Low-beta Plasma Research Articles

Spectrum for the nonlinear interaction between finite frequency pump inertial Alfvén wave and slow magnetosonic wave in low beta plasmas

Nonlinear interplay between the finite frequency inertial Alfvén wave and slow magnetosonic wave for low β-plasma (β≪me/mi) has been studied in the paper. The governing equation of slow magnetosonic wave has been derived in the presence of ponderomotive force associated with the finite frequency inertial Alfvén wave. A numerical simulation has been performed for the set of dimensionless governing equations representing finite frequency inertial Alfvén wave and slow magnetosonic wave for the parameters of auroral region. The localized structures and turbulence spectrum have been studied for the different angles of propagation (like θ=5°,25°,45°,75°) of slow magnetosonic wave. From the results, it has been observed that the localization becomes labyrinthine and varies with the change in the angle of propagation for the slow magnetosonic wave. Further, the spectral index follows the (∼k−3.8) for θ=5°, (∼k−4.05) for θ=25°, (∼k−4.2) for θ=45°, and (∼k−4.35) for θ=75°. Hence, one can conclude that the variation in the angle of propagation of slow magnetosonic wave affects the localization and spectral scaling. This variation may be responsible for the heating and acceleration of the plasma species in auroral region. The relevancy of the simulation results have been shown with the observation recorded by the spacecrafts such as FAST, Heos 2, Hawkeye 1, and Dynamics Explorer 1.

Particle Acceleration during Magnetic Reconnection in a Low-beta Plasma

Abstract Magnetic reconnection is a primary mechanism for particle energization in space and astrophysical plasmas. By carrying out two-dimensional (2D) fully kinetic simulations, we study particle acceleration during magnetic reconnection in plasmas with different plasma β (the ratio between the thermal pressure and the magnetic pressure). For the high-β cases, we do not observe significant particle acceleration. In the low-β regime ( β < 0.1 ), we find that reconnection is efficient at energizing both electrons and ions. While the distribution of accelerated particles integrated over the whole simulation box appears highly non-thermal, it is actually the superposition of a series of distributions in different sectors of a 2D magnetic island. Each of those distributions has only a small non-thermal component compared with its thermal core. By tracking a large number of particles, we show that particles get energized in X-line regions, contracting magnetic islands, and magnetic island coalescence regions. We obtain the particle energization rate j · E by averaging over particle drift motions and find that it agrees well with the particle kinetic energy change. We quantify the contribution of curvature drift, gradient drift, polarization drift, magnetization, non-gyrotropic effect, and parallel electric field in different acceleration regions. We find that the major energization is due to particle curvature drift along the motional electric field. The other particle motions contribute less but may become important in different acceleration regions. The highly efficient particle energization in low-β plasmas may help us understand the strong particle energization in solar flares and accretion disk coronae.

Polarization of obliquely propagating whistler mode waves based on linear dispersion theory

We discuss the variation of whistler mode wave electric and magnetic field polarizations as a function of propagation angle θkB0 with respect to the background magnetic field B0 using linear kinetic dispersion theory. The circular polarization of the whistler mode wave magnetic field at all propagation angles [Verkhoglyadova et al. J. Geophys. Res. 115, A00F19 (2010); P. M. Bellan, Phys. Plasmas 20, 082113 (2013)] is found to be valid only for cold plasma or low plasma beta conditions. The wave magnetic fields, on a plane orthogonal to the wave vector k, tend to become elliptically polarized with an increase in propagation angles for high beta plasma background conditions (βe≥0.1). The electric field polarization plane may not be orthogonal to wave vector k, especially for oblique propagations, and is found to be circularly polarized only at parallel propagation direction as reported by Verkhoglyadova et al. [J. Geophys. Res. 115, A00F19 (2010)] and Bellan [Phys. Plasmas 20, 082113 (2013)]. They become elliptically polarized with an increase in propagation angles. This is valid for arbitrary plasma beta conditions. The results are also analysed and compared for an inner magnetospheric plasma model with three electron species. The two major angles, Gendrin and resonance cone angles, are also discussed.

ENERGY DISSIPATION AND LANDAU DAMPING IN TWO- AND THREE-DIMENSIONAL PLASMA TURBULENCE

ABSTRACT Plasma turbulence is ubiquitous in space and astrophysical plasmas, playing an important role in plasma energization, but the physical mechanisms leading to dissipation of the turbulent energy remain to be definitively identified. Kinetic simulations in two dimensions (2D) have been extensively used to study the dissipation process. How the limitation to 2D affects energy dissipation remains unclear. This work provides a model of comparison between two- and three-dimensional (3D) plasma turbulence using gyrokinetic simulations; it also explores the dynamics of distribution functions during the dissipation process. It is found that both 2D and 3D nonlinear gyrokinetic simulations of a low-beta plasma generate electron velocity-space structures with the same characteristics as that of the linear Landau damping of Alfvén waves in a 3D linear simulation. The continual occurrence of the velocity-space structures throughout the turbulence simulations suggests that the action of Landau damping may be responsible for the turbulent energy transfer to electrons in both 2D and 3D, and makes possible the subsequent irreversible heating of the plasma through collisional smoothing of the velocity-space fluctuations. Although, in the 2D case where variation along the equilibrium magnetic field is absent, it may be expected that Landau damping is not possible, a common trigonometric factor appears in the 2D resonant denominator, leaving the resonance condition unchanged from the 3D case. The evolution of the 2D and 3D cases is qualitatively similar. However, quantitatively, the nonlinear energy cascade and subsequent dissipation is significantly slower in the 2D case.

Nonlinear asymmetric tearing mode evolution in cylindrical geometry

The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ′(w). For a low beta plasma without external heating, Δ′(w) can be approximately described by two terms, Δ′ql(w), ΔA′(w) [White et al., Phys. Fluids 20, 800 (1977); Phys. Plasmas 22, 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δql′ rigorously, for poloidal mode number m≥2. Δql′ is derived by solving the outer equation through the Frobenius method. Δ′ql is composed of four terms proportional to: constant Δ′0, w, wlnw, and w2. ΔA′ is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δql′ and ΔA′ is consistent with the more accurate expression calculated perturbatively [Arcis et al., Phys. Plasmas 13, 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the ΔA′ has to be considered in calculating island saturation.

Small amplitude Kinetic Alfven waves in a superthermal electron–positron–ion plasma

We are investigating the propagating properties of coupled Kinetic Alfven-acoustic waves in a low beta plasma having superthermal electrons and positrons. Using the standard reductive perturbation method, a nonlinear Korteweg-de Vries (KdV) type equation is derived which describes the evolution of Kinetic Alfven waves. It is found that nonlinearity and Larmor radius effects can compromise and give rise to solitary structures. The parametric role of superthermality and positron content on the characteristics of solitary wave structures is also investigated. It is found that only sub-Alfvenic and compressive solitons are supported in the present model. The present study may find applications in a low β electron–positron–ion plasma having superthermal electrons and positrons.

PLASMA COMPRESSION IN MAGNETIC RECONNECTION REGIONS IN THE SOLAR CORONA

ABSTRACT It has been proposed that particles bouncing between magnetized flows converging in a reconnection region can be accelerated by the first-order Fermi mechanism. Analytical considerations of this mechanism have shown that the spectral index of accelerated particles is related to the total plasma compression within the reconnection region, similarly to the case of the diffusive shock acceleration mechanism. As a first step to investigate the efficiency of Fermi acceleration in reconnection regions in producing hard energy spectra of particles in the solar corona, we explore the degree of plasma compression that can be achieved at reconnection sites. In particular, we aim to determine the conditions for the strong compressions to form. Using a two-dimensional resistive MHD numerical model, we consider a set of magnetic field configurations where magnetic reconnection can occur, including a Harris current sheet, a force-free current sheet, and two merging flux ropes. Plasma parameters are taken to be characteristic of the solar corona. Numerical simulations show that strong plasma compressions (≥4) in the reconnection regions can form when the plasma heating due to reconnection is efficiently removed by fast thermal conduction or the radiative cooling process. The radiative cooling process that is negligible in the typical 1 MK corona can play an important role in the low corona/transition region. It is found that plasma compression is expected to be strongest in low-beta plasma β ∼ 0.01–0.07 at reconnection magnetic nulls.

On the possibility for laboratory simulation of generation of Alfvén disturbances in magnetic tubes in the solar atmosphere

The paper deals with generation of Alfvén plasma disturbances in magnetic flux tubes through exploding laser plasma in magnetized background plasma. Processes with similar effect of excitation of torsion-type waves seem to provide energy transfer from the solar photosphere to the corona. The studies were carried out at experimental stand KI-1 representing a high-vacuum chamber 1.2 m in diameter, 5 m in length, external magnetic field up to 500 G along the chamber axis, and up to 2·10–6 Torr pressure in operating mode. Laser plasma was produced when focusing the CO2 laser pulse on a flat polyethylene target, and then the laser plasma propagated in θ-pinch background hydrogen (or helium) plasma. As a result, the magnetic flux tube 15–20 cm in radius was experimentally simulated along the chamber axis and the external magnetic field direction. Also, the plasma density distribution in the tube was measured. Alfvén wave propagation along the magnetic field was registered from disturbance of the magnetic field transverse component Bφ and field-aligned current Jz. The disturbances propagate at a near-Alfvén velocity 70–90 km/s and they are of left-hand circular polarization of the transverse component of magnetic field. Presumably, the Alfvén wave is generated by the magnetic laminar mechanism of collisionless interaction between laser plasma cloud and background. A right-hand polarized high-frequency whistler predictor was registered which propagated before the Alfvén wave at a velocity of 300 km/s. The polarization direction changed with the Alfvén wave coming. Features of a slow magnetosonic wave as a sudden change in background plasma concentration along with simultaneous displacement of the external magnetic field were found. The disturbance propagates at ~20–30 km/s velocity, which is close to that of ion sound at low plasma beta value. From preliminary estimates, the disturbance transfers about 10 % of the original energy of laser plasma.

Particle acceleration during magnetic reconnection in a low-beta pair plasma

Plasma energization through magnetic reconnection in the magnetically dominated regime featured by low plasma beta (β=8πnkT0/B2≪1) and/or high magnetization (σ=B2/(4πnmc2)≫1) is important in a series of astrophysical systems such as solar flares, pulsar wind nebula, and relativistic jets from black holes. In this paper, we review the recent progress on kinetic simulations of this process and further discuss plasma dynamics and particle acceleration in a low-β reconnection layer that consists of electron–positron pairs. We also examine the effect of different initial thermal temperatures on the resulting particle energy spectra. While earlier papers have concluded that the spectral index is smaller for higher σ, our simulations show that the spectral index approaches p = 1 for sufficiently low plasma β, even if σ∼1. Since this predicted spectral index in the idealized limit is harder than most observations, it is important to consider effects that can lead to a softer spectrum such as open boundary simulations. We also remark that the effects of three-dimensional reconnection physics and turbulence on reconnection need to be addressed in the future.

О возможности лабораторного моделирования процессов генерации альфвеновских возмущений в магнитных трубках в атмосфере Солнца

The paper deals with generation of Alfven plasma disturbances in magnetic flux tubes through exploding laser plasma in magnetized background plasma. Processes with similar effect of excitation of torsion-type waves seem to provide energy transfer from the solar photosphere to corona. The studies were carried out at experimental stand KI-1 represented a high-vacuum chamber of 1.2 m diameter, 5 m long, external magnetic field up to 500 Gs along the chamber axis, and up to 2·10–6 Torr pressure in operating mode. Laser plasma was produced when focusing the CO2 laser pulse on a flat polyethylene target, and then the laser plasma propagated in θ-pinch background hydrogen (or helium) plasma. As a result, the magnetic flux tube of 15–20 cm radius was experimentally simulated along the chamber axis and the external magnetic field direction. Also, the plasma density distribution in the tube was measured. Alfven wave propagation along the magnetic field was registered from disturbance of the magnetic field transverse component Bφ and field-aligned current Jz. The disturbances propagate at near-Alfven velocity of 70–90 km/s and they are of left-hand circular polarization of the transverse component of magnetic field. Presumably, Alfven wave is generated by the magnetic laminar mechanism of collisionless interaction between laser plasma cloud and background. The right-hand polarized high-frequency whistler predictor was registered which have been propagating before Alfven wave at 300 km/s velocity. The polarization direction changed with Alfven wave coming. Features of a slow magnetosonic wave as a sudden change in background plasma concentration along with simultaneous displacement of the external magnetic field were found. The disturbance propagates at ~20–30 km/s velocity, which is close to that of ion sound at low plasma beta value. From preliminary estimates, the disturbance transfers about 10 % of the original energy of laser plasma.

Laboratory astrophysics with laser-driven strong magnetic fields in China

In this paper, the recent studies of laboratory astrophysics with strong magnetic fields in China have been reviewed. On the Shenguang-II laser facility of the National Laboratory on High-Power Lasers and Physics, a laser-driven strong magnetic field up to 200 T has been achieved. The experiment was performed to model the interaction of solar wind with dayside magnetosphere. Also the low beta plasma magnetic reconnection (MR) has been studied. Theoretically, the model has been developed to deal with the atomic structures and processes in strong magnetic field. Also the study of shock wave generation in the magnetized counter-streaming plasmas is introduced.

Parametric Instabilities of Parallel Propagating Circularly Polarized Alfvén Waves: One-Dimensional Hybrid Simulations**Supported by the National Natural Science Foundation of China under Grant Nos 41331067, 41474125, 41274144, 41174124 and 41121003, the National Basic Research Program of China under Grant Nos 2013CBA01503 and 2012CB825602, and the Key Research Program of Chinese Academy of Sciences under Grant No KZZD-EW-01-4.

By performing one-dimensional (1-D) hybrid simulations, we analyze in detail the parametric instabilities of the Alfvén waves with a spectrum in a low beta plasma. The parametric instabilities experience two stages. In the first stage, the density modes are excited and immediately couple with the pump Alfvén waves. In the second stage, each pump Alfvén wave decays into a density mode and a daughter Alfvén mode similar to the monochromatic cases. Furthermore, the proton velocity beam will also be formed after the saturation of the parametric instabilities. When the plasma beta is high, the parametric decay in the second stage will be strongly suppressed.

Cut-off period for slow magnetoacoustic waves in coronal plasma structures

Context. There is abundant observational evidence of longitudinal compressive waves in plasma structures of the solar corona, which are confidently interpreted in terms of slow magnetoacoustic waves. The uses of coronal slow waves in plasma diagnostics, as well as analysis of their possible contribution to coronal heating and the solar wind acceleration, require detailed theoretical modelling. Aims. We investigate the effects of obliqueness, magnetic field, and non-uniformity of the medium on the evolution of long-wavelength slow magnetoacoustic waves guided by field-aligned plasma non-uniformities, also called tube waves. Special attention is paid to the cut-off effect due to the gravity stratification of the coronal plasma. Methods. We study the behaviour of linear tube waves in a vertical untwisted straight field-aligned isothermal plasma cylinder. We apply the thin flux tube approximation, taking into account effects of stratification caused by gravity. The dispersion due to the finite radius of the flux tube is neglected. We analyse the behaviour of the cut-off period for an exponentially divergent magnetic flux tube filled in with a stratified plasma. The results obtained are compared with the known cases of the constant Alfven speed and the pure acoustic wave. Results. We derive the wave equation for tube waves and reduce it to the form of the Klein–Gordon equation with varying coefficients, which explicitly contains the cut-off frequency. The cut-off period is found to vary with height, decreasing significantly in the low-beta plasma and in the plasma with the beta of the order of unity. The depressions in the cut-off period profiles can affect the propagation of longitudinal waves along coronal plasma structures towards the higher corona and can form coronal resonators.

Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows

In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (bg). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (βi = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (bg ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (bg ≳ 5). Kinetic PIC simulations using guide fields bg ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (βi = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (bg ≲ 3).

3D hybrid simulations of the interaction of a magnetic cloud with a bow shock

AbstractIn this paper, we investigate the interaction of a magnetic cloud (MC) with a planetary bow shock using hybrid simulations. It is the first time to our knowledge that this interaction is studied using kinetic simulations which include self‐consistently both the ion foreshock and the shock wave dynamics. We show that when the shock is in a quasi‐perpendicular configuration, the MC's magnetic structure in the magnetosheath remains similar to that in the solar wind, whereas it is strongly altered downstream of a quasi‐parallel shock. The latter can result in a reversal of the magnetic field north‐south component in some parts of the magnetosheath. We also investigate how the MC affects in turn the outer parts of the planetary environment, i.e., from the foreshock to the magnetopause. We find the following: (i) The decrease of the Alfvén Mach number at the MC's arrival causes an attenuation of the foreshock region because of the weakening of the bow shock. (ii) The foreshock moves along the bow shock's surface, following the rotation of the MC's magnetic field. (iii) Owing to the low plasma beta, asymmetric flows arise inside the magnetosheath, due to the magnetic tension force which accelerates the particles in some parts of the magnetosheath and slows them down in others. (iv) The quasi‐parallel region forms a depression in the shock's surface. Other deformations of the magnetopause and the bow shock are also highlighted. All these effects can contribute to significantly modify the solar wind/magnetosphere coupling during MC events.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionless and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.

Kinetic instability of drift magnetosonic wave in anisotropic low beta plasmas

The kinetic instability of the obliquely propagating drift magnetosonic wave for temperature anisotropic low beta plasmas is studied by using the gyro-kinetic model. The interplay between the temperature anisotropy and the density inhomogeneity free energy sources is discussed in order to provide stabilization of drift instability by the temperature anisotropy effect. It is shown that the anisotropy suppresses the growth rate when the anisotropy ratio Ae,i (=T⊥(e,i)/T∥(e,i)) is greater than unity, whereas it enhances the growth rate for Ae,i<1. Comparison of kinetic instability with reactive instability [Naim et al., Phys. Plasmas 21, 102112 (2014)] and the scaling of growth time with the diffusion and the anisotropy relaxation times are presented. Additionally, the stability analysis applicable to a wide range of plasma parameters is also performed.

Standing Slow MHD Waves in Radiatively Cooling Coronal Loops

The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops, namely, thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function, that ensures the temperature evolution of the background plasma due to radiation, coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglecting the magnetic field perturbation and, eventually, reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale, much larger than the oscillation period that subsequently enables using the WKB theory to study the properties of standing wave. The governing equation describing the time-dependent amplitude of waves is obtained and solved analytically. The analytically derived solutions are numerically evaluated to give further insight into the evolution of the standing acoustic waves. We find that the plasma cooling gives rise to a decrease in the amplitude of oscillations. In spite of the reduction in damping rate caused by rising the cooling, the damping scenario of slow standing MHD waves strongly increases in hot coronal loops.

Localization of 3D inertial Alfvén wave and generation of turbulence

The present paper deals with the nonlinear interaction of Inertial Alfven wave (IAW) and fast magnetosonic wave in the low beta plasma, where beta is the ratio of thermal pressure to the background magnetic pressure. In this paper, the localization and turbulent spectra of IAW along with the density dips correlated with the fast magnetosonic wave have been investigated. Variation of parallel electric field along and across the field lines has also been studied. Taking ponderomotive nonlinear effect in the dynamics of fast magnetosonic wave, couple of dimensionless equations has been derived. These coupled equations have been simulated numerically using the pseudo-spectral method. The obtained results reveal that the Kolmogorov scaling is followed by a steeper scaling in magnetic power spectrum, which is consistent with the observations by the FAST and Hawkeye spacecraft in auroral region. The relevance of present investigation has been discussed for auroral plasmas.

Localization of finite frequency inertial Alfvén wave and turbulent spectrum in low beta plasmas

In the present paper, we have investigated nonlinear interaction of inertial Alfven wave with ion acoustic wave, for low β-plasma (β≪m e /m i ) where β is the thermal to magnetic pressure ratio. We have developed the dynamical equation of inertial Alfven wave by considering the finite frequency as well as finite ion temperature correction. The dynamical equation of ion acoustic wave, propagating at an angle with respect to the background magnetic field, in the presence of ponderomotive nonlinearity due to inertial Alfven wave is also derived. Numerical simulation has been carried out to study the effect of nonlinear coupling between these waves which results in the formation of localized structures and turbulent spectrum, applicable to auroral region. The result reveals that the localized structures become complex and intense in nature (quasi-steady state). Further, we have studied the turbulent spectrum which follows spectral index (∼k −4.46) at smaller scales. Relevance of the obtained results has been shown with the observations reported by various spacecrafts like Hawkeye and HEOS-2 (Highly Eccentric Orbiting Satellite-2).