Electromagnetic ion/ion instabilities and their consequences in space plasmas: A review

This paper reviews recent research on the theory and computer simulations of electromagnetic ion/ion instabilities and their consequences in space plasmas. Ion/ion instabilities are growing modes in a collisionless plasma driven unstable by the relative streaming velocity v ₀of two distinct ion components such that v ₀is parallel or antiparallel to the uniform background magnetic field B ₀0. The space physics regimes which display enhanced fluctuations due to these instabilities and which are reviewed in this paper include the solar wind, the terrestrial foreshock, the plasma sheet boundary layer, and distant cometary environments.     

Transonic Flows in Two-Fluid Plasmas

Transonically rotating toroidal plasmas occur at all scales in the plasma universe and, recently, also in laboratory tokamak plasmas. This offers great opportunities for new insights of the effects of transonic transitions on the background equilibrium flows, and on the waves and instabilities excited. Transfer of knowledge and computational methods on MHD and two-fluid waves and instabilities in magnetically confined laboratory fusion plasmas to space and astrophysical plasmas is seriously hampered though by two related difficulties:

1. in contrast to laboratory plasmas, astrophysical plasmas always have sizeable plasma flows so that they can never be described as a static equilibrium;
2. these flows are usually ‘transonic’, i.e., surpass one of the critical speeds related to the different flow regimes with quite different physical characteristics.

Based on previously obtained MHD results on the stationary states and instabilities of transonically rotating accretion disks about compact objects, the extension to two-fluid plasmas is initiated: A variational principle for the computation of two-fluid stationary states is constructed which involves seven fields determining the different physical variables, and six arbitrary stream functions that should be determined by spatially resolved astrophysical observations. It exhibits all the intricacies due to the electron and ion flow excursions from the magnetic flux surfaces. New hyperbolic flow regimes are found with quite different properties than the MHD ones.     

Science Objectives and Rationale for the Radiation Belt Storm Probes Mission

The NASA Radiation Belt Storm Probes (RBSP) mission addresses how populations of high energy charged particles are created, vary, and evolve in space environments, and specifically within Earth’s magnetically trapped radiation belts. RBSP, with a nominal launch date of August 2012, comprises two spacecraft making in situ measurements for at least 2 years in nearly the same highly elliptical, low inclination orbits (1.1×5.8 RE, 10^°). The orbits are slightly different so that 1 spacecraft laps the other spacecraft about every 2.5 months, allowing separation of spatial from temporal effects over spatial scales ranging from ～0.1 to 5 RE. The uniquely comprehensive suite of instruments, identical on the two spacecraft, measures all of the particle (electrons, ions, ion composition), fields (E and B), and wave distributions (d E and d B) that are needed to resolve the most critical science questions. Here we summarize the high level science objectives for the RBSP mission, provide historical background on studies of Earth and planetary radiation belts, present examples of the most compelling scientific mysteries of the radiation belts, present the mission design of the RBSP mission that targets these mysteries and objectives, present the observation and measurement requirements for the mission, and introduce the instrumentation that will deliver these measurements. This paper references and is followed by a number of companion papers that describe the details of the RBSP mission, spacecraft, and instruments.     

The atmosphere of Venus

The investigations of Venus take a special position in planetary researches. It was just the atmosphere of Venus where first measurements in situ were carried out by means of the equipment delivered by a space probe (Venera 4, 1967). Venus appeared to be the first neighbor planet whose surface had been seen by us in the direct nearness made possible by means of the phototelevision device (Venera 9 and Venera 10, 1975). The reasons for the high interest in this planet are very simple. This planet is like the Earth by its mass, size and amount of energy obtained from the Sun and at the same time it differs sharply by the character of its atmosphere and climate. We hope that the investigations of Venus will lead us to define more precisely the idea of complex physical and physical-chemical processes which rule the evolution of planetary atmospheres. We hope to learn to forecast this evolution and maybe, in the far future, to control it. The last expeditions to Venus carried out in 1978 — American (Pioneer-Venus) and Soviet (Venera 11 and 12) — brought much news and it is interesting to sum up the results just now. The contents of this review are:

1. The planet Venus — basic astronomical data.
2. Chemical composition.
3. Temperature, pressure, density (from 0 to 100 km).
4. Clouds.
5. Thermal regime and greenhouse effect.
6. Dynamics.
7. Chemical processes.
8. Upper atmosphere.
9. Origin and evolution.
10. Problems for future studies

Here we have attempted to review the data published up to 1979 and partly in 1980. The list of references is not exhaustive. Publications of special issues of magazines and collected articles concerning separate space expeditions became traditional last time. The results obtained on the Soviet space probes Venera 9, 10 (the first publications) are collected in the special issues of Kosmicheskie issledovanija (14, Nos. 5, 6, 1975), analogous material about Venera 11, 12 is given at Pis'ma Astron. Zh. (5, Nos. 1 and 5, 1978), and in Kosmicheskie issledovanija (16, No. 5, 1979). The results of Pioneer-Venus mission are represented in two Science issues (203, No. 4382; 205, No. 4401) and special issue of J. Geophys. Res. (1980). We shall mention some articles to the same topic among previous surveys: (Moroz, 1971; Sagan, 1971; Marov, 1972; Hunten et al., 1977; Hoffman et al., 1977) and also the books by Kuzmin and Marov (1974) and Kondrat'ev (1977). Some useful information in the part of ground-based observations may be found in the older sources (for example, Sharonov, 1965; Moroz, 1967). For briefness we shall use as a rule the abbreviations of space missions names: V4 instead of Venera 4, M10 instead of Mariner 10 and so on. The first artificial satellites of Venus in the world (orbiters Venera 9 and 10) we shall mark as V9-O, V10-O unlike the descent probes V9, V10. Fly-by modules of Venera 11 and Venera 12 we shall mark as V11-F and V12-F. Pioneers descent probes — Large (Sounder), Day, Night and North — will be marked as P-L, P-D, P-Ni, P-No, orbiter as P-O, and bus as P-B.     

Solar Wind Turbulence and the Role of Ion Instabilities

Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling $k_{\perp}^{-5/3}$ for the perpendicular cascade and $k_{\|}^{-2}$ for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a ?3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to ?2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by $\sim k_{\perp}^{-\alpha}\exp(-k_{\perp}\ell_{d})$ , with α?8/3 and the dissipation scale ? _d close to the electron Larmor radius ? _d ?ρ _e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.     

The Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) NASA Mission-of-Opportunity

Two Wide-angle Imaging Neutral-atom Spectrometers (TWINS) is a NASA Explorer Mission-of-Opportunity to stereoscopically image the Earth’s magnetosphere for the first time. TWINS extends our understanding of magnetospheric structure and processes by providing simultaneous Energetic Neutral Atom (ENA) imaging from two widely separated locations. TWINS observes ENAs from 1–100 keV with high angular (～4°×4°) and time (～1-minute) resolution. The TWINS Ly-α monitor measures the geocoronal hydrogen density to aid in ENA analysis while environmental sensors provide contemporaneous measurements of the local charged particle environments. By imaging ENAs with identical instruments from two widely spaced, high-altitude, high-inclination spacecraft, TWINS enables three-dimensional visualization of the large-scale structures and dynamics within the magnetosphere for the first time. This “instrument paper” documents the TWINS design, construction, calibration, and initial results. Finally, the appendix of this paper describes and documents the Southwest Research Institute (SwRI) instrument calibration facility; this facility was used for all TWINS instrument-level calibrations.     

Low-Frequency Waves and Instabilities in Collisionless Plasmas

We present a theoretical overview of low-frequency waves and instabilities in collisionless, multi-component plasmas with gyrotropic ( ) thermal pressure. We show that the complete dispersion relation can be obtained in the framework of a mixed magnetohydrodynamic (MHD)-kinetic formalism, which uses the MHD mass, momentum, and induction equations, together with the kinetically corrected version of the double-adiabatic equations of state. The complete dispersion relation contains not only the three standard modes (fast, slow, and Alfvén) from double-adiabatic MHD, but also the mirror mode from kinetic theory. We examine the stability properties of these four modes, firstly in the case of a uniform medium, and secondly in the case of a stratified and rotating medium. We also discuss the connections with the quasi-interchange modes (interchange and translation) often referred to in the context of magnetospheric physics.     

Modelling Electrostatic Sheath Effects on Swarm Electric Field Instrument Measurements

The Electric Field Instrument (EFI) was designed to measure ionospheric ion flow velocities, temperatures and distribution functions at the ram face of the European Space Agency’s Swarm spacecraft. These flow velocities, combined with the known orbital velocity of the satellite and local magnetic field, will be used to infer local electric fields from the relation E=?v×B. EFI is among a class of many particle sensors and flow meters mounted on satellites to monitor in situ plasma conditions. The interpretation of the measurements made with EFI and similar sensors relies on a spacecraft sheath model. A common approach, valid in the relatively cold and dense ionospheric plasma, is to assume a potential drop in a thin sheath through which particle deflection and energisation can be calculated analytically. In such models, sheath effects only depend on the spacecraft floating potential, and on the angle of incidence of particles with respect to the normal to the surface. Corrections to measurements are therefore local as they do not depend on the geometry of nearby objects. In an actual plasma, satellites are surrounded by electrostatic sheaths with a finite thickness. As a result, local corrections to particle distribution functions can only be seen as an approximation. A correct interpretation of measured particle fluxes or particle distribution functions must, at least in principle, account for the extent and shape of the sheath in the vicinity of the measuring instrument. This in turn requires a careful analysis of the interaction of the satellite with the surrounding plasma, while accounting for detailed aspects of the geometry, as well as for several physical effects. In this paper, the validity of the thin sheath model is tested by comparing its predictions with detailed PIC (Particle In Cell) calculations of satellite-plasma interaction. Deviations attributed to sheath finite thickness effects are calculated for EFI measurements, with representative plasma parameters encountered along the planned Swarm orbit. Finite thickness effects of the plasma sheaths are found to induce EFI velocity measurement errors not exceeding 37 m/s, with larger errors occurring in plasmas that are simultaneously tenuous (10⁹ m^?3 or lower) and warm (0.5 eV or higher).     

Conjugate features of magnetospheric electron dynamics observed at balloon altitudes

Analysis of recent observations (from balloons, spacecraft, and surface observatories) demonstrate regional, shell, and nearpoint conjugacy at L ～ 7 during precipitative events which were characterized by local acceleration as well as release of gradient-drifted electrons injected during substorms. A number of new features of magnetospheric dynamics relating to substorm development and sudden-commencement effects, have been brought to light which, though poorly understood at present, may prove of considerable importance and are worthy of further investigation.

1. During the initial period of instability in substorm evolution, preceding the slower magnetotail convective injection, precipitation of waves of electrons in rapid polewards motion exhibit L-shell conjugacy near midnight.
2. Transient, large scale expansions of the magnetospheric electron population accompanied by temporally imbedded substorms display large scale regional conjugacy and are simultaneously observed as similarly transient intensity dropouts at balloon altitudes.
3. Precipitation from gradient-drifting electrons in the dayside magnetosphere exhibits near point-conjugacy, at least down to the order of 50 km and quite probably less.

Similarly tight conjugacy applies to the release of electrons showing a specific local response to sudden commencements.

1. Analysis of the approach to and attainment of spectral equilibrium in the precipitation observed from drifting electrons may provide information about either, or both, the source spectrum at injection and the process of local release.
2. The specific precipitation effect sometimes observed at the time of an SC remains a rather puzzling feature, although it seems clear now that the acceleration and/or release process responsible is of a highly local nature and works selectively at small pitch angles well within the magnetospheric boundary. Coupling of the interplanetary shock with the magnetosphere must be an important aspect, but the details are not clear as yet.
3. On at least one occasion, a large part (perhaps all) of the magnetospheric electron population varied in a nearly synchronous manner in response to solar wind induced distortions during the variable compressive phase of a sudden commencement geomagnetic storm.

In the ongoing effort to identify and understand acceleration and release mechanisms involved in magnetospheric dynamics, balloon-borne experiments will continue to be useful, providing essential information presently unattainable by other means.     

Gravity Probe B Data Analysis

This is the first of five connected papers detailing progress on the Gravity Probe B (GP-B) Relativity Mission. GP-B, launched 20 April 2004, is a landmark physics experiment in space to test two fundamental predictions of Einstein’s general relativity theory, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection began 28 August 2004 and science operations were completed 29 September 2005. The data analysis has proven deeper than expected as a result of two mutually reinforcing complications in gyroscope performance: (1) a changing polhode path affecting the calibration of the gyroscope scale factor C _g against the aberration of starlight and (2) two larger than expected manifestations of a Newtonian gyro torque due to patch potentials on the rotor and housing. In earlier papers, we reported two methods, ‘geometric’ and ‘algebraic’, for identifying and removing the first Newtonian effect (‘misalignment torque’), and also a preliminary method of treating the second (‘roll-polhode resonance torque’). Central to the progress in both torque modeling and C _g determination has been an extended effort on “Trapped Flux Mapping” commenced in November 2006. A turning point came in August 2008 when it became possible to include a detailed history of the resonance torques into the computation. The East-West (frame-dragging) effect is now plainly visible in the processed data. The current statistical uncertainty from an analysis of 155 days of data is 5.4 marc-s/yr (～14% of the predicted effect), though it must be emphasized that this is a preliminary result requiring rigorous investigation of systematics by methods discussed in the accompanying paper by Muhlfelder et al. A covariance analysis incorporating models of the patch effect torques indicates that a 3–5% determination of frame-dragging is possible with more complete, computationally intensive data analysis.     

Electric Fields and Magnetic Fields in the Plasmasphere: A Perspective From CLUSTER and IMAGE

The electric field and magnetic field are basic quantities in the plasmasphere measured since the 1960s. In this review, we first recall conventional wisdom and remaining problems from ground-based whistler measurements. Then we show scientific results from Cluster and Image, which are specifically made possible by newly introduced features on these spacecraft, as follows. 1. In situ electric field measurements using artificial electron beams are successfully used to identify electric fields originating from various sources. 2. Global electric fields are derived from sequences of plasmaspheric images, revealing how the inner magnetospheric electric field responds to the southward interplanetary magnetic fields and storms/substorms. 3. Understanding of sub-auroral polarization stream (SAPS) or sub-auroral ion drifts (SAID) are advanced through analysis of a combination of magnetospheric and ionospheric measurements from Cluster, Image, and DMSP. 4. Data from multiple spacecraft have been used to estimate magnetic gradients for the first time.     

The Supermassive Black Hole—Galaxy Connection

The observed scaling relations imply that supermassive black holes (SMBH) and their host galaxies evolve together. Near-Eddington winds from the SMBH accretion discs explain many aspects of this connection. The wind Eddington factor \(\dot{m}\) should be in the range ～1–30. A factor \(\dot{m}\sim 1\) give black hole winds with velocities v～0.1c, observable in X-rays, just as seen in the most extreme ultrafast outflows (UFOs). Higher Eddington factors predict slower and less ionized winds, observable in the UV, as in BAL QSOs. In all cases the wind must shock against the host interstellar gas and it is plausible that these shocks should cool efficiently. There is detailed observational evidence for this in some UFOs. The wind sweeps up the interstellar gas into a thin shell and propels it outwards. For SMBH masses below a certain critical (M–σ) value, all these outflows eventually stall and fall back, as the Eddington thrust of the wind is too weak to drive the gas to large radii. But once the SMBH mass reaches the critical M–σ value the global character of the outflow changes completely. The wind shock is no longer efficiently cooled, and the resulting thermal expansion drives the interstellar gas far from the black hole, which is unlikely to grow significantly further. Simple estimates of the maximum stellar bulge mass M _b allowed by self-limited star formation show that the SMBH mass is typically about 10^?3 M _b at this point, in line with observation. The expansion-driven outflow reaches speeds v _out?1200 km?s^?1 and drives rates \(\dot{M}_{\mathrm{out}}\sim 4000~\mathrm {M}_{\odot }\,\mathrm{yr}^{-1}\) in cool (molecular) gas, giving a typical outflow mechanical energy L _mech?0.05L _Edd, where L _Edd is the Eddington luminosity of the central SMBH. This is again in line with observation. These massive outflows may be what makes galaxies become red and dead, and can have several other potentially observable effects. In particular they have the right properties to enrich the intergalactic gas with metals. Our current picture of SMBH-galaxy coevolution is still incomplete, as there is no predictive theory of how the hole accretes gas from its surroundings. Recent progress in understanding how large-scale discs of gas can partially cancel angular momentum and promote dynamical infall offers a possible way forward.     

Identifications of some highly-ionized iron and nickel lines in the 200–400 Å region of the solar spectrum

A number of previously unclassified multiplets of Fexiv, xiii, xii, and xi produced by transitions of the type 3s ²3p ⁿ -3s3p ⁿ⁺¹ are identified in the XUV spectrum of the Sun. The iron lines account for most of the previously unidentified strong lines between 330 and 370 Å. Solar observations of especial value for the investigation of the 300–400 Å region were the slitless spectroheliograms of September 22, 1968 (Purcell and Tousey, 1969) and November 4, 1969 (Tousey, 1971) — on which the image of a flare was recorded. Other solar identifications in the same spectral region include the resonance lines of Nixvii and Nixviii, and one 3p-3d multiplet of Fexiii. The solar blend at 417 Å involving the Fexv inter-combination line and Sxiv is resolved.     

Basic Physical Mechanism of Fast Reconnection Evolution in Space Plasmas

Large dissipative events, such as solar flares and geomagnetic substorms, may result from sudden onset of fast (explosive) magnetic reconnection. Hence, it is a long-standing problem to find the physical mechanism that makes magnetic reconnection explosive; in particular, how can the fast magnetic reconnection explosively evolve in space plasmas? In this respect, we have proposed the spontaneous fast reconnection model as a nonlinear instability that grows by the positive feedback between plasma microphysics (anomalous resistivity) and macrophysics (global reconnection flow). On the basis of MHD simulations, we demonstrate for a variety of physical situations that the fast reconnection mechanism involving slow shocks in fact evolves explosively as a nonlinear instability and is sustained quasi-steadily on the nonlinear saturation phase. Also, distinct plasma processes, such as large-scale plasmoid propagation, magnetic loop development and loop-top heating, and asymmetric fast reconnection evolution, directly result from the spontaneous fast reconnection model. Obviously, MHD simulations are very useful in understanding the basic physics of explosive fast reconnection evolution in space plasmas. However, they cannot treat the details of microphysics near an X neutral point, which should be precisely studied in the coming 21st century.     

Measurements of quasi-static electric fields between 3 and 7 Earth radii on GEOS-1

Quasi-static electric fields have been measured with two spherical probes supported by cable booms providing a baseline of 42 m for the measurement. The performance of the experiment is outlined to demonstrate that electric fields can be measured with accuracies of ±0.7 mV m^-1 and ±1.0 mV m^-1 in the dawn-dusk and satellite-sun directions respectively. These uncertainties can be considerably reduced under favourable plasma conditions. Examples of typical observations are described.

1. The average electric field is always characterized by an irregular structure with time scales 0.5–5 min and with amplitudes of a few mV m^-1.
2. During substorms dawn-dusk electric fields up to 20–30 mV m^-1 have been observed over intervals of 30–60 s.
3. Oscillating electric fields with peak-to-peak amplitudes up to 10 mV m^-1 and periods of 3–10 min have been observed following magnetospheric disturbances.

The observations are discussed in terms of plasma motions and possible spatial scale sizes of the phenomena, standing magnetospheric wave modes and electrostatic potentials.     

He-like Ions as Practical Astrophysical Plasma Diagnostics: From Stellar Coronae to Active Galactic Nuclei

We review X-ray plasma diagnostics based on the line ratios of He-like ions. Triplet/singlet line intensities can be used to determine electronic temperature and density, and were first developed for the study of the solar corona. Since the launches of the X-ray satellites Chandra and XMM-Newton, these diagnostics have been extended and used (from C?v to Si?xiii) for a wide variety of astrophysical plasmas such as stellar coronae, supernova remnants, solar system objects, active galactic nuclei, and X-ray binaries. Moreover, the intensities of He-like ions can be used to determine the ionization process(es) at work, as well as the distance between the X-ray plasma and the UV emission source for example in hot stars. In the near future thanks to the next generation of X-ray satellites (e.g., Astro-H and IXO), higher-Z He-like lines (e.g., iron) will be resolved, allowing plasmas with higher temperatures and densities to be probed. Moreover, the so-called satellite lines that are formed closed to parent He-like lines, will provide additional valuable diagnostics to determine electronic temperature, ionic fraction, departure from ionization equilibrium and/or from Maxwellian electron distribution.     

Algol,Beta Lyrae,and W Serpentis: Some new results for three well studied eclipsing binaries

The properties of the eclipsing binaries Algol, Beta Lyrae, and W Serpentis are discussed and new results are presented. The physical properties of the components of Algol are now well determined. High resolution spectroscopy of the H-alpha feature by Richards et al. and by Gillet et al. and spectroscopy of the ultraviolet resonance lines with the International Ultraviolet Explorer satellite reveal hot gas around the BBV primary. Gas flows also have been detected apparently originating from the low mass, cooler secondary component and flowing toward the hotter star through the Lagrangian L1 point. Analysis of 6 years of multi-bandpass photoelectric photometry of Beta Lyrae indicates that systematic changes in light curves occur with a characteristic period of -275 ± 25 days. These changes may arise from pulsations of the B8II star or from changes in the geometry of the disk component. Hitherto unpublished u, v, b, y, and H-alpha index light curves of W Ser are presented and discussed. W Ser is a very complex binary system that undergoes complicated, large changes in its light curves. The physical properties of W Ser are only poorly known, but it probably contains one component at its Roche surface, rapidly transfering matter to a component which is embedded in a thick, opaque disk. In several respects, W Ser resembles an upscale version of a cataclysmic variable binary system.     

CLUSTER and IMAGE: New Ways to Study the Earth’s Plasmasphere

Ground-based instruments and a number of space missions have contributed to our knowledge of the plasmasphere since its discovery half a century ago, but it is fair to say that many questions have remained unanswered. Recently, NASA’s Image and ESA’s Cluster probes have introduced new observational concepts, thereby providing a non-local view of the plasmasphere. Image carried an extreme ultraviolet imager producing global pictures of the plasmasphere. Its instrumentation also included a radio sounder for remotely sensing the spacecraft environment. The Cluster mission provides observations at four nearby points as the four-spacecraft configuration crosses the outer plasmasphere on every perigee pass, thereby giving an idea of field and plasma gradients and of electric current density. This paper starts with a historical overview of classical single-spacecraft data interpretation, discusses the non-local nature of the Image and Cluster measurements, and emphasizes the importance of the new data interpretation tools that have been developed to extract non-local information from these observations. The paper reviews these innovative techniques and highlights some of them to give an idea of the flavor of these methods. In doing so, it is shown how the non-local perspective opens new avenues for plasmaspheric research.     

Particle code simulations with injected particles

As problems we are interested in become more complex, we often find our simulations stretching the limits of available computer resources. For example, an interesting problem is simulation of dissipation processes in sub-critical collisionless shocks. To simulate this system our simulation box must contain the shock and its upstream and downstream regions over the entire length of a run. If the shock moves with any appreciable speed the box must then be considerably larger than the shock thickness making it hard to resolve the shock front itself with a reasonable number of grid points. A solution to this problem is to run the simulation in the frame of reference of the shock. Particles are injected upstream of the shock and leave the simulation box downstream. With the shock stationary in the simulation box, we only need to contain enough of the up and downstream regions for the fields, etc., to settle down and separate the shock from the box boundaries. In this tutorial we consider some basic algorithms used in a practical particle injection code, such as the two dimensional WAVE code used at Los Alamos. We will try to present these ideas in a simple format general enough to be easily included in any particle code. Topics covered are:

1. Smoothly Injecting Particles.
2. Generating the Distribution Functions.
3. Time Dependent Injection Density.
4. Boundary Conditions on Fields and Particles.

(Flux and Charge Conservation)