A comparison of global models for the solar wind interaction with Mars

We present initial results from the first community-wide effort to compare global plasma interaction model results for Mars. Seven modeling groups participated in this activity, using MHD, multi-fluid, and hybrid assumptions in their simulations. Moderate solar wind and solar EUV conditions were chosen, and the conditions were implemented in the models and run to steady state. Model output was compared in three ways to determine how pressure was partitioned and conserved in each model, the location and asymmetry of plasma boundaries and pathways for planetary ion escape, and the total escape flux of planetary oxygen ions. The two participating MHD models provided similar results, while the five sets of multi-fluid and hybrid results were different in many ways. All hybrid results, however, showed two main channels for oxygen ion escape (a pickup ion ‘plume’ in the hemisphere toward which the solar wind convection electric field is directed, and a channel in the opposite hemisphere of the central magnetotail), while the MHD models showed one (a roughly symmetric channel in the central magnetotail). Most models showed a transition from an upstream region dominated by plasma dynamic pressure to a magnetosheath region dominated by thermal pressure to a low altitude region dominated by magnetic pressure. However, calculated escape rates for a single ion species varied by roughly an order of magnitude for similar input conditions, suggesting that the uncertainties in both the current and integrated escape over martian history as determined by models are large. These uncertainties are in addition to those associated with the evolution of the Sun, the martian dynamo, and the early atmosphere, highlighting the challenges we face in constructing Mars’ past using models.     

Oscillatory cosmic-ray shock structures

A multiple scales analysis is used to derive a mixed Burgers-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evolution of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behaviour. For low cosmic-ray pressures, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfvén waves are discussed and a modulational stability analysis is presented.     

The influence of the anomalous cosmic-ray component on the dynamics of the solar wind

It is well known that both the galactic and anomalous cosmic rays show positive intensity gradients in the outer heliosphere which are connected with corresponding pressure gradients. Due to an efficient dynamical coupling between the solar wind plasma and these highly energetic media by means of convected MHD turbulences, there exists a mutual interaction between these media. As one consequence of this scenario the enforced pressure gradients influence the distant solar wind expansion. Here we concentrate in our theoretical study on the interaction of the solar wind only with the anomalous cosmic-ray component. We use the standard two-fluid model in which the cosmic-ray fluid modifies the solar wind flow via the cosmic-ray pressure gradient. Then we derive numerical solutions in the following steps: first we calculate an aspherical pressure distribution for the anomalous cosmic rays, describing their diffusion in an unperturbed radial solar wind. Second, we then consider the perturbation of the solar wind flow due to these induced anomalous cosmic-ray pressure gradients. Within this context we especially take account of the action of a non-spherical geometry of the heliospheric shock which may lead to pronounced upwinddownwind asymmetries in the pressures and thereby in the resulting solar wind flows. As we can show in our model, which fits the available observational data, radial decelerations of the distant solar wind by between 5 to 11% are to be expected, however, the deviations of the bulk solar wind flow from the radialdirections are only slightly pronounced.     

Non-Equilibrium Distribution Functions in the Heliospheric Interface and Their Relaxation by Local Wave–Particle Interactions

The partially ionized local interstellar medium, before interacting with the heliospheric plasma on the upwind side, most probably undergoes an outer bow shock. After conversion into a sub-magnetosonic plasma flow, it then passes around the heliopause. While the ionized component at the bow shock undergoes abrupt changes of its dynamical properties, the neutral component first continues to flow downstream of the shock with its unperturbed properties. Consequently, the two fluids immediately after the bow shock passage are out of dynamical and thermodynamical equilibrium. Neutral atoms move with a higher bulk velocity and are cooler than the ions. Due to intensive local charge-exchange couplings between neutral atoms and protons these different properties tend to mix each other via momentum and energy exchanges. It turns out that the charge exchange period is shorter than the relaxation period. Hence the distribution functions cannot relax rapidly enough to their highest-entropy forms, i.e. shifted Maxwellians. Here we study the transport processes of newly injected ions in velocity space considering their quasi-linear and non-linear interactions with the ambient MHD turbulence in the plasma interface region. For that purpose we study the turbulence levels in the helio-sheath plasma region. We calculate the expected deviations from equilibrium distributions of ionic and atomic species in the outer heliospheric interface. It clearly turns out from these studies that non-relaxated non-equilibrium distribution functions have to be expected both for O-/H-ions and atoms in this region. This has inherent implications for the diagnostics of interstellar parameters, deduced from observations made further inwards from the interface region.     

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Effects of cosmic rays and density inhomogeneity of the circumstellar medium on the formation of a supernova shell

We consider the self-similar problem of a supernova explosion in a radially inhomogeneous medium by taking into account the generation of accelerated relativistic particles. The initial density of the medium is assumed to decrease with distance from the explosion center as a power law, ρ ₀ = A/r ^θ. We use a two-fluid approach in which the total pressure in the medium is the sum of the circumstellar gas pressure and the relativistic particle pressure. The relativistic particle pressure at the shock front is specified as an external parameter. This approach is applicable in the case where the diffusion coefficient of accelerated particles is small and the thickness of the shock front is much smaller than its radius. We have numerically solved a system of ordinary differential equations for the dimensionless quantities that describe the velocity and density behind the shock front as well as the nonrelativistic gas and relativistic particle pressures for various parameters of the inhomogeneity of the medium and various compression ratios of the medium at the shock front. We have established that the shock acceleration of cosmic rays affects most strongly the formation of a supernova shell (making it thinner) in a homogeneous circumstellar medium. A decrease in the circumstellar matter density with distance from the explosion center causes the effect of shock-accelerated relativistic particles on the supernova shell formation to weaken considerably. Inhomogeneity of the medium makes the shell thicker and less dense, while an increase in the compression ratio of the medium at the shock front causes the shell to become thinner and denser. As the relativistic particle density increases, the effect of circumstellar matter inhomogeneity on the shell formation becomes weaker.     

A class of semi-analytical solutions for a rotating toroidal plasma

In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P _s andf ² are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.     

A model for thinning of the plasma sheet

A one-dimensional model for thinning of the plasma sheet is developed on the basis of launching a fast mode MHD rarefaction wave propagating in the tailward direction along the plasma sheet. Behind the rarefaction wave the pressure is reduced, leading to thinning of the plasma sheet and also to an Earthward plasma flow with a speed on the order of the sound speed a₀. The plasma sheet thickness is reduced by a factor of 2 if an Earthward plasma flow speed of 0.8a₀ is induced. The predictions of the model are in reasonable agreement with observations.     

Compaction by impact of unconsolidated lunar fines

New Hugoniot and release adiabate data for 1.8 g cm^?3 lunar fines (sample, 70051) in the ç2 to ç70 kbar range demonstrate that upon shock compression intrinsic crystal density (ç3.1 g cm^?3) is achieved undershock stresses of 15 to 20 kbar. Release adiabate determinations indicate that measurable irreversible compaction occurs upon achieving shock pressures above ç4 kbar. For shocks in the ç7 to 15 kbar range, the inferred,post-shock, specific volumes observed decrease nearly linearly with increasing peak shock pressures. Upon shocking to ç15 kbar the post-shock density is approximately that of the intrinsic minerals. If the present data for sample 70051 are taken to be representative of the response to impact of unconsolidated regolith material on the Moon, it is inferred that the formation of appreciable quantities of soil breccia can be associated with the impact of meteoroids or ejecta at speeds of as low as ç1 km s^?1.     

Kink instability of a non-static plasma column

Starting with MHD equations we study the linear theory of stability of a plasma column with flow. From the dispersion equation derived, we calculate the dispersion curves and thereby estimate the effect of a flow in the linear theory. We find that, like the toroidal component of the magnetic field, a flow promotes instability: the rate of growth of instability may be increased by one or two orders of magntiude and the wavelength range for instability is also increased. When the flow velocity is large, the m=o and m=1 modes may appear almost together. Finally, a qualitative interpretation of three typical solar events is given on the basis of our results.     

Plasma jet and shock formation during current loop coalescence in solar flares

We report on the results of plasma jet and shock formation during the current loop coalescence in solar flares. It is shown by a theoretical model based on the ideal MHD equation that the spiral, two-sided plasma jet can be explosively driven by the plasma rotational motion induced during the two current loop coalescence process. The maximum velocity of the jet can exceed the Alfvén velocity, depending on the plasma (= c _s ² v _A ² ) ratio. The acceleration time getting to the maximum jet velocity is quite short and le than 1 s. The rebound following the plasma collapse driven by magnetic pinch effect can strongly induce super-Alfvénic flow. We present the condition of the shock formation. We briefly discuss the high-energy particle acceleration during the plasma collapse as well as by the shocks.     

High‐pressure phase transitions of α‐quartz under nonhydrostatic dynamic conditions: A reconnaissance study at PETRA III

Hypervelocity collisions of solid bodies occur frequently in the solar system and affect rocks by shock waves and dynamic loading. A range of shock metamorphic effects and high‐pressure polymorphs in rock‐forming minerals are known from meteorites and terrestrial impact craters. Here, we investigate the formation of high‐pressure polymorphs of α‐quartz under dynamic and nonhydrostatic conditions and compare these disequilibrium states with those predicted by phase diagrams derived from static experiments under equilibrium conditions. We create highly dynamic conditions utilizing a mDAC and study the phase transformations in α‐quartz in situ by synchrotron powder X‐ray diffraction. Phase transitions of α‐quartz are studied at pressures up to 66.1 and different loading rates. At compression rates between 0.14 and 1.96 GPa s^?1, experiments reveal that α‐quartz is amorphized and partially converted to stishovite between 20.7 GPa and 28.0 GPa. Therefore, coesite is not formed as would be expected from equilibrium conditions. With the increasing compression rate, a slight increase in the transition pressure occurs. The experiments show that dynamic compression causes an instantaneous formation of structures consisting only of SiO₆ octahedra rather than the rearrangement of the SiO₄ tetrahedra to form a coesite. Although shock compression rates are orders of magnitude faster, a similar mechanism could operate in impact events.     

Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate because of a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock-heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron–ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.     

A study of the observed shift in the peak position of olivine Raman spectra as a result of shock induced by hypervelocity impacts

Kuebler et al. (2006) identified variations in olivine Raman spectra based on the composition of individual olivine grains, leading to identification of olivine composition from Raman spectra alone. However, shock on a crystal lattice has since been shown to result in a structural change to the original material, which produces a shift in the Raman spectra of olivine grains compared with the original unshocked olivine (Foster et al. 2013). This suggests that the use of the compositional calculations from the Raman spectra, reported in Kuebler et al. (2006), may provide an incorrect compositional value for material that has experienced shock. Here, we have investigated the effect of impact speed (and hence peak shock pressure) on the shift in the Raman spectra for San Carlos olivine (Fo₉₁) impacting Al foil. Powdered San Carlos olivine (grain size 1–10 μm) was fired at a range of impact speeds from 0.6 to 6.1 km s^?1 (peak shock pressures 5–86 GPa) at Al foil to simulate capture over a wide range of peak shock pressures. A permanent change in the Raman spectra was found to be observed only for impact speeds greater than ~5 km s^?1. The process that causes the shift is most likely linked to an increase in the peak pressure produced by the impact, but only after a minimum shock pressure associated with the speed at which the effect is first observed (here 65–86 GPa). At speeds around 6 km s^?1 (peak shock pressures ~86 GPa), the shift in Raman peak positions is in a similar direction (red shift) to that observed by Foster et al. (2013) but of twice the magnitude.     

Perpendicular flow deviation in a magnetized counter-streaming plasma

Charged dust exists in various regions in the Solar System. How this charged dust interacts with the surrounding plasma is not well understood. In this study we neglect the charging process and treat the charged dust as a fluid interacting with the ambient magnetized plasma fluid. The model reproduces the expected plasma deceleration with both positively charged and negatively charged dust, but a new effect arises. Negatively charged dust causes the magnetic field to bend in the direction of the convection electric field, while positively charged dust causes the opposite magnetic field bending. Consequently, the interaction does not only result in a perpendicular shift in the downstream current system, but also a rotation in these currents. We present quantitative results using the multi-fluid MHD code BATSRUS for both subsonic and supersonic interactions. We find that the same perpendicular bending exists for all counter-streaming interaction problems, independent of the shape of the dust cloud. The new model can be applied to plasma interaction studies including, but not limited to, charged dust particles in the solar wind, cometary plasma, the Enceladus plume, and active plasma releases, such as the Active Magnetospheric Particle Tracer Experiment (AMPTE) mission. The predicted behavior is consistent with observations at Enceladus.     

Stratification of optical emission from NGC 6888 as a trace of the interaction between Wolf-Rayet stellar wind and the shell of a red supergiant

We suggest a model that explains the stratification peculiarities of the [O III] and Hα line emission from some of the ring nebulae around Wolf-Rayet stars. These peculiarities lie in the fact that the [O III] line emission regions are farther from the central star than the Hα regions, with the distance between them reaching several tenths of a parsec. We show that the radiative shock produced by a Wolf-Rayet stellar wind and propagating with a velocity of ～100 km s^?1 cannot explain such large distances between these regions due to the low velocity of the gas outflow from the shock front. The suggested model takes into account the fact that the shock produced by a Wolf-Rayet stellar wind propagates in a two-phase medium: a rarefied medium and dense compact clouds. The gas downstream of a fast shock traveling in a rarefied gas compresses the clouds. Slow radiative shocks are generated in the clouds; these shocks heat the latter to temperatures at which ions of doubly ionized oxygen are formed. The clouds cool down, radiating in the lines of this ion, to temperatures at which Balmer line emission begins. The distance between the [O III] and Hα line emission regions is determined by the cooling time of the clouds downstream of the slow shock and by the velocity of the fast shock. Using the ring nebula NGC 6888 as an example, we show that the gas downstream of the fast shock must be at the phase of adiabatic expansion rather than deceleration with radiative cooling, as assumed previously.     

Ion composition and chemistry in the coma of Comet 1P/Halley—A comparison between Giotto's Ion Mass Spectrometer and our ion-chemical network

In order to understand the cometary plasma environment it is important to track the closely linked chemical reactions that dominate ion evolution. We used a coupled MHD ion-chemistry model to analyze previously unpublished Giotto High Intensity Ion Mass Spectrometer (HIS-IMS) data. In this way we study the major species, but we also try to match some minor species like the CH_x and the NH_x groups. Crucial for this match is the model used for the electrons since they are important for ion-electron recombination. To further improve our results we included an enhanced density of supersonic electrons in the ion pile-up region which increases the local electron impact ionization. In this paper we discuss the results for the following important ions: C⁺, CH⁺, CH⁺₂, CH⁺₃, N⁺, NH⁺, NH⁺₂, NH⁺₃, NH⁺₄, O⁺, OH⁺, H₂O⁺, H₃O⁺, CO⁺, HCO⁺, H₃CO⁺, and CH₃OH⁺₂. We also address the inner shock which is very distinctive in our MHD model as well as in the IMS data. It is located just inside the contact surface at approximately 4550 km. Comparisons of the ion bulk flow directions and velocities from our MHD model with the data measured by the HIS-IMS give indication for a solar wind magnetic field direction different from the standard Parker angle at Halley's position. Our ion-chemical network model results are in a good agreement with the experimental data. In order to achieve the presented results we included an additional short lived inner source for the C⁺, CH⁺, and CH⁺₂ ions. Furthermore we performed our simulations with two different production rates to better match the measurements which is an indication for a change and/or an asymmetric pattern (e.g. jets) in the production rate during Giotto's fly-by at Halley's comet.