The formation of a collisionless shock is the result of a balance between nonlinear steepening and processes that counteract this steepening. Dispersive shocks are shocks in which dispersive processes counterbalance the front steepening and are formed when the dispersive spatial scale exceeds scales associated with resistive processes. Oblique dispersive shocks are characterized by a phase standing wave precursor adjacent to the magnetic ramp. The whistler critical Mach number is defined as the maximum Mach number for which a linear whistler wave can phase stand upstream of the shock front. It was widely accepted that if the Mach number exceeds , linear whistler waves propagating along the shock normal are not able to "phase stand" in the upstream flow, and "& mldr;the shock will be initiated by a monotonic ramp." (Kennel et al., 1985, https://doi.org/10.1029/gm034p0001). In this study, we present results of numerical simulations and observations of shocks with that reveal the occurrence of an alternative scenario. For both the shock resulting from kinetic particle-in-cell simulations and that observed by MMS, the propagation direction of the precursor deviates from the shock normal direction. As a result, the velocity of the surface of constant phase along the shock normal exceeds the phase speed of these waves. It is shown that the propagation of the surface of constant phase along the shock normal occurs at a velocity that is nearly equal to the shock speed. Hence, these waves are "phase standing along the shock normal" in spite of .

The mechanism by which some magnetically complex active regions evolve toward highly eruptive states while others remain relatively quiet remains an open question under active debate. In our previous studies, we showed that analysing magnetic parameters from the photosphere into the lower corona using potential field (PF), linear force-free field (LFFF), and nonlinear force-free field (NLFFF) extrapolations reveals important height-dependent behaviour, but these conclusions were based on five flaring and one nonflaring active regions. Here, we extend this investigation by doubling the sample to ten magnetically complex active regions and expanding the flaring range to span C- to X-class flaring activity. We derive three global diagnostic parameters and seven height-dependent morphological diagnostics, evaluated on horizontal layers every similar to 360 km from the photosphere up to 7 Mm. We find that while the NLFFF-based NF2 model generally yields stronger magnetic fields and allows eruptive signatures to persist above the photosphere, PF and LFFF are able to model very similar large-scale morphological trends. This finding suggests that much of the relevant structural information may already be captured by PF and LFFF, methods considered less complex than NF2. Therefore, here, we incorporate seven additional regions from a previous work consistent with LFFF data, yielding a combined sample of 17 magnetically complex active regions. Across this expanded data set, we observe that the most eruptive active regions (9 out of 17) tend to maintain a larger number of magnetic parameters (between 7 and 9) above their pre-eruptive thresholds over broader height ranges.

A number of mechanisms have been suggested to operate within the terrestrial bow shock to redistribute energy contained in the incoming solar wind flow. The majority of mechanisms involve the generation of turbulence while some are based on particle motion alone. In this paper, we investigate the possible occurrence of the Electron Trajectory Instability, that results from short scale electric field gradients. Spike-like bipolar features in electric field measurements are a commonly observed signature within the terrestrial bow shock. They are usually associated with the passage of electrostatic solitary waves associated with phase space holes in the particle distribution. Using electric field measurements, we compare different interferometric methods to determine the propagation direction, velocity, and spatial scale of these features. Based on these results, it appears that the instability criterion for the Electron Trajectory Instability is fulfilled and the electron trajectories will diverge in the presence of these structures.

The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically.

The primary scientific goal of ICARUS (Investigation of Coronal AcceleRation and heating of solar wind Up to the Sun), a mother-daughter satellite mission, proposed in response to the ESA "Voyage 2050" Call, will be to determine how the magnetic field and plasma dynamics in the outer solar atmosphere give rise to the corona, the solar wind, and the entire heliosphere. Reaching this goal will be a Rosetta Stone step, with results that are broadly applicable within the fields of space plasma physics and astrophysics. Within ESA's Cosmic Vision roadmap, these science goals address Theme 2: "How does the Solar System work?" by investigating basic processes occurring "From the Sun to the edge of the Solar System". ICARUS will not only advance our understanding of the plasma environment around our Sun, but also of the numerous magnetically active stars with hot plasma coronae. ICARUS I will perform the first direct in situ measurements of electromagnetic fields, particle acceleration, wave activity, energy distribution, and flows directly in the regions in which the solar wind emerges from the coronal plasma. ICARUS I will have a perihelion altitude of 1 solar radius and will cross the region where the major energy deposition occurs. The polar orbit of ICARUS I will enable crossing the regions where both the fast and slow winds are generated. It will probe the local characteristics of the plasma and provide unique information about the physical processes involved in the creation of the solar wind. ICARUS II will observe this region using remote-sensing instruments, providing simultaneous, contextual information about regions crossed by ICARUS I and the solar atmosphere below as observed by solar telescopes. It will thus provide bridges for understanding the magnetic links between the heliosphere and the solar atmosphere. Such information is crucial to our understanding of the plasma physics and electrodynamics of the solar atmosphere. ICARUS II will also play a very important relay role, enabling the radio-link with ICARUS I. It will receive, collect, and store information transmitted from ICARUS I during its closest approach to the Sun. It will also perform preliminary data processing before transmitting it to Earth. Performing such unique in situ observations in the area where presumably hazardous solar energetic particles are energized, ICARUS will provide fundamental advances in our capabilities to monitor and forecast the space radiation environment. Therefore, the results from the ICARUS mission will be extremely crucial for future space explorations, especially for long-term crewed space missions.

Space weather forecasting is of global interest, and its importance is well established in research community and recognized by government, industries and stockholders. Over the past years, many types of predictive models have been developed in the literature. There is a general agreement that forecasting models should not only provide point prediction but also inform the uncertainty associated with the prediction. This study presents a novel method bases on quantile regression and complex dynamic modelling for measuring uncertainties in space weather forecasting. The approach is implemented using Quantile regression and Nonlinear AutoRegressive Moving Average with Exogenous inputs (NARMAX) methods (for short the approach is called Q-NARMAX). The method is applied to Disturbance storm index (Dst) observations to examine its interpretability and capability for uncertainty analysis. Results show that the proposed Q-NARX model can produce excellent predictions of the Dst index, and meanwhile provides a measure for assessing the uncertainty in the forecast. The innovative integration of quantile regression, complex dynamic modelling and nonlinear system identification techniques enables the proposed work to have following attractive advantages and properties: 1) it can produce excellent prediction accuracy for space weather forecasting, 2) it uses transparent models to approximate (represent) black-box systems, enabling to interpret the dependent relationship between space weather indices (system outputs) and their drivers (system inputs), and 3) more importantly, it allows for uncertainty assessment and analysis of models and forecasts.

Different modeling methodologies possess different strengths and weakness. For instance, data based models may provide superior accuracy but have a limited spatial coverage while physics based models may provide lower accuracy but provide greater spatial coverage. This study investigates the coupling of a data based model of the electron fluxes at geostationary orbit (GEO) with a numerical model of the radiation belt region to improve the resulting forecasts/pastcasts of electron fluxes over the whole radiation belt region. In particular, two coupling methods are investigated. The first assumes an average value for L* for GEO, namely LGEO∗ ${L}_{\mathit{GEO}}^{\ast }$ = 6.2. The second uses a value of L* that varies with geomagnetic activity, quantified using the Kp index. As the terrestrial magnetic field responds to variations in geomagnetic activity, the value of L* will vary for a specific location. In this coupling method, the value of L* is calculated using the Kp driven Tsyganenko 89c magnetic field model for field line tracing. It is shown that this addition can result in changes in the initialization of the parameters at the Versatile Electron Radiation Belt model outer boundary. Model outputs are compared to Van Allen Probes MagEIS measurements of the electron fluxes in the inner magnetosphere for the March 2015 geomagnetic storm. It is found that the fixed LGEO∗ ${L}_{\mathit{GEO}}^{\ast }$ coupling method produces a more realistic forecast.

Within the inner magnetosphere, the occurrence of plasma waves and/or magnetic field structures plays an important role in the dynamics of the particle populations, accelerating some particles to higher energies while scattering others. The 2013 Cluster Inner Magnetosphere Campaign was designed to investigate this process based on observations made at small separation scales. In addition, it provides an ideal opportunity for the study of small-scale structures. This paper presents observations of previously unreported small-scale magnetic field structures and investigates their characteristics and spatial properties. These structures, seen in the STAFF-SC data set, are characterized by a rotation in the field direction and are observed to have spatial sizes of a few tens of kilometers, with a central core region around 10 km and are probably filamentary current structures. Using a variance analysis, it was determined that the maximum variance direction was close to being perpendicular to the external magnetic field. Based on the size of the central core region the current density is of the order of 10-40 nAm-2. While they may affect the profile of these structures, data calibration effects were ruled out as their origin.

Equatorial magnetosonic waves (EMS), together with chorus and plasmaspheric hiss, play key roles in the dynamics of energetic electron fluxes in the magnetosphere. Numerical models, developed following a first principles approach, that are used to study the evolution of high energy electron fluxes are mainly based on quasilinear diffusion. The application of such numerical codes requires statistical models for the distribution of key magnetospheric wave modes to estimate the appropriate diffusion coefficients. These waves are generally statistically modeled as a function of spatial location and geomagnetic indices (e.g., AE, Kp, or Dst). This study presents a novel dynamic spatiotemporal model for EMS wave amplitude, developed using the Nonlinear AutoRegressive Moving Average eXogenous machine learning approach. The EMS wave amplitude, measured by the Van Allen Probes, are modeled using the time lags of the solar wind and geomagnetic indices as inputs as well as the location at which the measurement is made. The resulting model performance is assessed on a separate Van Allen Probes data set, where the prediction efficiency was found to be 34.0% and the correlation coefficient was 56.9%. With more training and validation data the performance metrics could potentially be improved, however, it is also possible that the EMS wave distribution is affected by stochastic factors and the performance metrics obtained for this model are close to the potential maximum.

The following topics are dealt with: learning (artificial intelligence); fault diagnosis; feature extraction; production engineering computing; neural nets; condition monitoring; nonlinear control systems; support vector machines; wind turbines; mechanical engineering computing.

Magnetosonic waves play an important role on the overall dynamics of relativistic radiation belt electrons. Numerical codes modeling the evolution of the radiation belts often account for wave‐particle interaction with magnetosonic waves. The diffusion coefficients incorporated in these codes are generally estimated based on the results of statistical surveys of the occurrence and amplitude of these waves. These statistical models assume that the spectrum of the magnetosonic waves can be considered as continuous in frequency space. This assumption can only be valid if the discrete nature of the waves satisfy the Chirikov overlap criterion. Otherwise, the assumption of a continuous frequency spectrum could produce erroneous results in wave models and hence estimates of the electron diffusion coefficients used in numerical models of the inner magnetosphere. Recently, it was demonstrated, through a case study conducted on a single short (10 s) period snapshot within a longer wave event, that the discrete nature of the equatorial magnetosonic waves do satisfy the Chirikov overlap criterion and so the assumption of a continuous frequency spectrum is valid for the calculation of diffusion coefficients. This paper expands this study to a broader range of time with many magnetosonic wave events to determine whether the discrete nature of the waves always satisfy the Chirikov overlap criterion. The results show that most, but not all, discrete magnetosonic emissions satisfy the Chirikov overlap criterion. Therefore, the use of the continuous spectrum, employed in quasi‐linear theory, may not always be justified.

The occurrence of nonlinear interactions between discrete wave frequencies has been shown to play a significant role in the propagation and evolution of some plasma wave modes. In this paper we take advantage of closely spaced Cluster measurements to investigate the possibility nonlinear interactions occurring between the discrete emissions that are observed in a region of Equatorial Magnetosonic Wave generation. Based on transfer function analysis, it is shown that the role of nonlinear interactions plays a negligible role in the wave evolution as the emissions propagate from one satellite to the other. A bicoherence analysis of the individual signals also fails to find the existence of nonlinear interactions in the evolution of equatorial magnetosonic waves.

Collisionless shocks are ubiquitous throughout the universe: around stars, supernova remnants, active galactic nuclei, binary systems, comets, and planets. Key information is carried by electromagnetic emissions from particles accelerated by high Mach number collisionless shocks. These shocks are intrinsically nonstationary, and the characteristic physical scales responsible for particle acceleration remain unknown. Quantifying these scales is crucial, as it affects the fundamental process of redistributing upstream plasma kinetic energy into other degrees of freedom-particularly electron thermalization. Direct in situ measurements of nonstationary shock dynamics have not been reported. Thus, the model that best describes this process has remained unknown. Here, we present direct evidence demonstrating that the transition to nonstationarity is associated with electron-scale field structures inside the shock ramp.