On Weibull's Spectrum of Nonrelativistic Energetic Particles at IP Shocks: Observations and Theoretical Interpretation

Some interplanetary shocks are associated with short-term and sharp particle flux enhancements near the shock front. Such intensity enhancements, known as shock-spike events (SSEs), represent a class of relatively energetic phenomena as they may extend to energies of some tens of MeV or even beyond. Here we present an SSE case study in order to shed light on the nature of the particle acceleration involved in this kind of event. Our observations refer to an SSE registered on 2011 October 3 at 22:23 UT, by STEREO B instrumentation when, at a heliocentric distance of 1.08 au, the spacecraft was swept by a perpendicular shock moving away from the Sun. The main finding from the data analysis is that a Weibull distribution represents a good fitting function to the measured particle spectrum over the energy range from 0.1 to 30 MeV. To interpret such an observational result, we provide a theoretical derivation of the Weibull spectrum in the framework of the acceleration by "killed" stochastic processes exhibiting power-law growth in time of the velocity expectation, such as the classical Fermi process. We find an overall coherence between the experimental values of the Weibull spectrum parameters and their physical meaning within the above scenario. Hence, our approach based on the Weibull distribution proves to be useful for understanding SSEs. With regard to the present event, we also provide an alternative explanation of the Weibull spectrum in terms of shock-surfing acceleration

STATISTICS OF THE VELOCITY GRADIENT TENSOR IN SPACE PLASMA TURBULENT FLOWS

In the last decade, significant advances have been presented for the theoretical characterization and experimental techniques used to measure and model all of the components of the velocity gradient tensor in the framework of fluid turbulence. Here, we attempt the evaluation of the small-scale velocity gradient tensor for a case study of space plasma turbulence, observed in the Earth's magnetosheath region by the CLUSTER mission. In detail, we investigate the joint statistics P(R, Q) of the velocity gradient geometric invariants R and Q, and find that this P(R, Q) is similar to that of the low end of the inertial range for fluid turbulence, with a pronounced increase in the statistics along the so-called Vieillefosse tail. In the context of hydrodynamics, this result is referred to as the dissipation/dissipation-production due to vortex stretching

the weibull functional form for the energetic particle spectrum at interplanetary shock waves

Transient interplanetary shock waves are often associated with high energy particle enhancements, which are called energetic storm particle (ESP) events. Here we present a case study of an ESP event, recorded by the SEPT, LET and HET instruments onboard the STEREO B spacecraft, on 3 October 2011, in a wide energy range from 0.1 MeV to ~ 30 MeV. The obtained particle spectrum is found to be reproduced by a Weibull like shape. Moreover, we show that the Weibull spectrum can be theoretically derived as the asymptotic steady state solution of the diffusion loss equation by assuming anomalous diffusion for particle velocity. The evaluation of Weibull's parameters obtained from particle observations and the power spectral density of the turbulent fluctations in the shock region, support this scenario and suggest that stochastic acceleration can contribute significantly to the acceleration of high energetic particles at collisioness shock waves

RADIAL EVOLUTION OF SOLAR WIND TURBULENCE DURING EARTH AND ULYSSES ALIGNMENT OF 2007 AUGUST

At the end of 2007 August, during the minimum of solar cycle 23, a lineup of Earth and Ulysses occurred, giving the opportunity to analyze, for the first time, the same plasma sample at different observation points, namely at 1 and 1.4 AU. In particular, it allowed us to study the radial evolution of solar wind turbulence typical of fast wind streams as proposed in a Coordinated Investigation Programme for the International Heliophysical Year. This paper describes both the macrostructure and the fluctuations at small scales of this event. We find that soon after detecting the same fast stream, the Advanced Composition Explorer (ACE) observed a change of magnetic polarity being the interplanetary current sheet located between the orbits of the two spacecraft. Moreover, we observe that the compression region formed in front of the fast stream detected at ACE's location evolves in a fast forward shock at Ulysses' orbit. On the other hand, small-scale analysis shows that turbulence is evolving. The presence of a shift of the frequency break separating the injection range from the inertial range toward lower frequencies while distance increases is a clear indication that nonlinear interactions are at work. Moreover, we observe that intermittency, as measured by the flatness factor, increases with distance. This study confirms previous analyses performed using Helios observations of the same fast wind streams at different heliocentric distances, allowing us to relax about the hypothesis of the stationarity of the source regions adopted in previous studies. Consequently, any difference noticed in the solar wind parameters would be ascribed to radial (time) evolution

Recurrent flares in active region NOAA 11283

Context. Flares and coronal mass ejections (CMEs) are solar phenomena that are not yet fully understood. Several investigations have been performed to single out their related physical parameters that can be used as indices of the magnetic complexity leading to their occurrence. Aims. In order to shed light on the occurrence of recurrent flares and subsequent associated CMEs, we studied the active region NOAA 11283 where recurrent M and X GOES-class flares and CMEs occurred. Methods. We use vector magnetograms taken by HMI/SDO to calculate the horizontal velocity fields of the photospheric magnetic structures, the shear and the dip angles of the magnetic field, the magnetic helicity flux distribution, and the Poynting fluxes across the photosphere due to the emergence and the shearing of the magnetic field. Results. Although we do not observe consistent emerging magnetic flux through the photosphere during the observation time interval, we detected a monotonic increase of the magnetic helicity accumulated in the corona. We found that both the shear and the dip angles have high values along the main polarity inversion line (PIL) before and after all the events. We also note that before the main flare of X2.1 GOES class, the shearing motions seem to inject a more significant energy than the energy injected by the emergence of the magnetic field. Conclusions. We conclude that the very long duration (about 4 days) of the horizontal displacement of the main photospheric magnetic structures along the PIL has a primary role in the energy release during the recurrent flares. This peculiar horizontal velocity field also contributes to the monotonic injection of magnetic helicity into the corona. This process, coupled with the high shear and dip angles along the main PIL, appears to be responsible for the consecutive events of loss of equilibrium leading to the recurrent flares and CMEs

Bowshock-ANN_Test-Set

The present data set consists of a list of 944 terrestrial bow shock crossings observed by IMP-8, GEOTAIL, MAGION, CLUSTER-1, THEMIS-B and THEMIS-C spacecraft during the period 1973-2009. For each crossing, in addition to the time and position, are provided the respective upstream proton ram pressure and alfvénic Mach number

Bowshock-ANN_Test-Set

The present data set consists of a list of 944 terrestrial bow shock crossings observed by IMP-8, GEOTAIL, MAGION, CLUSTER-1, THEMIS-B and THEMIS-C spacecraft during the period 1973-2009. For each crossing, in addition to the time and position, are provided the respective upstream proton ram pressure and alfvénic Mach number