Vlasov Simulations Research Articles

Auto-resonant stimulated Brillouin backscattering in supersonic flowing plasmas by fully kinetic Vlasov simulations

The auto-resonant behavior of ion acoustic waves (IAWs) driven by stimulated Brillouin backscattering in supersonic flowing plasmas is self-consistently investigated by Vlasov simulations. Vlasov simulations show that the peak amplitude of the auto-resonant growing IAWs in the positive flow gradient is much larger than that in the negative flow gradient, which is contrary to the previous analysis (Wang et al 2018 Plasma Phys. Control. Fusion 60 025016). It is found that the IAW phase velocity remains unchanged in supersonic flowing plasmas, which significantly influences wave-particle interaction by changing the Landau damping and the coefficient of the kinetic nonlinear frequency shift in different position. As a result, the Landau damping of IAWs in the peak region in the negative case is stronger than that in the positive case, which has never been considered before. After considering its effects on particle trapping and, particularly, Landau damping of IAWs, theoretical predictions from three-wave mode equations are consistent with results by Vlasov simulations.

Gyrokinetic microinstability analysis of high-Ti and high-Te isotope plasmas in Large Helical Device

Transport and confinement characteristics, and microinstabilities for high- and high- isotope plasmas in Large Helical Device are explored by using the gyrokinetic Vlasov simulation GKV with hydrogen isotope ions and real-mass kinetic electrons. The experimental data indicate that the thermal diffusivity is reduced in the deuterium-dominated plasmas, where the deviation from the gyro-Bohm scaling in the overall tendency and the strong anomaly of the electron heat transport are identified. Linear gyrokinetic analyses identify that the growth rates of the ion temperature gradient and trapped electron mode (TEM) instabilities in the deuterium plasmas are reduced due to the change in the profile gradients and/or the isotope ion mass, and the radial dependence of the mixing-length diffusivity is qualitatively consistent with the experimental tendency. Also, TEM-like turbulent fluctuations are examined by the using the phase contrast imaging measurement and the linear gyrokinetic calculation for the high- deuterium plasma.

A performance comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensions

The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov–Poisson equation. More specifically, our goal is to compare the performance of the more recently developed semi-Lagrangian discontinuous Galerkin scheme to cubic spline interpolation, which is widely used in Eulerian Vlasov simulation. To that end, we perform simulations for nonlinear Landau damping and a two-stream instability and provide benchmarks for the SeLaLib and SLDG codes, both on a workstation and using MPI on a cluster. In addition, we will present results for the graphic processing unit (GPU) implementation contained in SLDG.We find that the semi-Lagrangian discontinuous Galerkin scheme shows a moderate improvement in run time for nonlinear Landau damping and a substantial improvement for the two-stream instability. It should be emphasized that these results are markedly different from results obtained in the asymptotic regime, which favor spline interpolation. Thus, we conclude that the traditional approach of evaluating numerical methods is misleading, even for short time simulations. In addition, the absence of any global communication in the semi-Lagrangian discontinuous Galerkin method gives it a decisive advantage for scaling to more than 256 cores.

Coherent phase space structures in a 1D electrostatic plasma using particle-in-cell and Vlasov simulations: A comparative study

We present a quantitative comparative study of the formation of coherent phase space structures in one dimension using two widely followed approaches in kinetic simulations of collision-less plasmas, namely, Monte Carlo based Particle-In-Cell (PIC) simulations and phase space grid based Eulerian Vlasov-Poisson simulations. Using a newly developed PIC solver, we demonstrate that, while for linear regimes, there is a ready quantitative agreement between Vlasov-Poisson and PIC solvers, whereas for weakly nonlinear regimes and late time simulations, for comparable field resolutions, Vlasov-Poisson simulation results are found to be relatively noise-free as compared to PIC results with a large number of PIC particles. As an extreme case, we address using high resolution PIC simulations, the formation of giant phase space vortices obtained recently using the Vlasov-Poisson method [P. Trivedi and R. Ganesh, Phys. Plasmas 23, 062112 (2016)] for an infinitesimal amplitude external drive. For identical parameters and numerical resolution, we present a qualitative and quantitative comparison between PIC results of driven giant phase space structures and those of the Vlasov method, for a Maxwellian plasma.

Anti-Langmuir decay instability in Langmuir decay instability cascade

Backward stimulated Raman scattering (BSRS) with Langmuir decay instability (LDI) and anti-Langmuir decay instability (ALDI or anti-LDI) has been researched by Vlasov simulation. The decay productions of anti-LDI in LDI cascade and their evolution with time are demonstrated for the first time. The BSRS reflectivity will be decreased largely through LDI cascade and ALDI in the small wave-number region. Different mechanisms to saturate BSRS in CH (or H) and C plasmas have been demonstrated. The dominant saturation mechanism of BSRS in CH (or H) plasmas is LDI cascade and ALDI. However, in C plasmas, due to very weak Landau damping of ion acoustic waves, LDI cascade will promote stimulated Brillouin scattering (SBS) excitation, then SBS will compete with BSRS and saturate BSRS in the later stage. The proportion of the hot electrons is decreased largely through LDI cascade and ALDI. These results give an effective mechanism to suppress BSRS and hot electron generation in the small wave-number region, which are of important significance in the inertial confinement fusion.

Implementation of a gyrokinetic collision operator with an implicit time integration scheme and its computational performance

We have implemented the Sugama collision operator in the gyrokinetic Vlasov simulation code, GKV, with an implicit time-integration scheme. The new method is versatile and independent of the details of the linearized collision operator, by means of an operator splitting, an implicit time integrator, and an iterative Krylov subspace solver. Numerical tests demonstrate stable computation over the time step size restricted by the collision term. An efficient implementation for parallel computation on distributed memory systems is realized by using the data transpose communication, which makes the iterative solver free from inter-node communications during iteration. Consequently, the present approach achieves enhancement of computational efficiency and reduction of computational time to solution simultaneously, and significantly accelerates the total performance of the application.

General self-similar solution for expansion of non-Maxwellian plasmas

In this work, self-similar expansion of one-dimensional collisionless plasma into a vacuum has been calculated for non-Maxwellian particles. It is known that, during the expansion, the initial Maxwellian electron velocity distribution function (DF) is deformed. In this paper, this deformation is illustrated by the Vlasov simulation of plasma expansion. A part of deformation is associated with the appearance of high energy (super thermal) electrons. Therefore, a more complete and realistic plasma model has to include the effect of the super thermal electrons. It is found that the resulting DF of simulation has good consistency with the generalized Lorentzian (kappa) DF. Then the self-similar calculations were carried out for cold ions while the electrons having Lorentzian DF. Finally, it was found that, by increasing the population of energetic electrons, the expansion takes place faster and the ions are accelerated to higher energies.

Temperature gradient driven heat flux closure in fluid simulations of collisionless reconnection

Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, vol. 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (Phys. Rev. Lett., vol. 64, 1990, 3019). Here, their approach is analysed on the basis of heat flux data from a Vlasov simulation. As a result, we propose a new local closure in which heat flux is driven by temperature gradients. This way, a more realistic approximation of Landau damping in the collisionless regime is achieved. Previous issues are addressed and the agreement with kinetic simulations in different reconnection set-ups is improved significantly. To the authors’ knowledge, the new fluid model is the first to perform well in simulations of the coalescence of large magnetic islands.

Erratum: “Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer” [Phys. Plasmas 24, 102904 (2017)

Erratum: “Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer” [Phys. Plasmas <b>24</b>, 102904 (2017)

Negative Potential Solitary Structures in the Magnetosheath With Large Parallel Width

AbstractWe report multispacecraft observations by the Magnetospheric MultiScale (MMS) mission of large (80–155 λDe parallel to B) electrostatic solitary waves (ESWs). Observations of the same ESWs at different positions and times enable unprecedented accuracy in determining the size, velocity, and evolution of these nonlinear structures. This particular event is a short series of negative potential solitary waves in the magnetosheath. The observed structures differ in amplitude and speed, merging or colliding with one another. A Vlasov simulation supports initial wave growth by a cold feature in the electron distribution function. Such cold electrons are likely the result of mixing between the cold magnetospheric and warm magnetosheath plasma along a reconnection separatrix. ESW speed and perpendicular size are inconsistent with ion phase space holes. Solving Poisson's equation for the measured potential, we find a reduction in electron density rather than an enhancement expected from an electron soliton. These ESWs have an unusual combination of properties on both ion and electron scales, likely supported by a complex electron distribution in the nonlinear state.

Vlasov simulations of electron acceleration by radio frequency heating near the upper hybrid layer

It is shown by using a combination of Vlasov and test particles simulations that the electron distribution function resulting from energization due to Upper Hybrid (UH) plasma turbulence depends critically on the closeness of the pump wave to the double resonance, defined as ω ≈ ωUH ≈ nωce, where n is an integer. For pump frequencies, away from the double resonance, the electron distribution function is very close to Maxwellian, while as the pump frequency approaches the double resonance, it develops a high energy tail. The simulations show turbulence involving coupling between Lower Hybrid (LH) and UH waves, followed by excitation of Electron Bernstein (EB) modes. For the particular case of a pump with frequency between n = 3 and n = 4, the EB modes cover the range from the first to the 5th mode. The simulations show that when the injected wave frequency is between the 3rd and 4th harmonics of the electron cyclotron frequency, bulk electron heating occurs due to the interaction between the electrons and large amplitude EB waves, primarily on the first EB branch leading to an essentially thermal distribution. On the other hand, when the frequency is slightly above the 4th electron cyclotron harmonic, the resonant interaction is predominantly due to the UH branch and leads to a further acceleration of high-velocity electrons and a distribution function with a suprathermal tail of energetic electrons. The results are consistent with ionospheric experiments and relevant to the production of Artificial Ionospheric Plasma Layers.

Two‐Dimensional Vlasov Simulations of Fast Stochastic Electron Heating in Ionospheric Modification Experiments

AbstractIonospheric heating experiments using high‐frequency ordinary (O)‐mode electromagnetic waves have shown the induced formation of magnetic field‐aligned density striations in the ionospheric F region, in association with lower hybrid (LH) and upper hybrid (UH) turbulence. In recent experiments using high‐power transmitters, the creation of new plasma regions and the formation of descending artificial ionospheric layers (DAILs) have been observed. These are attributed to suprathermal electrons ionizing the neutral gas, so that the O‐mode reflection point and associated turbulence is moving to a progressively lower altitude. We present the results of two‐dimensional (2‐D) Vlasov simulations used to study the mode conversion of an O‐mode pump wave to trapped UH waves in a small‐scale density striation of circular cross section. Subsequent multiwave parametric decays lead to UH and LH turbulence and to the excitation of electron Bernstein (EB) waves. Large‐amplitude EB waves result in rapid stochastic electron heating when the wave amplitude exceeds a threshold value. For typical experimental parameters, the electron temperature is observed to rise from 1,500 K to about 8,000 K in a fraction of a millisecond, much faster than Ohmic heating due to collisions which occurs on a timescale of an order of a second. This initial heating could then lead to further acceleration due to Langmuir turbulence near the critical layer. Stochastic electron heating therefore represents an important potential mechanism for the formation of DAILs.

Transition of backward stimulated Raman scattering from absolute to convective instability via density modulation

The effect of a static sinusoidal density modulation on the temporal growth rate of backward stimulated Raman scattering (BSRS) is discussed by kinetic theory and Vlasov simulation. One-dimensional Vlasov simulations show that the temporal growth rate will decrease with the increasing density modulation amplitude ε, which is consistent with the kinetic theory. Moreover, the transition from an absolute instability to a convective instability via the density modulation is also observed from the variation of the temporal growth rate of BSRS. The temporal growth rate in the case of density modulation wave-number ks=0.1kl (kl is wave-number of Langmuir wave) decreases faster with increasing ε than that in the case of ks=0.5kl because of the generation of more modes, which will make Landau damping of Langmuir waves stronger. In addition to the generation of other modes, the decrease of the resonant region where BSRS occurs with the increasing density modulation amplitude ε is also a reason for the reduction of the temporal growth rate.

Non-MHD effects in the nonlinear development of the MHD-scale Rayleigh-Taylor instability

The nonlinear evolution of the Rayleigh-Taylor instability (RTI) at a density shear layer transverse to magnetic field in a collisionless plasma is investigated by means of a fully kinetic Vlasov simulation with two spatial and two velocity dimensions. The primary RTI in the MHD regime develops symmetrically in a coordinate axis parallel to gravity as seen in the previous MHD simulations. The primary RTI in the Hall-MHD regime develops asymmetrically in a coordinate axis parallel to gravity. A compressible flow is formed at the secondary density shear layer by the Hall effect, which generates a strong scalar pressure gradient of ions. A Hall electric field due to the diamagnetic current results in the asymmetric flow at the tip of the finger structure. In the primary RTI with the ion gyro kinetic effect, secondary RTI with a wavelength shorter than the wavelength of the primary RTI is generated at the saturation stage of the primary RTI. A seed perturbation for the secondary RTI is excited by another secondary instability due to the coupling between the electron stress tensor and the Hall electric field. The heat flux term plays an important role in the time development of the total pressure. On the other hand, the contribution of the ion stress tensor is small in both the electric current and the total pressure.

Beam-plasma instability and density holes: Langmuir wave-packet formation and particle acceleration

The role of density perturbations of the background plasma in the development of Langmuir waves generated by beam-plasma instabilities is a very debated issue in space physics. The presence of clumpy electrostatic wave-packets (in particular Langmuir waves), from in situ observations, is indeed puzzling. Several processes have been proposed to explain the formation of waveforms, such as Stochastic Growth Theory and trapping in eigenmodes. Here we explore another mechanism considering the seeding of the beam-plasma instability by density holes. We have performed several 1D-1V Vlasov simulations in the electrostatic limit. We show that in the presence of a density hole, a large amplitude solitary wave-packet of Langmuir waves is formed and that it evolves towards clumpier waveforms. Moreover, the large-amplitude wave-packets generated near the hole can reach saturation and accelerate the electrons of the beam: their velocity distribution is strongly distorted, leading to a multi-peaked structure that generates new unstable modes having phase velocities both larger and smaller than the average speed of the beam. The relationship between the wave amplitude and the characteristics of the density hole is also described, showing how the electron beam may select specific holes to generate enhanced localised Langmuir wave-packets.

Harmonic effects on ion-bulk waves and simulation of stimulated ion-bulk-wave scattering in CH plasmas

Ion-bulk (IBk) wave, a novel branch with a phase velocity close to the ion’s thermal velocity, discovered by Valentini et al (2011 Plasma Phys. Control. Fusion 53 105017), is recently considered as an important electrostatic activity in solar wind, and thus of great interest to space physics and also inertial confinement fusion. The harmonic effects on IBk waves has been researched by Vlasov simulation for the first time. The condition of excitation of the large-amplitude IBk waves is given. The nature of nonlinear IBk waves in the condition of (klor is the wave number at loss-of-resonance point) is undamped Bernstein–Greene–Kruskal-like waves with harmonic superposition. Only when the wave number k of IBk waves satisfies , can a large-amplitude and mono-frequency IBk wave be excited. A novel stimulated scattering from IBk modes called stimulated ion-bulk-wave scattering (SIBS) or stimulated Feng scattering (SFS) has been proposed and also verified by Vlasov–Maxwell code. In CH plasmas, in addition to the stimulated Brillouin scattering from multi ion-acoustic waves, there exists SIBS simultaneously. This research gives an insight into the SIBS in the field of laser plasma interaction.

Effect of density modulation on backward stimulated Raman Scattering in a laser-irradiated plasma

The influence of an arbitrary static sinusoidal density modulation on Raman backscattering is discussed theoretically and numerically. One-dimensional Vlasov simulations show a suppression of convective gain of seed with large modulation amplitude ϵ or small modulation vector ks, which is consistent with the modulation theory, namely, the generation of harmonics. However, this initial suppression is soon replaced by a periodic enhancement of reflectivity in the nonlinear stage due to the different performance of Langmuir wave propagation in density peaks and valleys. Modulation effects are also instantiated in electron acceleration. With large ks, finite orders of harmonics may lead to obvious layers of the phase island structure, and local phase island mixing occurs when the wave amplitude increases. With small ks, electrons could be accelerated by a series of adjacent harmonics from low phase velocity to high phase velocity step by step, which may produce a large number of superthermal electrons even with relativistic kinetic energy.

Vlasov models for kinetic Weibel-type instabilities

The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and relativistic Vlasov–Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multi-stream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model, including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three-dimensional case.

Vlasov simulations of thermal plasma waves with relativistic phase velocity in a Lorentz boosted frame.

For certain classes of relativistic plasma problems, performing numerical calculations in a Lorentz boosted frame can be even more advantageous for gridded momentum-space-time (e.g., Vlasov) problems than has been demonstrated for position space-time problems and result in a potential reduction in the number of calculations needed by a factor ∼γ_{b}^{6}. In this study, the Lorentz boosted frame technique was applied to the problem of warm wave-breaking limits of plasma waves with relativistic phase velocity. The numerical results are consistent with analytic conclusions. By appropriate normalization and for sufficiently warm plasma, the dynamics for the Vlasov equation in different Lorentz frames were found to be independent of γ_{p}.

Secondary instabilities in the collisionless Rayleigh-Taylor instability: Full kinetic simulation

The nonlinear evolution of the Rayleigh-Taylor instability (RTI) at a density shear layer transverse to magnetic field in collisionless plasma is investigated by means of a fully kinetic Vlasov simulation with two spatial and two velocity dimensions. The primary RTI in the MHD regime develops symmetrically in a coordinate axis parallel to gravity as seen in the previous MHD simulations. Small-scale secondary instabilities are generated due to secondary velocity shear layers formed by the nonlinear development of the primary RTI. The secondary instabilities take place asymmetrically in the coordinate axis parallel to gravity. It is suggested that these secondary instabilities correspond to the electron Kelvin-Helmholtz instability generated by the electron velocity shear, whose development depends on the polarity of the inner product between the magnetic field and the vorticity of the velocity shear layer.