High-Mach-number collisionless schock dynamics: theory and simulations versus multi-point measurements in space
V. Krasnoselskikh (team leader), S. Bale (team co-leader), M. Balikhin, D. Burgess, M. Gedalin, T. Horbury, H. Kucharek, B. Lembege, V. Lobzin, C. Mazelle, S. Schwartz, M. Scholer
Collisionless shocks are very ubiquitous in space plasmas and play a fundamental role in a number of astrophysical environments, among which are the heliosphere, supernova remnants (SNR), gamma ray bursts (GRB), jets from black holes, and others. They are intensively studied experimentally in the near-Earth environment aboard satellites (Cluster, ISEE, AMPTE, Wind, Polar and many others), in the interplanetary space, and in the vicinity of other planets (Ulysses, Voyager, and Phobos), as well as by means of remote sensing techniques making use of radio observations of the Sun and astrophysical objects such as supernova remnants, jets etc. The most of astrophysical shocks are presumably high-Mach-number shocks.
Shock waves are usually considered to be nonlinear waves that cause irreversible changes of state of the media and from macroscopic point of view they are stationary. However, in the very beginning of the collisionless shock physics it was hypothesized that high-Mach-number shocks can be nonstationary. Later the first unambiguous evidence of the nonstationarity was obtained in the laboratory experiments and in the space observations in 70-80s. The four-spacecraft Cluster mission gives much more opportunities for experimental studies of the Earth’s bow shock nonstationarity, because multispacecraft measurements provide a good opportunity to discriminate temporal and spatial variations. The first results of Cluster measurements reveal several examples of nonstationary shock and recently the first unambiguous evidence of shock front reformation was found. However, despite of several decades of studies, there are a lot of open questions related to different aspects of nonstationarity, including front rippling and reformation. The topics we are going to work on are:
Collisionless shocks play a fundamental role in space plasmas from plasma astrophysics to solar and planetary physics. They are intensively studied in the near-Earth environment and in the vicinity of other planets, as well as in the interplanetary space, in the solar atmosphere and in astrophysical objects (supernova remnants, jets etc.). A fundamental topic of collisionless shock physics is to determine the shock front structure and its dynamics, as well as to identify the main physical processes affecting both the structure and dynamics. This topic is of crucial importance both from fundamental and practical point of view. Shock waves are involved in a huge variety of processes in the geospace environment, in the heliosphere, in interstellar space, and in different astrophysical objects. For practice, the knowledge of shock wave physics is necessary to predict space weather hazards caused by disturbances on the Sun and in the interplanetary space.
From the very beginning of the collisionless shock studies it was found that there exists a set of critical Mach numbers corresponding to qualitative changes of shock front structure and of the main dissipative and dispersive effects that form this structure. Most of the shocks in the solar wind as well as planetary bow shocks are supercritical or ion-reflection shocks. This means that shock Mach number exceeds the so-called 2nd critical Much number and ion reflection with subsequent energyzation make a significant contribution into slowing down of the incoming flow and dissipation of its kinetic energy.
In the shocks with Mach numbers larger than this critical one, the conductivity and viscosity cannot provide sufficient dissipation. A new dissipation mechanism should be invoked and one of these mechanisms was found to be an ion reflection. However, for the purely perpendicular case it was also indicated that there can exist the saturation of the number of reflected ions (Kennel et al., 1985, Hada et al., 2003).
However, in the very beginning of the collisionless shock physics Paul et al. [1967] hypothesized that high-Mach-number shocks can be nonstationary, and the first unambiguous evidence of the nonstationarity was obtained by Morse et al. [1972] in the laboratory experiments.
In the 1980s, new evidence of shock front nonstationarity were found. In particular, Vaisberg et al. [1984] reported low frequency oscillations of the ion flux in the Earth’s bow shock. Later Bagenal et al. [1987] observed a similar phenomenon in the Uranian bow shock. On the other hand, with the help of 1-D full particle simulation, a periodic self-reformation of the shock front associated with ion reflection for supercritical shock has been evidenced for the first time by Biskamp and Welter [1982]. Additional indications of these processes were found by Lembege and Dawson [1987a] for purely perpendicular shock and by Lembege and Dawson [1987b] for oblique. All these simulations used 1-D full particle code and were rather short (1/2 of upstream ion gyroperiod) but large enough to evidence it. Lembege and Savoini [1992] using improved 2D full particle simulations have analyzed in details this periodic self-reformation and have shown that this process is not an artefact of using 1D code but persists quite well even for moderate (but supercritical) Mach number and as resistive effects are fully included. This self-reformation takes place over the characteristic ion gyroperiod. It is characterized by strong variations of the fields in the vicinity of the ramp and by quasi-periodic bursty ion reflection. However, this periodic process does not exist for angles θBn below a critical value [Lembege and Savoini, 1992].
Numerical simulations performed by Leroy et al. [1982] with the use of the 1-D hybrid code showed that the front structure of perpendicular shocks varies with time, for example, the maximum value of the magnetic field (overshoot) exhibits temporal variations with a characteristic time of the order of ion gyroperiod, the magnitude of these variations being about of 20% with typical parameters for the Earth bow shock (MA = 8 and be,i = 0.6, where MA is the Alfvén Mach number, be,i is the ratio of the thermal and magnetic pressures). They also found that for MA =10 and be,i = 0.1 the ion reflection was bursty, oscillating between 0% and 70-75%. Hybrid modeling of perpendicular shocks with very high Mach numbers was carried out for the first time by Quest [1986]. He found that the ion reflection in the shocks can be periodic, the stages with 100% ion reflection alternating with the stages of 100% ion transmission. As a result, instead of a stationary structure, observed was a periodic wave breaking and shock front reformation. Later Hellinger et al. [2002] reexamined the properties of perpendicular shocks with the use of the 1-D hybrid code and observed the front reformation for a wide range of parameters if upstream protons are relatively cold and/or Mach number is high. The 1-D full particle simulation performed by Hada et al. [2003] with unrealistic electron to ion mass ratio confirmed that the periodic self-reformation of the shock front takes place if the βi is relatively low and/or Mach number is high.
Scholer et al. [2003] and Scholer and Matsukiyo [2004] using 1-D full-particle simulations with the physical ion to electron mass ratio reproduced the reformation of exactly and approximately perpendicular high-Mach-number shocks in plasmas with bi < 0.4 and demonstrated an importance of modified two-stream instability for the reformation process. With the help of a 1-D full particle simulation, Muschietti and Lembege [2006] have shown that electron cyclotron drift instability is excited in the foot region of a strictly perpendicular shock, but does not inhibit the periodic self-reformation of the shock front.
Krasnoselskikh [1985] and Galeev et al. [1988a,b] proposed models describing the shock front instability due to domination of nonlinearity over dispersion and dissipation. This instability results in a gradient catastrophe within a finite time interval. Several aspects of the model, including the role of nonlinear whistler oscillations and existence of a critical Mach number above which a nonstationarity appears, were developed in further detail and more rigorously by Krasnoselskikh et al. [2002] and complemented by numerical simulations with the use of the 1-D full particle electromagnetic code with a small ratio of electron and ion masses, me/mi = 0.005. It was shown that the transition to nonstationarity is always accompanied by disappearance of the phase-standing whistler wave train within the shock front. Moreover, for large Mach numbers the nonstationarity manifests itself as a quasi-periodic ramp reformation, which influences considerably the ion reflection that is also nonstationary and sometimes the ions are reflected from both old and new ramps simultaneously.
The four-spacecraft Cluster mission gives much more opportunities for experimental studies of the shocks. The first examples of some aspects of shock nonstationarity were presented by Horbury et al. [2001]. They analyzed magnetic field data for two quasiperpendicular shocks, with moderate and high Alfvén Mach number. While for moderate MA the shock profiles measured by different spacecraft were approximately the same, with the exception of a small-amplitude wave activity in the foot, for high MA the amplitude of the fluctuations attains ~10 nT, making profiles considerably different for different spacecraft. However, Horbury et al. [2001] argue that these fluctuations stop before the ramp and do not appear to disrupt the shock structure; on the other hand, they don't reject an opportunity that the fluctuations may be signatures of the unsteady shock reformation. Recently Lobzin et al. [2007], using Cluster observations, provided a convincing evidence that high-Mach-number quasiperpendicular shocks are nonstationary, moreover, a quasi-periodic shock front reformation takes place.
Computer simulations of high-Mach-number shocks in two-dimensional geometry led to the discovery of large-scale “ripples” [Winske and Quest, 1988; Thomas, 1989]. These ripples have a characteristic scale of 5 c/ωpi and move along the shock surface with a velocity comparable with Alfven velocity. Lowe and Burgess [2003] argue that the ripples can be considered as a surface mode. The mechanism of shock front instability leading to rippling is not understood. Winske and Quest [1988] found the resemblance between the ripples and waves generated by Alfven ion cyclotron instability. Shocks ripples have been also evidenced and analyzed by Lembege and Savoini [1992] using a 2-D full particle simulations both for strictly perpendicular and quasi-perpendicular shocks. For perpendicular shocks, these ripples have been identified as due to low-hybrid waves generated by cross-field currents instabilities at the front. However, all these ripples have rather complicated structure and could no be analyzed with the use of simple models.
Modern computer hardware allows one to extend considerably the previous simulations of high-Mach-number shocks. In particular, D. Burgess plans to begin 3D hybrid simulations. Probably, these studies will shed more light upon the nature of shock front nonstationarity and rippling.
While the shock front rippling was observed in numerical simulations, both hybrid and full-particle ones, up to now there exist only one experimental evidence that this phenomenon does exist. Moullard et al. [2006] analyzed a single event when during ~ 1 hour time interval Cluster spacecraft “touched” the bow shock and than crossed it twice during ~10 minutes. This shock is almost perpendicular, high-beta, and high-Mach-number one, with Mf = 11. It was found the observed within the front oscillations of the magnetic field and plasma density can be interpreted as a wave moving along the shock surface, and the velocity of this wave seems to make an acute angle with the upstream magnetic field, < 40˚, and vary within the range from 2 to 4 VAd, where VAd is the downstream Alfven velocity. The wavelength value estimated by Moullard is 1000-2000 km. Later Burgess [2006] performed a simulation of rippling to analyze the problems of interpretation of multipoint observations. However, a single case study cannot be considered as a convincing evidence favoring shock front rippling. In addition, a lot of questions remain open, in particular, is it a common structure and how does it depend on plasma and shock parameters? The data obtained by multi-spacecraft missions like Cluster could give an opportunity to observe rippling of the Earth’s bow shock and to analyze it in more detail.
One of the most important topics in collisionless shocks physics is related to acceleration of particles (both ions and electrons) to high energies. These particles, in their turn, could result in a variety of instabilities, both in the shock front and quite far from it. The nature of these instabilities depend on a characteristic energy of accelerated particles and the shape of their distribution function. Obviously, the shock front nonstationarity can change considerably the properties of accelerated particles populations and thereby modify the “appearance” of the shock front and its vicinity. For example, Gedalin [2001] showed that the ripples result in the enhanced diffusion in the proton velocity space.
Expected output
The proposed team will perform a detailed study of various bow shock crossings by the Cluster spacecraft with respect to shock structure and dynamics (nonstationarity, upstream standing whistlers, shock front irregularities) as outlined in the Abstract. These shocks will be simulated by numerical full particle simulations and the results will be compared with the observations. Comparison with the available theoretical models will then lead to an extension or modification of the models. It is expected that this work will lead to several papers in the scientific literature, including an article in Space Science Reviews that will resume the current state of the studies on the subject concerned. The review is expected to be submitted at the first quarter of 2009. The team members will publicize their results at scientific meetings.
Why ISSI?
Presently expertise in theoretical modeling of the structure of collsionless shocks, in numerical modeling of such shocks, and in Cluster data analysis is distributed over various research institutions in Europe, the US, and Israel. For an important step towards an understanding of the shock structure and its dynamics it is higly desirable to bring together this expertise. Appropriate bow shock crossings by Cluster have to be selected and analyzed by the experimentalists. Given the individual shock parameters these shocks should be simulated by full particle simulations by the simulationists. Both observations and simulations will be compared with the available theoretical models. If necessary the theoretical models will then be extended or modified. This requires a team of experimenters, theoreticians and simulationists working closely together. The team members have different field of expertise including plasma theory, observations, data processing, and numerical simulations of space plasma phenomena. It is impossible to carry out such an ambitious project only by electronic communication. ISSI is the ideal environment to bring together the proposed team of experts from various countries.
List of confirmed participants (with appended short CVs)
Pr. S. Bale (UCB, Berkeley, USA),
Pr. M. Balikhin (University of Sheffield, Sheffield, UK),
Dr. D. Burgess (Astronomy Unit, Queen Mary, University of London),
Pr. M. Gedalin (Ben Gurion University of Beer-Sheva, Beer-Sheva, Israel),
Dr. T. Horbury (Imperial College, London, UK),
Dr. V. Krasnoselskikh (team leader, LPCE/CNRS-University of Orleans, Orleans, France),
Dr. H. Kucharek (University of New Hampshire, USA),
Dr. B. Lembege (CETP-CNRS-UVSQ-IPSL),
Dr. V. Lobzin (le Studium Institute for Advanced Studies, Orléans, France),
Dr. C. Mazelle (CESR/CNRS, Toulouse, France),
Pr. S. Schwartz (Imperial College, London, UK),
Pr. M. Scholer (Max-Planck-Institute, Garching, Germany, retired).
We suppose also to invite several experts to reinforce our team using another sources of funding.
Schedule of the project
To achieve the goals of the project we plan to organize three workshops/meetings of the team at ISSI. On the first workshop during first two days we shall form topical groups and formulate crucial issues to work on, then the work will be organized in the frame of these groups. We shall define the objectives to be achieved and will choose several shocks to perform comparative studies using data analysis, computer simulations, and theoretical analysis. The second meeting will be dedicated to compare the results of studies of different groups and putting them together. This comparison of the results will allow us to clarify where the theoretical models are in a good agreement with the observations and what are critical points of disagreement between the modeling and experiment. The third meeting will be partly organized in groups to finalize their results, but most of the work will be dedicated to organization and preparation of the whole review paper. The average number of people supposed to attend each meeting will be 10-12 people. The first meeting/workshop is supposed to be held at the end 2007 or at the beginning of 2008, the second one in the late spring or beginning of summer 2008, and the last one at the end of 2008. The review paper will be ready for publication within 3-4 months after the last meeting.
The workshops require Internet access and computer terminals for participants without laptops. Data are available to the group at no cost to ISSI.
We apply for a financial support for the meeting participants during their stay in Bern. The funding we ask ISSI is for 3 weeks duration meetings for 12 participants. Travel support is requested only for the team leader. If the funding will be smaller, we can consider an opportunity to organize the third “editorial” meeting with smaller number of participants.
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