Showing papers on "Oblique shock published in 2000"

Shock Wave—Turbulence Interactions

Abstract: ▪ Abstract The idealized interactions of shock waves with homogeneous and isotropic turbulence, homogeneous sheared turbulence, turbulent jets, shear layers, turbulent wake flows, and two-dimensional boundary layers have been reviewed. The interaction between a shock wave and turbulence is mutual. A shock wave exhibits substantial unsteadiness and deformation as a result of the interaction, whereas the characteristic velocity, timescales and length scales of turbulence change considerably. The outcomes of the interaction depend on the strength, orientation, location, and shape of the shock wave, as well as the flow geometry and boundary conditions. The state of turbulence and the compressibility of the incoming flow are two additional parameters that also affect the interaction.

Orientation dependence in molecular dynamics simulations of shocked single crystals

Abstract: We use multimillion-atom molecular dynamics simulations to study shock wave propagation in fcc crystals As shown recently, shock waves along the direction form intersecting stacking faults by slippage along {l_brace}111{r_brace} close-packed planes at sufficiently high shock strengths We find even more interesting behavior of shocks propagating in other low-index directions: for the case, an elastic precursor separates the shock front from the slipped (plastic) region Shock waves along the direction generate a leading solitary wave train, followed (at sufficiently high shock speeds) by an elastic precursor, and then a region of complex plastic deformation (c) 2000 The American Physical Society

Megahertz Pulse-Burst Laser and Visualization of Shock-Wave/Boundary-Layer Interaction

Abstract: The development and application of a Nd:YAG pulse-burst laser system, which is capable of operating at up to 1-MHz pulse repetition rate with high pulse energy and narrow spectral linewidth, is presented. The laser system can generate a burst of from 1 to 99 pulses over a maximum time interval of 100 µs. The average single pulse energy at 1:064µ is 10 mJ. This laser is paired with a new megahertz-rate charge-coupled device framing camera to obtain images of a Mach 2.5 e ow over a 14-deg angle wedge at a 500-kHz repetition rate. The sequential images clearly show the dynamic interaction between the incoming turbulent boundary layer and the unsteady oblique shock wave.

Restricted Shock Separation in Rocket Nozzles

Abstract: In overexpanded rocket nozzles the e ow separates from the nozzle wall at a certain pressure ratio of wall pressure to ambient pressure. Flow separation and its theoretical prediction have been the subject of several experimental and theoretical studies in the past decades. Two distinctive e ow separation phenomena, the freeshock and restricted-shock separation, were observed in experiments with nozzles. Both phenomena are discussed in detail, and the system of recompression shocks and expansion waves is described. For the free-shock case three different shock structures in theplume can occur, namely the regular shock ree ection, the Mach disk, or a cap-like shock pattern. Theappearanceofthesedifferentplumepatternsis discussed. Theseshock structuresareconserved for the full-e owing, but overexpanded, nozzle. Numerical results obtained for existing rocket nozzles, e.g., Space ShuttleMain EngineorVulcain, show a qualitativegood agreement with experimental photographs.Furthermore, an explanation for the appearance of restricted shock separation, which has been widely unknown up to now, is given, analyzing why and under what conditions it occurs. The type of nozzle contour strongly ine uences this form of e ow separation, and restricted shock separation also occursin full-scale, thrust-optimized rocket nozzles. Based on the results established for e ow separation, an outlook on the generation of side loads is given.

A proof of existence of perturbed steady transonic shocks via a free boundary problem

Abstract: We prove the existence of a solution of a free boundary problem for the transonic small-disturbance equation The free boundary is the position of a transonic shock dividing two regions of smooth flow Assuming inviscid, irrotational flow, as modeled by the transonic small-disturbance equation, the equation is hyperbolic upstream where the flow is supersonic, and elliptic in the downstream subsonic region To study the stability of a uniform planar transonic shock, we consider perturbation by a steady C1+ϵ upstream disturbance If the upstream disturbance is small in a C1 sense, then there is a steady solution in which the downstream flow and the transonic shock are Holder-continuous perturbations of the uniform configuration This result provides a new use of inviscid perturbation techniques to demonstrate, in two dimensions, the stability of transonic shock waves of the type that appear, for example, over the wing of an airplane, along an airfoil, or as bow shocks in a flow with a supersonic free-stream velocity © 2000 John Wiley & Sons, Inc

Shock-Wave–Vortex Interactions: Shock and Vortex Deformations, and Sound Production

Abstract: In this paper we study the interaction of a shock wave with a cylindrical vortex. The objective of the study is to characterize the shock and vortex deformations and the mechanism of sound generation. The approach relies on the solution of the two-dimensional Euler equations by means of a high order finite volume weighted-ENO scheme. In order to provide some guidance into the analysis we have also developed an acoustic analogy of the problem by formulating a wave equation for the pressure disturbance that is solved analytically by means of Green's functions. A systematic study has been conducted by investigating the effects of vortex intensity and shock strength. Specifically, we have determined the dependence of shock distortion and vortex compression, and its subsequent nutation upon shock and vortex strengths. The acoustic field generated through shock--vortex interactions has been found to evolve in three stages and to exhibit a three sound quadrupolar directivity. In the early stages of the interaction the sound generated due to shock distortion shows a dipolar character, which then changes to a quadrupolar one due to a restoring mechanism that acts during the interaction of the shock with the rear part of the vortex. In the third stage secondary sounds are formed, which also show a quadrupolar directivity. The acoustic analogy applied to weak shock--vortex interactions also confirms the numerically predicted sound generation mechanism.

Analysis of Transient Thermal Choking Processes in a Model Scramjet Engine

Abstract: Shadowgraph flow visualisation and floor static pressure measurements have been used to examine the transient behaviour of a thermally choked combusting flow. Experiments were performed to examine the effect of varying inlet Mach number and fuel-air equivalence ratio on the nature and extent of the interaction. In all cases a sudden increase in static pressure was measured, followed by a highly turbulent region of sonic flow which was seen to propagate upstream along the duct. The nature of the dominant processes causing this pressure discontinuity are still not certain. Some mechanisms which may contribute to this phenomenon are presented. These include separation of the boundary layer in the duct, formation of a detonation and formation of a near-normal shock wave by the region of thermally choked flow.

Analytical Study and Structure of a Stationary Radiative Shock

Abstract: In this paper we study the radiative shock that arises in certain situations in astrophysics (among others, supernovae, accretion flows, and stars formation). However, it is clear that the high-energy lasers (LIL, LMJ, NIF) will produce plasma flows with hydrodynamics dominated by radiation. Usually, only the radiation flux is considered, and the radiation pressure and energy are neglected. In this paper, in addition to the radiation flux, we take into account the total (matter plus radiation) energy density and pressure. We derive the corresponding generalized Rankine-Huguoniot equations, and it turns out that we can get analytically the structure of the radiative shock. It is shown that three distinct regimes arise; when the Mach number increases (but is small enough), the shock evolves from a continuous structure to a discontinuous one (a discontinuity appears between the shocked medium and the fluid at rest). It is seen then, that this discontinuity disappears for very high values of the Mach number. These behaviors are due to the presence of radiation. Moreover, a precursor develops into the unshocked medium, and scaling laws are derived to obtain the width of the shock and the length of the precursor in terms of the Mach number. Finally, the assumption of the LTE approximation is examined.

Experimental investigation of mixing and ignition of transverse jets in supersonic crossflows

Abstract: Ignition, flame-holding, and mixing enhancement are fundamental aspects of supersonic combustion and are critical to the development of hypersonic airbreathing propulsion engines. High velocities associated with supersonic/hypersonic flight speeds constrain the performance of propulsion systems because of the limited flow residence time inside the combustor. A useful hypervelocity propulsion system therefore requires enhanced mixing of fuel and air, injection with very low drag penalty, and effective distribution of fuel over the burner cross-section. One of the simplest approaches is the transverse injection of fuel from wall orifices. The interesting but rather complicated flow-field dynamics of transverse jets injected into a supersonic crossflow has been studied by many supersonic combustion researchers since 1960’s, but with limited freestream flow conditions. Most of the previous research was performed in conventional wind tunnels by accelerating cold air into supersonic conditions, namely in low velocity and low total enthalpy flow conditions. However, a real supersonic combustor environment at flight speeds beyond Mach 8 can only be simulated using impulse facilities due to the required high total enthalpies. Among various impulse facilities, expansion tubes are especially useful in providing high total enthalpy flows with the proper chemical composition, namely the absence of dissociated species. This research is focused on studying the near-field mixing and ignition properties of transverse fuel jets injected into realistic supersonic combustor flows. We use advanced flow visualization techniques, namely planar laser-induced fluorescence (PLIF) imaging of the hydroxyl radical (OH) and ultra-fast-framing-rate schlieren imaging. While schlieren indicates the location of shock waves, jet penetration and large scale flow features, OH-PLIF is used to map the regions of ignition. The first objective of the present work is to characterize the expansion tube facility

Numerical and experimental investigation of double-cone shock interactions

Abstract: A series of experiments was conducted in the Princeton University Mach 8 Wind Tunnel to study shock interactions on axisymmetric double-cone geometries. Schlieren images and surface-pressure data were taken. Two models were tested, which were expected to produce steady Type VI and Type V shock interactions. The experiments are compared to computational fluid dynamics calculations, and the features of these complicated flowfields are discussed. The comparison is excellent for the laminar Type VI shock interaction. The computations accurately reproduce the size of the separation zone and the surface pressure. However, for the Type V interaction the laminar computation overpredicts the size of the separation region. In addition, the experimental results for the Type V interaction show that the size of the separation region decreases with increasing Reynolds number, whereas the laminar computations predict the opposite trend. Turbulent computations show much better agreement with experimental data and reproduce the experimentally observed relationship between the size of the separation region and the Reynolds number, indicating that the reattachment shocks cause transition to turbulence in these flows

Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties

Abstract: This paper presents an adaptive lattice Boltzmann model of higher accuracy for viscous compressible flows with heat conduction. The proper heat conduction term in the energy equation is recovered by a modification of the kinetic energy transported by particles. The accuracy of the model is improved by introducing a term of fluctuating velocity in the collision-invariant vector. The Navier-Stokes equations are derived by the Chapman-Enskog method from the Bhatnagar-Gross-Krook Boltzmann equation. The advantage of an adaptive lattice Boltzmann model over the standard ones is that the particle velocities are no longer constant, varying with the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. To investigate the viscous and conductive properties of the model, a one-dimensional flow with a sinusoidal velocity distribution and Couette flow were simulated, showing good agreement with the analytical solutions. The simulation of an oblique shock impinging on a solid wall has captured the complex feature of the interaction between the shock and boundary layer.

Numerical Study of Shock-Reflection Hysteresis in an Underexpanded Jet

Abstract: Shock-ree ection hysteresis and plume structure in a low-density, axisymmetric highly underexpanded air jet is examined using a Navier ‐Stokes e ow solver. This type of jet is found in a number of applications, e.g., rocket exhausts and fuel injectors. The plume structure is complex, involving the interaction of several e ow features, making this a demanding problem. Two types of shock ree ection appear to occur in the plume, regular and Mach, depending on the jet pressure ratio. The existence of a dual solution domain where either type may occur has been predicted, in agreement with experiment where the same phenomenon has been observed for a nitrogen jet. There is a hysteresis in the shock-ree ection type; the ree ection type observed in the dual-solution domain depends on the time history of the plume development. A quasi-steady approach is employed to calculate the entire hysteresis loop. An implicit, multiblock structured, e nite volume e ow solver is used. The results of the computational study are used to examine the structure of the plume and are compared with experimental data where possible. Some e ow features not initially recognized from experiment have been identie ed, notably curvature of the Mach disk, recirculation behind the Mach disk, and the regular ree ection having Mach-ree ection characteristics.

The Galactic Shock Pump: A Source of Supersonic Internal Motions in the Cool Interstellar Medium

Abstract: We propose that galactic shocks propagating through interstellar density fluctuations provide a mechanism for the intermittent replenishment, or "pumping," of the supersonic motions and internal density enhancements observed pervasively within cool atomic and molecular interstellar structures, without necessarily requiring the presence of self-gravity, magnetic fields, or young stars. The shocks are assumed to be due to a variety of galactic sources on a range of scales. An analytic result for the kinematic vorticity generated by a shock passing through a radially stratified two-dimensional isobaric model cloud is derived, assuming that the Mach number is not so large that the cloud is disrupted, and neglecting the shock curvature and cloud distortion. Two-dimensional lattice gas hydrodynamic simulations at modest Mach numbers were used to verify the analytic result. The induced internal velocities are initially a significant fraction of the shock speed divided by the square root of the density contrast, accounting for both the observed line width amplitudes and the apparent cloud-to-cloud line width-density scaling. The line width-size relation could then be interpreted in terms of the well-known power spectrum of a system of shocks. The induced vortical energy should quickly be converted to compressible and MHD modes and so would be difficult to observe directly, even though it would still be the power source for the other modes. The shock pump thus produces density structure without the necessity of any sort of instability. We argue that the shock pump should lead to nested shock-induced structures, providing a cascade mechanism for supersonic "turbulence" and a physical explanation for the fractal-like structure of the cool interstellar medium. The average time between shock exposures for an idealized cloud in our Galaxy is estimated and found to be small enough that the shock pump is capable of sustaining the supersonic motions against readjustment and dissipation, except for the smallest structures. This suggests an explanation of the roughly spatially uniform and nearly sonic line widths in small "dense cores." We speculate that the avoidance of shock pumping may be necessary for a localized region to form stars and that the inverse dependence of probability of avoidance on region size may be an important factor in determining the stellar initial mass function.

Supersonic external-compression diffuser and method for designing same

Abstract: A supersonic external-compression inlet (20) comprises a generally scoop-shaped supersonic compression section for diffusing a supersonic free stream flow (24). The supersonic compression section includes a main wall having a leading edge (28) and a throat portion downstream of the leading edge (28), and side portions joined to opposite side edges of the main wall so as to form a generally scoop-shaped structure. The side portions advantageously extend into the supersonic flow stream far enough to encompass the initial oblique shock wave that is attached to the leading edge of the main wall. The main wall has an inner surface (22) formed generally as an angular sector of a surface of revolution, the inner surface (22) of the main wall coacting with inner surfaces of the side portions to define a three-dimensional external-compression surface. The supersonic external-compression inlet (20) also includes a subsonic diffuser section arranged to receive flow from the supersonic compression section and to diffuse the flow to a subsonic condition. A variable-geometry inlet includes an external ramp hinged about its forward edge and forming a portion of the inner surface of the scoop-shaped diffuser, pivotal movement of the external ramp serving to vary a throat size of the inlet. The subsonic diffuser (20) includes an internal ramp hinged about its aft edge for maintaining a smooth transition from the external ramp.

Observation of shock wave elimination by a plasma in a Mach-2.5 flow

Abstract: An experimental study on the influence of a plasma on the structure of an attached conical shock front appearing at the front end of a missile-shaped model has been carried out in a Mach-2.5 flow. The tip and the body of the model are designed as the cathode and anode for gaseous discharge, which produces a spraylike plasma moving around the tip. It is observed that the plasma has caused the shock front to separate from the model. The shock wave moves upstream in the form of a detached bow shock a sensible distance away from the model tip. The detached shock front appears to be highly dispersed in its new location as seen in the shadow video graphs of the flow. As the discharge current increases, experimental evidence shown in the video further reveals a distinct state of the flow without the presence of any shock wave.

Disintegration of trans‐Alfvénic shocks due to variable viscosity and resistivity

Abstract: The evolution of magnetohydrodynamic shock waves depends on dissipation properties of the medium. The increase or decrease of dissipation coefficients results in a larger or smaller thickness of fast and slow shocks. This is not the case for trans-Alfvenic shock waves (TASWs), i.e., such at which the flow velocity passes through the Alfven velocity. In the present paper, it is shown that the variation of dissipation coefficients may cause disintegration of TASWs or diffusion-like change of their upstream and downstream states. This mechanism is complementary to the accumulation of an Alfven-type perturbation inside the shock transition layer. It is also demonstrated that if this variation has a cyclic nature, the TASW undergoes oscillatory disintegration. In this process, it repeatedly transforms into another TASW and emits a nonlinear wave train consisting of shock and rarefaction waves. The implications for planetary bow shocks and shocks induced by CMEs are discussed. In the observational data the disintegration may show up as an unusual position of the bow shock under typical conditions of the solar wind and as a multiple, time-varying structure of the CME leading edge.

Experimental Studies of Laminar Separated Flows Induced by Shock Wave/Boundary Layer and Shock/Shock Interaction in in Hypersonic Flows for CFD Validation

Abstract: In this paper, we summarize the measurements made in a number of experimental programs designed to obtain fundamental measurements for code validation in regions of shock wave/laminar boundary layer interaction and shock/shock interaction flows at Mach numbers between 9 and 15 for a range of Reynolds numbers, some low enough to enable these flows to be computed using both DSMC and Navier-Stokes numerical schemes. Detailed measurements of heat transfer and pressure as well as Schlieren photographs of the flowfield geometry were obtained on a series of axisynunetric cone/cone and cylinder/flare configurations. The model configurations and the fieestream test conditions selected for these studies generated flows in which the regions up and downstream of the separated regions were attached, and the pressure and heat transfer in these regions could be easily predicted. Miniature highfrequency instrumentation was also used to obtain high spatially and temporally resolved measurements in regions of shock/shock interaction on a cylindrical leading edge placed downstream of a shock generator. Again, these studies were made over a large Reynolds number range to ensure that the flows selected for comparison with laminar numerical solutions remained fully laminar downstream of the interaction region. In this set of measurements we have also included measurements made in preliminary studies of real-gas effects on the characteristics of separated regions and the levels of heating generated in regions of shock/shock interaction.

An experimental study of oblique transition in a Blasius boundary layer flow

Abstract: Transition initiated by a pair of oblique waves was investigated experimentally in a Blasius boundary layer flow by using hot-wire measurements and flow visualisation. The oblique waves were generated by periodic blowing and suction through an array of pipes connecting to the flow through a transverse slit in the flat plate model. The structure of the flow field is described and the amplitude of individual frequency-spanwise wave number modes was determined from Fourier transforms of the disturbance velocity. In contrast to results from investigations of oblique transition at subcritical flow conditions, the transition process at the present conditions suggests the combined effect of non-modal growth of streaks and a second stage with exponential growth of oblique waves to initiate the final breakdown stage.

Supersonic Nonequilibrium Plasma Wind-Tunnel Measurements of Shock Modification and Flow Visualization

Abstract: Experiments conducted in a new, small-scale, nonequilibrium plasma wind tunnel recently developed at Ohio State University are discussed. The facility provides a steady-state supersonic e ow of cold nonequilibrium plasma with well-characterized, near uniform, properties. The plasma is produced in aerodynamically stabilized highpressureglowdischargethatformstheplenumofthesupersonicnozzle.Thepossiblemodie cation ofthesupersonic e ow due to ionization is studied by measuring the angle of oblique shocks attached to the wedge located in the nozzle test section. The results do not show any detectable shock weakening or attenuation in weakly ionized nitrogen plasma, compared to the measurements in a nonionized gas e ow. Experiments in supersonic e owing nitrogen and helium afterglow also demonstrate a novel technique for high-density supersonic e ow visualization. It allows identifying all key features of the supersonic e ow, including shocks, boundary layers, e ow separation regions, andwakesby recording intensevisibleradiation of theweakly ionizedplasmas.Interpretation ofradiation intensitydistributionsinnonequilibriumsupersonice owingafterglowmayprovideinformationonkeymechanisms of energy storage and ultraviolet radiation in high-altitude rocket plumes. In addition, these e ow visualization experiments can be used for validation of multidimensional computer e ow codes used for internal e ow simulation.

Second-type self-similar solutions to the ultrarelativistic strong explosion problem

Abstract: The well-known Blandford–McKee solution describes the ultrarelativistic flow in a spherical blast wave enclosed by a strong shock. It is valid when the density of the external medium into which the shock propagates varies with the distance r from the origin as r−k, for k 5−3/4≈4.13, are presented. In these solutions Γ varies as Γ2∝t−m with m=(3−23)k−4(5−33) so that the shock accelerates and the fraction of the flow energy contained in the vicinity of the shock decreases with time. The new solutions are shown to be in excellent agreement with numerical simulations of the flow equations. It is proved that no second-type self-similar solutions exist for k<5−3/4≈4.13.

Evolution of a shock wave in a granular gas

Abstract: Shock wave evolution arising during a steady one-dimensional motion of a piston in a granular gas, composed of inelastically colliding particles is treated by a computational fluid dynamics (CFD) method. It is shown that the flow reaches an asymptotic stationary (final) stage after large evolution time. At this stage particle kinetic energy dissipation leads to formation of two regions within the upstream flow: a fluidized region adjacent to the shock front and a “solid” region adjacent to the piston. In the latter the density is close to the maximum packing density and the kinetic energy of chaotic granular motion is almost zero. The shock wave velocity, mass, and the granular kinetic energy in the fluidized region are found to be constant values, whereas the mass of the solid region grows linearly with time. All properties calculated for the final evolution stage are in excellent agreement with the predictions of the asymptotic solution of the problem obtained earlier. We extend the existing hydrodynami...

Oblique shock reflection from an axis of symmetry

Abstract: An exploratory computational study of the reflection of an inward-facing conical shock wave from its axis of symmetry is presented. This is related to more complex practical situations in both steady and unsteady flows. The absence of a length scale in the problem studied makes features grow linearly with time. The ensuing flow is related to the Guderley singularity in a cylindrical imploding shock. The problem is explored by making a large number of computations of the Euler equations. Distinct reflection congurations are identied, and the regions of parameter space in which they occur are delineated.

Effect of reflection type on detonation initiation at shock-wave focusing

Abstract: . From practical and theoretical standpoints, the initiation of combustion in gaseous media due to the shock waves focusing process at various reflectors is a subject of much current interest. The complex gas flowfield coupled with chemical kinetics provides a wide spectrum of possible regimes of combustion, such as fast flames, deflagration, detonation etc. Shock wave reflection at concave surfaces or wedges causes converging of the flow and produces local zones with extremely high pressures and temperatures. The present work deals with the initiation of detonation due to shock waves focusing at parabolic and wedge reflectors. Particular attention has been given to the determination of the critical values of the incident shock wave (ISW) Mach number, parameters of the combustible mixture, and geometrical sizes of reflector at which different combustion regimes could be generated.

Three-dimensional effects in wind tunnel studies of shock wave reflection

Abstract: This paper concentrates on establishing the three-dimensional flow geometry associated with studies of shock wave reflection between two symmetrical wedges in supersonic flow. It considers the issue of hysteresis in such flows, and draws a distinction between three different aspects of hysteresis, associated with: ideal two-dimensional flow, flow with noise, and three-dimensional effects. The three-dimensional nature of the flow field is elucidated by the use of oblique shadowgraph photography where the optical axis of the shadowgraph system passes at an oblique angle, of as much as 55°, through the test section. The traces of the wave system reflecting off the tunnel window are identified and are used to assist in identification of wave profiles. The nature of the approach of the peripheral Mach reflections collapsing towards the centre of the flow becomes evident, as does the mechanism of transition from Mach reflection to regular reflection. Distinct evidence of the effects of flow perturbations at the mechanical equilibrium transition point are presented, as are changes in the rate of growth of the Mach stem near this point.It is shown that three-dimensional effects can have a major effect on the wedge angle for transition. In the present tests, at Mach 3.1 and a wedge aspect ratio of 0.5, this occurs at a wedge angle of about 5° higher than the theoretical maximum for the corresponding two-dimensional flow, where the dual solution domain extends over only two degrees.

V-waves, bow shocks, and wakes in supercritical hydrostatic flow

Abstract: The structure of the bow shock, V-wave, and the related wave drag and wake in supercritical ambient flow are investigated for homogeneous hydrostatic single-layer flow with a free surface over an isolated two-dimensional (i.e. h(x, y)) obstacle. The two control parameters for this physical system are the ratio of obstacle height to fluid depth and the Froude number F = U/√gH. Based on theoretical analysis and numerical modelling, a steady-state regime diagram is constructed for supercritical flow. This study suggests that supercritical flow may have an upstream bow shock with a transition from the supercritical state to the subcritical state near the centreline, and a V-shock in the lee without a state transition. Unlike subcritical flow, neither a flank shock nor a normal lee shock is observed, due to the local supercritical environment. Both the bow shock and V-shock are dissipative and reduce the Bernoulli constant, but the vorticity generation is very weak in comparison with subcritical ambient flow. Thus, in supercritical flow, wakes are weak and eddy shedding is absent.Formulae for V-wave shape and V-wave drag are given using linear theory. Both formulae compare well with numerical model runs for small obstacles.These results can be applied to air flow over mountains, river hydraulics and coastal ocean currents with bottom topographies.

Pick-up ion acceleration at the termination shock and the post-shock pick-up ion energy distribution

Abstract: It is discussed since quite some time in the literature that the solar wind termination shock may act as an efficient particle accelerator though the underlying physics of injecting particles into this shock acceleration process was not well un- derstood up to now Most of the earlier work required an ad-hoc prescription of the rate by which particles are injected into the process of diffusive shock acceleration Here we avoid this in- jection problem studying instead the single particle fate of pick- up ions arriving at the shock and undergoing multiple adiabatic reflections at the shock We start out from preaccelerated pick- up ions arriving with a known isotropic distribution function at the shock and suffering reflections or transmissions through the shock depending on their actual velocity space coordinates Upstream and downstream of the shock the ions in addition are subject to Fermi-2 acceleration processes described by means of a phase-space transport equation for a pitch-angle anisotropic distribution function As we can show the spectral energy distri- bution resulting for the downstream pick-up ions consists of two parts, the low energy keV-part which is due to directly transmit- ted ions and the high energy MeV-part which is due to multiply reflected ions We also show that the resulting spectrum is fairly sensitive to the location of the shock sector with respect to the upwind direction This fact is best reflected in corresponding energetic neutral atom (ENA) fluxes reaching the Earth from different directions and thus serves as a unique diagnostic tool for the remote study of the 3-d properties of the termination shock