Cluster at the Bow Shock Status and Outlook

M. Scholer1, M. F. Thomsen2, D. Burgess3, S. D. Bale4, M. A. Balikhin5, A. Balogh6, T. S. Horbury6, V. V. Krasnoselskikh7, H. Kucharek8, E. A. Lucek6, B. Lembege9, E. Mobius8 10, S. J. Schwartz3 11, and

When some dynamical energy release occurs in dilute astrophysical plasmas, collisionless shocks arise where the macroscopic flow is regulated by microscopic dissipation and where selective particle acceleration may occur. Collisionless shocks are found in the corona of the Sun, in the solar wind, in front of planetary magnetospheres, and in many other astrophysical settings. The two main questions in collisionless shock physics are: (1) how is dissipation achieved in a plasma where two-body Coulomb collisions are unimportant, and (2) how is part of the thermal plasma accelerated to high energies? The Earth's bow shock is a collisionless shock where these questions have been investigated in great detail for more than three decades by in situ observations. It turned out that physical processes at the bow shock occur on all spatial scales, from the electron inertial scale

I Max-Planck-Institut für extraterrestrische Physik, Garching, Germany

2Los Alamos National Laboratory, Los Alamos, NM, USA

3 Astronomy Unit, Queen Mary, University of London, London, UK

4 Department of Physics and Space Sciences Laboratory, University of California, Berkeley, CA, USA

5 Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK

6Space and Atmospheric Physics, The Blackett Laboratory, Imperial College London, London, UK

7LPCE/CNRS, Orleans, France

8Space Science Center, Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire, USA

9CETP/IPSL, Velizy, France

10Also Department of Physics, University of New Hampshire, Durham, New Hampshire, USA

II Now at Space and Atmospheric Physics, The Blackett Laboratory, Imperial College London, London, UK

Space Science Reviews 118: 223-227, 2005. DOI: 10.1007/s11214-005-3833-2

© Springer 2005

in the ramp of the quasi-perpendicular bow shock to many hundreds of ion iner-tial scales in the foreshock region of the quasi-parallel bow shock. Cluster with its multi-spacecraft capability provides the unique opportunity to unravel many of the outstanding questions in collisionless shock physics. But, as we have seen, when answering one question a plethora of new questions arises. The main achievements of Cluster concerning the Earth's bow shock so far are:

1. Determination of the length scales of the quasi-perpendicular bow shock associated with the shock ramp, overshoot/undershoot, and downstream wavetrain.

2. Detection of small scale electric field structures in the ramp of the quasi-perpendicular bow shock

3. Revealing the origin of field-aligned beams at the quasi-perpendicular bow shock

4. Determination of the internal structure of the short large-amplitude structures in the upstream region of the quasi-parallel bow shock

5. Determination of the mean free path of diffuse energetic ions upstream of the quasi-parallel bow shock

One of the important questions in collisionless shock physics is to which degree the steepening of a magnetosonic wave leading to the shock is balanced by either dissipation or dispersion. The relevant spatial scale associated with dispersion is the electron or ion inertial length, whereas dissipation due to gyroviscosity associated with gradients of the ion stress tensor introduces the gyroscale of the ions in the shock. Bale et al. (2003) have shown that the largest density transition scale of the quasi-perpendicular bow shock is, independent of shock (mgnetosonic) Mach number, the convected ion gyroradius. In contrast, the shock scale in units of the ion inertial scale increases with shock Mach number. The ion inertial scale seems to be appropriate at low Mach numbers only. This demonstrates the importance of gyroviscosity (within the fluid picture) for dissipation in quasi-perpendicular shocks. In astrophysical settings high Mach number, low beta shocks are of particular interest. It remains to be seen whether low beta shocks also scale with the convected ion gyroradius since some particle simulations predict, at least during short times, very small shock transition regions of the order of several electron scales.

The Bale et al. (2003) analysis captures only the largest transition scale at the shock. However, as demonstrated by the electric field measurements by Walker et al. (2004), there are fine-scale features of the electric field in the ramp of the quasi-perpendicular bow shock down to the electron inertial scale. These electric field excursions in the ramp have large amplitudes (up to 70 mVm-1), are layered, with normals in the general shock normal direction, and can contribute up to 50% to the cross shock potential. The origin and nature of these electric field structures is yet unclear and deserves further intense investigation. It will also be interesting to see whether and/or how these electric field structures influence the adiabaticity of the electrons when they pass through the shock ramp.

While it has been known since the ISEE era that the quasi-perpendicular bow shock is a source of field-aligned beams, the Cluster multi-spacecraft capability has now given important clues as to the production mechanism of these beams. During bow shock crossings often one spacecraft has been downstream of the shock while another spacecraft has been upstream and observed a field-aligned beam with speeds of about 1500 km/s. As shown by Kucharek et al. (2004) in the same velocity region the downstream distribution is virtually empty, indicating that these beams do not originate from leakage of downstream heated solar wind ions. In the ramp the gyrating ions are observed which are due to specular reflection. As these ions interact again during their orbital motion with the ramp magnetic field in such a way that their energy is constant in the de Hoffmann-Teller frame they can reach a region in phase space where they have a large velocity parallel to the field and can escape upstream in the form of field-aligned ion beams. However, details of this process have still to be worked out. The picture becomes more complicated due to the three-dimensional structure of the bow shock on smaller scales: for instance, ripples on the shock may change locally the magnetic field-shock normal angle which allows particles to escape which otherwise would have been transmitted downstream. Other open questions are: what determines the intensity of the field-aligned beam and what role does the cross-shock potential play in reflecting the particles? The large data base provided by Cluster constitutes an ideal platform to study these questions in the future in considerable detail.

The upstream region of the quasi-parallel shock is spatially extended and constitutes an inhomogeneous transition region. This region is dominated by diffuse backstreaming energetic ions, supposedly accelerated at the shock out of the solar wind thermal population, ultra-low frequency waves generated by these ions, and large amplitude magnetic pulsations (SLAMS) as the shock is approached. SLAMS are most probably vital for the thermalization process in quasi-parallel collisionless shocks, i.e., understanding their growth, shape and size will contribute to understanding in detail how the inhomogeneous components of the shock cause the ther-malization of the plasma. Observations by Cluster upstream of the quasi-parallel bow shock have revealed the internal structure of the SLAMS. It was anticipated that the spatial extent of SLAMS is of the order of one Earth radius. However, it has been found that the SLAMS are highly structured on a much smaller scale: Lucek et al. (2002) reported in SLAMS significant variations of the magnetic field magnitude when the tetrahedron scale was of the order of 600 km. SLAMS orientation has so far been difficult to determine: when the tetrahedron scale was 600 km the structures seen at different spacecraft were rather different, while at a tetrahedron scale of 100 km no information of the orientation over larger scales than the spacecraft separation scale can be made. From timing analysis it was con firmed that SLAMS are fast mode structures propagating sunward in the solar wind frame (Behlke et al., 2003; Stasiewicz et al., 2003). However, the motional electric field within the SLAMS is equal to the measured electric field, indicating that the plasma in the SLAMS moves with the same velocity as the structure itself. The quasi-parallel bow shock clearly contains multiple scale lengths, and further analysis of current Cluster data, together with future Cluster observations at intermediate and large scales can address some of the outstanding questions.

Diffuse energetic ions upstream of the quasi-parallel bow shock are strong evidence for first order Fermi (or diffusive) acceleration at the shock. First order Fermi acceleration requires that the particles cross and recross the shock many times, i.e., they have to be pitch angle scattered in the upstream and downstream medium or, in other words, the mean free path parallel to the magnetic field has to be sufficiently small. When particles diffuse from the shock along the magnetic field upstream against the convection of the solar wind the intensity has to fall off in the steady state exponentially with an e-folding distance given by the diffusion coefficient and the solar wind velocity. Cluster allows for the first time the direct determination of the e-folding distance of the diffuse ion density in the upstream region, and, in turn, a determination of the diffusion coefficient and the mean free path, respectively. During one particular event when the tetrahedron scale was about 5000 km the e-folding distance of the partial diffuse ion densities has been determined in several energy bands in the range between 10 and 32 keV. From the e-folding distances a mean free path from about 0.5 Earth radii at the lowest energy and 3 Earth radii at the highest energy has been determined (Kis et al., 2004). This shows that upstream ions indeed undergo diffusive spatial transport in the region of the quasiparallel shock and strongly supports the claim that the quasi-parallel bow shock accelerates these ions. An unsolved problem in collisionless shock physics is the so-called injection problem, i.e., how and why a certain part of the thermal solar wind is further accelerated at the shock. It is to be hoped that detailed Cluster studies of the quasi-parallel bow shock also help in unravelling this problem.

The future for Cluster studies of the Earth's bow shock is bright and exciting. The datasets used in the work reported here hold considerably more information waiting to be exploited to the full. Subsequent data will take advantage of novel separation strategies to explore new (mainly larger) scales and to target nearly planar surfaces, such as the bow shock, by correspondingly non-regular tetrahedral spacecraft configurations which take account of the fact that the scales along and perpendicular to the surface are not necessarily the same. The orbit evolution will cause Cluster to encounter the bow shock at lower latitudes and thus closer to the sub-solar regions. Under nominal solar wind conditions, the expected Mach numbers will be higher, as the solar wind velocity and shock normal will be more collinear. Quasi-parallel shock geometries will be more frequently encountered, due to the tendency for 'Parker spiral' interplanetary fields to be predominantly in the plane of the ecliptic. Finally, combined studies with other outer magneto-

spheric missions will provide new opportunities to apply existing, and new, multi-spacecraft techniques to the many outstanding issues.

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