Solar Wind Rest Frame Research Articles

The Link Between Individual Velocities in the Incident Plasma Flow and Ion Populations Upstream of Collisionless Shocks

AbstractThe interaction of the solar wind with Earth’s bow shock gives rise to several distinct ion populations upstream and downstream of the shock. Using numerical computation of trajectories in the de Hoffmann‐Teller frame of reference and previous analytical results, we investigate whether membership of these populations is determined by a particle’s incident velocity in the solar wind rest frame. The shock is assumed to be a planar surface acting as an electrostatic potential jump. Ions with insufficient energy to overcome this potential are assumed to reflect specularly. We find that ions escaping upstream come from the wings of the incident distribution, assumed to be Maxwellian, and have incoming velocities in the plasma rest frame that point upstream close to the magnetic field direction. Ions escaping after several reflections have more field‐aligned incident velocities in the upstream frame on average than those escaping after one reflection. Different ion populations occupy separate regions of the incident distribution.

Foreshock cavitons and spontaneous hot flow anomalies: a statistical study with a global hybrid-Vlasov simulation

Abstract. The foreshock located upstream of Earth's bow shock hosts a wide variety of phenomena related to the reflection of solar wind particles from the bow shock and the subsequent formation of ultra-low-frequency (ULF) waves. In this work, we investigate foreshock cavitons, which are transient structures resulting from the non-linear evolution of ULF waves, and spontaneous hot flow anomalies (SHFAs), which are thought to evolve from cavitons as they accumulate suprathermal ions while being carried to the bow shock by the solar wind. Using the global hybrid-Vlasov simulation model Vlasiator, we have conducted a statistical study in which we track the motion of individual cavitons and SHFAs in order to examine their properties and evolution. In our simulation run where the interplanetary magnetic field (IMF) is directed at a sunward–southward angle of 45∘, continuous formation of cavitons is found up to ∼11 Earth radii (RE) from the bow shock (along the IMF direction), and caviton-to-SHFA evolution takes place within ∼2 RE from the shock. A third of the cavitons in our run evolve into SHFAs, and we find a comparable amount of SHFAs forming independently near the bow shock. We compare the properties of cavitons and SHFAs to prior spacecraft observations and simulations, finding good agreement. We also investigate the variation of the properties as a function of position in the foreshock, showing that transients close to the bow shock are associated with larger depletions in the plasma density and magnetic field magnitude, along with larger increases in the plasma temperature and the level of bulk flow deflection. Our measurements of the propagation velocities of cavitons and SHFAs agree with earlier studies, showing that the transients propagate sunward in the solar wind rest frame. We show that SHFAs have a greater solar wind rest frame propagation speed than cavitons, which is related to an increase in the magnetosonic speed near the bow shock.

Effect of Upstream ULF Waves on the Energetic Ion Diffusion at the Earth's Foreshock. I. Theory and Simulation

Abstract Field-aligned diffusion of energetic ions in the Earth’s foreshock is investigated by using the quasi-linear theory (QLT) and test particle simulation. Non-propagating MHD turbulence in the solar wind rest frame is assumed to be purely transverse with respect to the background field. We use a turbulence model based on a multi-power-law spectrum including an intense peak that corresponds to upstream ULF waves resonantly generated by the field-aligned beam (FAB). The presence of the ULF peak produces a concave shape of the diffusion coefficient when it is plotted versus the ion energy. The QLT including the effect of the ULF wave explains the simulation result well, when the energy density of the turbulent magnetic field is 1% of that of the background magnetic field and the power-law index of the wave spectrum is less than 2. The numerically obtained e-folding distances from 10 to 32 keV ions match with the observational values in the event discussed in the companion paper, which contains an intense ULF peak in the spectra generated by the FAB. Evolution of the power spectrum of the ULF waves when approaching the shock significantly affects the energy dependence of the e-folding distance.

Modified ion-Weibel instability as a possible source of wave activity at Comet 67P/Churyumov-Gerasimenko

Abstract. We analytically discuss wave excitation in a homogeneous three component plasma consisting of solar wind protons, electrons and a beam of cometary water ions applied to the plasma environment of comet 67P/Churyumov-Gerasimenko. The resulting dispersion relations are studied in a solar wind rest frame, where a cometary current is solely generated by the water ion beam, and a cometary rest frame representing the rest frame of the Rosetta spacecraft. A modified ion-Weibel instability is excited by the cometary current and predominantly grows perpendicular to this current. The corresponding water ion mode is connected to a frequency of about 40 mHz in agreement with wave measurements of Rosetta's magnetometer in the cometary rest frame. Furthermore, the superposition of the strongest growing waves result in a fan-like phase structure close to the comet.

Characteristics of proton velocity distribution functions in the near-lunar wake from Chandrayaan-1/SWIM observations

Due to the high absorption of solar wind plasma on the lunar dayside, a large scale wake structure is formed downstream of the Moon. However, recent in-situ observations have revealed the presence of protons in the near-lunar wake (100 km to 200 km from the surface). The solar wind, either directly or after interaction with the lunar surface (including magnetic anomalies), is the source of these protons in the near-wake region. Using the entire data from the SWIM sensor of the SARA experiment onboard Chandrayaan-1, we analyzed the velocity distribution of the protons observed in the near-lunar wake. The average velocity distribution functions, computed in the solar wind rest frame, were further separated based on the angle between the upstream solar wind velocity and the IMF. Although the protons enter the wake parallel as well as perpendicular to the IMF, the velocity distribution were not identical for the different IMF orientations, indicating the control of IMF in the proton entry processes. Several proton populations were identified from the velocity distribution and their possible entry mechanism were inferred based on the characteristics of the velocity distribution. These entry mechanisms include (i) diffusion of solar wind protons into the wake along IMF, (ii) the solar wind protons with finite gyro-radii that are aided by the wake boundary electric field, (iii) solar wind protons with gyro-radii larger than lunar radii from the tail of the solar wind velocity distribution, and (iv) scattering of solar wind protons from the dayside lunar surface or from magnetic anomalies. In order to gain more insight into the entry mechanisms associated with different populations, backtracing is carried out for each of these populations. For most of the populations, the source of the protons obtained from backtracing is found to be in agreement with that inferred from the velocity distribution. There are few populations that could not be explained by the known mechanisms and remain unknown.

PULSED ALFVÉN WAVES IN THE SOLAR WIND

Using 3 s plasma and magnetic field data from the Wind spacecraft located in the solar wind well upstream from Earth, we report observations of isolated, pulse-like Alfvenic disturbances in the solar wind. These isolated events are characterized by roughly plane-polarized rotations in the solar wind magnetic field and velocity vectors away from the directions of the underlying field and velocity and then back again. They pass over Wind on timescales ranging from seconds to several minutes. These isolated, pulsed Alfven waves are pervasive; we have identified 175 such events over the full range of solar wind speeds (320-550 km s{sup -1}) observed in a randomly chosen 10 day interval. The large majority of these events are propagating away from the Sun in the solar wind rest frame. Maximum field rotations in the interval studied ranged from 6 Degree-Sign to 109 Degree-Sign . Similar to most Alfvenic fluctuations in the solar wind at 1 AU, the observed changes in velocity are typically less than that predicted for pure Alfven waves (Alfvenicity ranged from 0.28 to 0.93). Most of the events are associated with small enhancements or depressions in magnetic field strength and small changes in proton number density and/or temperature.more » The pulse-like and roughly symmetric nature of the magnetic field and velocity rotations in these events suggests that these Alfvenic disturbances are not evolving when observed. They thus appear to be, and probably are, solitary waves. It is presently uncertain how these waves originate, although they may evolve out of Alfvenic turbulence.« less

Quasi‐monochromatic ULF foreshock waves as observed by the four‐spacecraft Cluster mission: 1. Statistical properties

Cluster data are used to study the statistics of a particular type of foreshock wave: quasi‐monochromatic ultra‐low‐frequency (ULF) waves with characteristic periods of 30 s in the spacecraft frame. On the basis of a large set of foreshock observations made in 2001 with spacecraft separations ∼600 km, the intrinsic properties of the waves are found using a cross‐correlation timing analysis. This method, which allows the solar wind rest frame properties of the waves to be calculated with fewer assumptions when compared to previous dual spacecraft analysis, is described in detail. The performance of minimum variance analysis (MVA) as a wave analysis tool is investigated experimentally using this multispacecraft analysis. MVA estimates of propagation direction are shown to diverge from the multispacecraft estimate in the limit of linear wave polarization. Theoretical estimates of MVA error are also compared to the observations. Previously established wave properties derived from ISEE are independently tested; it is found that statistically, the waves propagate at frequencies an order of magnitude below the ion cyclotron frequency in the solar wind rest frame and have wavelengths of the order of an Earth radius. However, these statements mask the fact that there is significant variation about these average values that is physical in nature. The data are plotted in the ω − k plane and the average frequency and wave number are used to experimentally identify the “average” resonant beam speed. This beam speed is an order of magnitude greater than the local Alfvén speed in the solar wind rest frame. Furthermore, histograms of the inferred beam speed normalized to the solar wind speed are presented and compared to previously published plasma data. Finally, the spacecraft frame wave period is found to be proportional to the magnetic field strength in a manner consistent with previous analyses.

Two dimensional particle-in-cell simulations of the lunar wake

The solar wind plasma from the Sun interacts with the Moon, generating a wake structure behind it, since the Moon is to a good approximation an insulator, has no intrinsic magnetic field, and a very thin atmosphere. Following earlier one and one-half dimensional (112D) simulations, 212D simulations have been studied for the first time. 212D simulations in the solar wind rest frame with an initial circular void reveal structures similar to those found in the earlier simulations, indicating that the 112D simulations are a good approximation to the physics. The infilling of the wake was found to be anisotropic, with the infilling occurring predominantly parallel to the magnetic field. The 212D simulations that are stationary with respect to the Moon, allow the effect of solar wind magnetic fields oblique to the solar wind flow to be studied, and these reveal additional assymetries.

Detailed structure and dynamics in particle-in-cell simulations of the lunar wake

The solar wind plasma from the Sun interacts with the Moon, generating a wake structure behind it, since the Moon is to a good approximation an insulator, has no intrinsic magnetic field and a very thin atmosphere. The lunar wake in simplified geometry has been simulated via a 112D electromagnetic particle-in-cell code, with high resolution in order to resolve the full phase space dynamics of both electrons and ions. The simulation begins immediately downstream of the moon, before the solar wind has infilled the wake region, then evolves in the solar wind rest frame. An ambipolar electric field and a potential well are generated by the electrons, which subsequently create a counter-streaming beam distribution, causing a two-stream instability which confines the electrons. This also creates a number of electron phase space holes. Ion beams are accelerated into the wake by the ambipolar electric field, generating a two-stream distribution with phase space mixing that is strongly influenced by the potentials created by the electron two-stream instability. The simulations compare favorably with WIND observations.

Particle‐in‐cell simulations of the lunar wake with high phase space resolution

The evolution of the lunar wake in simplified geometry can be simulated via a 1½D electromagnetic particle‐in‐cell code. By using a sufficient number of particles per cell, we are able, for the first time, to resolve the full phase space dynamics of both electrons and ions. This simulation begins immediately downstream of the moon, before the solar wind has infilled the wake region, then evolves in the solar wind rest frame. The electrons immediately begin to move into the void but are trapped by two potential wells, thus generating vortices in phase space on both sides of the wake, between which counter‐streaming electron beams interact. Ion beams are generated after the lighter electrons have moved into the void, creating a two‐stream distribution which mixes in phase space due to the potentials created by the electron two‐stream instability. Other structures are also evident. The simulations are consistent with both WIND observations and the results of earlier electrostatic simulations which focus only on the ion dynamics.

Large‐amplitude MHD waves upstream of the Jovian bow shock: Reinterpretation

Observations of large‐amplitude MHD waves upstream of the Jovian bow shock have previously been interpreted as arising from a resonant electromagnetic ion beam instability (Goldstein et al., 1983). That interpretation was based on the conclusion that the observed fluctuations were predominantly right elliptically polarized in the solar wind rest frame. Because it has been noted by the authors that the fluctuations are, in fact, left elliptically polarized (Smith et al., 1983; Goldstein et al., 1983), a reanalysis of the observations is necessary. In this paper we investigate several mechanisms for producing left‐hand‐polarized MHD waves in the observed frequency range. Instabilities excited by protons appear unlikely to account for the observations. We conclude that a resonant instability excited by relativistic electrons streaming along the magnetic field away from Jupiter is a likely source of free energy consistent with the observations. Evidence for the existence of such a population of electrons has been found in both the low energy charged particle experiments and cosmic ray experiments on Voyager 2. This new interpretation is reminiscent of observations reported by Smith et al. (1976) using Pioneer data of left‐polarized (solar wind frame) MHD fluctuations in association with relativistic electrons.

Waves observed upstream of interplanetary shocks

The properties of waves with frequencies below 3 Hz observed upstream of low Mach number (2–3) interplanetary shocks are discussed. High‐frequency emissions (0.2–2 Hz in the spacecraft frame) are commonly detected immediately upstream (<2 RE) of the shocks, whereas lower frequency emissions (∼0.05 Hz) are found to extend upstream to much greater distances (typically 10 RE). Both emissions are right‐hand circularly or elliptically polarized and generally propagate within a 15° cone angle relative to the ambient magnetic field. The lack of a significant compressional component for either of these waves is in agreement with propagation parallel to the ambient magnetic field. Upstream waves are detected principally in association with quasi‐parallel shocks (θBn < 65°). Assuming the waves are propagating outward from the shock, an expression is derived for the wave frequency in the solar wind rest frame. The waves are found to have rest frame frequencies of 0.05–1 Hz and 10−3 to 10−2 Hz. Arguments are presented which exclude the possibility that the high‐frequency waves are standing whistler mode waves. The most likely source of these emissions is generation at the shock by 100 eV to 1 keV electrons and propagation of the whistler mode waves into the upstream region. The lower frequency 10−3 to 10−2 Hz waves propagate at speeds near the Alfvén velocity, and hence cannot outrun the super‐Alfvénic shocks. These waves must be locally generated by plasma instabilities in the upstream region. Generation by Landau electrons or ions can be ruled out due to the observation of parallel propagation of the waves. The most likely source is 1–10 keV cyclotron‐resonant ions propagating away from the shock. The upstream waves bear many similarities to those observed in the earth's foreshock. The frequencies, polarization, and typical upstream extent are nearly identical. It is also deduced that the lower frequency waves of both regions are generated by keV ions streaming away from the shock. There are some differences, however. Waves upstream of interplanetary shocks are found to propagate parallel to the magnetic field (<15°), are noncompressive (ΔB/B ≤ 0.25) and are generally lower in amplitude. Additionally, there are extraordinary interplanetary events, for which the scale of the upstream wave region is greatly extended (∼1300 RE or 0.04 AU) and the field takes on a more turbulent character. The latter events should be of interest in modeling Fermi acceleration of ions at collisionless shocks.

A model for generation of bow-shock-associated upstream waves

A model is proposed for the generation of upstream hydromagnetic waves by proton beams reflected at the earth's bow shock. It is assumed that the reflection process can produce some gyrophase bunching of the protons, thus creating a gyrophase disturbance that propagates with the beam as it streams back along interplanetary field lines. This leads to the production of driven hydromagnetic waves in the left-hand mode. The resulting theory predicts a wave amplitude, frequency, and polarization in the solar wind rest frame. The amplitude depends on the fraction of protons assumed to be phase coherent in their gyromotion and on the plasma beta, beam velocity, temperatures, and the Alfven Mach number. The theory also predicts the Doppler-shifted frequencies and the apparent sense of polarization that would be observed in satellite measurement frames.