Non-linear resonant excitation of whistler mode waves in the Earth's ionosphere

We examine the resonant non-linear interaction in the Earth's ionosphere of two powerful high frequency radio beams with frequencies f ₁ and f ₂ (both larger than the plasma frequency at F2_max) and wave numbers k ₁ and k ₂ such that a whistler mode wave can be excited with a frequency f ₃ = f ₁ — f ₂ and a wave number k ₃ = k ₁ – k ₂. The feasibility of an effective ground based installation, sited at low latitudes, is discussed and the field strength of the wave emerging from a 10 km wide ionospheric region illuminated by the beams is evaluated for a range of transmitted frequencies, beam orientations and plasma frequencies in the interaction region. It is suggested that the longitude dependence of the enhancement of VLF noise bands detected by the Ariel 3 satellite may be due to a non-linear interaction of this type between any two or more medium wavelength signals from areas where there is a high concentration of commercial broadcasting stations, such as the NE region of the U.S.A.     

Particle acceleration by magnetic reconnection and shocks during current loop coalescence in solar flares

This article reviews recent development of the theory of current loop coalescence and shock waves, giving particular attention to particle acceleration caused by these processes. First, explosive reconnection driven by the current loop coalescence and associated particle acceleration are studied by theoretical and magnetohydrodynamic simulation methods and the results are compared with observations of solar flares; this model gives a good explanation for the quasi-periodic structure of some solar flare bursts. Next follows a discussion of particle acceleration in association with fast magnetosonic shock waves. It is shown theoretically and by relativistic particle simulation that a quasi-perpendicular shock wave can accelerate trapped ions in the direction perpendicular to the ambient magnetic field up to speeds much greater than the Alfvén speed, . When the ambient magnetic field is rather strong ( _{ce pe} ), both ions and electrons can be accelerated to relativistic energies. For both the nonrelativistic and relativistic cases, the time needed for the acceleration is very short; it is for the ions. These results are compared with the rapid and simultaneous acceleration of ions and electrons in the impulsive phase of solar flares.     

Structure of reconnection layers in the magnetosphere

Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the earth's magnetosphere. In this paper, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al's model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number,M _c, such that for slow shocks with an intermediate Mach numberM _IM _c, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks withM _I<M _c, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical numberM _c in slow shocks.     

Review of the CIV phenomenon

Alfvén's Critical Ionization Velocity (CIV) phenomenon is reviewed, with the main emphasis on comparisons between experimental and theoretical results. The review covers (1) the velocity measurements in laboratory experiments, (2) the effect of wall interaction, (3) the experimental and theoretical limits to the magnetic field strength and the neutral density, (4) ionospheric release experiments, (5) theoretical models for electron energization in comparison to experimental results, and (6) CIV models. All laboratory investigations of the CIV are found to obey the three following simple rules of thumb: (1) if the magnetic field is so strong that V _A > 3V ₀, and if there is enough neutral gas that the Townsend condition is fulfilled, then the CIV effect occurs, (2) when it occurs, the threshold velocity (or E/B value) is within ± 50% of Alfvén's proposed value V _c , and (3) for weaker magnetic fields, the effect gradually becomes irreproducible or weak and disappears altogether for V _A < V ₀. The theoretical understanding of the process has grown rapidly during the last decade, mainly due to the introduction of computer simulation models which have to a large degree confirmed and extended earlier analytical theories. The CIV mechanism is not due to one single plasma process, but to several different mechanisms which are applicable in different parameter regimes and geometries. The computer simulations have shown that in order to understand the mechanism properly it is necessary to consider a large number of interlocking collisional and plasma processes. The theoretical development has reached the stage where it should be possible to adapt computer simulation models to specific experiments and predict ionization rates, plasma flow velocities, E/B values, particle distributions, and wave spectra. Such models should for the first time provide a really firm basis for extrapolations of the CIV process to space applications.     

Interaction of non-perpendicular/parallel solar wind shock waves with the earth's magnetosphere

The interaction of travelling interplanetary shock waves with the bow shock-magnetosphere system is considered. We consider the general case when the interplanetary magnetic field is oblique to the Sun-planetary axis, thus, the interplanetary shock is neither parallel nor perpendicular. We find that an ensemble of shocks are produced after the interaction for a representative range of shock Mach numbers. First, we find that the system S ₊ R _– CS _– S ₊ appears after the collision of travelling fast shock waves S ₊ (Mach number M = 2 to 7) with the bow shock. Here, S _– and R _– represent the slow shock wave and slow rarefaction wave, and C represents the contact surface. It is shown that in the presence of an interplanetary field that is inclined by 45° to the radial solar wind velocity vector, the waves R _– and S _– are weak waves and, to the first degree of approximation, the situation is similar to the previously studied normal perpendicular case. The configuration, R ₊ C _m S _– S ₊ or R ₊ C _m R _– S ₊ where C _m is the magnetopause, appears as the result of the fast shock wave's collision with the magnetopause. In this case the waves S _– and R _– are weak. The fast rarefaction wave reflected from the magnetosphere is developed similar to the case for the collision of a perpendicular shock. The shock wave intensity is varied for Mach numbers from 2 to 10. Thus, in the limits of the first approximation, the validity of the one-dimensional consideration of the nonstationary interaction of travelling interplanetary shock waves with the bow shock-magnetosphere system is proved. The appearance of the fast rarefaction wave, R ₄, decreasing the pressure on the magnetosphere of the Earth after the abrupt shock-like contraction, is proved. A possible geomagnetic effect during the global perturbation of the SSC or SI⁺ type is discussed.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

The Jovian magnetodisk

Magnetic field measurements made by the vector helium magnetometers on board Pioneers-10 and 11 reveal the existence of a current sheet (thickness 2R _J) carrying an eastward current. Self-consistent studies of the current sheet show that the magnitude of the current is of the order of 10⁺² Am⁺¹ and that the current is carried by a hot (T>1 keV) plasma, the density of which varies between 1 cm⁺³ at 30R _J to 10⁺² cm⁺³ at 80R _J. The current sheet is warped azimuthally and parallel to the magnetic dipole equator.The existence of an azimuthal field component indicates a poloidal plasma flow transporting some 10²⁹ ions per second from Jupiter into the outer magnetosphere. It is shown that, if the outer magnetosphere is in a steady state, this plasma must be transported outward within the current sheet by a diffusion process which is faster than the one responsible for particle transport in the inner magnetosphere but slower than Bohm diffusion. It is suggested that the diffusion is due to the observed mhd turbulence in the current sheet. Such a model requires the existence of open field lines along which particles can escape freely into interplanetary space.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Pulsars as gamma ray sources: Nebular shocks and magnetospheric gaps

I summarize the results of recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is primarily electrons and positrons with an admixture of heavy ions. Shocks which contain heavy ions that are a minority constituent by number but which carry most of the energy density in the upstream medium put 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) E ^-2, where N(E)dE is the number of particles with energy between E and E+dE. Synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front, provides the mechanism of thermalization and non-thermal particle acceleration. The maximum energy achievable by the pairs is _± m _± c ² = m _i c ² ₁/Z _i, where ₁ is the Lorentz factor of the upstream flow and Z _i is the atomic number of the ions. The shock's spatial structure contains a series of overshoots in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. These overshoots provide a new interpretation of the structure of the inner regions of the Crab Nebula, in particular of the wisps, surface brightness enhancements near the pulsar. The wisps appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure ₁ 4 × 10⁶, the upstream magnetic field B ₁ to be 3 × 10^-5 Gauss, as well as to show that the total ion flow is 3 × 10³⁴ elementary charges/sec, in good agreement with the total current flow predicted by the early Goldreich and Julian (1969) model. The total pair outflow is shown to be about 5 × 10³⁷ pairs per second, in good agreement with the particle flux required to explain the nebular X—ray source.The energetics of particle acceleration within the magnetospheres of rotation powered pulsars and the consequences for pulsed gamma ray emission are also briefly discussed. The gamma ray luminosity above 100 MeV is shown to scale in proportion to _R ^1/2 , as is in accord with some of the simplest ideas about polar cap models. Models based on acceleration in the outer magnetosphere are also briefly discussed.     

Electric currents and voltage drops along auroral field lines

The current state of knowledge concerning Birkeland currents (j _∥) and parallel electric field (E _∥) is briefly reviewed. Four types of j _∥ are discussed-the primary ‘region 1’ sheets, the ‘region 2’ sheets which parallel them and which seem to close in the partial ring current, the cusp currents which appear to correlate with interplanetary B _y, and the ‘Harang filament’. The energy required by E _∥ and by the associated particle acceleration processes seems to be derived from j _∥. Much of the evidence for e _∥ comes from particles, from ‘inverted V’ spectra, rising ion beams and expanded loss cones, while ‘conies’ may signify acceleration by Electrostatic Ion Cyclotron (EIC) waves, associated with beams accelerated by E _∥. Different theoretical studies predict for E _∥ a smooth, disordered or abrupt structure, and evidence for all 3 types can be deduced from S3-3 electric field probe observations.

     

Wave motions in the atmosphere and related ionospheric phenomena

We review important studies in the field of stratosphere-ionosphere coupling, including recent studies of wave motions of planetary waves, atmospheric tides and internal gravity waves in the atmosphere. The interrelation between stratospheric sudden warmings and winter anomaly of radio absorption, a dynamical model of stratospheric sudden warmings and some production mechanisms of intensified electron density in the D region are discussed. Other topics presented are atmospheric tides in the lower thermosphere including dynamo action, and internal gravity waves, by which we intend to explain travelling ionospheric disturbances in the F ₂ region and sporadic E layer at midlatitude (wave-enhanced sporadic E). Thermospheric winds are also reviewed and wind effects on the F ₂ layer are discussed. For each atmospheric event systematic observations of suitable physical quantities with proper time and spatial intervals are desirable.     

The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential B _z and transverse magnetic field components B _x are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field B _x also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ₁ being dependent on the exponent α as: for protons and for electrons in a strong guiding field (β > 10⁻²) and for electrons in a moderate or weak guiding field (β > 10⁻⁴). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as for protons and for electrons in weaker guiding fields and as for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.     

Dynamics of the geomagnetic storm

This paper is intended as a critical review of current ideas concerning the mechanisms responsible for the geomagnetic storm.The dynamical theory of the geomagnetic storm phenomenon is formulated as a problem in elasticity. The observed variations in the field are the strains produced by particle stresses exerted by gases in interplanetary space, by gases enmeshed in the field, and by the gases in the ionosphere. The stresses exerted by interplanetary gases are principally inward, resulting in the initial phase increase of the horizontal component. The stresses exerted by gases enmeshed in the field are principally outward, resulting in the main phase decrease of the horizontal component. The transient sudden commencement is a hydromagnetic wave phenomenon.The main phase is most simply explained by the shock heating of the ions to kev energies at 3 – 5 R _E during the active phase of the storm. The recovery follows then from charge exchange with the ambient neutral hydrogen. The predicted more rapid recovery at sunspot minimum has been verified observationally.This work was supported by the National Aeronautics and Space Administration under grant NASA-NsG-96-60.     

Ion Acoustic Waves in the Heliosphere

Observations of ion acoustic waves in the solar wind during the first and second orbit of the Ulysses spacecraft are presented. The observations show variations of the wave activity with the heliolatitude and with the phase of the solar cycle. The interrelationships between the wave intensity and the electron heat flux and the ratio of electron to proton temperature, T _e/T _p, are examined. This revised version was published online in August 2006 with corrections to the Cover Date.     

Initial results from the ISEE-1 and -2 plasma wave investigation

In this paper we present an initial survey of results from the plasma wave experiments on the ISEE-1 and -2 spacecraft which are in nearly identical orbits passing through the Earth's magnetosphere at radial distances out to about 22.5R _e . Essentially every crossing of the Earth's bow shock can be associated with an intense burst of electrostatic and whistler-mode turbulence at the shock, with substantial wave intensities in both the upstream and downstream regions. Usually the electric and magnetic field spectrum at the shock are quite similar for both spacecraft, although small differences in the detailed structure are sometimes apparent upstream and downstream of the shock, probably due to changes in the motion of the shock or propagation effects. Upstream of the shock emissions are often observed at both the fundamental, f _- ^p , and second harmonic, 2f _p ^- , of the electron plasma frequency. In the magnetosphere high resolution spectrograms of the electric field show an extremely complex distribution of plasma and radio emissions, with numerous resonance and cutoff effects. Electron density profiles can be obtained from emissions near the local electron plasma frequency. Comparisons of high resolution spectrograms of whistler-mode emissions such as chorus detected by the two spacecraft usually show a good overall similarity but marked differences in detailed structure on time scales less than one minute. Other types of locally generated waves, such as the (n+1/2)f _- ^g electron cyclotron waves, show a better correspondence between the two spacecraft. High resolution spectrograms of kilometric radio emissions are also presented which show an extremely complex frequency-time structure with many closely spaced narrow-band emissions.     

Experimental technique for the investigation of artificially generated disturbances in planar laminar hypersonic boundary layers

A new experimental method to introduce artificially disturbances into flat plate boundary layers was studied in the Ludwieg-tube wind tunnel of the DLR in Göttingen at a free-stream Mach number of M₁ = 5. For the investigations, a 500 mm long and 20 mm thick flat plate model was used which spanned the test section 400 mm in width. As disturbance source a spark device flush mounted to the model surface close to its leading edge was utilized. The hot wire measurements of natural and forced disturbances in the boundary layer of the flat plate were conducted at different streamwise positions. The charge conditions of the wind tunnel used were almost constant at p_charge ≈ 5 bar and T_charge ≈ 393 K. This resulted in a unit Reynolds number of $\text{Re}{}_1\text{/l ≈ 6.74 1 10}{}^6\text{m}{}^{\mathrm{-1}}$ and a mass flow of ρ₁u₁ = 30.34 kg/m²s. To check the flow quality of the tunnel and the laminar characteristic of the boundary layer optically, Schlieren pictures were taken prior to each measurement campaign. The artificially inserted wave packets were successfully measured at different streamwise and spanwise locations downstream of the spark source. The main wave parameters, e.g. wave numbers and wave inclination angle were deduced from the measurements.     

Microscopic structure of the solar wind

As the solar wind flows out from the coronal base the coulomb collision frequencies rapidly become small and particle-particle collisions can no longer maintain local statistical equilibrium. At 1 AU the particle distribution functions have important non-Maxwellian characteristics and the firehose instability, a cyclotron resonance whistler-mode instability, and several heat flux current instabilities should be operative. Superthermal particle populations also provide large wave levels, and other forms of enhanced plasma turbulence develop at shock fronts and discontinuities. This report contains a review of the theoretical concepts and a progress report on the experimental study of interplanetary wave-particle interactions.Prepared for Space Science Reviews.     

Role of ionospheric effects and plasma sheet dynamics in the formation of auroral arcs

At the ionospheric level, the substorm onset (expansion phase) is marked by the initial brightening and subsequent breakup of a pre-existing auroral arc. According to the field line resonance (FLR) wave model, the substorm-related auroral arc is caused by the field-aligned current carried by FLRs. The FLRs are standing shear Alfvén wave structures that are excited along the dipole/quasi-dipole lines of the geomagnetic field. The FLRs (that can cause auroral arc) thread from the Earthward edge of the plasma sheet and link the auroral arc to the plasma sheet region of 6–15 R _E. The region is associated with magnetic fluctuations that result from the nonlinear wave-wave interactions of the cross-field current-instability. The instability (excited at the substorm onset) disrupts the cross-tail current which is built up during the growth phase of the substorms and results in magnetic fluctuations. The diversion of the current to polar regions can lead to auroral arc intensification. The current FLR model is based on the amplitude equations that describe the nonlinear space-time evolution of FLRs in the presence of ponderomotive forces exerted by large amplitude FLRs (excited during substorms). The present work will modify the FLR wave model to include the effects arising from magnetic fluctuations that result from current disruption near the plasma sheet (6–15 R _E). The nonlinear evolution of FLRs is coupled with the dynamics of plasma sheet through a momentum exchange term (resulting from magnetic fluctuations due to current disruption) in the generalized Ohm's law. The resulting amplitude equations including the effects arising from magnetic fluctuations can be used to study the structure of the auroral arcs formed during substorms. We have also studied the role of feedback mechanism (in a dipole geometry of the geomagnetic field) in the formation of the discrete auroral arc observed on the nightside magnetosphere. The present nonlinear dispersive model (NDM) is extended to include effects arising from the low energy electrons originating from the plasma sheet boundary layer. These electrons increase the ionospheric conductivity in a localized patch and enhance the field-aligned current through a feedback mechanism. The feedback effects were studied numerically in a dipole geometry using the the NDM. The numerical studies yield the magnitude of the field-aligned current that is large enough to form a discrete auroral arc. Our studies provide theoretical support to the observational work of Newell et al. that the feedback instability plays a major role in the formation of the discrete auroral arcs observed on the nightside magnetosphere.     

High temporal resolution observations of electron heating at the bow shock

High temporal resolution measurements of solar wind electrons at the Earth's bow shock on the dawn side have been made with the LASL/MPI fast plasma experiments on ISEE-1 and 2. One dimensional, 1-d, temperatures, T _e , and densities, N _e , are obtained every 0.3 s and 2-d values are obtained every 3 s. Profiles of T _e and N _e at the shock usually are found to be similar to one another and also to the profile of the magnetic field magnitude. The time scale of electron thermalization varies from about 0.5 s to greater than 1 min, depending importantly on the shock motion and the orientation of the magnetic field. Typical thermalization times from 05:00–12:00 LT are 10 s, considerably shorter than proton thermalization times at the shock. This time scale corresponds to a distance of 100 km, comparable to but somewhat larger than the typical ion inertial length. The electron thermalization times are significantly longer than some of the values frequently cited in the past. At the end of the electron thermalization there typically is an overshoot in electron thermal pressure followed by an undershoot which give the pressure profile of the shock the appearance of a damped wave. Ion thermalization is essentially completed by the time the electron pressure wave is damped. The most probable value of the electron temperature ratio across the shock is 1.7, and this value is relatively independent of the Sun-Earth-satellite angle, _ss , for _ss between 25° and 100°.The Los Alamos Scientific Laboratory requests that the publisher identify this article as work performed under the auspices of the Department of Energy.By acceptance of this article, the publisher recognizes that the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.     

Energetic particles at high latitudes

We review work on diffusion coefficients of energetic particles with an attempt to extract implications on their behaviour at high latitudes. In the ecliptic plane results from solar energetic particle propagation between the Sun and about 5 AU can be described by an effective radial mean free path _r which is approximately constant as a function of distancer. When particle propagation in three dimensions in the heliosphere is considered it is not sufficient to consider _r only. Jovian electrons can be used as probes to determine the parameters of three-dimensional diffusion. In the polar regions diffusion is dominated by its parallel component. Some predictions how should vary with latitude are discussed. For different choices of this variation we present expectations for intensity-time profiles of solar particle events during the Ulysses polar passages.     

Plasma waves at the dayside magnetopause

Experimental investigations of plasma waves at the magnetopause, including recent results from the AMPTE/IRM satellite, show that both E and B fluctuations typically have a featureless spectrum which monotonically decreases with frequency; integrated rms amplitudes are typically a few mV m^-1 for E and 10 nT for B, though in particular E can be as much as an order of magnitude larger in exceptional cases. Surveys show a lack of correlation between wave parameters and the magnetopause parameters. Under the assumption that crossing the diffusion region would give a pronounced signature in the waves, the survey data allow an upper limit to be placed on the latitudinal extent of the diffusion region, which is about 1000 km — implying that it is not surprising that the wave data surveys have so far failed to detect it. The observed wave turbulence levels have been used to estimate diffusion coefficients under different assumptions for the wave mode, but the resulting diffusion coefficient is always too small to explain either reconnection or boundary layer formation. Recent work of Galeev et al. (1986) indicates that the dominant diffusion process may be magnetic field migration, which is a macroscopic process involving the interaction of tearing mode islands. Assuming this mode to be present at the observed level of B, a particle diffusion coefficient of nearly 10⁹ m² s^-1 is obtained. Another macroscopic diffusive process which could occur at the magnetopause is stochastic E × B scattering, which also implies a diffusion coefficient the order of 10⁹ m² s^-1 if the observed E spectrum is assumed to be a turbulent cascade consisting of convective cells.     

Substorm-associated injections of energetic ions observed by GEOS-1 and ATS-6 in and near synchronous altitude

Energetic ion measurements of GEOS-1 and ATS-6 are analysed for the period of geomagnetic activity following the arrival of a solar wind shock at 0027 UT on July 29, 1977. GEOS crossed the magnetopause at 6.9 R _E and 0027 UT (1312 LT). Although the difference in local time to ATS at 6.6 R _E is only 2 h ATS seems to remain well inside the magnetopause. During the second orbital pass on this day GEOS crossed the geostationary orbit at the onset time of a major substorm developing at 1120 UT. At this time the local time difference of GEOS and ATS was 12 h. The considerably different energy dispersions are discussed. An azimuthal anisotropy of approximately 20% observed in the GEOS data is interpreted to be the result of a particle density gradient.NOAA-SEL, Boulder, Colo., U.S.A.