present preliminary calculations in inhomogeneous interstellar medium combining two or three different phases where we obtain the same trends.

Bremsstrahlung emission and collisional damping rate for Langmuir waves

The emission of electrostatic Langmuir waves by collisional process, termed electrostatic bremsstrahlung emission, and the collisional damping of Langmuir waves, which can be considered as the inverse electrostatic bremsstrahlung process, are rigorously discussed. Some inaccuracies in the previous formalisms are also corrected. It is shown that the improved formulae in the case of Maxwellian particle distributions are given in forms where they satisfy Kirchhoff’s law in the balanced form.