Right-hand Resonant Instability Research Articles

Electromagnetic Ion–Ion Instabilities in Space Plasmas: Effects of Suprathermal Populations

Abstract In collision-poor plasmas from space, three distinct ion–ion instabilities can be driven by the proton beams streaming along the background magnetic field: left-hand resonant, nonresonant, and right-hand resonant instabilities. These instabilities are in general investigated considering only idealized proton beams with Maxwellian velocity distributions, and ignoring the implications of suprathermal populations, usually reproduced by the Kappa power laws. Moreover, the existing theories minimize the kinetic effects of electrons, assuming them isotropic and Maxwellian distributed. In an attempt to overcome these limitations, in the present paper we present the results of an extended investigation of ion–ion instabilities, which show that their dispersion and stability properties (e.g., growth rates, wave frequencies, and the unstable wavenumbers) are highly sensitive to the influence of suprathermal populations and anisotropic electrons. These results offer valuable explanations for the origin of the enhanced low-frequency fluctuations, frequently observed in space plasmas and associated with proton beams.

Laboratory Observations of Ultra-Low Frequency Analogue Waves Driven by the Right-Hand Resonant Ion Beam Instability.

The Right-Hand Resonant Instability (RHI) is one of several electromagnetic ion/ion beam instabilities responsible for the formation of parallel magnetized collisionless shocks and the generation of ultra-low frequency (ULF) waves in their foreshocks. This instability has been observed for the first time under foreshock-relevant conditions in the laboratory through the repeatable interaction of a preformed magnetized background plasma and a super-Alfvénic laser-produced plasma. This platform has enabled unprecedented volumetric measurements of waves generated by the RHI, revealing filamentary current structures in the transverse plane. These measurements are made in the plasma rest frame with both high spatial and temporal resolution, providing a perspective that is complementary to spacecraft observations. Direct comparison of data from both the experiment and the Wind spacecraft to 2D hybrid simulations demonstrates that the waves produced are analogous to the ULF waves observed upstream of the terrestrial bow shock.

Electromagnetic Structure and Electron Acceleration in Shock–Shock Interaction

Abstract A shock–shock interaction is investigated by using a one-dimensional full particle-in-cell simulation. The simulation reproduces the collision of two symmetrical high Mach number quasi-perpendicular shocks. The basic structure of the shocks and ion dynamics is similar to that obtained by previous hybrid simulations. The new aspects obtained here are as follows. Electrons are already strongly accelerated before the two shocks collide through multiple reflection. The reflected electrons self-generate waves upstream between the two shocks before they collide. The waves far upstream are generated through the right-hand resonant instability with the anomalous Doppler effect. The waves generated near the shock are due to firehose instability and have much larger amplitudes than those due to the resonant instability. The high-energy electrons are efficiently scattered by the waves so that some of them gain large pitch angles. Those electrons can be easily reflected at the shock of the other side. The accelerated electrons form a power-law energy spectrum. Due to the accelerated electrons, the pressure of upstream electrons increases with time. This appears to cause the deceleration of the approaching shock speed. The accelerated electrons having sufficiently large Larmor radii are further accelerated through the similar mechanism working for ions when the two shocks are colliding.

Hybrid simulations of a parallel collisionless shock in the large plasma device

We present two-dimensional hybrid kinetic/magnetohydrodynamic simulations of planned laser-ablation experiments in the Large Plasma Device. Our results, based on parameters that have been validated in previous experiments, show that a parallel collisionless shock can begin forming within the available space. Carbon-debris ions that stream along the magnetic-field direction with a blow-off speed of four times the Alfvén velocity excite strong magnetic fluctuations, eventually transferring part of their kinetic energy to the surrounding hydrogen ions. This acceleration and compression of the background plasma creates a shock front, which satisfies the Rankine–Hugoniot conditions and can therefore propagate on its own. Furthermore, we analyze the upstream turbulence and show that it is dominated by the right-hand resonant instability.

Vlasiator: First global hybrid-Vlasov simulations of Earth's foreshock and magnetosheath

We present results from a new hybrid-Vlasov simulation code, Vlasiator, designed for global magnetospheric simulations. Vlasiator represents ions by a six-dimensional distribution function propagated using a finite volume approach. The distribution functions are self-consistently coupled to electromagnetic fields with electrons modeled as a charge-neutralizing fluid. A novel sparse representation of the distribution function reduces the computational demands of the problem by up to two orders of magnitude. The capabilities of the code are demonstrated by reproducing characteristics of the ion/ion right-hand resonant beam instability, as well as key features of the collisionless bow shock and magnetosheath in front of the Earth's magnetosphere in global five-dimensional (two in ordinary space, three in velocity space) simulations. We find that Vlasiator reproduces the ion velocity distribution functions with quality comparable to spacecraft observations.

Evaluation of magnetic helicity density in the wave number domain using multi-point measurements in space

Abstract. We develop an estimator for the magnetic helicity density, a measure of the spiral geometry of magnetic field lines, in the wave number domain as a wave diagnostic tool based on multi-point measurements in space. The estimator is numerically tested with a synthetic data set and then applied to an observation of magnetic field fluctuations in the Earth foreshock region provided by the four-point measurements of the Cluster spacecraft. The energy and the magnetic helicity density are determined in the frequency and the wave number domain, which allows us to identify the wave properties in the plasma rest frame correcting for the Doppler shift. In the analyzed time interval, dominant wave components have parallel propagation to the mean magnetic field, away from the shock at about Alfvén speed and a left-hand spatial rotation sense of helicity with respect to the propagation direction, which means a right-hand temporal rotation sense of polarization. These wave properties are well explained by the right-hand resonant beam instability as the driving mechanism in the foreshock. Cluster observations allow therefore detailed comparisons with various theories of waves and instabilities.

Observations of linear and nonlinear processes in the foreshock wave evolution

Abstract. Waves in the foreshock region are studied on the basis of a hypothesis that the linear process first excites the waves and further wave-wave nonlinearities distribute scatter the energy of the primary waves into a number of daughter waves. To examine this wave evolution scenario, the dispersion relations, the wave number spectra of the magnetic field energy, and the dimensionless cross helicity are determined from the observations made by the four Cluster spacecraft. The results confirm that the linear process is the ion/ion right-hand resonant instability, but the wave-wave interactions are not clearly identified. We discuss various reasons why the test for the wave-wave nonlinearities fails, and conclude that the higher order statistics would provide a direct evidence for the wave coupling phenomena.

Generation of nonlinear Alfvén and magnetosonic waves by beam–plasma interaction

One-dimensional (1-D) and two-dimensional (2-D) hybrid simulations are carried out to study the interaction between a background plasma and an ion beam, whose velocity is parallel to the ambient magnetic field B0. It is found that the beam–plasma interaction and the associated wave evolution can be divided into four phases. The simulation results in phase 1 in the early stage of wave evolution are consistent with the linear theory. Right-hand nonresonant instabilities are present and dominant in cases with a relatively strong ion beam (e.g., the ratio of beam ion density to background ion density >0.06 for beam velocity =10VA, where VA is the Alfvén speed), while right-hand resonant instabilities are present in the weak beam cases. During phases 2 and 3, the waves grow to form nonlinear structure, and are then saturated. A detailed analysis shows that the wave evolution in these phases is through secondary instabilities associated with parametric decay or the wave modulation. In addition, it is shown for the first time from the self-consistent simulation that in the final phase, nonlinear shear Alfvén waves with right-hand polarization in the magnetic field are generated. The magnetohydrodynamic (MHD) wave conditions of the Alfvén mode are satisfied. These Alfvén waves propagate mainly with k⋅B0>0, and the dispersion relation ω=kVA cos α is satisfied, where α is the angle between the wave vector k and B0. On the other hand, fast magnetosonic/whistler waves and slow mode waves are formed in the final phase of weak beam cases. In the 2-D simulations, field-aligned filaments (with k∼k⊥) in the density and magnetic field can be present due to the 2-D effects, in addition to the Alfvén, fast, and slow modes. The heating rate of background ions and its dependence on the wave propagation direction are also examined.

Three-dimensional simulation of the electromagnetic ion/ion beam instability: cross field diffusion

Abstract. In a system with at least one ignorable spatial dimension charged particles moving in fluctuating fields are tied to the magnetic field lines. Thus, in one-and two-dimensional simulations cross-field diffusion is inhibited and important physics may be lost. We have investigated cross-field diffusion in self-consistent 3-D magnetic turbulence by fully 3-dimensional hybrid simulation (macro-particle ions, massless electron fluid). The turbulence is generated by the electromagnetic ion/ion beam instability. A cold, low density, ion beam with a high velocity stream relative to the background plasma excites the right-hand resonant instability. Such ion beams may be important in the region of the Earth's foreshock. The field turbulence scatters the beam ions parallel as well as perpendicular to the magnetic field. We have determined the parallel and perpendicular diffusion coefficient for the beam ions in the turbulent wave field. The result compares favourably well (within a factor 2) with hard-sphere scattering theory for the cross-field diffusion coefficient. The cross-field diffusion coefficient is larger than that obtained in a static field with a Kolmogorov type spectrum and similar total fluctuation power. This is attributed to the resonant behaviour of the particles in the fluctuating field.

Ion-beam–plasma electromagnetic instabilities

It is well known that ion-beam–plasma interactions can destabilize right- and left-hand polarized electromagnetic waves. Owing to the fact that these instabilities have mostly been studied numerically by solving the hot-plasma dispersion relation, their fluid nature has often gone unnoticed. Choosing the ion background to be the rest frame, it is shown that the right-hand polarized instabilities are the result of a merging of the magnetosonic/electron-cyclotron branch of the dispersion relation with the ion beam. For any given ion-beam density and sufficiently large beam velocity, there are always two right- and two left-hand polarized instabilities leading to forward-propagating electromagnetic waves. It is also shown that all right-hand polarized instabilities are resonant instabilities, satisfying ω−kU+Ωp ≈ 0 around their maximum growth rate (ω and k are the frequency and the wavenumber respectively, U is the beam velocity, and Ωp is the proton gyrofrequency). Likewise, when the two left-hand instabilities are simultaneously present, they are also resonant instabilities satisfying ω ≈ Ωp. The high-frequency right-hand resonant instability (ω [Gt ] Ωp) has a maximum growth rate that depends only on the ratio between the beam density and the total density. The range of the unstable spectrum decreases with increasing beam velocity, leading to highly monochromatic radiation.

Identification of low-frequency kinetic wave modes in the Earth's ion foreshock

Abstract. In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ωr « Ωp) waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock) the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions). Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when other properties can diverge from those of the theoretical modes.

Observations of upstream ions, solar wind ions and electromagnetic waves in the Earth's foreshock

Theoretical work, together with analysis of ISEE data has led to the view that the right-hand resonant ion beam instability is probably responsible for transforming field aligned beam distributions into gyrophase-bunched distributions associated with large amplitude circularly polarised electromagnetic waves. We describe AMPTE-UKS observations of gyrophase-bunched distributions and associated waves and discuss whether they are consistent with the right-hand resonant instability hypothesis.

Nonlinear evolution of electromagnetic ion beam instabilities

An ion beam streaming along a magnetic field is known to be mainly unstable to two field‐aligned, low‐frequency electromagnetic instabilities: the ion/ion right‐hand resonant instability and ion/ion nonresonant instability. A comparative study of the two instabilities by means of linear analysis and simulation is carried out to investigate and contrast their properties. Linear analysis demonstrates that the nonresonant instability becomes resonant if the density of the ion beam is sufficiently high. When the relative drift speed between the ion beam and the ambient ions is 10 υA, where υA is the Alfvén speed, the nonresonant instability undergoes a transition to a resonant interaction at nb/no≃0.065, nb(no) being the beam (total ion) density. Hybrid simulations carried out for the densities of nb/no = 0.02, 0.1, and 0.25 show both the resonant and nonresonant instabilities result in the formation of nonlinear pulses called pulsations but with distinct features. For example, the pulsations generated by the resonant instability have positive correlation with the ion density, while those generated by the nonresonant instability are likely to have relatively weak negative correlation. Furthermore, the waves generated by the nonresonant instability are subject to a parametric decay instability and tend to form a state of condensate where the turbulence becomes nearly monochromatic. These features can be utilized to differentiate between pulsations produced by the two instabilities in space and, in particular, short large amplitude magnetic structures.

Nonlinear magnetosonic waves and mirror mode structures in the March 1991 Ulysses interplanetary event

In examining the March 23–25, 1991 Ulysses (2.2 AU) high speed solar wind events, we find two distinct plasma wave modes: steepened magnetosonic waves with whistler precursors and mirror mode structures. These two modes are locally generated by plasma instabilities, presumably associated with anisotropies existing in the energetic shock particles and solar wind plasma, respectively. The magnetosonic waves are generated by a right‐hand resonant instability associated with a ∼ 40 keV ion beam.By an extrapolation of the results presented here, assuming microflares and nanoflares at the Sun generate shocks in the lower corona and these shocks accelerate energetic ions, we suggest that the ions, via the right‐hand resonant instability, generate magnetosonic waves which steepened to form “microshocks” (such as shown here). These shocks could, in turn, accelerate more energetic ions, leading to a shock/energetic ion/magnetosonic wave cascade. These newly formed magnetosonic waves and shocks presumably could propagate in a broad range of directions, leading to energy dissipation over a large region of the outer corona.

Nonlinear generation of whistler waves by an ion beam

We propose and simulate with an electromagnetic hybrid code a new mechanism for whistler wave generation by an ion beam. First, a field‐aligned ion beam becomes unstable to the electromagnetic ion/ion right‐hand resonant instability which generates large amplitude MHD‐like waves. These waves then trap the ion beam and increase its effective temperature anisotropy. As a result, the growth rates of the electron/ion whistler instability are significantly enhanced, and whistlers start to grow above the noise level. At the same time, because of the reduced parallel drift speed of the ion beam, the frequencies of the whistlers are also downshifted. We also performed full particle simulations to isolate and separately investigate the electron/ion whistler instability. The results are in agreement with the assumption of fluid electrons in the hybrid simulations and with the linear theory of the instability.

Electromagnetic ion beam instabilities: II

This paper extends the results of Gary et al. [Phys. Fluids 27, 1852 (1984)]. That paper examined the linear theory of electromagnetic instabilities driven by an ion beam streaming along a magnetic field in a homogeneous Vlasov plasma, emphasizing the parametric dependence of the instability growth rates. This paper considers the parametric dependence of the real frequency at maximum growth of two such instabilities with right-hand polarization. It is shown that the right-hand resonant ion beam instability can have maximum growth at frequencies near the ion-cyclotron frequency if the beam–main component relative drift speed is about twice the Alfvén speed and at least one of the following conditions holds: the ion beta or the beam–main component relative temperature are sufficiently small, or the perpendicular-to-parallel beam temperature ratio is sufficiently large. These results support the identification of the right-hand resonant instability as the source of the large amplitude magnetic fluctuations observed upstream of slow shocks in the Earth’s magnetotail.