A stationary bow shock model for plasmas: The spherical blunt obstacle problem

We present an analytic model of a stationary bow shock which describes the interaction between a supermagnetosonic ambient wind and an obstacle with spherical-like frontal shape. We develop expressions for the bow shock’s geometry and the physical properties of the plasma sheath as functions of the upstream conditions. The solution is limited to magnetic fields parallel to the upstream velocity. The model allows to use any value of the upstream alfvenic and sonic Mach numbers and the polytropic index (γ$\gamma$), pointing out the influence of γ$\gamma$ for the magnetosheath compression and the bow shock shape. When both Mach numbers are small, the upstream magnetic field intensity affects also the bow shock shape. We compare our results with other models finding important consistencies. We also compare our results with in-situ data, we fund a reasonable qualitative agreement; however, it seems that our model underestimates the magnetosheath size.     

Fluctuations of cosmic rays and IMF in the vicinity of interplanetary shocks

Fluctuations of cosmic rays and interplanetary magnetic field upstream of interplanetary shocks are studied using data of ground-based polar neutron monitors as well as measurements of energetic particles and solar wind plasma parameters aboard the ACE spacecraft. It is shown that coherent cosmic ray fluctuations in the energy range from 10 keV to 1 GeV are often observed at the Earth’s orbit before the arrival of interplanetary shocks. This corresponds to an increase of solar wind turbulence level by more than the order of magnitude upstream of the shock. We suggest a scenario where the cosmic ray fluctuation spectrum is modulated by fast magnetosonic waves generated by flux of low-energy cosmic rays which are reflected and/or accelerated by an interplanetary shock.     

Energetic positive ions in the cometary “foreshock” region

Ions produced by ionization of the cometary neutrals interact with the solar wind protons to produce large amplitude oscillations of the ambient magnetic field. Such oscillations are convected towards the comet at the unperturbed solar wind speed far from the shock and at a lower speed closer to the shock (due to the solar wind mass loading); hence, they can energize the incoming ions by Fermi acceleration. The spatial extension of the acceleration region is of the order of 10⁶ km and the resulting energy spectrum is harder than in the Earth's bow shock case. The energization of cometary ions produces an additional deceleration of the solar wind. It is suggested that Comet Halley may be the most efficient “cosmic ray shock” in the solar system.     

Swarm – An Earth Observation Mission investigating Geospace

The Swarm mission was selected as the 5th mission in ESA’s Earth Explorer Programme in 2004. This mission aims at measuring the Earth’s magnetic field with unprecedented accuracy. This will be done by a constellation of three satellites, where two will fly at lower altitude, measuring the gradient of the magnetic field, and one satellite will fly at higher altitude. The measured magnetic field is the sum of many contributions including both magnetic fields and currents in the Earth’s interior and electrical currents in Geospace. In order to separate all these sources electric field and plasma measurements will also be made to complement the primary magnetic field measurements. Together these will allow the deduction of information on a series of solid earth processes responsible for the creation of the fields measured. The completeness of the measurements on each satellite and the constellation aspect, however, implies simultaneous observations of a unique set of important electrodynamical parameters crucial for the understanding of the physical processes in Geospace, which are an important part of the objectives of the International Living With a Star Programme, ILWS. In this paper an overview of the Swarm science objectives, the mission concept, the scientific instrumentation, and the expected contribution to the ILWS programme will be summarized.     

On the large-scale structure of the tail current as measured by THEMIS

The magnetic field structure and the spatial characteristics of the large-scale currents in the magnetospheric tail were studied during quiet and moderately disturbed geomagnetic conditions in 2009. The magnetic field of the currents other than the tail current was calculated in terms of a paraboloid model of the Earth’s magnetosphere, A2000, and was subtracted from measurements. It was found on the base of obtained tail current magnetic field radial distribution that the inner edge of the tail current sheet is located in the night side magnetosphere, at distances of about 10 R_E and of about 7 R_E during quiet and disturbed periods respectively. During the disturbance of February 14, 2009 (Dst_min ∼ −35 nT), the B_x and the B_z component of the tail current magnetic field near its inner edge were about 60 nT, and −60 nT that means that strong cross-tail current have been developed. The tail current parameters at different time moments during February 14, 2009 have been estimated. Solar wind conditions during this event were consistent with those during moderate magnetic storms with minimum Dst of about −100 nT. However, the magnetospheric current systems (magnetopause and cross-tail currents) were located at larger geocentric distances than typical during the 2009 extremely quiet epoch and did not provide the expected Dst magnitude. Very small disturbance on the Earth’s surface was detected consistent with an “inflated” magnetosphere.     

Small-scale deformation of the bow shock

The prediction of the bow shock location is a proof of our understanding of the processes governing the solar wind – magnetosphere interaction. However, the models describing the bow shock location as a function of upstream parameters are based on a statistical processing of bow shock crossings observed by a single spacecraft. Such crossings locate the bow shock in motion, i.e., in a non-equilibrium state and this fact can be a source of significant errors. We have carefully analyzed a long interval of simultaneous observations of the bow shock and magnetopause and another interval of bow shock observations at two well-separated points. Our results suggest that often a small-scale deformation of the bow shock front due to magnetosheath fluctuations is the most appropriate interpretation of observations. Since the low-frequency magnetosheath variations exhibit largest amplitudes, a simultaneous bow shock displacement over a distance of 10–15 R_E can be observed. We suggest that bow shock models can be probably improved if the tilt angle would be implemented as a parameter influencing the bow shock location in high latitudes.     

Plasma flow variations and energetic protons upstream of the earth’s bow shock: A statistical study

Foreshock is a special region located upstream of the Earth’s bow shock characterized by the presence of various plasma waves and fluctuations caused by the interaction of the solar wind plasma with particles reflected from the bow shock or escaping from the magnetosphere. On the other hand, foreshock fluctuations may modify the bow shock structure and, being carried through the magnetosheath, influence the magnetopause. During the years 1995–2000, the INTERBALL-1 satellite made over 10,000 hours of plasma and energetic particles measurements in the solar wind upstream of the Earth’s bow shock. We have sorted intervals according to the level of solar wind ion flux fluctuations and/or according to the flux of back-streaming energetic protons. An analysis of connection between a level of ion flux fluctuations and fluxes of high-energy protons and their relation to the IMF orientation is presented.     

Neutron monitor asymptotic directions of viewing during the event of 13 December 2006

During the recent ground level enhancement of 13 December 2006, also known as GLE70, solar cosmic ray particles of energy bigger that ∼500 MeV/nucleon propagated inside the Earth’s magnetosphere and finally accessed low-altitude satellites and ground level neutron monitors. The magnitude and the characteristics of this event registered at different neutron monitor stations of the worldwide network can be interpreted adequately on the basis of an estimation of the solar particle trajectories in the near Earth interplanetary space. In this work, an extended representation of the Earth’s magnetic field was realized applying the Tsyganenko 1989 model. Using a numerical back-tracing technique the solar proton trajectories inside the magnetospheric field of the Earth were calculated for a variety of particles, initializing their travel at different locations, covering a wide range of energies. In this way, the asymptotic directions of viewing were calculated for a significant number of neutron monitor stations, providing crucial information on the Earth’s “magnetospheric optics” for primary solar cosmic rays, on the top of the atmosphere, during the big solar event of December 2006. The neutron monitor network has been treated, therefore, as a multidimensional tool that gives insights into the arrival directions of solar cosmic ray particles as well as their spatial and energy distributions during extreme solar events.     

Two-dimensional phase plane structure and the stability of the orbital motion for space debris in the geosynchronous ring

Based on the orbital resonance model, we study the two-dimensional phase plane structure of the motion of space debris orbiting the geosynchronous ring under the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ of the Earth’s gravitational field. We present the main characteristic parameters of the two-dimensional phase plane structure. We also analyze the stability of the two-dimensional phase plane structure with numerical method. Our main findings indicate that the combined effects of the tesseral harmonics J₂₂, J₃₁ and J₃₃ fully determine the two-dimensional phase plane structure of the space debris, and it remains robust under the effect of the Earth’s actual gravitational field, the luni-solar perturbations and the solar radiation pressure with the normal area-to-mass ratios.     

Rapid and Asymmetric Response of the Earth's Bow Shock:Multipoint Observations

We analyze observations of three bow shock crossings which occurred during 2007, using upstream data from STEREO A/B, ACE and WIND, combined with multi-point THEMIS and Cluster data, and TC-1 data located near noon. During the crossing of 7 May 2007, we find that following a rapid reduction in solar wind ram pressure and subsequent pressure pulse seen by ACE and WIND upstream, the bow shock responds asymmetrically from dawn to dusk. Cluster data on the dawn-side suggest the bow shock is significantly flared and responds rapidly to the pulse arrival, while TC-1 at noon, and THEMIS on the dusk-side, are well matched to the model bow shock, but show a delayed response. The crossings observed on 21 May and 2 June show contrasting response matching the model boundary for northward Interplanetary Magnetic Field (IMF). The IMF and solar wind plasma data suggest that the bow shock crossing at dawn-dusk side and subsolar point were mainly caused by large and smaller scale features of the solar wind ram pressure rise rather than the influence of IMF.      

Radiation from relativistic shocks in turbulent magnetic fields

Using our new 3-D relativistic particle-in-cell (PIC) code parallelized with MPI, we investigated long-term particle acceleration associated with a relativistic electron–positron jet propagating in an unmagnetized ambient electron–positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic shock compression. In the jet (reverse) shock behind the bow (forward) shock the strongest electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to calculate radiation from first principles that goes beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations. Initially we calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We then used the technique to calculate emission from electrons in a small simulation system. From these simulations we obtained spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields with red noise. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger simulation system may generate a jitter/synchrotron spectrum.     

Thermal neutrons’ response to the GLEs

Thermal neutrons’ flux near the Earth’s crust is very sensitive regarding different processes and phenomena both in the near-Earth space and in the Earth’s crust by reason of the dual nature of the thermal neutron flux. Its first source is associated with high-energy particles of cosmic rays penetrating into the Earth’s atmosphere and interacting with its elements. The second source originates from the radioactive gases contained in the Earth’s crust. So the contributions of these two sources are specified by the Earth’s crust conditions and its movements, on one hand and variations of high-energy particles flux near the Earth.     

地球弓激波的三维模拟

利用磁流体动力学(MHD)全球模拟结果,根据弓激波的跃变特性确定出弓激波位置,建立了一个新的综合考虑了快磁声马赫数、太阳风动压、行星际磁场强度以及磁层顶曲率半径的弓激波三维位型模型.将新模型与以往模型的模拟结果进行比较发现,新的弓激波全球模型结果可靠,解决了部分现有模型不能描述弓激波三维位型的问题.研究结果表明,在行星际磁场北向时,随着快磁声马赫数的增大,弓激波日下点距离减小,但是在行星际磁场南向时,快磁声马赫数的变化对弓激波日下点距离影响不大;弓激波位型在赤道面与子午面上存在明显的不对称性,而且随着行星际磁场的转向,这种非对称性也会发生相应改变;行星际磁场南向,B_z值较小时,子午面内弓激波位型已经不是简单的抛物线,出现了明显的类似于极尖区磁层顶的凹陷变化区.      

行星际起伏向磁层顶的输运

时间尺度为分钟数量级的太阳风速度和行星际磁场大幅度扰动实际上始终存在于行星际空间的。这些扰动一直传输到紧贴磁层边界面外侧的区域。它们在磁鞘等离子体和磁层顶的相互作用过程中可能起很重要的作用。行星际起伏中的磁场分量在通过地球弓激波时首先经历一次跳跃,然后一部分扰动被带到磁层边界面处。在边界面附近磁场扰动幅度被大大地放大了。弓激波上游的太阳风条件控制了放大因子。本文所作的数值模拟研究结果表明,如果上游有大幅度的扰动,在边界面附近就有大幅度的Alfven起伏的磁场分量。当上游磁场接近垂直于日地联线时,放大因子变得相当大,而且放大因子随上游的等离子体β值和/或Alfven马赫数的增加而增加。上游各向异性对放大因子的影响不大。在磁层边界附近存在大幅度起伏表明这里不存在稳定的片流。      

Cosmic ray anisotropies in the outer heliosphere

The observation of the directional distribution of energetic and cosmic ray particles has been done with the Voyager spacecraft over a long period. Since 2002, when the first flux enhancements of charged particles associated with the approach of Voyager 1 to the solar wind termination shock were observed, these anisotropy measurements have become of special interest. They play an important role to understand the magnetic field and shock structure and the basics of the modulation of cosmic ray and anomalous particles at and beyond the termination shock. They also serve as motivation to study the spatial behavior of galactic and anomalous cosmic ray anisotropies with numerical modulation models in order to illustrate how the radial anisotropy, at different energies, change from upstream to downstream of the termination shock. Observations made by Voyager 1 indicate that the termination shock is a complicated region than previously thought, hence the effects of the latitude dependence of the termination shock’s compression ratio and injection efficiency on the radial anisotropies of galactic and anomalous protons will be illustrated. We find that the magnitude and direction of the radial anisotropy strongly depends on the position in the heliosphere and the energy of particles. The effect of the TS on the radial anisotropy is to abruptly increase its value in the heliosheath especially in the A > 0 cycle for galactic protons and in both polarity cycles for anomalous protons. Furthermore, the global effect of the latitude dependence of the shock’s compression ratio is to increase the radial anisotropy for galactic protons throughout the heliosphere, while when combined with the latitude dependence of the injection efficiency this increase depends on modulation factors for anomalous protons and can even alter the direction of the radial anisotropy.     

Energetic ion acceleration and transport in the upstream region of Jupiter: Voyager 1 and 2

Long-lived upstream energetic ion events at Jupiter appear to be very similar in nearly all respects to upstream ion events at earth. A notable difference between the two planetary systems is the enhanced heavy ion compositional signature reported for the Jovian events. This compositional feature has suggested that ions escaping from the Jovian magnetosphere play an important role in forming upstream ion populations at Jupiter. In contrast, models of energetic upstream ions at earth emphasize $\text{in situ}$ acceleration of reflected solar wind ions within the upstream region itself. Using Voyager 1 and 2 energetic (? 30 keV) ion measurements near the magnetopause, in the magnetosheath, and immediately upstream of the bow shock, we examine the compositional patterns together with typical energy spectra in each of these regions. We find characteristic spectral changes late in ion events observed upstream of the bow shock at the same time that heavy ion fluxes are enhanced and energetic electrons are present. A model involving upstream Fermi acceleration early in events and emphasizing energetic particle escape in the prenoon part of the Jovian magnetosphere late in events is presented to explain many of the features in the upstream region of Jupiter.     

Measurements of the radiation quality factor Q at aviation altitudes during solar minimum (2006–2008)

In radiation protection, the Q-factor has been defined to describe the biological effectiveness of the energy deposition or absorbed dose to humans in the mixed radiation fields at aviation altitudes. This particular radiation field is generated by the interactions of primary cosmic particles with the atoms of the constituents of the Earth’s atmosphere. Thus the intensity, characterized by the ambient dose equivalent rate H∗(10), depends on the flight altitude and the energy spectra of the particles, mainly protons and alpha particles, impinging on the atmosphere. These charged cosmic projectiles are deflected both by the interplanetary and the Earth’s magnetic field such that the corresponding energy spectra are modulated by these fields. The solar minimum is a time period of particular interest since the interplanetary magnetic field is weakest within the 11-year solar cycle and the dose rates at aviation altitudes reach their maximum due to the reduced shielding of galactic cosmic radiation. For this reason, the German Aerospace Center (DLR) performed repeated dosimetric on-board measurements in cooperation with several German airlines during the past solar minimum from March 2006 to August 2008. The Q-factors measured with a TEPC range from 1.98 at the equator to 2.60 in the polar region.     

The evolution of mirror type magnetic fluctuations in the magnetosheath based on multipoint observations

Two orbits were selected in January–February 2006 when the separation between the Cluster spacecraft was large and mirror type magnetic field fluctuations were observed by all spacecraft in different regions of the terrestrial magnetosheath. Minimum variance analysis was applied to find the mirror type fluctuations, and the amplitude of the fluctuations was determined individually. Mirror mode structures are moving along the streamlines frozen in the plasma. A model was developed for the calculation of plasma flowtime from the bow shock to the observation point. The growth rate of the field strength perturbations was estimated by comparing the amplitudes of fluctuations observed simultaneously at distant locations (∼10,000 km) based on the assumption that δB ∼ exp(γt). The obtained growth rate values were about an order of magnitude smaller than those provided by linear models and they decreased in the inner regions of the magnetosheath, indicating some saturation in the growth of the waves when proceeding towards the magnetopause. The results of these two case studies suggest that mirror type fluctuations originate from the compression region downstream of the quasi-perpendicular bow shock, and the growth of the fluctuations cannot be described by linear approximations.     

Jovian periodicities (∼10 h, ∼40 min) on Ulysses’ Distant Jupiter Encounter observations around the Halloween CIR events

We analyzed data from four different instruments (HI-SCALE, URAP, SWOOPS, VHM/FGM) onboard Ulysses spacecraft (s/c) and we searched for possible evidence of Jovian emissions when the s/c approached Jupiter during the times of Halloween events (closest time approach/position to Jupiter: February 5, 2004/R = 1683 R_J,θ = ∼49°). In particular, we analyzed extensively the low energy ion measurements obtained by the HI-SCALE experiment in order to examine whether low energy ion/electron emissions show a symmetry, and whether they are observed at north high latitudes upstream from the jovian bow shock, as is known to occur in the region upstream from the south bow shock as well ( Marhavilas et al., 2001). We studied the period from October 2003 to March 2004, as Ulysses moved at distances 0.8–1.2 AU from the planet at north Jovicentric latitudes <75°, and we present here an example of characteristic Jovian periodicities in the measurements around a CIR observed by Ulysses on days ∼348–349/2003 (R = 1894 R_J,θ = 72°). We show that Ulysses observed low energy ion (∼0.055–4.7 MeV) and electron (>∼40 keV) flux and/or spectral modulation with the Jupiter rotation period (∼10 h) as well as variations with the same period in solar wind parameters, radio and magnetic field directional data. In addition, characteristic strong ∼40 min periodic variations were found superimposed on the ∼10 h ion spectral modulation. Both the ∼10 h and ∼40 min ion periodicities in HI-SCALE measurements were present in several cases during the whole period examined (October 2003 to March 2004) and were found to be more evident during some special conditions, for instance during enhanced fluxes around the start (forward shock) and the end (reverse shock) of CIRs. We infer that the Jovian magnetosphere was triggered by the impact of the CIRs, after the Halloween events, and it was (a) a principal source of forward and reverse shock-associated ion flux structures and (b) the cause of generation of ∼10 h quasi-periodic magnetic field and plasma modulation observed by Ulysses at those times.     

Determination of reconnected flux via remote sensing

Magnetic reconnection is one of the most fundamental processes in the magnetosphere. We present here a simple method to determine the essential parameters of reconnection such as reconnected flux and location of the reconnection site out of single spacecraft data via remote sensing. On the basis of a time-dependent reconnection model, the dependence of the reconnected flux on the magnetic field z-component B_z is shown. The integral of B_z over time is proportional to the reconnected flux and depends on the distance between the reconnection site and the actual position where B_z is measured. This distance can be estimated from analysis of magnetic field B_z data. We apply our method to Cluster measurements in the Earth’s magnetotail.