Magnetic helicity generation in the frame of Kazantsev model

Using a magnetic dynamo model, suggested by Kazantsev (J. Exp. Theor. Phys. 1968, vol. 26, p. 1031), we study the small-scale helicity generation in a turbulent electrically conducting fluid. We obtain the asymptotic dependencies of dynamo growth rate and magnetic correlation functions on magnetic Reynolds numbers. Special attention is devoted to the comparison of a longitudinal correlation function and a function of magnetic helicity for various conditions of asymmetric turbulent flows. We compare the analytical solutions on small scales with numerical results, calculated by an iterative algorithm on non-uniform grids. We show that the exponential growth of current helicity is simultaneous with the magnetic energy for Reynolds numbers larger than some critical value and estimate this value for various types of asymmetry.     

Using wavelet‐domain adaptive filtering to improve signal‐to‐noise ratio of nuclear magnetic resonance log data from tight gas sands

In tight gas sands, the signal‐to‐noise ratio of nuclear magnetic resonance log data is usually low, which limits the application of nuclear magnetic resonance logs in this type of reservoir. This project uses the method of wavelet‐domain adaptive filtering to denoise the nuclear magnetic resonance log data from tight gas sands. The principles of the maximum correlation coefficient and the minimum root mean square error are used to decide on the optimal basis function for wavelet transformation. The feasibility and the effectiveness of this method are verified by analysing the numerical simulation results and core experimental data. Compared with the wavelet thresholding denoise method, this adaptive filtering method is more effective in noise filtering, which can improve the signal‐to‐noise ratio of nuclear magnetic resonance data and the inversion precision of transverse relaxation time T₂ spectrum. The application of this method to nuclear magnetic resonance logs shows that this method not only can improve the accuracy of nuclear magnetic resonance porosity but also can enhance the recognition ability of tight gas sands in nuclear magnetic resonance logs.     

Numerical simulations of MHD dynamos

The generation of magnetic fields in space plasmas and in astrophysics is usually described within the framework of magnetohydrodynamics. Turbulent helical flows produce magnetic fields very efficiently, with correlation length scales larger than those characterizing the flow. Within the context of the solar magnetic cycle, a turbulent dynamo is responsible for the so-called alpha effect, while the Omega effect is associated to the differential rotation of the Sun.We present direct numerical simulations of turbulent magnetohydrodynamic dynamos including two-fluid effects such as the Hall current. More specifically, we study the evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence, and explore the conditions for exponential growth of the magnetic energy. In all the cases considered, we find that the dynamo saturates at the equipartition level between kinetic and magnetic energy, and the total energy reaches a Kolmogorov power spectrum.     

A shell model for anisotropic magnetohydrodynamic turbulence

Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B ₀, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 10⁵ have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B ₀ with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.     

Evolution of non-linear α 2-dynamos and taylor's constraint

A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?²-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10^?3 to 5.0× 10^?5, for?α?=α ₀cos?θ?sin?π?(r?r_i ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?₀. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.     

Large-scale convective dynamos in a stratified rotating plane layer

We study the effect of stratification on large-scale dynamo action in convecting fluids in the presence of background rotation. The fluid is confined between two horizontal planes and both boundaries are impermeable, stress-free and perfectly conducting. An asymptotic analysis is performed in the limit of rapid rotation (τ???1 where τ is the Taylor number). We analyse asymptotic magnetic dynamo solutions in rapidly rotating systems generalising the results of Soward [A convection-driven dynamo I. The weak field case. Philos. Trans. R. Soc. Lond. A 1974, 275, 611–651] to include the effects of compressibility. We find that in general the presence of stratification delays the efficiency of large-scale dynamo action in this regime, leading to a reduction of the onset of dynamo action and in the nonlinear regime a diminution of the large-scale magnetic energy for flows with the same kinetic energy.     

Convective dynamos with intermediate and strong fields

Abstract

The weak-field Benard-type dynamo treated by Soward is considered here at higher levels of the induced magnetic field. Two sources of instability are found to occur in the intermediate field regime M ～ T ^1/12, where M and T are the Hartmann and Taylor numbers. On the time scale of magnetic diffusion, solutions may blow up in finite time owing to destabilization of the convection by the magnetic field. On a faster time scale a dynamic instability related to MAC-wave instability can also occur. It is therefore concluded that the asymptotic structure of this dynamo is unstable to virtual increases in the magnetic field energy.

In an attempt to model stabilization of the dynamo in a strong-field regime we consider two approximations. In the first, a truncated expansion in three-dimensional plane waves is studied numerically. A second approach utilizes an ad hoc set of ordinary differential equations which contains many of the features of convection dynamos at all field energies. Both of these models exhibit temporal intermittency of the dynamo effect.     

An improved input energy spectrum verified by the shake table tests

Input energy is the principal component of the energy balance equation. It is beneficial to determine, through its components, how the recoverable and irrecoverable energies are distributed within the structural elements. Several equations and attenuation relations to define mass-normalized input energy spectra exist in the literature. They are mainly proposed for elastic systems subjected to far-fault EQs. There is a lack of experimental verification of these proposed spectra. In this paper, experimental assessment was performed to the existing spectra, and further improvements were accomplished. For this purpose, steel cantilever columns were tested on the shake table for two specific historical EQs coincidently having similar spectral acceleration values. Based on the experimental results, a three-part mass-normalized relative input energy spectrum was formulated including soil type, EQ (corner period, intensity, duration, spectral acceleration, and velocity), and structural behavioral characteristics (period and structural damping). The proposed input energy spectrum was experimentally calibrated and numerically validated for various EQs featuring near- and far-field types. Analytical and experimental comparisons were made between the previously developed spectrum and the newly proposed one. The validation studies and the statistical evaluations exposed that the proposed spectrum yielded better agreement with the experimental and numerical results.     

Driving Galactic Turbulence by Supernova Explosions

We investigate the general properties of supernova driven interstellar turbulence using local three-dimensional MHD simulations under Galactic conditions. Our model includes the effects of large-scale shear due to Galactic differential rotation, density stratification, compressibility, magnetic fields, heating via supernova explosions and parameterized radiative cooling of the interstellar medium. In addition to investigating isolated supernova explosions we allow for multiple supernovae distributed randomly in the Galactic disc and exponentially in the vertical direction. Single supernova explosions drive a strong shock, the lifetime of which is approximately 2 Myr in our model. This stage is found to be characterized by a kinetic energy spectrum in the diffuse gas with spectral index consistent with k = –2. Large-scale shear and Coriolis force act on the supernova remnant producing some vorticity inside it, but this process was found to be very weak. In the case of multiple supernova explosions, older remnants have an important role causing density fluctuations in the interstellar medium. In this clumpy medium, the propagation velocity of the shock fronts changes due to the changing density, and vorticity is generated. In the absence of these supernova interactions the kinetic energy spectrum shows a relatively wide shock spectrum with spectral index k = –2, but when the supernova interactions become dominant the classical k = –5/3 spectrum is observed.     

Broken ergodicity in magnetohydrodynamic turbulence

Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B _o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B _o?=?0 and weakly broken when B _o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B _o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.     

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell-i

Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 10⁵, Prandtl number P = 1, and Rayleigh number R between 1 |MX 10⁴ and 4 |MX 10⁴ (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 10⁴, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 10⁴, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 10⁴, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 10⁴, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 10⁴, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 10⁴ maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 10⁴.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.     

Topological invariants of field lines rooted to planes

Abstract

Two open curves with fixed endpoints on a boundary surface can be topologically linked. However, the Gauss linkage integral applies only to closed curves and cannot measure their linkage. Here we employ the concept of relative helicity in order to define a linkage for open curves. For a magnetic field consisting of closed field lines, the magnetic helicity integral can be expressed as the sum of Gauss linkage integrals over pairs of lines. Relative helicity extends the helicity integral to volumes where field lines may cross the boundary surface. By analogy, linkages can be defined for open lines by requiring that their sum equal the relative helicity.

With this definition, the linkage of two lines which extend between two parallel planes simply equals the number of turns the lines take about each other. We obtain this result by first defining a gauge-invariant, one-dimensional helicity density, i.e. the relative helicity of an infinitesimally thin plane slab. This quantity has a physical interpretation in terms of the rate at which field lines lines wind about each other in the direction normal to the plane. A different method is employed for lines with both endpoints on one plane; this method expresses linkages in terms of a certain Gauss linkage integral plus a correction term. In general, the linkage number of two curves can be put in the form L=r + n, |r|≦1J2, where r depends only on the positions of the endpoints, and n is an integer which reflects the order of braiding of the curves.

Given fixed endpoints, the linkage numbers of a magnetic field are ideal magneto-hydrodynamic invariants. These numbers may be useful in the analysis of magnetic structures not bounded by magnetic surfaces, for example solar coronal fields rooted in the photosphere. Unfortunately, the set of linkage numbers for a field does not uniquely determine the field line topology. We briefly discuss the problem of providing a complete and economical classification of field topologies, using concepts from the theory of braid equivalence classes.     

Continuous wavelet transform,theoretical aspects and application to aeromagnetic data at the Huanghua Depression,Dagang Oilfield,China

We use the continuous wavelet transform based on complex Morlet wavelets, which has been developed to estimate the source distribution of potential fields. For magnetic anomalies of adjacent sources, they always superimpose upon each other in space and wavenumber, making the identification of magnetic sources problematic. Therefore, a scale normalization factor, a^?n, is introduced on the wavelet coefficients to improve resolution in the scalogram. By theoretical modelling, we set up an approximate linear relationship between the pseudo‐wavenumber and source depth. The influences of background field, random noise and magnetization inclination on the continuous wavelet transform of magnetic anomalies are also discussed and compared with the short‐time Fourier transform results. Synthetic examples indicate that the regional trend has little effect on our method, while the influence of random noise is mainly imposed on shallower sources with higher wavenumbers. The source horizontal position will be affected by the change of magnetization direction, whereas the source depth remains unchanged. After discussing the performance of our method by showing the results of various synthetic tests, we use this method on the aeromagnetic data of the Huanghua depression in central China to define the distribution of volcanic rocks. The spectrum slices in different scales are used to determine horizontal positions of volcanic rocks and their source depths are estimated from the modulus maxima of complex coefficients, which is in good accordance with drilling results.     

The effect of time-dependent γ-pumping on buoyant magnetic structures

ABSTRACT

In this paper, we explore for the first time the interactions of the net downward, time-dependent, γ-pumping overlying an imposed layer of magnetic fluid, in a polytropic atmosphere. Our calculations show that an equipartition of energy, between the magnetic and kinetic components, must be reached for buoyancy-driven magnetic structures to rise into the pumping region. However, structures do not rise unhindered, as in a previous investigation. We show that the evolution and other features of the emerging magnetic flux structures are significantly affected by the temporal variation of the γ-pumping. The rate of emerging structures, the strength of magnetic concentrations and the extent to how far magnetic field can travel were all found to depend on the timescale of the γ-pumping.     

Chaotic mixing of tracer and vorticity by modulated travelling Rossby waves

Abstract

We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading “chaotic advection” or “Lagrangian turbulence.” A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k ^{? l} at shortwaves—precisely as for mixing by homogeneous, isotropic two dimensional turbulence,—even though the physics of the present case is very different. We have produced two independent arguments accounting for this behavior.

We then examine integrations of the unforced barotropic vorticity equation with initial conditions chosen to give a large scale streamline geometry similar to that analyzed in the passive case. It is found that vorticity mixing proceeds along lines similar to passive tracer mixing. Broad regions of homogenized vorticity ultimately surround the separatrices of the large scale streamline pattern, with vorticity gradients limited to nonchaotic regions (regions of tori) in the corresponding passive problem.

Vorticity in the chaotic zone takes the form of an arrangement of strands which become progressively finer in scale and progressively more densely packed; this process transfers enstrophy to small scales. Although the enstrophy cascade is entirely controlled by the large scale wave, the shortwave enstrophy spectrum ultimately takes on the classical k ^{? l} form. If one accepts that the enstrophy cascade is indeed mediated by chaotic advection, this is the expected behavior. The extreme form of nonlocality (in wavenumber space) manifest in this example casts some doubt on the traditional picture of enstrophy cascade in the Atmosphere, which is based on homogeneous two dimensional turbulence theory. We advance the conjecture that these transfers are in large measure attributable to large scale, low frequency, planetary waves.

Upscale energy transfers amplifying the large scale wave do indeed occur in the course of the above-described process. However, the energy transfer is complete long before vorticity mixing has gotten very far, and therefore has little to do with chaotic advection. In this sense, the vorticity involved in the enstrophy cascade is “fossil vorticity,” which has already given up its energy to the large scale.

We conclude with some speculations concerning statistical mechanics of two dimensional flow, prompted by our finding that flows with identical initial energy and enstrophy can culminate in very different final states. We also outline prospects for further applications of chaotic mixing in atmospheric problems.     

Relationship between global seismicity and solar activities

The relations between sunspot numbers and earthquakes (M≧6), solar 10.7 cm radio flux and earthquakes, solar proton events and earthquakes have been analyzed in this paper. It has been found that: (1) Earthquakes occur frequently around the minimum years of solar activity. Generally, the earthquake activities are relatively less during the peak value years of solar activity, some say, around the period when magnetic polarity in the solar polar regions is reversed. (2) the earthquake frequency in the minimum period of solar activity is closely related to the maximum annual means of sunspot numbers, the maximum annual means of solar 10.7 cm radio flux and solar proton events of a whole solar cycle, and the relation between earthquake and solar proton events is closer than others. (3) As judged by above interrelationship, the period from 1995 to 1997 will be the years while earthquake activities are frequent. In the paper, the simple physical discussion has been carried out. These results supported the exploration and studies of some researchers to a certain extent. This work is supported by Foundation of the Chinese Academy of Sciences (major item).     

Large-eddy simulations of convection-driven dynamos using a dynamic scale-similarity model

Dynamo simulations require sub-grid scale (SGS) models for the momentum and heat flux, the Lorentz force, and the magnetic induction. Previous large eddy simulations (LES) using the scale similarity model have represented many aspects of the SGS motion. However, discrepancies are observed due to interchanging the order of filtering operation and spatial differentiation. In this study, we implement a correction term for this commutation error specifically for the scale-similarity model. Furthermore, we implement a dynamic scheme to evaluate time-dependent coefficients for the SGS models. We perform dynamo simulations in a rotating plane layer with different spatial resolutions, and compare results for the time dependence of the large-scale magnetic field. Simulations are performed at two different Rayleigh numbers, using constant values for the other dimensionless numbers (Ekman, Prandtl, and magnetic Prandtl numbers). Both cases show that the dynamic LES can accurately represent the large-scale magnetic field, whereas the dynamo failed in the direct simulations without the SGS terms at the same spatial resolutions. We conclude that the dynamic versions of the SGS and commutation error correction are essential for successful dynamos on coarser grids.     

双能CT的基本原理、应用和未来展望(英文)

断层影像(CT)的图像对比度与扫描所用的X光源能谱分布有很大关系。传统CT使用具有能谱分布的一个光源进行成像,有时会出现信息模糊致使两种不同材料在CT图像上完全相同。双能CT使用两个不同分布的能谱对物体进行成像,能够消除单能谱情况下的信息模糊。虽然双能CT的基本概念由来已久,但最近商业系统的出现使双能CT迅速成为一个热点。我们首先概述了双能CT的基本物理原理和双能信号处理方法,包括促使双能CT进入现代医学成像的关键技术。其次,双能CT的应用已非常广泛,本文从其在临床应用角度进行了详细介绍使读者有所了解。最后,我们简要探讨了当前的两个技术发展领域:光子技术探测器和技术合成CT。     

Injection and acceleration of H+ and He2+ at Earth’s bow shock

We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in order to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth’s bow shock. The shocks propagate into a medium containing magnetic fluctuations, which are initially superimposed on the background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He²⁺ is included self-consistently. The upstream differential intensity spectra of H⁺ and He²⁺ can be well represented by exponentials in energy. The e-folding energy E_c is a function of time: E_c increases with time. Furthermore the e-folding energy (normalized to the shock ramming energy E_p) increases with increasing Alfvén Mach number of the shock and with increasing fluctuation level of the initially superimposed turbulence. When backstreaming ions leave the shock after their first encounter they exhibit already a spectrum which extends to more than ten times the shock ramming energy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contribute to ion injection. Acceleration models that permit thermal particles to scatter like the non-thermal population do not describe the correct physics.