Trapping Of Energetic Particles Research Articles

Efficient Nonthermal Ion and Electron Acceleration Enabled by the Flux-Rope Kink Instability in 3D Nonrelativistic Magnetic Reconnection.

The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux ropes and undergo further acceleration. As a consequence, both ions and electrons develop clear power-law energy spectra that contain a significant fraction of the released energy. The low-energy bounds are determined by the injection physics, while the high-energy cutoffs are limited only by the system size. These results have strong relevance to observations of nonthermal particle acceleration in space and astrophysics.

A Focused Transport-based Kinetic Fractional Diffusion-advection Equation for Energetic Particle Trapping and Reconnection-related Acceleration by Small-scale Magnetic Flux Ropes in the Solar Wind

Abstract Analysis of energetic particle inner heliospheric spacecraft data increasingly suggests the existence of anomalous diffusion phenomena that should be addressed to achieve a better understanding of energetic particle transport and acceleration in the expanding solar wind medium. Related to this is fast-growing observational evidence supporting the long-standing prediction from magnetohydrodynamic (MHD) theory and simulations of the presence of an inner heliospheric, dominant quasi-two-dimensional MHD turbulence component that contains coherent contracting and merging (reconnecting) small-scale magnetic flux rope (SMFR) structures. This suggests that energetic particle trapping in SMFRs should play a role in anomalous diffusion in the solar wind that warrants further investigation. However, progress in studying such anomalous energetic particle transport phenomena in the solar wind is hampered by the lack of a fundamental derivation of a general fractional kinetic transport equation linking macroscopic energetic particle fractional transport to the microscopic physics of energetic particle interaction with SMFR structures. Here, we outline details of how one can derive a closed ensemble-averaged focused transport equation in the form of a general kinetic fractional diffusion-advection equation from first principles following the nonlinear Eulerian correlation function closure approach of Sanchez et al. With this equation one can model the anomalous diffusion of energetic particles in ordinary, momentum, and pitch-angle space in response to particle trapping in numerous SMFRs advected with the solar wind flow.

Stability analysis of secondary modes, driven by the phase space island

We present a new theoretical approach, based on the Hamiltonian formalism, to investigate the stability of islands in phase space, generated by trapping of energetic particles (EPs) in plasma waves in a tokamak. This approach is relevant to MHD modes driven by EPs (EP-MHD) such as toroidal Alfvén eigenmodes (TAEs), EP-driven geodesic acoustic modes (EGAMs) or fishbones. A generic problem of a single isolated EP-MHD mode is equivalent to and hence can be replaced by a 2D Hamiltonian dynamics in the vicinity of the phase space island. The conventional Langmuir wave/bump-on-tail problem is then used as a representative reduced model to describe the dynamics of the initial EP-MHD.Solving the Fokker–Planck equation in the presence of pitch angle scattering, velocity space diffusion and drag and retaining plasma drifts in a model, we find a ‘perturbed’ equilibrium, associated with these phase space islands. Its stability is then explored by addressing the Vlasov/Fokker–Planck–Poisson system. The Lagrangian of this system provides the dispersion relation of the secondary modes and allows an estimate of the mode onset. The secondary instabilities have been confirmed to be possible but under certain conditions on the primary island width and in a certain range of mode numbers. The threshold island width, below which the mode stability is reached, is calculated. The secondary mode growth rate is found to be maximum when the associated resonant velocity approaches the boundary of the primary island. This, in turn, leads to a conclusion that the onset of the secondary mode can be prevented provided the primary wave number is the lowest available.

Damage-free surface treatment of polyethersulfone films using magnetized plasma generated by low-frequency (60 Hz) power

ABSTRACTSurface treatments of polyethersulfone (PES) films were performed using the magnetized plasma generated by low-frequency (60Hz) power for applying them to the flexible substrates of solar cells and electronic displays. The contact angle between the water droplet and PES films was observed to change from 80° to 30° after the plasma treatment. This indicates that the surface of the PES films changed from hydrophobic to hydrophilic. The surface roughness of the films did not change after the plasma treatment, and this indicates that the magnetized plasma did not damage the surface of the films. The trapping of energetic particles by the magnetic field is thought to be responsible for this result. It is concluded that the plasma treatment by using the magnetized plasma is useful for the surface modification of the polymeric materials suitable for flexible substrates of solar cells and electronic displays.

Local modulation and trapping of energetic particles by coherent magnetic structures

AbstractRecent observational studies show strong statistical associations between features of interplanetary suprathermal energetic particle (EP) data and rapid changes in the interplanetary vector magnetic field. The latter are connected to intermittency and coherent magnetic structures, including classical discontinuities. Here we discuss these observations in the context of two appealing theoretical ideas: First, magnetic structures bounding flux tubes can cause local or temporary topological trapping, thus influencing EP transport. Second, charged particles may be accelerated by interacting with dynamic flux tubes, either through reconnection, trapping in secondary islands, or a betatron mechanism. We present observations that support interpretation in terms of trapping boundaries associated with changes in EP flux and also find a case in which an EP peak lies near a coherent magnetic structure that is not a shock, with changing particle anisotropy consistent with outflow from the structure, suggestive of local particle acceleration.

Kinetic simulations of ring current evolution during the Geospace Environment Modeling challenge events

We investigate the temporal and spatial evolution of the ring current during two storms selected for study by the Geospace Environment Modeling (GEM) program using our kinetic drift‐loss model coupled with a time‐dependent plasmasphere model. We use geosynchronous data from LANL satellites to model the inflow of plasma from the magnetotail. We compare results from simulations using either Volland‐Stern (VS) or Weimer (W01) model of the convection electric field and investigate the relative effect of magnetospheric convection and radial diffusion on the storm‐time injection and trapping of energetic particles and ring current asymmetry. Model comparisons with in situ Cluster, NOAA, and Polar energetic particle observations show overall better agreement with W01 than with VS model. On the other hand, VS model reproduced better the evolution of the plasmapause as observed by IMAGE. Additional ring current ion injections caused by radial diffusion near Dst minima improved the agreement with observations. Radial diffusion did not affect much ring current buildup during the main phase of the storms and the ring current fluxes remained asymmetric, in good agreement with NOAA data. We calculated the excitation of electromagnetic ion cyclotron (EMIC) waves self‐consistently with the evolving plasma populations, and the resulting precipitating fluxes of resonant protons. These fluxes increased significantly within regions of enhanced plasma wave excitation near the plasmapause or inside plasmaspheric plumes and reduced the total H+ energy by ∼10% during the storm recovery phase. Initial results from self‐consistent magnetic field calculations are presented as well. We found that while the magnitude of the ring current fluxes was reduced when adiabatic drifts in a self‐consistent magnetic field were calculated, their morphology was not affected significantly and the local time of the equatorial flux peaks remained almost unchanged.

Anomalous and classical diffusion of cosmic rays due to nonlinear two‐dimensional structures and random magnetic fields

Magnetic field turbulence in the heliosphere is modeled by two‐dimensional coherent vortex structures and random‐phase linear wave fields added to a background magnetic field. Energetic particle trapping and acceleration by interaction with the turbulent fields are studied numerically. The corresponding radial and field‐aligned diffusion coefficients are estimated. Different diffusion regimes (subdiffusion, superdiffusion, classical diffusion) are controlled by the following parameters: the ratio between amplitudes of the random component and the regular vortex field, ε1, and the ratio between the average particle gyroradius and the magnetic field correlation length, ε2. The anomalous diffusion regime occurs when the correlation length of magnetic field disturbances is about the same or larger than the particle gyroradius (ε2 ≤ 1). Applications of our results to cosmic ray transport are discussed.

Relativistic model of ring current and radiation belt ions and electrons: Initial results

We present first results from our global drift‐loss model extended to relativistic energies and electrons, investigating the effect of magnetospheric convection and radial diffusion on the storm time injection and trapping of energetic particles during the October 2001 geomagnetic storm. We show that magnetospheric convection is the dominant injection mechanism during the rapid main phase creating a very asymmetric ring current distribution for both ions and electrons. Radial diffusion injects particles with higher energies (≥80 keV) deep into the magnetosphere (L < 4) and increases the total ring current energy content by about 15% near minimum Dst, causing the ring current to become symmetric only during the storm recovery phase. We evaluate the electron contribution to the ring current during this storm and find it highly variable, being small (∼2%) during quiet time and the largest near Dst peaks, resulting in ∼10% of the total ring current ion energy content.

Cusp region radiation belts in the dayside magnetosphere

The possibility of quasi-stable trapping of charged particles of hundreds keV–MeV energy on the front side Earth magnetosphere is explored in this article by numerical modeling of the single particle orbits in the geomagnetic field utilizing empirical Tsyganenko model. On the front side magnetosphere the remote equatorial magnetic field lines are compressed to balance the solar wind pressure and exhibit two minima in the geomagnetic field strength magnitude along the field line in high latitudes on both sides of the equator which results in stable confinement structures in the north or/and the south hemispheres, providing energetic particle trapping for times from several minutes to durations of seasonal scale. Simulation of the energetic proton orbits in magnetosphere passing through the regions of magnetic field minima with different disturbance level and the Earth's tilt shows when and where these trapped radiation zones could exist. It is noted that the existence of this adiabatic confinement zone depends on the tilt of the geomagnetic dipole axis to the Sun–Earth direction. As a result the northern polar cap (cusp) confinement zone appears only during a summer solstice and similarly the southern hemisphere capture zone appears during a winter solstice. During equinox the confinement zones exist in both hemispheres in the disturbed magnetospheric conditions, however, they are less pronounced. The zones are essentially restricted to the sunlit magnetosphere. They form a kind of cusp radiation belt, where a proton drifts with a period of several minutes, conserving its 1st and the 2nd adiabatic invariants. The latitudinal width of the belt is very thin, about 2–5 latitudinal degrees. The particle orbits passing through opposite off-equatorial field minimum reveal another effect: a bound of the geomagnetic equatorial plane on the day sector. These and other features of the confinement zones in the two minima off-equatorial magnetic field regions are discussed.

Energetic Electrons as a Field Line Topology Tracer in the High Latitude Boundary/CUSP Region: Cluster Rapid Observations

Energetic electrons (e.g., 50 keV) travel along field lines with a high speed of around 20 R E s −1. These swift electrons trace out field lines in the magnetosphere in a rather short time, and therefore can provide nearly instantaneous information about the changes in the field configuration in regions of geospace. The energetic electrons in the high latitude boundary regions (including the cusp) have been examined in detail by using Cluster/RAPID data for four consecutive high latitude/cusp crossings between 16 March and 19 March 2001. Energetic electrons with high and stable fluxes were observed in the time interval when the IMF had a predominately positive B z component. These electrons appeared to be associated with a lower plasma density exhibiting no obvious tailward plasma flow (< 20 keV). On the other hand, no electrons or only spike-like electron events have been observed in the cusp region during southward IMF. At that time, the plasma density was as high as that in the magnetosheath and was associated with a clear tailward flow. The fact that no stable energetic electron fluxes were observed during southward IMF indicates that the cusp has an open field line geometry. The observations indicate that both the South and North high latitude magnetospheric boundary regions (including both North and South cusp) can be energetic particle trapping regions. The energetic electron observations provide new ways to investigate the dynamic cusp processes. Finally, trajectory tracing of test particles has been performed using the Tsyganenko 96 model; this demonstrates that energetic particles (both ions and electrons) may be indeed trapped in the high latitude magnetosphere.

Seasonal cusp radiation belt on dayside magnetosphere

The possibility of quasi-stable trapping of charged particles of hundreds keV to MeV energy on the frontside Earth magnetosphere is explored in by numerical modeling of the single particle orbits in the geomagnetic field utilizing empirical Tsyganenko magnetic field model. Due to solar wind pressure the remote magnetic field lines on the frontside of the magnetosphere exhibit two minima in the geomagnetic field strength along the field line in high latitudes on the both sides of the equator. These minima may result in stable confinement structures, a kind of radiation belts, in the northern or/and the southern hemispheres, providing energetic particle trapping for times from several minutes to duration of seasonal scale. Simulation of energetic proton orbits passing through the regions of the magnetic field minima with different disturbance level and the Earth’s tilt reveals conditions in which these trapped radiation zones could result. It is shown that the existence of the adiabatic confinement zones strongly depends on the seasonal inclination of the Earth’s rotation axis. As a result the northern cusp confinement zone appears only in a summer solstice and similarly the southern cusp capture zone appears only in a winter solstice. In equinox time the confinement zones exist in both hemispheres in the disturbed magnetospheric conditions, however, they are less pronounced. The zones are essentially restricted to the sunlit magnetosphere. They form a kind of cusp radiation ring/belt, where a proton drifts with a period of several minutes, conserving its 1 st and the 2 nd adiabatic invariants. The latitudinal width of the ring is very thin, about 2-5 latitudinal degrees. The proton orbits passing through the off-equatorial field minimum opposite to those cusp belts reveal another interesting effect: a bound of the geomagnetic equatorial plane on the day sector. These and other features of the confinement zones in the two minima off-equatorial magnetic field regions are discussed.

Extended gamma-ray emission of the solar flares in june 1991

During the solar flares on 9, 11, and 15 June 1991 the COMPTEL instrument measured extended {radiation in the 2.223 MeV neutron-capture line, in prompt nuclear deexcitation lines and in pion-decay ra- diation for several hours after the flares. The long-term time proles can be described by a double exponential decay with decay constants on the order of 10 min for the fast and several 100 min for the slow components. We studied the 11 June 1991 flare in more detail and found that during the extended phase the accelerated proton and ion spectrum is harder, the e/p ratio is lower, and the emission prole is smoother, compared to those of the impulsive phase. Pion-decay radiation was not detected before the onset of the extended emission phase. When comparing the three flares to one another, we found a striking similarity in the time proles of the nuclear line and the neutron capture line emission. However, the pion-decay radiation varied in intensity signicantly from flare to flare. The impulsive-phase emissions of the flares show no such similarity. Our measurements indicate that the processes taking place during the extended phase dier from those during the impulsive phase, or in other {ray line flares. Based on these results long-term trapping of energetic particles from the impulsive phase seems unlikely, as opposed to continuous particle acceleration.

Coronal Trapping of Energetic Flare Particles:Yohkoh/HXT Observations

We examine spectroscopic data from the Yohkoh Hard X-Ray Telescope in a search for spectral evidence of the coronal trapping of energetic particles during solar flares. Two distinct particle populations with significantly different spectral properties are found to be present in three of the six flares studied; the first population is trapped in the corona, where it encounters a "thick-thin" target, while the second population precipitates directly to the footpoints. In the remaining three events, a single population of energetic particles appear to be responsible for the observed hard X-ray emission, either via thermal bremsstrahlung (one case) or nonthermal thin-target emission (two cases). For the three events in which a trapped population is observed, the spectroscopic observations imply first that there is likely to be a single acceleration mechanism for both the trapped and the precipitating populations and second that the magnetic field geometry in these flares is conducive to trapping in a confined region high in the corona, above the soft X-ray loops. Both conditions are consistent with magnetic reconnection models of flares in which energetic particles are trapped between MHD slow-mode shocks attached to the reconnection region and a fast-mode shock formed by the reconnection outflow jet.

An assessment of a magnetospheric model by tracing the energetic particle trapping boundary

We use the two most recent empirical magnetosphere models of Tsyganenko [1987; 1989] to find the energy dependent boundary of isotropic precipitation due to the nonadiabatic particle motion in the nightside current sheet. Model predictions are compared with the earlier published satellite observations of this boundary at low altitudes. A dramatic difference has been found between the predicted position of the isotropy boundary based on T87 and T89 model. The most recent magnetosphere model of Tsyganenko featuring the warped current sheet with thickness dependent both on XGSM and YGSM predicts that the isotropy boundary is situated at much lower latitudes than inferred from the previous models. This is in agreement with observations. However, even this model with very stretched tail magnetic field lines has difficulties in explaining the frequently observed very steep profile of critical rigidity vs L.

Magnetic trapping of energetic particles on open dayside boundary layer flux tubes

Both simple as well as detailed empirical magnetic models of the Earth's dayside magnetosphere suggest that field lines near the magnetopause boundary in the noon quadrant (∼09:00 to ∼15:00 M.L.T.) possess an unusual property due to the compressive effect of the impinging solar wind flow, namely that the equatorial region represents a local maximum in the magnetic field strength, and not a minimum as elsewhere in the magnetosphere. In this region the field lines therefore possess off-equatorial field strength minima, which occur at increasingly high latitudes as the boundary is approached. These field lines can therefore support two distinct particle populations, those which bounce across the equator between mirror points on either side, and those which are trapped about the off-equatorial field strength minima and are confined to one side of the equator. When these field lines become magnetically open due to the occurrence of magnetic reconnection at the equatorial magnetopause, the former particles will rapidly escape into the magnetosheath by field-aligned flow, while the latter population may be sustained within the boundary layer over many bounce periods, as the flux tubes contract and move tailward. Consequently, trapped distributions of energetic particles may commonly occur on open field lines in the dayside boundary layer in the noon quadrant, particularly at high latitudes. The existence of such particles is thus not an infallible indicator of the presence of closed magnetic field lines in this region. At earlier and later local times, however, the boundary layer field lines revert to possessing a minimum in the field strength at the equator. These field lines are not, therefore, generally expected to sustain a significant trapped particle population once they become open due to near-equatorial reconnection.

A theory of diffuse emission bursts triggered by coherent VLF signals propagating parallel to the geomagnetic field

Satellite and ground‐based studies have demonstrated that coherent VLF signals propagating in the terrestrial magnetosphere can trigger diffuse and structured emission bursts. A triggering mechanism for diffuse emissions which may operate when the coherent signal propagates parallel to the geomagnetic field is investigated in this note. The theory is based on the concept that trapping of energetic particles in the potential wells of the coherent signal alters the gradient of the particle distribution function with respect to parallel velocity. If, as a result of trapping, the gradient becomes sufficiently steep, broad band wave growth takes place as predicted by established theory. The resulting pitch angle diffusion of particles produces a more stable configuration in which the steep gradient is reduced towards that corresponding to the marginally stable distribution. For initially positive gradients in the energetic electron distribution function with respect to parallel velocity, wave growth takes place above the frequency of the causative coherent signal. The theory predicts that the bandwidth of emissions triggered in this way should rapidly increase with time and may reach maximum widths of several hundred hertz.

Nonlinear pitch angle scattering and trapping of energetic particles during Landau resonance interactions with whistler mode waves

The time averaged equations of motion derived by Inan and Tkalcevic (1982) are used in a test particle study of Landau resonant interactions of whistler mode waves and energetic particles in the magnetopshere. By computing individual particle trajectories it is shown that the pitch angle scattering and energy exchange is significantly different for the two classes of particles, trapped and untrapped. The trapped particles are characterized by a bounded phase variation, whereas the nontrapped particles exhibit unbounded phase variation. The threshold wave electric field intensities necessary for trapping are determined. Full distribution test particle simulation is carried out to determine the precipitated electron flux that would be induced as a result of these interactions. It is shown that for typical parameters the resulting precipitation fluxes for Landau resonance interactions are much smaller than those induced in gyroresonance interactions, even for wave field intensities that are much higher than the trapping threshold.

Energetic particle losses and trapping boundaries as deduced from calculations with a realistic magnetic field model

An interpretation of the stable trapping boundaries of energetic electrons and protons during quiet periods is given basing on a realistic magnetospheric magnetic field model. Particle losses are explained in terms of an ionospheric and drift loss cone filling due to a non-adiabatic pitch-angle scattering in the nightside magnetotail current sheet. The proposed mechanism is shown to provide a good agreement of the observed and calculated positions of the energetic particle trapping boundaries, as well as their energy dependence. The obtained results can be applied as a tool for investigating the magnetospheric magnetic field structure using the particle data of low-altitude satellites.

Nightside energetic particle decreases at the synchronous orbit

More than 100 cases of major decreases of proton and electron fluxes at the synchronous orbit have been observed and interpreted as a movement of the energetic particle trapping boundary earthward of 6.6 earth radii before the substorm expansion phase. These events are observed only between 1700 and 0800 LT and are consistent with the existence of a westward magnetospheric electric field of a few tenths of a millivolt per meter before substorm expansion. Most substorm particle events seen on the nightside do not exhibit this behavior, presumably because the trapping boundary moves inside 6.6 earth radii only during major events. Such events show evidence of particle acceleration, which probably was concentrated at higher L values, near the instantaneous location of the trapping boundary.