The paper develops a theoretical relationship between the polytropic index and the temperature anisotropy that may characterize space plasmas. The derivation is based on the correlation among the kinetic energies of particles with velocities described by anisotropic kappa distributions. The correlation coefficient depends on the effective dimensionality of the velocity distribution function, having its shape determined by the temperature anisotropies caused by the ambient magnetic field; on the other hand, the effective dimensionality is directly dependent on the polytropic index. This analysis leads to the connection between the correlation coefficient, effective dimensionality of velocity space, and the polytropic index, with the ratio of temperature anisotropy. Moreover, a data and statistical analysis is performed to test the application of the theoretically developed model, in the solar wind proton plasma near 1 AU. The derived theoretical relationship is in good agreement with observations, showing that the lowest and classical value of the adiabatic polytropic index occurs in the isotropic case, while higher indices characterize anisotropic plasmas. Finally, possible extensions of the theory considering (i) non-adiabatic polytropic behavior, and (ii) more general distributions, are further discussed.
We combine different measurements of the polytropic index of the proton plasma in the heliosphere: i) near-adiabatic index in the inner heliosphere ~1AU, ii) subadiabatic indices in the outer heliosphere ~20-40AU, and iii) near-zero indices in the inner heliosheath. These observations are unified by a single theoretical model of the polytropic index throughout its radial extent in the heliosphere; the corresponding fitting reveals the decreasing trend of the polytropic index with increasing heliocentric distance R. We anticipate that with increasing R, (i) the Debye length and mean-free-path d…
A polytropic process describes the transition of a fluid from one state to another through a specific relationship between the fluid density and temperature. The value of the polytropic index that governs this relationship determines the heat transfer and the effective degrees of freedom during the process. In this study, we analyze solar wind proton plasma measurements, obtained by the Faraday cup instrument on-board Parker Solar Probe. We examine the large-scale variations of the proton plasma density and temperature within the inner heliosphere explored by the spacecraft. We also address a …
Interplanetary Coronal Mass Ejections (ICMEs) and High Speed Streams (HSSs) are noteworthy drivers of disturbance of interplanetary space. Interaction between them can cause several phenomena, such as; generation of waves, enhanced geo-effectiveness, particle acceleration, etc. However, how does thermodynamic properties vary during the ICME-HSS interaction remain an open problem. In this study, we investigated the polytropic behavior of plasma during an ICME-HSS interaction observed by STEREO and Wind spacecraft. We find that the ICME observed by the STEREO-A has polytropic index $α= 1.0$, i.e…
Polytropic stellar wind models with strongly localized heating
Ruhr-Universität Bochum（波鸿鲁尔大学）；Ilia State University（伊利亚国立大学）；Evgeni Kharadze Georgian National Astrophysical Observatory（叶夫根尼·哈拉泽格鲁吉亚国家天文台）；Institut für Weltraumforschung, Österreichische Akademie der Wissenschaften（奥地利科学院空间研究所）；Institute of Radio Astronomy, National Academy of Sciences of Ukraine（乌克兰国家科学院无线电天体物理研究所）
The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth's magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this …
The acceleration of the solar coronal plasma to supersonic speeds is one of the most fundamental yet unresolved problem in heliophysics. Despite the success of Parker's pioneering theory on an isothermal solar corona, the realistic solar wind is observed to be non-isothermal, and the decay of its temperature with radial distance usually can be fitted to a polytropic model. In this work, we use Parker Solar Probe data from the first nine encounters to estimate the polytropic index of solar wind protons. The estimated polytropic index varies roughly between 1.25 and 1.5 and depends strongly on s…
Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the cas…
Recent Very Long Baseline Interferometry observations of the relativistic jet in the M87 radio galaxy at 43 GHz show gradual relativistic acceleration of the plasma and suggest a linear dependence of Lorentz factor on jet radius at scales up to 8 marcsec (0.65 pc) from the core (2.5 marcsec in projection). General analysis of integrals of motion being unaltered along the jet and reflecting fundamental conservation laws shows that the above dependence implies a polytropic equation of state with index 4/3. The inferred value of the polytropic index appears independent of the exact nature of forc…
In collision-poor plasmas from space, e.g., the solar wind and planetary magnetospheres, the kinetic anisotropy of the plasma particles is expected to be regulated by the kinetic instabilities. Driven by an excess of ion (proton) temperature perpendicular to the magnetic field $(~T_\perp >T_\parallel)$, the electromagnetic ion-cyclotron (EMIC) instability is fast enough to constrain the proton anisotropy, but the observations do not conform to the instability thresholds predicted by the standard theory for bi-Maxwellian models of the plasma particles. This paper presents an extended investigat…
Turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two dimensional, particle-in-cell (PIC) plasma simulations with realistic electron-proton mass ratio and a guide field out of the simulation plane. A fluctuation power spectrum with approximately power law form is created down to scales of order the electron gyroradius. In the dynamic magnetic …
We perform fully-kinetic particle-in-cell simulations of an hot plasma that expands radially in a cylindrical geometry. The aim of the paper is to study the consequent development of the electron temperature anisotropy in an expanding plasma flow as found in a collisionless stellar wind. Kinetic plasma theory and simulations have shown that the electron temperature anisotropy is controlled by fluctuations driven by electromagnetic kinetic instabilities. In this study the temperature anisotropy is driven self-consistently by the expansion. While the expansion favors an increase of parallel anis…
A relationship is derived between power anisotropy and wavevector anisotropy in turbulent fluctuations. This can be used to interpret plasma turbulence measurements, for example in the solar wind. If fluctuations are anisotropic in shape then the ion gyroscale break point in spectra in the directions parallel and perpendicular to the magnetic field would not occur at the same frequency, and similarly for the electron gyroscale break point. This is an important consideration when interpreting solar wind observations in terms of anisotropic turbulence theories. Model magnetic field power spectra…
The nature of MHD turbulence is analyzed through both temporal and spatial magnetic fluctuation spectra. A magnetically turbulent plasma is produced in the MHD wind-tunnel configuration of the Swarthmore Spheromak Experiment (SSX). The power of magnetic fluctuations is projected into directions perpendicular and parallel to a local mean field; the ratio of these quantities shows the presence of variance anisotropy which varies as a function of frequency. Comparison amongst magnetic, velocity, and density spectra are also made, demonstrating that the energy of the turbulence observed is primari…
Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the …
Turbulence in space plasmas usually exhibits two regimes separated by a spectral break that divides the so called inertial and kinetic ranges. Large scale magnetic fluctuations are dominated by non-linear MHD wave-wave interactions following a -5/3 or -2 slope power-law spectrum. After the break, at scales in which kinetic effects take place, the magnetic spectrum follows a steeper power-law $k^{-α}$ shape given by a spectral index $α> 5/3$. Despite its ubiquitousness, the possible effects of a turbulent background spectrum in the quasilinear relaxation of solar wind temperatures are usually n…
Using a hybrid kinetic magnetohydrodynamic formalism incorporating the effects of pressure anisotropy, we simulate the evolution of a turbulent collisionless plasma in six different models covering the sub/super-sonic and sub/super-Alfvénic regimes. Based on the power spectrum of the simulated magnetic field, we compute the particle diffusion coefficients for protons with kinetic energy in the $50-500$ MeV range, and compare them to those obtained within standard magnetohydrodynamics. Our results show that the differences in the statistical properties of the magnetic field, generated by pressu…
In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A = T_{\perp}/T_\parallel>$ (with $\perp, \parallel$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the ki…
We investigate properties of a solar wind-like plasma including a secondary alpha particle population exhibiting a parallel temperature anisotropy with respect to the background magnetic field, using linear and quasi-linear predictions and by means of one-dimensional hybrid simulations. We show that anisotropic alpha particles can drive a parallel fire hose instability analogous to that generated by protons, but that, remarkably, the instability can be triggered also when the parallel plasma beta of alpha particles is below unity. The wave activity generated by the alpha anisotropy affects the…
We investigate the role of kinetic instabilities driven by a proton anisotropy on the onset of magnetic reconnection by means of 2-D hybrid simulations. The collisionless tearing of a current sheet is studied in the presence of a proton temperature anisotropy in the surrounding plasma. Our results confirm that anisotropic protons within the current sheet region can significantly enhance/stabilize the tearing instability of the current. Moreover, fluctuations associated to linear instabilities excited by large proton temperature anisotropies can significantly influence the stability of the plas…
Collisionless shocks follow the Rankine-Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent Particle-in-Cell simulations reveal a significant departure from magnetohydrodynamics behavior for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we …
Using hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvénic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfvénic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale "critical balance"…
We study the stability of large amplitude, circularly polarized Alfvén waves in an anisotropic plasma described by the double-adiabatic/CGL closure, and in particular the effect of a background thermal pressure anisotropy on the well-known properties of Alfvén wave parametric decay in Magnetohydrodynamics (MHD). Anisotropy allows instability over a much wider range of values of parallel plasma beta ($β_\parallel$) when $ξ=p_{0\bot}/p_{0\parallel} > 1$. When the pressure anisotropy exceeds a critical value, $ξ\geqξ^*$ with $ξ^*\simeq2.7$, there is a new regime in which the parametric instabilit…
The nonlinear state of a high-beta collisionless plasma is investigated when an imposed linear shear amplifies or diminishes a uniform magnetic field, driving pressure anisotropies and hence firehose/mirror instabilities. The evolution of the resulting microscale turbulence is considered when the shear is switched off or reversed after one shear time (mimicking local behaviour of a macroscopic flow), so a new macroscale configuration is superimposed on the microscale state left behind by the previous one. There is a threshold value of plasma beta: when $β\llΩ/S$ (ion cyclotron frequency/shear …
Using high-resolution data from Solar Orbiter, we investigate the plasma conditions necessary for the proton temperature anisotropy driven mirror-mode and oblique firehose instabilities to occur in the solar wind. We find that the unstable plasma exhibits dependencies on the angle between the direction of the magnetic field and the bulk solar wind velocity which cannot be explained by the double-adiabatic expansion of the solar wind alone. The angle dependencies suggest that perpendicular heating in Alfvénic wind may be responsible. We quantify the occurrence rate of the two instabilities as a…
In order to resolve and characterize anisotropy in turbulent plasma flows a proper estimation of the background magnetic field is crucially important. Various approaches to calculate the background magnetic fields, ranging from local fields to globally averaged fields, are commonly used in the analysis of turbulent data. Here we investigate how the uncertainty in the orientation of a scale dependent background magnetic field influences the ability to resolve anisotropy. Therefore we introduce a quantitative measure, the angle uncertainty, which characterizes the uncertainty of the orientation …
