Search

Multi-input single-output (MISO) nonlinear autoregressive moving average with exogenous inputs (NARMAX) models have been derived to forecast the > 0.8 MeV and > 2 MeV electron fluxes at geostationary Earth orbit (GEO). The NARMAX algorithm is able to identify mathematical model for a wide class of nonlinear systems from input–output data. The models employ solar wind parameters as inputs to provide an estimate of the average electron flux for the following day, i.e. the 1-day forecast. The identified models are shown to provide a reliable forecast for both > 0.8 and > 2 MeV electron fluxes and are capable of providing real-time warnings of when the electron fluxes will be dangerously high for satellite systems. These models, named SNB3GEO > 0.8 and > 2 MeV electron flux models, have been implemented online at http://www.ssg.group.shef.ac.uk/USSW/UOSSW.html.

The interaction of CMEs with the solar wind can lead to the formation of interplanetary shocks. Ions accelerated at these shocks contribute to the solar energetic protons observed in the vicinity of the Earth. Recently a joint analysis of Venus Express (VEX) and STEREO data by Russell et al. (2009) have shown that the formation of strong shocks associated with Co-rotating Interaction Regions (CIRs) takes place between the orbits of Venus and the Earth as a result of coalescence of weaker shocks formed earlier. The present study uses VEX and Advanced Composition Explorer (ACE) data in order to analyse shocks associated with CMEs that erupted on 29 and 30 July 2007 during the solar wind conjunction period between Venus and the Earth. For these particular cases it is shown that the above scenario of shock formation proposed for CIRs also takes place for CMEs. Contradiction with shock formation resulting from MHD modelling is explained by inability of classical MHD to account for the role of wave dispersion in the formation of the shock.

The standard timing accuracy for the Cluster mission is ±2 ms. However for inter-spacecraft comparisons of waveform data, a much higher accuracy is needed – for example a timing error of 1 ms results in a phase error of 65° for a signal at 180 Hz. Most Cluster data are recorded on an onboard solid state recorder and time-stamped using an onboard clock which is calibrated to coordinated universal time (UTC). Until recently, the error of this onboard clock was allowed to increase to the ±2 ms limit before a new calibration was applied. However, the timing error for real-time data is estimated to be only ~11 μs, so these data may be used to prepare a time correction data set which allows the standard timing accuracy to be improved considerably. This paper describes the details of the preparation and validation of this data set. Two independent source data sets are used: telemetry to European Space Agency (ESA) ground stations supporting the main operations of the Cluster spacecraft, and the real-time telemetry to the NASA Deep Space Network (DSN) stations supporting the Wide-Band Plasma Wave Investigation.

The nonlinear autoregressive moving average with exogenous inputs (NARMAX) system identification technique is applied to various aspects of the magnetospheres dynamics. It is shown, from an example system, how the inputs to a system can be found from the error reduction ratio (ERR) analysis, a key concept of the NARMAX approach. The application of the NARMAX approach to the Dst (disturbance storm time) index and the electron fluxes at geostationary Earth orbit (GEO) are reviewed, revealing new insight into the physics of the system. The review of studies into the Dst index illustrate how the NARMAX approach is able to find a coupling function for the Dst index from data, which was then analytically justified from first principles. While the review of the electron flux demonstrates how NARMAX is able to reveal new insight into the physics of the acceleration and loss processes within the radiation belt.

Low frequency waves in the foot of a supercritical quasi-perpendicular shock front have been observed since the very early in situ observations of the terrestrial bow shock (Guha et al., 1972). The great attention that has been devoted to these type of waves since the first observations is explained by the key role attributed to them in the processes of energy redistribution in the shock front by various theoretical models. In some models, these waves play the role of the intermediator between the ions and electrons. It is assumed that they are generated by plasma instability that exist due to the counter-streaming flows of incident and reflected ions. In the second type of models, these waves result from the evolution of the shock front itself in the quasi-periodic process of steepening and overturning of the magnetic ramp. However, the range of the observed frequencies in the spacecraft frame are not enough to distinguish the origin of the observed waves. It also requires the determination of the wave vectors and the plasma frame frequencies. Multipoint measurements within the wave coherence length are needed for an ambiguous determination of the wave vectors. In the main multi-point missions such as ISEE, AMPTE, Cluster and THEMIS, the spacecraft separation is too large for such a wave vector determination and therefore only very few case studies are published (mainly for AMPTE UKS AMPTE IRM pair). Here we present the observations of upstream low frequency waves by the Cluster spacecraft which took place on 19 February 2002. The spacecraft separation during the crossing of the bow shock was small enough to determine the wave vectors and allowed the identification of the plasma wave dispersion relation for the observed waves. Presented results are compared with whistler wave dispersion and it is shown that contrary to previous studies based on the AMPTE data, the phase velocity in the shock frame is directed downstream. The consequences of this finding for both types of models that were developed to explain the generation of these waves are discussed.

Multi-point wave observations on Cluster spacecraft are used to infer the dispersion relation of electromagnetic ion cyclotron (EMIC) waves. In this study we use a phase differencing method and observations from STAFF and WHISPER during a well-studied event of 30 March 2002. The phase differencing method requires the knowledge of the direction of the wave vector, which was obtained using minimum variance analysis. Wave vector amplitudes were calculated for a number of frequencies to infer the dispersion relation experimentally. The obtained dispersion relation is largely consistent with the cold plasma dispersion relation. The presented method allows inferring the dispersion relation experimentally. It can be also used in the future to analyse the hot plasma dispersion relation of waves near the local gyrofrequency that can occur under high plasma beta conditions.

The theory of the Weibel instability is generalized for the case of a plasma immersed in a nonzero external magnetic field. It is shown that the presence of this external field modifies the dispersion relation for this mode which now possesses a nonzero frequency. The explicit expression for the real and imaginary parts of the frequency is then calculated. It turns out that the linear growth rate remains unchanged, whereas the frequency becomes nonzero due to the finite value of the electron cyclotron frequency. The frequency of the Weibel mode is found to be proportional to the electron temperature anisotropy. The formal similarity of the Weibel and drift-mirror instabilities is outlined.

Ducted propagation of whistler waves in the terrestrial magnetosphere-ionosphere system was discussed and studied long before the first in-situ spacecraft measurements. While a number of implicit examples of the existence of ducted propagation have been found, direct observation of ducts has been hampered by the low sampling rates of measurements of the plasma density. The present paper is based on Cluster observations of chorus waves. The ability to use measurements of the spacecraft potential as a proxy for high time resolution electron density measurements is exploited to identify a number of cases when increased chorus wave power, observed within the radiation belts, is observed simultaneously with density enchantments. It is argued that the observation of ducted propagation of chorus implies modification of numerical models for plasma-wave interactions within the radiation belts.

The NARMAX OLS-ERR methodology is applied to identify a mathematical model for the dynamics of the Dst index. The NARMAX OLS-ERR algorithm, which is widely used in the field of system identification, is able to identify a mathematical model for a wide class of nonlinear systems using input and output data. Solar wind-magnetosphere coupling functions, derived from analytical or data based methods, are employed as the inputs to such models and the outputs are geomagnetic indices. The newly deduced coupling function, p1/2V4/3BTsin6(θ/2), has been implemented as an input to model the Dst dynamics. It was shown that the identified model has a very good forecasting ability, especially with the geomagnetic storms.

Cluster four point measurements provide a comprehensive dataset for the separation of temporal and spatial variations, which is crucial for the calculation of the cross shock electrostatic potential using electric field measurements. While Cluster is probably the most suited among present and past spacecraft missions to provide such a separation at the terrestrial bow shock, it is far from ideal for a study of the cross shock potential, since only 2 components of the electric field are measured in the spacecraft spin plane. The present paper is devoted to the comparison of 3 different techniques that can be used to estimate the potential with this limitation. The first technique is the estimate taking only into account the projection of the measured components onto the shock normal. The second uses the ideal MHD condition E·B = 0 to estimate the third electric field component. The last method is based on the structure of the electric field in the Normal Incidence Frame (NIF) for which only the potential component along the shock normal and the motional electric field exist. All 3 approaches are used to estimate the potential for a single crossing of the terrestrial bow shock that took place on the 31 March 2001. Surprisingly all three methods lead to the same order of magnitude for the cross shock potential. It is argued that the third method must lead to more reliable results. The effect of the shock normal inaccuracy is investigated for this particular shock crossing. The resulting electrostatic potential appears too high in comparison with the theoretical results for low Mach number shocks. This shows the variability of the potential, interpreted in the frame of the non-stationary shock model.

Single spacecraft measurements from the Cluster 3 satellite are used to identify nonlinear processes in ion-sound turbulence observed within the front of the quasiperpendicular terrestrial bow shock. Ion sound waves possess spatial scales that are too small for the efficient use of multipoint measurements on inter-satellite separation scales. However, it is shown how frequency domain modelling can be applied to single spacecraft electric field data obtained using the EFW internal burst mode. The resulting characteristics of the nonlinear processes are used to argue about the possible wave sources and investigate their dynamics.

In situ measurements of the magnetic field are vital to the study of many fundamental problems in planetary research. Therefore the magnetometer experiment is a key element of the payload of Venus Express. In addition to the interaction of the solar wind with Venus, these measurements are crucial for the study of atmospheric escape and detection of lightning. However, the methodology for the magnetic field measurements had to be different to the traditional approach, because Venus Express is not a magnetically clean spacecraft. A technique based on two-point simultaneous measurements of the magnetic field and systems identification software is used to separate the natural magnetic field from the spacecraft generated interference. In this paper an overview of the techniques developed to separate these two field types and the results achieved for 1 Hz Venus Express data are presented. Previous publications suggest that the resulting Venus Express cleaned data is of comparable quality to measurements made from onboard magnetically clean spacecraft (Zhang et al., 2008a, b; Slavin et al., 2009).

A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.

The primary process occurring at a collisionless shock is the redistribution of the bulk upstream energy into other degrees of freedom. One part of this process results in the acceleration of electrons at the shock front. Accelerated electrons are observed at the terrestrial and other planetary shocks, comets, and their effects are observed in astrophysical phenomena such as supernova remnants and jets in the form of X-ray bremsstrahlung radiation. One of the physical models for electron acceleration at supercritical shocks is based on low-hybrid turbulence due to the presence of reflected ions in the foot region. Since lower hybrid waves propagate almost perpendicular to the magnetic field they can be simultaneously in resonance with both the unmagnetised ions (ω=Vik⊥) and magnetised electrons (ω=Vek||). In this paper, Cluster observations of the electric field are used to study the occurrence of lower hybrid waves in the front of the terrestrial bow shock. It is shown that the lower hybrid waves exist as isolated wave packets. However, the very low level of the observed lower hybrid turbulence is too small to impart significant energisation to the electron population.

Lion roars are intense, short duration packets of whistler mode waves, observed in the magnetosheath. They are typically seen coincident with the magnetic field minima of mirror mode waves. The orbit of the Double Star TC-1 spacecraft (570 km by 78970 km, inclination at 28.5 degrees) is ideal for observations of lion roars as the spacecraft is in the magnetosheath more than 50% of the time when the apogee is on the dayside. The STAFF/DWP experiment provides the spectral matrix of the three magnetic components at 27 frequencies in the range 10 Hz to 4 kHz, with one second time resolution, and also the waveform up to 180 Hz at a low duty cycle. The characteristics of lion roars observed are reported. The maximum lion roar intensities appear higher than reported by most previous studies. The electron temperature anisotropy is estimated from the lion roar frequency ratios, and is in reasonably good agreement with plasma measurements. This indicates the presence of a trapped electron component in the mirror mode.

The four point measurements available from the Cluster mission enable spatiotemporal effects in data sets to be resolved. One application of these multipoint measurements is the determination of the wave vectors and hence the identification of wave modes that exist within the plasma. Prior to multi-satellite missions, wave identification techniques were based upon the interpretation of observational data using theoretically defined relations. However, such techniques are limited by the quality of the data and the type of plasma model employed. With multipoint measurements, wave modes can be identified and their wave directions determined purely from the available observations. This paper takes two such methods, a phase differencing technique and k-filtering and compares their results. It is shown that both methods can resolve the k vector for the dominant mirror mode present in the data. The phase differencing method shows that the nature of the wave environment is constantly changing and as such both methods result in an average picture of the wave environment in the period analysed. The k-filtering method is able to identify other modes that are present.

This paper investigates the short scale structures that are observed in the electric field during crossings of the quasi-perpendicular bow shock using data from the Cluster satellites. These structures exhibit large amplitudes, as high as 70 m Vm-1 and so make a significant contribution to the overall change in potential at the shock front. It is shown that the scale size of these short-lived electric field structures is of the order of a few c/ωpe. The relationships between the scale size and the upstream Mach number and θBn are studied. It is found that the scale size of these structures decreases with increasing plasma β and as θBn→90°. The amplitude of the spikes remains fairly constant with increasing Ma and appears to increase as θBn→90°.

A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves Vint = Vacos(θ).

We study numerically in detail the behaviour of electrons in the strongly inhomogeneous static magnetic and electric fields, which are typical for thin quasiperpendicular collisionless shocks. We pay particular attention to the dependence of the final electron velocities on their initial velocities, for different shock widths. Electrons are completely magnetized when the shock is wide, but become demagnetized, and the energies that they acquire rapidly increase with the steepening of the field structure. One of the clear manifestations of the electron demagnetization is the loss of even approximate one-to-one correspondence of the downstream perpendicular velocity to the upstream perpendicular velocity. Electron reflection occurs despite the large cross-shock potential which accelerates electrons along the magnetic field (the regime of complete magnetization) or across the shock (strong demagnetization). The reflected ion fraction is sensitive to the potential, magnetic field jump, and ramp width.

We study the collisionless dynamics of electrons in the shock ramp using the numerical trajectory analysis in the model electric and magnetic fields of the shock. Even with very modest assumptions about the cross-shock potential the electron trajectories are very sensitive to the width of the ramp. The character of electron motion changes from the fully adiabatic (with conservation of v2 /B) when the ramp is wide, to the nonadiabatic one, when the ramp becomes sufficiently narrow. The downstream electron distribution also changes drastically, although this change depends on the initial electron temperature.

The ESA/NASA Cluster mission has four identical satellites and is due for launch at the end of 1995. It will provide a unique opportunity to study medium scale processes in the region from inside the magnetopause to the solar wind. The polar orbit will allow measurements in the cusp and along auroral field lines, both regions where turbulence is to be expected. Five of the eleven instruments on each payload form the Wave Experiment Consortium (WEC); EFW, STAFF, VMISPER, WBD and DWP. The WEC is capable of a wide variety of wave and turbulence measurements. This paper outlines these capabilities and describes the form of the data which will be collected. The paper gives a discussion of how the WEC data may be analysed so as to give an insight into the non-linear processes which occur in these regions of the space plasmas. There are many ways in which a plasma may be considered to behave in a non-linear manner. We concentrate on how the spatio-temporal turbulence in the plasma may be investigated so as to yield the energy spectrum with respect to both the frequency and wave number.

AbstractThe nonlinear theory of large-amplitude magnetosonic (MS) waves in high? space plasmas is revisited. It is shown that solitary waves can exist in the form of ?bright? or ?dark? solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory?Guest?Harris (DGH) or Kennel?Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by ?distributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a ?bright? soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall?MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined. [ABSTRACT FROM AUTHOR]

A theory for the parametric interaction of inertial Alfvén wave (IAW) packets with large-scale convective cells accounting for the nonzero ratio of the Alfvén and light velocities is presented. It is shown that in the auroral plasma cavity where the Alfvén velocity has its maximum value, the parametric interaction of IAWs with convective cells is substantially reduced. In this region the Alfvén velocity is comparable to the speed of light and thus the displacement current cannot be neglected. This current plays a stabilizing role and results in a decline of the parametric instability growth rate. On the contrary, the incorporation of the finite width of the IAW packet leads to increase in the convective cell growth rate. A compact expression for the instability growth rate and the optimal conditions for the fastest growing convective mode are derived. The relevance of the theory to recent spacecraft measurements in the Earth’s ionosphere is pointed out. [ABSTRACT FROM AUTHOR]