Field Line Curvature Radius Research Articles

Conditions of Loss Cone Filling by Scattering on the Curved Field Lines for 30 keV Protons During Geomagnetic Storm as Inferred From Numerical Trajectory Tracing

AbstractThe rate of pitch angle scattering on the curved magnetic field lines is well parameterized by the ratio of the minimum field line curvature radius to the maximum effective particle gyroradius (K = RC/rg). The critical value of this ratio (Kcr) corresponding to the loss cone filling is of special interest since it corresponds to the low altitude isotropic boundaries (IBs). The early theoretical estimates gave Kcr = 8, whereas recent estimations of the K parameter on the field lines corresponding to the observed IBs during the geomagnetic storms revealed KIB values in the range of 3–30. We numerically trace the trajectories of the 30 keV protons in the magnetic field of the global magnetohydrodynamic simulation of the intense storm in order to infer statistical distribution of Kcr. The electric field and effects of nonstationarity are neglected in this study. It is found that although the Kcr values do show some variations during the course of the storm, its range is rather narrow 4 < Kcr < 8. The result suggests that higher KIB values found in the observational studies, if not caused by the magnetosphere‐ionosphere mapping error, should be attributed to some other mechanism of pitch angle scattering. The Kcr values tend to be lower (4–6) during the main phase because the region of low K values approaches the Earth and the equatorial loss cone size becomes larger due to a larger equatorial magnetic field in the near‐earth region. The remaining variation of Kcr is explained by the presence of the guide component of the magnetic field.

Ballooning instability of azimuthally small scale coupled Alfvén and slow magnetoacoustic modes in two-dimensionally inhomogeneous magnetospheric plasma

This paper investigates the conditions of the ballooning instability of the coupled Alfvén and slow magnetoacoustic modes in the dipole model of Earth's magnetosphere taking into account plasma and magnetic field inhomogeneity in the direction along the magnetic field lines. The diamagnetic condition (meaning vanishing perturbation of the total pressure) is satisfied. It was shown that the instability develops on the slow magnetoacoustic oscillation branch, but the instability threshold is determined by the coupling with the Alfvén mode. The symmetric (with respect to the magnetic equator) modes were found to be more unstable than antisymmetric ones. In this case, the instability threshold depends on plasma compressibility: the finite sound velocity raises the instability threshold. For all other equal conditions, the instability threshold decreases with the decrease in the field line curvature radius on the equator.

Formation of 30 KeV Proton Isotropic Boundaries During Geomagnetic Storms

AbstractWe study the origin of the 30 keV proton isotropic boundary (IB) in the nightside auroral zone during geomagnetic storms, particularly, to address the recent results that the adiabaticity parameter K (ratio of the magnetic field line curvature radius to the particle gyroradius at the equator) on the IB field line can be much larger comparing to its theoretical estimate K ∼ 8 for the field line curvature (FLC) scattering mechanism. During nine storms in 2011–2013, we investigate ∼2,000 IBs observed by low‐altitude Polar Operational Environmental Satellites (POES) satellites and apply the TS05 magnetospheric model to estimate the K value in the equatorial part of the IB field line. The statistical distribution of the estimated K parameter, while being rather broad, is centered on K = 9–13. For smaller subset of ∼250 IBs, the concurrent magnetic field measurements on board Time History of Events and Macroscale Interaction During Substorms probes in the equatorial magnetotail were used to correct the estimated K‐values accounting for the TS05 deviations from the real magnetic configuration. After correction, the K distribution becomes narrower, being still centered on K = 9–12. Different estimates give percentages of events with K < 13, which can be attributed to IBs formed by FLC scattering, between 60% and 80%. Finally, we have not found any dependence of the K distribution on magnetic local time and IB latitude, except for events with IB located at extremely low latitudes (<59°). These findings imply that the FLC scattering is a dominant mechanism of IB formation operating in a variety of magnetospheric conditions.

Formation of Dawn‐Dusk Asymmetry in Earth's Magnetotail Thin Current Sheet: A Three‐Dimensional Particle‐In‐Cell Simulation

AbstractUsing a three‐dimensional particle‐in‐cell simulation, we investigate the formation of dawn‐dusk asymmetry in Earth's magnetotail. The magnetotail current sheet is compressed by an external driving electric field down to a thickness on the order of ion kinetic scales. In the resultant thin current sheet (TCS) where the magnetic field line curvature radius is much smaller than ion gyroradius, a significant portion of the ions becomes unmagnetized and decoupled from the magnetized electrons, giving rise to a Hall electric field Ez and an additional cross‐tail current jy caused by the unmagnetized ions being unable to comove with the electrons in the Hall electric field. The Hall electric field transports via E × B drift magnetic flux and magnetized plasma dawnward, causing a reduction of the current sheet thickness and the normal magnetic field Bz on the duskside. This leads to an even stronger Hall effect (stronger jy and Ez) in the duskside TCS. Thus, due to the internal kinetic effects in the TCS, namely, the Hall effect and the associated dawnward E × B drift, the magnetotail dawn‐dusk asymmetry forms in a short time without any global, long‐term effects. The duskside preference of reconnection and associated dynamic phenomena (such as substorm onsets, dipolarizing flux bundles, fast flows, energetic particle injections, and flux ropes), which has been pervasively observed by spacecraft in the past 20 years, can thus be explained as a consequence of this TCS asymmetry.

Extent of ECH wave emissions in the Earth's magnetotail

AbstractThe exact role of electrostatic electron cyclotron harmonic (ECH) waves in driving diffuse aurora has been controversial for many years. Using THEMIS observations from five magnetotail seasons, we investigate the occurrence rate distribution of ECH waves and the extent of individual wave intensifications under various plasma sheet conditions. Both are critical for modeling these waves' contributions to electron scattering and to diffuse auroral emissions. Single‐spacecraft data analysis shows that ECH waves occur frequently in the midnight and postmidnight magnetotail and that their occurrence rates decrease with increasing radial distance from Earth. More than 50% of ECH wave events (continuous intervals of wave activity) occur during local plasma sheet activations, evidenced by energetic electron injections and dipolarization fronts. Excluding ECH wave emissions concurrent with such local plasma sheet activations (known to peak in occurrence rate near premidnight), we find that quiet plasma sheet ECH wave emissions exhibit preference for dawn. This preference suggests a close relationship between these waves and the drift paths of injected electrons. Dual‐spacecraft data analysis shows that the Z‐extent is ~0.5 RE, the Y‐extent is ~2 RE, and the X‐extent is at least 4 RE. During locally quiet plasma sheet conditions, ECH waves exhibit a smaller Z‐ and X‐extent, but the Y‐extent is similar during all the conditions. In order to investigate the mechanism leading to the different Z‐extents under various plasma sheet conditions, we use ray tracing to model the wave power distribution as a function of distance from the neutral sheet. We find a linear correlation between the wave Z‐extent and field line curvature radius (Rc). A Z‐extent of ~0.2 RE (consistent with observations) corresponds to Rc~0.9 RE. Our results suggest that ECH intensification following dipolarizing flux bundles is in part due to increased Rc, which enables intensification to higher amplitudes over a larger volume, explaining the increased occurrence rate and extent of active‐time wave events.

Radio pulsar activity and the crustal Hall drift

Models of pulsar radio emission that are based on an inner accelerating region require the existence of very strong and small scale surface magnetic field structures at or near the canonical polar cap. The aim of this paper is to identify a mechanism that creates such field structures and maintains them over a pulsar's lifetime. The likely physical process that can create the required 'magnetic spots' is the Hall drift occurring in the crust of a neutron star. It is demonstrated, that the Hall drift can produce small scale strong surface magnetic field anomalies (spots) on timescales of $10^4$ years by means of non-linear interaction between poloidal and toroidal components of the subsurface magnetic field. These anomalies are characterized by strengths of about $10^{14}$ G and curvature radii of field lines of about $10^6$ cm, both of which are fundamental for generation of observable radio emission.

Multiprobe estimation of field line curvature radius in the equatorial magnetosphere and the use of proton precipitations in magnetosphere‐ionosphere mapping

Nonadiabatic, chaotic motion of ions under a curved geomagnetic field geometry is well recognized as a key mechanism that leads to the pitch angle scattering of protons in the equatorial magnetosphere. The efficiency of such proton pitch angle scattering process is energy dependent and controlled by the radius of curvature of the magnetic field line (RCMFL). The protons scattered into the loss cone will precipitate into the ionosphere and excite proton auroras there. In this study, we propose techniques to calculate the RCMFL based upon multiprobe measurements under different probe geometries. We also demonstrate how to use the obtained RCMFL to evaluate the proton precipitation fluxes, and further use the proton precipitation features to help estimate the magnetosphere‐ionosphere mapping. Our procedures are summarized as follows: (1) We calculate the RCMFL using Time History of Events and Macroscale Interactions during Substorms (THEMIS) multiprobe measurements. (2) With the obtained RCMFL, we evaluate the scattering efficiency and in turn the loss cone fluxes of the magnetospheric protons at different energy levels. (3) The above evaluation of the in situ loss cone fluxes is compared to the ionospheric measurements of proton precipitation fluxes in various energy ranges and/or the optical proton auroras to estimate the possible footprint of THEMIS probes in the ionosphere.

MAGNETIC PROPERTIES OF INNER MAGNETOSPHERE DURING GEOMAGNETIC STORMS INFERRED FROM A TSYGANENKO MAGNETIC FIELD MODEL

In this paper we report some properties of inner magnetospheric structure inferred from the T01_s code, one of the latest magnetospheric models by Tsyganenko. We have constructed three average storms representing moderate, strong, and severe intensity storms using 95 actual storms. The three storms are then modelled by the T01_s code to examine differences in magnetic structure among them. We find that the magnetic structure of intense storms is strikingly different from the normal structure. First, when the storm intensity is large, the field lines anchored at dayside longitudinal sectors become warped tailward to align to the solar wind direction. This is particularly so for the field lines anchored at the longitudinal sectors from postnoon through dusk. Also while for the moderate storm the equatorial magnetic field near geosynchronous altitude is found to be weakest near midnight sector, this depression region expands into even late afternoon sector during the severe storm. Accordingly the field line curvature radius at the equator in the premidnight geosynchronous region becomes unusually small, reaching down to a value less than 500 km. We attribute this strong depression and the dawn-dusk asymmetry to the combined effect from the enhanced tail current and the westward expansion/rotation of the partial ring current.

Validity of the fluid description of critical β and Alfvén time scale of ballooning instability onset in the near-Earth collisionless high-β plasma

For a realistic, highly stretched, two‐dimensional tail configuration, in which the pressure gradient force is balanced with the curved field line tension force at the equator, the growth rates and the real frequencies of the ideal magnetohydrodynamic (MHD) and two component fluid (nonideal MHD) ballooning modes, in which the phrase “two component fluid” means that the Hall and the electron pressure gradient terms are included in the generalized Ohm's law, the ion bounce frequency ωbi, the ion magnetic drift frequency ωdi, the ion diamagnetic drift frequency ω*i, and the ion cyclotron frequency ωci are calculated numerically at the equator as a function of X from the near‐Earth tail (X = −15 RE) to the midtail (X = −30 RE). Contrary to the well‐known dipole field case, in which the bounce frequency decreases with increasing ∣X∣, the ion bounce frequency increases with ∣X∣ for the tail configuration. The ion magnetic drift frequency dominated by the curvature drift frequency also increases with increasing ∣X∣. The exact growth rates of the ideal and nonideal ballooning modes, γe and γne, which are nearly equal, are given by 1.22VA/Rc, where VA is the Alfvén velocity and Rc is the field line curvature radius at the equator, and satisfy ωbi, ωdi, ω*i < γe < ωci on average in the near‐Earth tail at X ∼ −15 RE. Also, the ion motion remains adiabatic in the near‐Earth tail at X ∼ −15 RE. Therefore it is a posteriori verified that the fluid or MHD description of the linear stability of the ballooning instability is valid, and the critical β and the Alfvén time scale τA ∼ Rc/VA of the ballooning instability onset obtained by the fluid theory are validated in the near‐Earth tail as close as 15 RE from the Earth. Despite the plasma being collisionless and high‐β in the near‐Earth tail, the subtle collisionless kinetic effects due to the field line curvature in high‐β collisionless plasma are not significant enough to invalidate the fluid description in the near‐Earth tail. The Alfvén time scale of an e‐folding growth of the Alfvén wave trapped within Rc in the equatorial region is of the order of a few tens of seconds or less in the near‐Earth tail. It is faster than the bounce time of the bulk of ions and can explain the observed rapid time scale of a substorm onset. There is excellent agreement between the critical β and the Alfvén time scale obtained analytically for the two component fluid plasma and those obtained by a three‐dimensional particle simulation.

Suprathermal electron acceleration in magnetic reconnection

The suprathermal electrons of ≥20 keV that extend from the hot thermal electron with 2–3 keV temperature are sometimes observed in Earth's magnetosphere in association with reconnection. We study the origin of the hot and suprathermal electrons in terms of the kinetic magnetic reconnection process by using the two‐dimensional particle‐in‐cell simulation. We find that the hot and suprathermal electrons can be formed in the nonlinear evolution of a large‐scale magnetic reconnection. The electrons are, at the first stage, accelerated in the elongated, thin, X‐type current sheet. Next the preheated/accelerated electrons are transported to the stronger magnetic field region produced by piling up of magnetic field lines due to colliding of the fast reconnection outflow with the preexisting plasma. In this region they are further accelerated owing to the ∇B drift and the curvature drift. The mirror force of the reconnecting magnetic fields, the effective pitch angle scattering that occurs when the Larmor radius is comparable to the magnetic field line curvature radius, and the broadband waves excited by the Hall electric current are the other important agents to control the particle acceleration.

Conditions for the validity of the incompressible assumption for the ballooning instability in the long‐thin magnetospheric equilibrium

Conditions under which the compressibility can be neglected for the magnetospheric ballooning instability, which arises in the shear Alfvén branch, are clarified in the context of ideal magnetohydrodynamic plasmas and stochastic plasmas by using the normal mode analysis and the energy principle. An expansion in the small parameter, which is equal to the ratio of the ∇⊥B0 scale length to the field line curvature radius, shows that the incompressible assumption is valid for the ballooning instability with long‐thin perturbations in the low‐frequency regime and in the long‐thin magnetospheric equilibrium, in which the field line curvature radius is much larger than the ∇⊥B0 scale length. When the long‐thin assumption for the equilibrium is not satisfied near the equator, the calculation of the energy functional for a trial function shows that the strongly localized ballooning mode is essentially incompressible if the plasma β at the equator is much larger than 6/Γ, where Γ is the ratio of specific heats. For the stochastic plasmas near the equator the strongly localized ballooning mode is essentially incompressible irrespective of the β value. These results justify the incompressible assumption made in a previous ballooning stability analysis for the long‐thin magnetospheric equilibrium. It is suggested that before the substorm onset, the near‐Earth plasma sheet becomes more taillike, and the long‐thin assumption for the equilibrium becomes more likely to be satisfied on average, and thus the near‐Earth plasma sheet becomes more favorable to the onset of the ballooning instability without the strong stabilizing influence of the compressibility.

Magnetotail particle distributions associated with pitch angle isotropization

We present modeled ion distributions in the near-Earth magnetotail expected to be associated with high latitude pitch angle isotropization. The model consists of a magnetic field reversal and a plasma source such that particles have a ratio of the minimum field line curvature radius to maximum gyroradius near unity, a nonadiabatic regime. For precipitating particles observed at the edge of the field reversal, we find structuring in the ion distribution consisting of peaks and valleys in the pitch angle distribution, particularly for intermediate values of field line curvature, which is consistent with the near-Earth tail region. The structures are non-Maxwellian and not gyrotropic. They are resolvable by instruments such as the GEOTAIL spacecraft CPI detector and can be used as a remote sensing method for fields in this regime between adiabatic motion and current sheet motion.

Pitch angle scattering near energy resonances in the geomagnetic tail

In sharp field reversals where the particle Larmor radius is larger than the magnetic field line curvature radius, particles may not conserve their magnetic moment (first adiabatic invariant). We examine the pitch angle scattering which affects the particles under such conditions. We show that this scattering alternatively leads to a clear three‐branch pattern of magnetic moment variations or to unstructured variations. The three‐branch pattern is characterized by systematic enhancements of magnetic moment at relatively small (up to ∼30°) pitch angles, negligible change at large pitch angles and, in between, either enhancement or damping depending on phase. We show that this three‐branch pattern emerges near the energy resonances reported by Burkhart and Chen [1991], where particles escape after transient oscillations inside the reversal. Away from resonance, the three‐branch pattern gradually expands and affects an increasing volume of the velocity space. Such a structuring of pitch angle scattering is similar to that obtained in weak field reversals (i.e., for Larmor radii comparable to the field line curvature radius), even though the particle orbits in sharp and weak reversals are significantly different. This fact allows us to extend the centrifugal impulse model developed for weak reversals to sharp ones. In this model, nonadiabatic behavior is viewed as the result of perturbation of the particle gyromotion by an impulsive centrifugal force. We demonstrate that this model reproduces essential features of the particle dynamics in sharp reversals and, in particular, the energy resonance phenomenon. We show that in a like manner to weak reversals, three‐branch dynamics in sharp reversals has significant implications for particle injection into the loss cone and gyrophase bunching near the magnetotail midplane.

Ion and electron distribution functions in the distant magnetotail: modeling of Geotail observations

Ion and electron distribution functions measured by the Geotail spacecraft in the distant magnetotail are investigated considering single‐particle dynamics in sharp field reversals. The observed H+ distribution functions exhibit two components, namely, a low‐energy core and a high‐energy population propagating tailward. In agreement with previous studies, we show that ion dynamics in a two‐dimensional (2‐D) reconnection field geometry naturally leads to such distributions and that the neutral line location can be analytically inferred from the velocity space structure. As for electron distribution functions, Geotail observations reveal characteristic “flattop” profiles with enhanced flux in the parallel direction at low energies and in the perpendicular direction at high energies. We interpret these distributions as the result of the electron chaotic behavior in the reconnection region. This chaotic regime, which occurs when the particle Larmor radius is comparable to the magnetic field line curvature radius, can lead to prominent pitch angle scattering. Near the neutral line, we show that at a given energy, this regime yields flux depletion in the parallel direction and enhancement in the perpendicular one. The flattop profile arises from this behavior affecting only the (relatively) high‐energy part of the electron distribution. Conversely, the threshold energy above which electrons exhibit such a behavior contains information on the field reversal characteristics. The electron distribution functions obtained numerically are in agreement with the observations, which support this interpretation framework and allow us to estimate the thickness of the neutral sheet.

Characteristics of electrons at the trapping boundary of the radiation belt

New measurements are presented of the L‐dependent energy threshold for electron flux isotropy observed near midnight from low‐altitude satellites. These data provide the basis for an important remote sensing of the geomagnetic field configurations near the outer edge of the radiation belt. The threshold energy for isotropy observed at low altitudes is interpreted as providing a measure of the effective scale length of inhomogeneity of the geomagnetic field near the equator at high altitude. The data presented were obtained with electron spectrometers on the UARS satellite providing flux and energy spectrum measurements for energies between 30 keV and 5 MeV simultaneously at a variety of pitch angles. On certain orbits the UARS satellite achieved fine L shell resolution and nearly simultaneous measurements at different local times. With this previously unavailable L shell resolution the threshold energy for isotropy versus L shell curves near midnight have shown slopes steeper than 20 MeV per unit L on 20% of the cases, using the International Geomagnetic Reference Field (IGRF) 85 magnetic field model. On 66% of the satellite passes the slopes at the two boundary crossings within 01 to 06 hours in magnetic local time and about 10 min in elapsed time were within a factor of 3 of each other. The L shell at which isotropy occurs above a given threshold energy is found to be generally lower and the slope steeper at times of high geomagnetic disturbance. For the analysis presented here, if isotropy occurs when the radius of field line curvature is less than 10 times the gyroradius of the particles, the scale lengths of inhomogeneities were always found to be less than 2900 km, and in 99% of the cases the scale lengths were greater than 73 km.

Gyrophase effects in the centrifugal impulse model of particle motion in the magnetotail

We investigate the dynamics of charged particles in a magnetic field reversal in the particular case where the Larmor radius is comparable to the magnetic field line curvature radius. In the current interpretation framework based upon the parameter κ (defined as the square root of the minimum curvature radius‐to‐maximum Larmor radius ratio), this situation corresponds to κ of the order of 1. We show that this nonadiabatic regime, which lies at the transition between adiabatic motion (κ ≫ 1) and the nonadiabatic one characterized by oscillations about the field minimum (κ < 1), results from prominent centrifugal effects in the field reversal. To model these effects, we develop a simple analytical description which is based upon an impulsive centrifugal force perturbing the particle gyromotion on the time scale of the cyclotron turn. Comparisons with numerical calculations of ion trajectories demonstrate that this centrifugal impulse model adequately describes both the magnetic moment variations and the gyrophase variations experienced by the particles. As for the magnetic moment, three distinct behaviors (negligible change, strong phase dependence with possible damping, and systematic enhancement) are identified depending upon pitch angle. As for the gyration phase, important bunching effects are obtained which are interpreted as being due to the action of the impulsive centrifugal force. These phase bunching effects are enhanced as the κ parameter approaches unity. In the limit κ ∼ 1, a strong imbalance is obtained between the two phase sectors corresponding to duskward and dawnward motions. This imbalance, which extends over a few tenths of an Earth radius in the Z direction, leads to the formation of a thin current sheet in the vicinity of the magnetotail midplane.

Energetic particle precipitation in the substorm growth phase measured by EISCAT and Viking

Particle precipitation into the evening auroral oval in the 1–2 hours preceding substorm onset has been studied using measurements from the EISCAT incoherent scatter radar, complemented by measurements from the Viking satellite. The ionization between 100 and 160 km altitude is found to correspond to precipitation of approximately Maxwellian populations of ions with average energies of 10–20 keV and of electrons with average energies of 1–3 keV. A high‐energy tail in the electron precipitation is found to account for the ionization below 100 km altitude in the equatorward and poleward parts of the precipitation zone. A distinct population of high‐energy electrons, with energies of several tens of keV or more, is, however, required to explain the ionization profiles in the center of the zone. The ions and separate population of high‐energy electrons are precipitated from close to the respective stable trapping boundaries (where the particle pitch angle distribution changes from isotropic to trapped). It is suggested that the latter electrons are scattered into the loss cone as the magnetic field becomes more taillike during the substorm growth phase and the radius of field line curvature in the equatorial plane becomes unusually small. The southward drifting band of high radio wave absorption, which has previously been identified by many authors as a characteristic feature of the substorm growth phase in riometer records, is found in the cases presented here to be explained mainly by the separate, high‐energy electron population. The lower‐energy electron population has the spectral characteristics expected for a plasma sheet origin but is found both equatorward and poleward of the trapping boundary for >100‐keV electrons. Southward drifting auroral arcs which also characterize the substorm growth phase are found to be located immediately poleward of the zone of higher‐energy electron precipitation, i.e., immediately poleward of the stable trapping boundary for >10‐keV electrons. This suggests that the latitude at which a substorm is initiated, which is often that of a previously southward drifting arc, may be controlled by the presence of the trapping boundary.