A collisionless shock is often regarded as a discontinuity with a plasma flow across it. Plasma parameters before the shock (upstream) and behind the shock (downstream) are related by the Rankine-Hugoniot relations (RH) which essentially are the mass, momentum, and energy conservation laws. Standard RH assume the upstream and downstream regions are uniform, that is, the fluctuations of the plasma parameters and magnetic field are negligible. Observations show that there exist shocks in which these fluctuations remain large well behind the shock. The pressure and energy of these fluctuations have to be included in the total pressure and energy. Here we lay down a basis of theory taking into account persisting non-negligible turbulence. The theory is applied to the case where only downstream magnetic turbulence is substantial. It is shown that the density and magnetic field compression ratios may significantly deviate from those predicted by the standard RH. Thus, turbulent effects should be taken into account in observational data analyses.
The density compression ratio N = nd/nu (left column) and the magnetic compression ratio R = Bd/Bu (right column), as functions of the Alfvénic Mach number M, for two cases: a) θu = 60°, β = 0.2 (top row), and b) θu = 20°, β = 2 (bottom row). In both case presence of fluctuations results in the increase of the compression ratios.
Full Article: Gedalin, M. (SHARP) (2023). Rankine-Hugoniot relations in turbulent shocks. Frontiers in Physics, 11, doi: 10.3389/fphy.2023.1325995
The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically.
Three components and the magnitude of the magnetic field in the VSO coordinate system as observed during the Venusian bow shock crossing on 2011 July 26. The transition is highlighted by the gray shaded area.
Full Article: Balikhin, M. A., Gedalin, M. (SHARP), Walker, S. N., Agapitov, O. V., Zhang, T. (2023). Structure of a quasi-parallel shock front. The Astrophysical Journal, 959, doi: 10.3847/1538-4357/ad0b7
Context. Solar Orbiter, a mission developed by the European Space Agency, explores in situ plasma across the inner heliosphere while providing remote-sensing observations of the Sun. The mission aims to study the solar wind, but also transient structures such as interplanetary coronal mass ejections and stream interaction regions. These structures often contain a leading shock wave that can differ from other plasma shock waves, such as those around planets. Importantly, the Mach number of these interplanetary shocks is typically low (1–3) compared to planetary bow shocks and most astrophysical shocks. However, our shock survey revealed that on 30 October 2021, Solar Orbiter measured a shock with an Alfvén Mach number above 6, which can be considered high in this context.
Aims. Our study examines particle observations for the 30 October 2021 shock. The particles provide clear evidence of ion reflection up to several minutes upstream of the shock. Additionally, the magnetic and electric field observations contain complex electromagnetic structures near the shock, and we aim to investigate how they are connected to ion dynamics. The main goal of this study is to advance our understanding of the complex coupling between particles and the shock structure in high Mach number regimes of interplanetary shocks.
Methods. We used observations of magnetic and electric fields, probe-spacecraft potential, and thermal and energetic particles to characterize the structure of the shock front and particle dynamics. Furthermore, ion velocity distribution functions were used to study reflected ions and their coupling to the shock. To determine shock parameters and study waves, we used several methods, including cold plasma theory, singular-value decomposition, minimum variance analysis, and shock Rankine-Hugoniot relations. To support the analysis and interpretation of the experimental data, test-particle analysis, and hybrid particle in-cell simulations were used.
Results. The ion velocity distribution functions show clear evidence of particle reflection in the form of backstreaming ions several minutes upstream. The shock structure has complex features at the ramp and whistler precursors. The backstreaming ions may be modulated by the complex shock structure, and the whistler waves are likely driven by gyrating ions in the foot. Supra-thermal ions up to 20 keV were observed, but shock-accelerated particles with energies above this were not.
Evolution of ion VDFs across the shock. Panel a shows a reduced distribution of the phase-space density along the shock normal, and we plot in panel b the magnetic field in shock coordinates. The bottom panels show ion VDFs in the plane (panels c to i) and at various locations from upstream to downstream of the shock front. refers to Bu. An ion population (in all the VDFs) that is separate from the solar wind beam is noticeable.
Full Article: Dimmock, A. P. (SHARP), Gedalin, M. (SHARP), Lalti, A. (SHARP), Trotta, D., Khotyaintsev, Yu. V. (SHARP), Graham, D. B. (SHARP), Johlander, A., Vainio, R., Blanco-Cano, X., Kajdič, P., Owen, C. J. and Wimmer-Schweingruber, R. F. (2023). Backstreaming ions at a high Mach number interplanetary shock – Solar Orbiter measurements during the nominal mission phase. Astronomy and Astrophysics, 679, doi: 10.1051/0004-6361/202347006
In fast collisionless shocks, the density and magnetic field increase and the plasma is heated. The compression and heating are ultimately determined by the Rankine–Hugoniot relations connecting the upstream and downstream parameters. The standard Rankine–Hugoniot relations take into account only mean upstream and downstream parameters. Observations at the Earth’s bow shock show that the downstream magnetic field does not always relax to a uniform state, but large amplitude magnetic oscillations persist. Here, these Rankine–Hugoniot relations are extended to such turbulent shocks where the mean downstream magnetic field is accompanied by magnetic fluctuations. It is shown that the turbulent magnetic field pressure may substantially exceed the pressure of the mean field, while the density compression and heating may be only weakly affected. Thus, strong amplification of the rms magnetic field can be achieved at the expense of a modest reduction of plasma heating.
Left: dependence of the density compression N = ρd/ρu on the turbulent magnetic pressure . Right: dependence of the normalized downstream ion temperature on the turbulent magnetic pressure . The range of X in the figure is limited by the condition X < P.
Full Article: Gedalin, M. (SHARP) (2023). Rankine–Hugoniot Relations and Magnetic Field Enhancement in Turbulent Shocks. The Astrophysical Journal, 958, doi: 10.3847/1538-4357/ad0461
Diffusive shock acceleration requires the production of backstreaming superthermal ions (injection) as a first step. Such ions can be generated in the process of scattering of ions in the superthermal tail off the shock front. Knowledge of the scattering of high-energy ions is essential for matching conditions of upstream and downstream distributions at the shock transition. Here we analyze the generation of backstreaming ions as a function of their initial energy in a model stationary shock and in a similar rippled shock. Rippling substantially enhances ion reflection and the generation of backstreaming ions for slightly and moderately superthermal energies, and thus is capable of ensuring ion injection into a further diffusive shock acceleration process. For high-energy ions, there is almost no difference in the fraction of backstreaming ions produced and the ion distributions between the planar stationary shock and the rippled shock.
Left column: the distribution of the forward-moving incident ions fu(v∥, v⊥). Upper middle: the distribution of the ions far downstream of the shock fd(v∥, v⊥) without rippling. Bottom middle: the distribution of the ions far downstream of the shock fd(v∥, v⊥) in the rippled shock. Upper right (empty in this case): the distribution of the backstreaming ions fb(v∥, v⊥) without rippling. Bottom right: the distribution of the backstreaming ions fb(v∥, v⊥) in the rippled shock. The initial ion distribution is isotropic with vp = 0.5.
Full Article: Gedalin, M. (SHARP), Ganushkina, N. (SHARP), Pogorelov, N. V., Roytershteyn, V. (2023). Scattering of Superthermal Ions at Shocks: Dependence on Energy. The Astrophysical Journal, 957, doi: 10.3847/1538-4357/ad04dd
Synchrotron radiation from relativistic electrons is usually invoked as responsible for the nonthermal emission observed in supernova remnants. Diffusive shock acceleration is the most popular mechanism to explain the process of particles acceleration and within its framework a crucial role is played by the turbulent magnetic field. However, the standard models commonly used to fit X-ray synchrotron emission do not take into account the effects of turbulence in the shape of the resulting photon spectra. An alternative mechanism that properly includes such effects is the jitter radiation, which provides for an additional power law beyond the classical synchrotron cutoff. We fitted a jitter spectral model to Chandra, NuSTAR, SWIFT/BAT, and INTEGRAL/ISGRI spectra of Cassiopeia A (Cas A) and found that it describes the X-ray soft-to-hard range better than any of the standard cutoff models. The jitter radiation allows us to measure the index of the magnetic turbulence spectrum νB and the minimum scale of the turbulence across several regions of Cas A, with best-fit values νB ∼ 2 − 2.4 and km.
Chandra and NuSTAR exposure/vignetting-corrected images of Cas A. Leftmost panel: Chandra/ACIS-S count-rate image in the 0.5–8 keV band with a pixel size of 1” and a square root scale. Other panels: exposure/vignetting-corrected and mosaicked NuSTAR images of Cas A in various energy bands, reported on the images in units of keV, with a square root scale.
Full Article: Greco, E. (SHARP), Vink, J. (SHARP), Ellien, A. (SHARP) and Ferrigno, C. (2023). Jitter Radiation as an Alternative Mechanism for the Nonthermal X-Ray Emission of Cassiopeia A. The Astrophysical Journal, 956, doi: 10.3847/1538-4357/acf567
SciFest is a science festival that covers disciplines such as natural sciences, technology, medicine, pharmacy, social sciences and humanities. The goal of the festival is to get the public interested in research and science.
Andrew Dimmock and Daniel Graham attended the SciFest science festival at the IRF stand. Here they talked to the general public of all ages from school children to adults about different aspects of space physics such as satellites, solar wind, space weather, and solar system bodies. The festival also involved practical demonstrations such as how to build a magnetosphere.
The structure of a collisionless shock affects ion motion in the shock front and is affected by the formed ion distribution. In high-Mach-number shocks, a significant fraction of incident ions are reflected by the macroscopic electric and magnetic fields in the shock front. Ions are non-specularly reflected by the combined electric deceleration and magnetic deflection. Here, a first analytical description of the non-specular reflection is presented. The contribution of the increasing magnetic field is evaluated and shown to enhance reflection. The distribution of non-specularly reflected ions ahead of the ramp is calculated and their velocities at the re-entry to the shock are found numerically. Dependence on the angle between the shock normal and the upstream magnetic field vector is illustrated.
Normalized 1-D reduced distribution function f(x,vx) for non-specularly reflected ions only with M=5, s=0.5, β=0.5 and θBn=65∘; (a) A=0.75, (b) A=0.375. Ions which have positive vx, return to the shock and cross it again.
Full Article: Sharma, P. (SHARP) and Gedalin, M. (SHARP) (2023). Non-specular ion reflection at quasiperpendicular collisionless shock front. Journal of Plasma Physics, 89(5), doi: 10.1017/S002237782300096X
plane (panels c to i) and 
at various locations from upstream to downstream of the shock front. 
refers to Bu. An ion population (in all the VDFs) that is separate from the solar wind beam is noticeable.
. Right: dependence of the normalized downstream ion temperature 
on the turbulent magnetic pressure 
. The range of X in the figure is limited by the condition X < P.
across several regions of Cas A, with best-fit values νB ∼ 2 − 2.4 and 
km.
