Perpendicular Shocks Research Articles

Contributions to the cross shock electric field at supercritical perpendicular shocks: impact of the pickup ions

A particle-in-cell code is used to examine contributions of the pickup ions (PIs) and the solar wind ions (SWs) to the cross shock electric field at the supercritical, perpendicular shocks. The code treats the pickup ions self-consistently as a third component. Herein, two different runs with relative pickup ion density of 25% and 55% are presented in this paper. Present preliminary results show that: (1) in the low percentage (25%) pickup ion case, the shock front is nonstationary. During the evolution of this perpendicular shock, a nonstationary foot resulting from the reflected solar wind ions is formed in front of the old ramp, and its amplitude becomes larger and larger. At last, the nonstationary foot grows up into a new ramp and exceeds the old one. Such a nonstationary process can be formed periodically. hen the new ramp begins to be formed in front of the old ramp, the Hall term mainly contributed by the solar wind ions becomes more and more important. The electric field Ex is dominated by the Hall term when the new ramp exceeds the old one. Furthermore, an extended and stationary foot in pickup ion gyro-scale is located upstream of the nonstationary/self-reforming region within the shock front, and is always dominated by the Lorentz term contributed by the pickup ions; (2) in the high percentage (55%) pickup ion case, the amplitude of the stationary foot is increased as expected. One striking point is that the nonstationary region of the shock front evidenced by the self-reformation disappears. Instead, a stationary extended foot dominated by Lorentz term contributed by the pickup ions, and a tationary ramp dominated by Hall term contributed by the solar wind ions are clearly evidenced. The significance of the cross electric field on ion dynamics is also discussed.

On the universality of nonthermal electron acceleration due to quasi-turbulent wakefields

Nonthermal acceleration of relativistic electrons in a wakefield induced by large amplitude light waves is discussed. It is considered that large amplitude light waves are excited as the precursor waves in the upstream of relativistic perpendicular shocks in the universe, and that the wakefield is excited by the light ponderomotive force. Thus, the wakefield acceleration is possible in the astrophysical circumstances. We model such shock environments in a laboratory plasma by substituting an intense laser pulse for the large amplitude light waves. By performing 2-D particle-in-cell simulations, we discuss the properties of the wakefield acceleration in various laser and plasma conditions. With the relativistic intensities of the laser pulses, the electrons are nonthermally accelerated by the wakefield. When the pulse length and the spot size are comparable to the electron inertial scale, the energy distribution functions of the electrons can be monoenergetic. On the other hand, when the pulse spatial scales are much larger than the electron inertial scale, which occurs in the case of the shock precursor light waves, the distribution functions are universally represented by power law spectra with an index of 2, independent of the laser intensity, the plasma density, and the laser pulse size.

Microinstabilities at perpendicular collisionless shocks: A comparison of full particle simulations with different ion to electron mass ratio

A full particle simulation study is carried out for studying microinstabilities generated at the shock front of perpendicular collisionless shocks. The structure and dynamics of shock waves are determined by Alfvén Mach number and plasma beta, while microinstabilities are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the plasma-to-cyclotron frequency. Thus, growth rates of microinstabilities are changed by the ion-to-electron mass ratio, even with the same Mach number and plasma beta. The present two-dimensional simulations show that the electron cyclotron drift instability is dominant for a lower mass ratio, and electrostatic electron cyclotron harmonic waves are excited. For a higher mass ratio, the modified two-stream instability is dominant and oblique electromagnetic whistler waves are excited, which can affect the structure and dynamics of collisionless shocks by modifying shock magnetic fields.

Modified two‐stream instability at perpendicular collisionless shocks: Full particle simulations

A full particle simulation study is carried out for studying microinstabilities generated in self‐consistently excited perpendicular collisionless shocks. The present two‐dimensional simulation with a high ion‐to‐electron mass ratio shows that the modified two‐stream instability can be generated by the interaction of incoming and reflected ions with electromagnetic whistler mode waves propagating in the direction quasi‐perpendicular to the ambient magnetic field. Properties of the excited whistler mode waves are consistent with the linear dispersion analysis based on the simulated velocity distribution functions. It is also found that the excited waves have an electron‐scale wavelength in the shock‐normal direction and an ion‐scale wavelength in the shock‐tangential direction, suggesting that the electron‐scale microturbulences and the ion‐scale shock structures are coupled with each other through the modified two‐stream instability.

A Shannon entropy approach to the temporal evolution of SEP energy spectrum

The kinetic energy spectra of solar energetic parti- cle (SEP) events contain information on the particle acceler- ation mechanisms. A novel approach is proposed to investi- gate the time evolution of the spectral shape for the 20 Febru- ary 2002 SEP event. Proton differential fluxes recorded by the ERNE instrument aboard SOHO, in the energy range 1.67 112 MeV, are analyzed. The solar source is associated with this SEP event by studying solar and interplanetary con- ditions during the considered time period. The energy spec- trum evolution is studied by evaluating the time history of Shannon's differential entropy derived from the SEP fluxes. Our findings suggest that particle acceleration in the consid- ered event is produced by a perpendicular shock in the solar corona. Moreover, dropouts in the particle flux are clearly identified up to energies of at least 10 MeV.

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

AbstractRelativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ≪1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron–ion shock front. This potential is responsible for electron energization.

Solving the relativistic Rankine-Hugoniot condition in the presence of a magnetic field in the astrophysical scenario of a neutron star

Rankine-Hugoniot condition has been solved to study phase transition in astrophysical scenario mainly in the case of phase transition from neutron star (NS) to quark star (QS). The phase transition is brought about by a combustion front, which travels from the center to the surface. The equations of state and temperature plays a huge role in determining the nature of the front propagation, which brings about the phase transition in neutron stars (NSs). Magnetic field has been introduced and the modified conservation condition for the perpendicular and oblique shocks is obtained. Numerical solution of the perpendicular shock has been shown in the figures, which finds that the magnetic field helps in shock generation. It indirectly hints at the instability of the matter and thereby the NS for very high magnetic field, implying that NSs can only support finite magnetic field strength.

Solar wind parameters and geomagnetic indices for four different interplanetary shock/ICME structures

[1] Interplanetary shocks associated with coronal mass ejections (CMEs) have very profound effects on geomagnetic storms. In order to investigate the role of the interplanetary shock properties and pre-conditions, we present a statistical study of 280 interplanetary shocks and their associated geomagnetic activities during 1998–2007. The results show that perpendicular shocks can cause more intense geomagnetic activities compared with parallel ones under the same IMF pre-condition. Through a southward IMF pre-condition, interplanetary shocks and driven ICMEs can intensify geomagnetic storms significantly. It is revealed that interplanetary shocks would intensify negative IMF Bz pre-condition by a factor of 3 to 6. This effect would enhance geomagnetic storms greatly. The result shows that there are 74% of intense (Dst ≤ −100 nT) and 69% of super (Dst ≤ −200 nT) geomagnetic storms related to a negative IMF Bz pre-condition.

Acceleration of heavy ions by perpendicular collisionless shocks: Impact of the shock front nonstationarity

[1] Both hybrid/full particle simulations and recent experimental results have clearly evidenced that the front of a supercritical quasi-perpendicular shock can be nonstationary. One responsible mechanism proposed for this nonstationarity is the self-reformation of the front itself being due to the accumulation of reflected ions. Important consequences of this nonstationarity are that not only the amplitude but also the spatial scales of fields components at the shock front (ramp and foot) are strongly varying within each cycle of the self-reformation. On the other hand, several studies have been made on the acceleration and heating of heavy ions but most have been restricted to a stationary shock profile only. Herein, one-dimensional test particle simulations based on shock profiles fields produced in PIC simulation are performed in order to investigate the impact of the shock front nonstationarity on heavy ion acceleration (He, O, Fe). Reflection and acceleration mechanisms of heavy ions (with different initial thermal velocities and different charge-mass ratios) interacting with a nonstationary shock front (self-reformation) are analyzed in detail. Present preliminary results show that: (1) the heavy ions suffer both shock drift acceleration (SDA) and shock surfing acceleration (SSA) mechanisms; (2) the fraction of reflected heavy ions increases with initial thermal velocity, charge-mass ratio and decreasing shock front width at both stationary shocks (situation equivalent to fixed shock cases) and nonstationary shocks (situation equivalent to continuously time-evolving shock cases); (3) the shock front nonstationarity (time-evolving shock case) facilitates the reflection of heavy ions; (4) a striking feature is the formation of an injected monoenergetic heavy ions population which persists in the shock front spectrum for different initial thermal velocities and ions species. The impact of the shock front nonstationarity on the heavy ions spectra within the shock front region and the downstream region are detailed separately. Present results are compared with previous experimental analysis and theoretical models of solar energetic particles (SEP) events. The variations of Fe/O spectra in high energy part have been retrieved, and the nonstationary effects of shock front strongly amplify these variations.

A statistical physics perspective on the evolution of ion distributions across low Mach number quasi-perpendicular collisionless shocks

[1] The heating of directly transmitted ions at low Mach number, perpendicular and quasi-perpendicular shocks has been the subject of previous statistical physics studies. In this paper, we use a Hamiltonian formulation of the ion kinetics for a quasi-perpendicular shock model to derive the general solution to Liouville's equation as a function of six invariants, finding forms of these invariants in terms of the upstream parameters. The ion distribution is expressed as a function of one of these invariants, subject to a Maxwellian upstream boundary condition, and the evolution of the distribution through and downstream of the shock is studied. The momentum-space volume within surfaces of constant probability (related to the temperature) is shown to be inversely proportional to an average value of the canonical momentum associated with motion in the direction normal to the shock plane, generalizing a previous result to three-dimensional phase space. We also study the evolution of the distribution properties numerically, in particular noting that the “twisting” of these surfaces in phase space is the result of the unequal guiding center motion of different parts of the distribution (which is not the case for a fully perpendicular shock). This property provides insight into the damping of oscillations in the mean momentum and the temperature for a quasi-perpendicular model (as the distribution is spread about the central value through gyration) and the observed T⊥ > T∥ anisotropy.

Impact of the nonstationarity of a supercritical perpendicular collisionless shock on the dynamics and energy spectra of pickup ions

[1] Both hybrid and full particle simulations and recent experimental results have clearly evidenced that the front of a supercritical quasi-perpendicular shock can be nonstationary. One proposed mechanism responsible for this nonstationarity is the self-reformation of the shock front being due to the accumulation of reflected ions. On the other hand, a large number of studies have been made on the acceleration and heating of pickup ions (PIs) but most have been restricted to a stationary shock profile only. Herein, one-dimensional test particle simulations based on shock profiles issued from one-dimensional particle-in-cell simulation are performed in order to investigate the impact of the shock front nonstationarity (self-reformation) on the acceleration processes and the resulting energy spectra of PIs (protons H+) at a strictly perpendicular shock. PIs are represented by different shell distributions (variation of the shell velocity radius). The contribution of shock drift acceleration (SDA), shock surfing acceleration (SSA), and directly transmitted (DT) PI's components to the total energy spectra is analyzed. Present results show that (1) both SDA and SSA mechanisms can apply as preacceleration mechanisms for PIs, but their relative energization efficiency strongly differs; (2) SDA and SSA always work together at nonstationary shocks (equivalent to time-varying shock profiles) but SDA, and not SSA, is shown to dominate the formation of high-energy PIs in most cases; (3) the front nonstationarity reinforces the formation of SDA and SSA PIs in the sense that it increases both their maximum energy and their relative density, independently on the radius of PI's shell velocity; and (4) for high shell velocity around the shock velocity, the middle energy range of the total energy spectrum follows a power law Ek−1.5. This power law is supported by both SDA and DT ions (within two separate contributing energy ranges) for a stationary shock and mainly by SDA ions for a nonstationary shock. In both cases, the contribution of SSA ions is comparatively weak.

JUMP CONDITIONS FOR RELATIVISTIC MAGNETOHYDRODYNAMIC SHOCKS IN A GYROTROPIC PLASMA

We study the jump conditions of a relativistic magnetohydrodynamic shock wave in a gyrotropic plasma and solve these relations for a parallel and a perpendicular shock. A closure for the system of jump conditions is obtained by using the constraints of the firehose and mirror instability which operates in anisotropic, gyrotropic plasmas. All postshock quantities are expressed in terms of the compression ratio and dimensionless upstream quantities.

Effect of Injection Angle in Mixing and Combustion Characteristics of Scramjet Combustor

Effect of injection angle in mixing and combustion in a scramjet combustor is numerically simulated. Three dimensional Navier Stokes equations alongwith k-e turbulence model are solved using commercial CFD software. Both infinitely fast rate kinetics and single step finite rate kinetics are used to model chemical kinetics. Turbulence chemistry interaction is modeled by Eddy Dissipation Concept (EDC). Good agreement between the computed and experimental results for angular injection (30°) and perpendicular injection forms the basis of further analysis. More flow blockage has caused significant upstream interaction for perpendicular injection and terminal shock is seen to anchor upstream of combustor step; while for angular injection, the flow field is predominantly supersonic. Single step finite rate chemistry show comparatively low pressure and lesser upstream interaction because of the presence of backward reaction. Thermochemical variables are analysed to study the effect of angle of injection on nature...

Experimental evidence of nonthermal acceleration of relativistic electrons by an intensive laser pulse

Nonthermal acceleration of relativistic electrons is investigated with an intensive laser pulse. An energy distribution function of energetic particles in the universe or cosmic rays is well represented by a power-law spectrum, therefore, nonthermal acceleration is essential to understand the origin of cosmic rays. A possible candidate for the origin of cosmic rays is wakefield acceleration at relativistic astrophysical perpendicular shocks. The wakefield is considered to be excited by large-amplitude precursor light waves in the upstream of the shocks. Substituting an intensive laser pulse for the large amplitude light waves, we performed a model experiment of the shock environments in a laboratory plasma. An intensive laser pulse was propagated in a plasma tube created by imploding a hollow polystyrene cylinder, as the large amplitude light waves propagated in the upstream plasma at an astrophysical shock. Nonthermal electrons were generated, and the energy distribution functions of the electrons have a power-law component with an index of ~2. We described the detailed procedures to obtain the nonthermal components from data obtained by an electron spectrometer.

Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations

Abstract. We have performed full particle electromagnetic simulations of a quasi-perpendicular shock. The shock parameters have been chosen to be appropriate for the quasi-perpendicular Earth's bow shock observed by Cluster on 24 January 2001 (Lobzin et al., 2007). We have performed two simulations with different ion to electron mass ratio: run 1 with mi/me=1840 and run 2 with mi/me=100. In run 1 the growth rate of the modified two-stream instability (MTSI) is large enough to get excited during the reflection and upstream gyration of part of the incident solar wind ions. The waves due to the MTSI are on the whistler mode branch and have downstream directed phase velocities in the shock frame. The Poynting flux (and wave group velocity) far upstream in the foot is also directed in the downstream direction. However, in the density and magnetic field compression region of the overshoot the waves are refracted and the Poynting flux in the shock frame is directed upstream. The MTSI is suppressed in the low mass ratio run 2. The low mass ratio run shows more clearly the non-stationarity of the shock with a larger time scale of the order of an inverse ion gyrofrequency (Ωci): the magnetic field profile flattens and steepens with a period of ~1.5Ωci−1. This non-stationarity is different from reformation seen in previous simulations of perpendicular or quasi-perpendicular shocks. Beginning with a sharp shock ramp the large electric field in the normal direction leads to high reflection rate of solar wind protons. As they propagate upstream, the ion bulk velocity decreases and the magnetic field increases in the foot, which results in a flattening of the magnetic field profile and in a decrease of the normal electric field. Subsequently the reflection rate decreases and the whole shock profile steepens again. Superimposed on this 'breathing' behavior are in the realistic mass ratio case the waves due to the MTSI. The simulations lead us to a re-interpretation of the 24 January 2001 bow shock observations reported by Lobzin et al. (2007). It is suggested that the high frequency waves observed in the magnetic field data are due to the MTSI and are not related to a nonlinear phase standing whistler. Different profiles at the different spacecraft are due to the non-stationary behavior on the larger time scale.

Anomalous deformation of the Earth's bow shock in the lunar wake: Joint measurement by Chang’E-1 and SELENE

Because the solar wind (SW) flow is usually super-sonic, a fast-mode bow shock (BS) is formed in front of the Earth's magnetosphere, and the Moon crosses the BS at both dusk and dawn flanks. On the other hand, behind of the Moon along the SW flow forms a tenuous region called lunar wake, where the flow can be sub-Alfvénic (and thus sub-sonic) because of its low-density status. Here we report, with joint measurement by Chang’E-1 and SELENE, that the Earth's BS surface is drastically deformed in the lunar wake. Despite the quasi-perpendicular shock configuration encountered at dusk flank under the Parker-spiral magnetic field, no clear shock surface can be found in the lunar wake, while instead gradual transition of the magnetic field from the upstream to downstream value was observed for a several-minute interval. This finding suggests that the ‘magnetic ramp’ is highly broadened in the wake where a fast-mode shock is no longer maintained due to the highly reduced density. On the other hand, observations at the 100 km altitude on the dayside show that the fast-mode shock is maintained even when the width of the downstream region is smaller than a typical scale length of a perpendicular shock. Our results suggest that the Moon is not so large to eliminate the BS at 100 km altitude on the dayside, while the magnetic field associated with the shock structure is drastically affected in the lunar wake.

Heliosheath fluctuations near the perpendicular termination shock: Two‐dimensional hybrid simulations

The two‐dimensional Los Alamos hybrid simulation code is used to study the excitation of fluctuations and the associated ion dynamics at the high Alfvén‐Mach heliospheric termination shock and in the near‐shock heliosheath. This simulation represents the electrons as a zero‐mass fluid, addresses only a perpendicular shock, and considers the upstream ions to consist of a cool solar wind component and a more energetic pickup component. The shock yields two strongly heated downstream components: the more dense thermals and the more tenuous suprathermals, each with strong T⊥ > T∥ anisotropies. In the downstream, relatively homogeneous sheath plasma, linear dispersion theory predicts that each component anisotropy drives both the Alfvén‐cyclotron instability and the proton mirror instability. The simulation demonstrates that Alfvén‐cyclotron modes dominate mirror‐like modes in the downstream, in contrast to earlier two‐dimensional hybrid simulations of high‐Mach quasi‐perpendicular shocks without pickup ions, in which the Alfvén‐cyclotron and mirror modes were excited to comparable intensities. A hypothesis is presented that the presence of pickup ions implies a relatively low magnetosonic Mach number at termination shocks, thereby favoring the excitation of the Alfvén‐cyclotron instability. The primary consequence of wave‐particle interactions from this instability is pitch angle scattering, so the energetic part of the ion perpendicular velocity distribution in the heliosheath is depleted by comparison with the distribution computed from a comparable one‐dimensional hybrid simulation.

Hybrid simulations of the termination shock: Suprathermal ion velocity distributions in the heliosheath

The Los Alamos hybrid simulation code is used to examine kinetic properties of pickup ions at the heliospheric termination shock and in the downstream heliosheath. All simulations are one‐dimensional in spatial variations, represent the electrons as a zero‐mass fluid, and address only perpendicular shocks. Interpretation of measurements from the IBEX and Voyager spacecraft depend sensitively on the properties of the suprathermal ions downstream of the termination shock, so this research addresses three topics concerning such ions. First, a careful examination of pickup ion trajectories shows that their initial acceleration does not require specular reflection at the shock, as is sometimes assumed, but is the consequence of gyromotion by selected ions at the shock. The primary factor in this energy gain is a gyro‐phase‐dependent interaction with the motional electric field upstream of, and the magnetic field at, the shock. Second, shock simulations are carried out in which the upstream pickup ions are assumed to have four different types of velocity distributions. The downstream ion perpendicular velocity distributions f(v⊥) are similar in each of the runs and may be approximately characterized as a thermal Maxwellian and a suprathermal distribution. The only significant difference among the four downstream distributions is in the tails of the suprathermal component. Third, simulations are carried out for three different upstream Mach numbers; the results show that faster solar wind flows lead to increased fluxes of ions in the tails of the suprathermal component and are generally consistent with energetic neutral atom observations by the IBEX spacecraft.

Non adiabatic electron behavior through a supercritical perpendicular collisionless shock: Impact of the shock front turbulence

Adiabatic and nonadiabatic electrons transmitted through a supercritical perpendicular shock wave are analyzed with the help of test particle simulations based on field components issued from 2 − D full‐particle simulation. A previous analysis (Savoini et al., 2005) based on 1 − D shock profile, including mainly a ramp (no apparent foot) and defined at a fixed time, has identified three distinct electron populations: adiabatic, overadiabatic, and underadiabatic, respectively, identified by μds/μus ≈ 1, >1 and <1, where μus and μds are the magnetic momenta in the upstream and downstream regions. Presently, this study is extended by investigating the impact of the time evolution of 2 − D shock front dynamics on these three populations. Analysis of individual time particle trajectories is performed and completed by statistics based on the use of different upstream velocity distributions (spherical shell of radius vshell and a Maxwellian with thermal velocity vthe). In all statistics, the three electron populations are clearly recovered. Two types of shock front nonstationarity are analyzed. First, the impact of the nonstationarity along the shock normal (due to the front self‐reformation only) strongly depends on the values of vshell or vthe. For low values, the percentages of adiabatic and overadiabatic electrons are almost comparable but become anticorrelated under the filtering impact of the self‐reformation; the percentage of the underadiabatic population remains almost unchanged. In contrast, for large values, this impact becomes negligible and the adiabatic population alone becomes dominant. Second, when 2 − D nonstationarity effects along the shock front (moving rippling) are fully included, all three populations are strongly diffused, leading to a larger heating; the overadiabatic population becomes largely dominant (and even larger than the adiabatic one) and mainly contributes to the energy spectrum.

On the reformation at quasi‐ and exactly perpendicular shocks: Full particle‐in‐cell simulations

A full particle‐in‐cell (PIC) simulation study is carried out on the reformation at quasi‐ and exactly perpendicular collisionless shocks with a relatively low Alfven Mach number (MA = 5). Previous self‐consistent one‐dimensional (1‐D) hybrid and full PIC simulations have demonstrated that ion kinetics are essential for the nonstationarity of perpendicular collisionless shocks. These results showed that reflection of ions at the shock front is responsible for the periodic collapse and redevelopment of a new shock front on a timescale of the ion cyclotron period, which is called the shock reformation. Recent 2‐D hybrid and full PIC simulations, however, suggested that the shock reformation does not take place at exactly perpendicular shocks with MA ∼ 5. By contrast, another 2‐D hybrid PIC simulation showed that the shock reformation persists at quasi‐perpendicular shocks with MA ∼ 5. Although these two works seem to be inconsistent with each other, the reason is not well understood because of several differences in numerical simulation conditions. Thus this paper gives a direct comparison between full PIC simulations of quasi‐ and exactly perpendicular shocks with almost the same condition. It is found that the time development of the shock magnetic field averaged over the shock‐tangential direction shows the transition from the reformation to no‐reformation phase. On the other hand, local shock magnetic field shows the evident appearance and disappearance of the shock front, and the period becomes longer in the no‐reformation phase than in the reformation phase.