We give a systematic theoretical analysis of trapped nonadiabatic charged particle motion in two‐dimensional taillike magnetic field reversals. Particle dynamics is shown to be controlled by the curvature parameter κ, i.e., the ratio κ² = Rmin/ρmax between the minimum radius of curvature of the magnetic field and the maximum Larmor radius in it for a particle of given energy. κ≫1 corresponds to the usual adiabatic case with the magnetic moment μ as a first‐order invariant of motion. As κ decreases toward unity, the particle motion becomes stochastic due to deterministic chaos, caused by the overlapping of nonlinear resonances between the bounce‐ and the gyro‐motion. We determine the threshold of deterministic chaos and derive the related pitch angle diffusion coefficient which describes statistically the particle behavior in the limit κ → 1. Such behavior, which for κ ≅ 1 becomes strongly chaotic, applies, e.g., to thermal electrons in Earth's magnetotail and makes its collisionless tearing mode instability possible. We also show that in sharply curved field reversals, i.e., for κ<1, both a new kind of adiabaticity and a partially adiabatic but weakly chaotic type of motion appear. The latter is strongly effected by separatrix‐crossings in the phase space, which lead to a qualitatively different chaotic behavior compared with the case κ>1. Both types of trapped particle motion in sharply curved magnetic field reversals κ<1 are closely connected with fast oscillations perpendicular to the reversal plane. However, the trajectories are adiabatic only in the case that they permanently remain crossing the reversal plane. The adiabatic are of a ring type, i.e., they resemble rings in phase space and also in real physical space. For ring‐type orbits the action integral over the fast oscillations is an adiabatic invariant in the usual sense. On the other hand, the most common particle trajectories in a sharply curved field reversal with κ<1 are essentially of a cucumberlike quasi‐adiabatic type. For quasi‐adiabatic cucumberlike orbits the action integral over the fast oscillations is an adiabatic invariant only in a piecemeal way between successive traversals in the phase space of the fast motion of a separatrix between orbits which do and those, which do not cross the reversal plane. Due to the effect of separatrix traversals the slow motion shifts between different cucumber orbits with a conservation of the action integral on average but with its chaotic phase space diffusion even for very small perturbation parameters κ. The case κ<1 is applicable, e.g., to thermal ions and high‐energy electrons in Earth's magnetotail. Our findings lead to a systematic interpretation of particle observations in Earth's magnetotail and of numerous numerical calculations, carried out in the past. They also explain rather well, e.g., the pitch angle diffusion of plasma sheet particles, the isotropization of the plasma sheet electron distribution immediately before a substorm and provide with the transition to chaos a mechanism for the on...

Abstract. The advanced energetic particle spectrometer RAPID on board Cluster can provide a complete description of the relevant particle parameters velocity, V , and atomic mass, A, over an energy range from 30 keV up to 1.5 MeV. We present the first measurements taken by RAPID during the commissioning and the early operating phases. The orbit on 14 January 2001, when Cluster was travelling from a perigee near dawn northward across the pole towards an apogee in the solar wind, is used to demonstrate the capabilities of RAPID in investigating a wide variety of particle populations. RAPID, with its unique capability of measuring the complete angular distribution of energetic particles, allows for the simultaneous measurements of local density gradients, as reflected in the anisotropies of 90 • particles and the remote sensing of changes in the distant field line topology, as manifested in the variations of loss cone properties. A detailed discussion of angle-angle plots shows considerable differences in the structure of the boundaries between the open and closed field lines on the nightside fraction of the pass and the magnetopause crossing. The 3 March 2001 encounter of Cluster with an FTE just outside the magnetosphere is used to show the first structural plasma investigations of an FTE by energetic multi-spacecraft observations.Correspondence to: U. Mall (mall@linmpi.mpg.de) Key words. Magnetospheric physics (energetic particles, trapped; magnetopause, cusp and boundary layers; magnetosheath) The instrumentThe RAPID spectrometer (Research with Adaptive Particle Imaging Detectors), described in detail by Wilken et al. (1995), is an advanced particle detector for the analysis of suprathermal plasma distributions in the energy range from 20-400 keV for electrons, 30 keV-1500 keV for hydrogen, and 10 keV/nucleon-1500 keV for heavier ions. Innovative detector concepts, in combination with pinhole acceptance, allow for the measurement of angular distributions over a range of 180 • in the polar angle for electrons and ions. Identification of the ion species is based on a two-dimensional analysis of the particle's velocity and energy. Electrons are identified by the well-known energy-range relationship. Table 1 list the main parameters of the RAPID instrument.The energy signals in RAPID are analyzed in 8 bit ADCs. With a mapping process the 256 channels are reduced to 8 channels in the case of the ion sensor and into 9 channels in the case of the electron sensor. The resulting energy channel limits are listed in Table 2.

Magnetic reconnection is commonly considered as a mechanism of solar (eruptive) flares. A deeper study of this scenario reveals, however, a number of open issues. Among them is the fundamental question, how the magnetic energy is transferred from large, accumulation scales to plasma scales where its actual dissipation takes place. In order to investigate this transfer over a broad range of scales we address this question by means of a high-resolution MHD simulation. The simulation results indicate that the magnetic-energy transfer to small scales is realized via a cascade of consecutive smaller and smaller flux-ropes (plasmoids), in analogy with the vortex-tube cascade in (incompressible) fluid dynamics. Both tearing and (driven) "fragmenting coalescence" processes are equally important for the consecutive fragmentation of the magnetic field (and associated current density) to smaller elements. At the later stages a dynamic balance between tearing and coalescence processes reveals a steady (power-law) scaling typical for cascading processes. It is shown that cascading reconnection also addresses other open issues in solar flare research such as the duality between the regular largescale picture of (eruptive) flares and the observed signatures of fragmented (chaotic) energy release, as well as the huge number of accelerated particles. Indeed, spontaneous current-layer fragmentation and formation of multiple channelised dissipative/acceleration regions embedded in the current layer appears to be intrinsic to the cascading process. The multiple small-scale current sheets may also facilitate the acceleration of a large number of particles. The structure, distribution and dynamics of the embedded potential acceleration regions in a current layer fragmented by cascading reconnection are studied and discussed.

This paper discusses kinetic modeling of the properties of magnetotail formation from a plasma mantle source and develops a unified view of the structure of the central part of the magnetotail plasma sheet as well as the structure of its boundary layer. Trajectories of mantle protons in the presence of a uniform dawn‐dusk electric field have been traced using the Tsyganenko magnetic field model for quiet periods of magnetospheric activity. The most important portion of the particle trajectories is each particle's first interaction with the sharp reversal of the magnetic field in the tail midplane, because this interaction results in particle energization and chaotic scattering. The closer this interaction takes place to the X line, the larger a particle's energy will become. The intensity of the chaotic scattering in the tail midplane depends also on the position in the tail at which it occurs. The energization and scattering result in a significant restructuring of the tail ion distributions, both in space and in velocity coordinates. Our model shows the evolution of the global structure of the tail with a clearly defined central plasma sheet and plasma sheet boundary layer developing from its beginnings as a plasma “nucleus” in the distant tail current sheet. This large‐scale restructuring is accompanied by the creation of small‐scale features in the particle distribution functions. For example, the model not only correctly reproduces the spatial distribution and velocity dispersion of the fast ion beams moving both earthward and tailward in the plasma sheet boundary layer, but also indicates that these beams should be highly structured spatially into 5‐6 smaller beamlets with distinct velocities. In addition the model shows that complementary ring distribution structures should also exist in the central plasma sheet. Our analysis indicates that the ion distribution functions in the central plasma sheet should take a rather specific form in velocity space with loss regions oriented predominantly orthogonal to the magnetic field. Our results also emphasize the importance of counterstreaming populations, not only in the boundary layer, but also in the central part of the plasma sheet. Analytical calculations indicate that the properties of chaotic scattering in the magnetotail under realistic conditions (x dependence of the normal magnetic field and dawn‐dusk electric field) are quite different from those predicted by earlier simple xindependent models. Finally the model results are compared with recent observations of ion distribution functions and their moments for various regions of the magnetotail, and quantitative estimates from the model are shown to be in good agreement with observations. Small‐scale structuring and the presence of counterstreaming are also discussed, as well as their possible importance in explaining the observed intermittency in the plasma sheet bulk flows.

Linear prediction filtering techniques have shown that the magnetospheric response to energy transfer from the solar wind contains both driven and unloading components. Filter elements ordered with respect to geomagnetic activity have shown a peak at 20 minutes due to the driven component and a second peak at 1 hour which has been interpreted in terms of the magnetotail unloading component. The peak at 1 hour was found to increase in strength with increasing activity up to a critical activity level beyond which the peak vanished. We study these features of geomagnetic activity in terms of a nonlinear dynamical model of the magnetospheric system. We base our model on the leaky faucet analogy of plasmoid formation (Hones, 1979) and the dripping faucet experiment and model of Shaw (1984). We have constructed a mechanical analogue to the magnetosphere which models both the driven and the loading‐unloading energy release mechanisms. This model is elementary, but is dynamically complete in that it is able to represent the entire cycle of substorm growth, expansion, and recovery. The model is able to explain many of the features of the linear filter results. In particular, the model suggests that the disappearance of the 1 hour peak is due to a chaotic transition beyond which the loading‐unloading mechanism continues, but aperiodically. This work suggests that, using the tools of chaos theory, we may gain considerable insight into the stormtime behavior of the magnetosphere.