Hybrid Vlasov Research Articles

Target surface area effects on hot electron dynamics from high intensity laser–plasma interactions

Reduced surface area targets were studied using an ultra-high intensity femtosecond laser in order to determine the effect of electron sheath field confinement on electron dynamics. X-ray emission due to energetic electrons was imaged using a imaging crystal. Electrons were observed to travel along the surface of wire targets, and were slowed mainly by the induced fields. Targets with reduced surface areas were correlated with increased hot electron densities and proton energies. Hybrid Vlasov–Fokker–Planck simulations demonstrated increased electric sheath field strength in reduced surface area targets.

A kinetic model of plasma turbulence

A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of theproper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropyT⊥/T∥(where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given byT⊥/T∥and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas.

Extended fluid models: Pressure tensor effects and equilibria

We consider the use of “extended fluid models” as a viable alternative to computationally demanding kinetic simulations in order to manage the global large scale evolution of a collisionless plasma while accounting for the main effects that come into play when spatial micro-scales of the order of the ion inertial scale di and of the thermal ion Larmor radius ϱi are formed. We present an extended two-fluid model that retains finite Larmor radius (FLR) corrections to the ion pressure tensor while electron inertia terms and heat fluxes are neglected. Within this model we calculate analytic FLR plasma equilibria in the presence of a shear flow and elucidate the role of the magnetic field asymmetry. Using a Hybrid Vlasov code, we show that these analytic equilibria offer a significant improvement with respect to conventional magnetohydrodynamic shear-flow equilibria when initializing kinetic simulations.

Hybrid Vlasov–Fokker–Planck–Maxwell simulations of fast electron transport and the time dependance of K-shell excitation in a mid-Z metallic target

Using a hybrid Vlasov–Fokker–Planck–Maxwell code coupled to calculations using a modified relativistic binary-encounter Bethe model of ionizing collisions we study the time and space dependence of Kα photon generation by a fast electron beam injected into a solid density copper plasma target. The electron beam is chosen to be representative of that expected to be generated by a picosecond duration, ∼1019 W cm−2 intensity laser. Kα photons are produced as electrons reflux laterally across the target and are slowed and thermalized by collisions with, and Ohmic heating of, the background fluid over a ∼10 ps timescale, which dictates the timescale for Kα emission. The results show reasonable agreement with recent experimental results in terms of both the yield and time dependance. We show how lateral expansion of the electrons can be imaged in the Kα radiation.

Hybrid simulation of stimulated Brillouin scattering in laser fusions

In laser plasmas interactions, the simulation of stimulated Brillouin scattering takes a long time. In order to decrease the simulation time, a hybrid Vlasov code is developed, in which the electrons are treated as Boltzmann fluid. The two-ion beam instability is simulated, and the simulation results are compared with the theoretical results. Stimulated Brillouin scattering is also simulated, the results show the code correctness.

Excitation of nonlinear electrostatic waves with phase velocity close to the ion-thermal speed

Recent hybrid Vlasov–Maxwell simulations predicted the presence of a significant level of electrostatic activity, consisting of ion-acoustic waves and of a new branch of waves (called ion-bulk (IBk) waves), at short spatial scalelengths in the tail of the solar-wind turbulent cascade along the direction of the ambient magnetic field. These waves, driven by particle trapping processes, have phase speed comparable to the ion-thermal speed and acoustic dispersion. In this paper, the hybrid Vlasov–Maxwell code redesigned in the electrostatic configuration is used to reproduce the excitation of the IBk waves. An external driver electric field is applied to the plasma ions in order to create a population of trapped particles. This inhibits Landau damping that would otherwise suppress these low phase speed oscillations. The aim of this work is to show that the IBk waves, like ordinary linear modes, can be excited by general type drivers (even of low amplitude) applied to the plasma. Finally, Vlasov–Poisson simulations, with kinetic ions and Boltzmann electrons, are used to point out the limitations of the quasi-neutrality assumption, on which the hybrid model is based.

Nonlinear evolution of electromagnetic ion cyclotron waves

Hybrid Vlasov–Fourier modeling is used to investigate the nonlinear evolution of electromagnetic ion cyclotron (EMIC) waves driven by proton temperature anisotropy in plasmas with a population of He+ ions and a cold proton background. In the pure proton–electron plasma, most of the free energy is converted into high-amplitude waves and currents. In the nonlinear stage, within a few hundred proton gyroperiods after the saturation, the wave spectrum shifts toward lower wave numbers and frequencies, from ω∼0.6Ωp to below ω∼0.25Ωp. In the presence of even a small population of He+ ions almost all of the free energy is used in He+ heating. The wave activity in the saturated state moves from the linearly unstable upper branch to the linearly stable lower one. In the presence of a background of cold protons, the waves can propagate in the frequency stop-band. Our results demonstrate that linear stability theory cannot be used to estimate the characteristics of the expected saturated wave spectra in the terrestrial magnetosphere. Significantly, our nonlinear simulations produce wave spectra which are in close agreement with the EMIC waves observed in situ by satellites as well as by ground-based magnetometers positioned at the ends of the magnetic field lines.

Hybrid Vlasov simulations for alpha particles heating in the solar wind

AbstractHeating and acceleration of heavy ions in the solar wind and corona represent a long-standing theoretical problem in space physics and are distinct experimental signatures of kinetic processes occurring in collisionless plasmas. To address this problem, we propose the use of a low-noise hybrid-Vlasov code in four dimensional phase space (1D in physical space and 3D in velocity space) configuration. We trigger a turbulent cascade injecting the energy at large wavelengths and analyze the role of kinetic effects along the development of the energy spectra. Following the evolution of both proton and α distribution functions shows that both the ion species significantly depart from the maxwellian equilibrium, with the appearance of beams of accelerated particles in the direction parallel to the background magnetic field.

Numerical study of ion-cyclotron resonant interaction via hybrid-Vlasov simulations

Hybrid Vlasov–Maxwell numerical simulations are used to investigate the collisionless resonant interaction of ions with ion-cyclotron waves in parallel propagation with respect to a background magnetic field. In linear regime, analytical results on wave damping, obtained by integrating the linearized Vlasov equation through the well-known characteristics method, are compared with the numerical results. Then, the ion heating process and the consequent generation of temperature anisotropy in the direction perpendicular to the background magnetic field are investigated numerically in detail. In nonlinear regime, the numerical results show that the distribution of particle velocities is strongly distorted due to the resonant ion-cyclotron interaction with the formation of diffusive plateaus in the longitudinal direction (with respect to the ambient field) and significantly departs from the Maxwellian equilibrium. These results are relevant in many plasma physics environments, such as the solar wind, where the process of ion-cyclotron heating and the generation of temperature anisotropy and non-Maxwellian velocity distributions are routinely recovered in many in situ measurements, or the laboratory plasmas, where the resonant interaction of ions with ion-cyclotron waves is the primary source of auxiliary heating in the confining apparatus.

The kinetic nature of turbulence at short scales in the solar wind

The analysis of the transition from the large-scale fluid regime to the short-scale kinetic range of wavelengths in the development of the turbulent cascade of energy is nowadays subject of fervent discussion in the space plasmas scientific community. We make use of Hybrid Vlasov–Maxwell simulations where the full kinetic dynamics of ions is taken into account, while electrons are treated as a fluid. We investigate the development of turbulence in the solar wind, in 1D–3V phase space configuration and in the frequency range across the ion cyclotron frequency. These simulations allow for the analysis of the role of kinetic effects in the short-scale region of the energy spectra in the direction parallel to the background magnetic field. Our numerical results show the presence of a significant electrostatic activity at small wavelengths, triggered by the resonant interaction of ions with longitudinal waves. Our model does not allow to take into account the evolution of the turbulent spectra in the plane perpendicular to the ambient field, due to limited dimensionality in phase space. On the other hand, this model permits to isolate and study the possibility of transferring the electromagnetic large-scale energy on the small-scale kinetic electrostatic component of the spectrum. Peculiar features observed in the spacecraft data in the solar wind are qualitatively reproduced within the hybrid-Vlasov model, such as the generation of perpendicular temperature anisotropy and accelerated longitudinal beams of ions in the distribution of particle velocities as well as the appearance of a marked peak of electrostatic activity in the short-scale termination of the turbulent spectra.

Electrostatic Short-Scale Termination of Solar-Wind Turbulence

Recent hybrid Vlasov simulations [F. Valentini, Phys. Rev. Lett. 101, 025006 (2008)10.1103/PhysRevLett.101.025006] have shown that the short-scale termination of solar-wind turbulence is characterized by the occurrence of longitudinal electrostatic fluctuations. Beside the ion-acoustic branch, in agreement with solar-wind observations, a novel branch of acoustic-like waves, with phase velocity close to the ion thermal speed, has been recovered in the simulations. In this Letter, we show that these waves turn out to be Bernstein-Greene-Kruskal-like solutions of the hybrid Vlasov-Maxwell equations, driven by kinetic effects of resonant particle trapping. We also discuss the development of the solar-wind turbulent spectra across the ion inertial length and especially stress the fact that turbulence privileges acoustic paths to develop towards short wavelengths.

A Hilbert-Vlasov code for the study of high-frequency plasma beatwave accelerator

High-frequency beatwave simulations relevant to the University of California at Los Angeles (UCLA) experiment with relativistic eulerian hybrid Vlasov code are presented. These Hilbert-Masov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by beatwave experiment for a high ratio of driver frequency to plasma frequency /spl omega//sub pump///spl omega//sub plasma//spl ap/33. The present model allows us to extend detailed modeling to frequency ratios greater than the current practical maximum of 10 or so, for Vlasov or particle-in-cell (PIC) codes, by replacing the Maxwell equations by mode equations for the electromagnetic Vlasov code. Numerical results, including beat frequency chirping (i.e., pump frequency linearly decreasing with time), show that the amplitude limit due to relativistic detuning can be enhanced with accelerated particles up to the ultrarelativistic energies with a high-acceleration gradient of more than 25 GeV/m.

One-dimensional simulations of Langmuir collapse in a radiation-driven plasma

Langmuir collapse in a radiation-driven plasma is simulated in one dimension using both the hybrid Vlasov model and the modified Zakharov model. In the hybrid model, the electrons are described by the Vlasov equation and the ions are described by the fluid equations. Two numerical runs with different parameters are performed: (a) a weakly driven case, and (b) a strongly driven case. The comparisons of the results between the two models for each case are carried out in detail. It is found that the dynamic behavior of the plasma can be changed dramatically by varying the external driving field. The electron temperature increases only ∼10% in the weakly driven case, while it increases ∼200% in the strongly driven case during a single Langmuir collapse. The two models agree with each other during the first collapse after the saturation of modulational instability. Dynamic differences appear after the first collapse, caused by the electron heating in the hybrid model, which is not accounted for in the standard isothermal Zakharov model.