Tsyganenko Magnetic Field Model Research Articles

Analysis of the Tsyganenko Magnetic Field Model Accuracy during Geomagnetic Storm Times Using the GOES Data

Because of the small number of spacecraft available in the Earth’s magnetosphere at any given time, it is not possible to obtain direct measurements of the fundamental quantities, such as the magnetic field and plasma density, with a spatial coverage necessary for studying, global magnetospheric phenomena. In such cases, empirical as well as physics-based models are proven to be extremely valuable. This requires not only having high fidelity and high accuracy models, but also knowing the weakness and strength of such models. In this study, we assess the accuracy of the widely used Tsyganenko magnetic field models, T96, T01, and T04, by comparing the calculated magnetic field with the ones measured in-situ by the GOES satellites during geomagnetically disturbed times. We first set the baseline accuracy of the models from a data-model comparison during the intervals of geomagnetically quiet times. During quiet times, we find that all three models exhibit a systematic error of about 10% in the magnetic field magnitude, while the error in the field vector direction is on average less than 1%. We then assess the model accuracy by a data-model comparison during twelve geomagnetic storm events. We find that the errors in both the magnitude and the direction are well maintained at the quiet-time level throughout the storm phase, except during the main phase of the storms in which the largest error can reach 15% on average, and exceed well over 70% in the worst case. Interestingly, the largest error occurs not at the Dst minimum but 2–3 hours before the minimum. Finally, the T96 model has consistently underperformed compared to the other models, likely due to the lack of computation for the effects of ring current. However, the T96 and T01 models are accurate enough for most of the time except for highly disturbed periods.

Observing the cold plasma in the Earth's magnetosphere with the EMMA network

We illustrate a semi-automated procedure to detect the field line resonance (FLR) frequencies and the derived equatorial plasma mass densities in the inner magnetosphere from ULF measurements recorded at the European quasi-Meridional Magnetometer Array (EMMA). FLR frequencies are detected using the standard technique based on cross-phase and amplitude ratio spectra from pairs of stations latitudinally separated. Equatorial plasma mass densities are then inferred by solving the toroidal MHD wave equation using the TS05 Tsyganenko magnetic field model and assuming a 1/r dependence of the mass density along the field line. We also present a statistical analysis of the results obtained from 165 non-consecutive days of observations at 8 station pairs covering the range of magnetic L -shells 2.4-5.5 and encompassing a wide range of geomagnetic conditions. The rate of FLR detection maximizes around local noon at each pair of stations, reaching the highest values (~95%) around L = 3. A clear diurnal modulation of the FLR frequency is observed at all L values. At the lowest latitudes, the variation is characterized by a rapid decrease in the early morning hours, a stagnation in the middle of the day, and an increase in the evening hours. At higher latitudes, a continuous and more pronounced decrease of the FLR frequency is observed during all daytime hours reflecting a permanent state of recovery of flux tubes depleted by events of enhanced magnetospheric convection. Consistently, the radial profiles of the inferred equatorial mass density show a density increase from morning to afternoon which gets more pronounced with increasing distance and with the level of the preceding geomagnetic activity. The results also confirm the formation of the plasmapause at geocentric distances that decrease as the disturbance level increases. Mean mass density distributions in the equatorial plane are also shown in 2-D maps for different geomagnetic conditions, as well as for a representative stormy day.

A case study of the plasma in the magneto-sheath using the numerical magnetosheath-magnetosphere model and THEMIS measure-ments

This paper presents a case study of the plasma parameters in the magnetosheath, based on THEMIS measurements. As a theoretical tool we apply the self-consistent magnetosheath-magnetosphere model. A specific aspect of the model is that the positions of the bow shock and the magnetopause are self-consistently determined. In the magnetosheath the distribution of the velocity, density and temperature is calculated, based on the gas-dynamic theory. The magnetosphere module allows for the calculation of the magnetopause currents, confining the magnetic field into an arbitrary non-axisymmetric magnetopause. The variant of the Tsyganenko magnetic field model is applied as an internal magnetic field model. As solar wind monitor we use measurements from the WIND spacecraft. The results show that the model quite well reproduces the values of the ion density and velocity in the magnetosheath. The simlicity of the model allows calulations to be perforemed on a personal computer, which is one of the mean advantages of our model.

Strong diffusion limit in the realistic magnetosphere: Dependence on geomagnetic condition and spatial location

AbstractAs an essential concept of resonant wave‐particle interactions, the strong diffusion limit DSD is an important variable to explore the efficiency of wave‐induced pitch angle scattering for particle precipitation loss to the atmosphere. Determined by the size of equatorial loss cone on a given field line and the bounce period at a given energy, the value of DSD sets a lower limit to the precipitation timescale for loss cone filling, regardless of the strength of wave‐particle interactions. However, no efforts have ever been made to evaluate DSD in the realistic magnetosphere considering the impact of various geomagnetic activities. To perform a systematic exploration of the dependence of DSD on geomagnetic condition, spatial location, and global magnetic field model, we have numerically computed DSD using the dipolar and non‐dipolar Tsyganenko magnetic field models under three representative (quiet, moderate, and active) geomagnetic conditions. Use of more realistic Tsyganenko magnetic field models introduces non‐negligible or considerable differences in DSD magnitude from that obtained using a dipolar field. The difference can be over an order of magnitude at the field lines with equatorial crossings ≥6 Re during geomagnetically disturbed times. We also report that in the realistic magnetosphere both DSD magnitude and its variations have a strong dependence on the spatial location. Computed DSD shows the maximum tending to occur on the dayside (MLT = 12 and 16) and the minimum DSD more likely to occur at MLT = 00. Compared to the dipolar results, largest deviation in DSD occurs for MLT = 00, 04, and 20, while DSD variations on the dayside are relatively small. Our results demonstrate that accurate evaluation of DSD besides scattering rates in the realistic magnetosphere, especially at high spatial locations and under geomagnetically disturbed conditions for which a dipolar approximation fails, can make an important contribution to quantifying the wave effect on particle resonant diffusion, which should be incorporated into future modeling efforts for comprehending the role of resonant wave‐particle interactions and the dynamics of magnetospheric electrons under a variety of geomagnetic conditions.

Chorus-driven resonant scattering of diffuse auroral electrons in nondipolar magnetic fields

[1] We perform a comprehensive analysis of resonant scattering of diffuse auroral electrons by oblique nightside chorus emissions present along a field line with an equatorial crossing of 6 RE at 00:00 MLT, using various nondipolar Tsyganenko magnetic field models. Bounce-averaged quasi-linear diffusion coefficients are evaluated for both moderately and actively disturbed geomagnetic conditions using the T89, T96, and T01s models. The results indicate that inclusion of nondipolar magnetic field leads to significant changes in bounce-averaged rates of both pitch angle and momentum diffusion for 200 eV to 10 keV plasma sheet electrons. Compared to the results using a dipole field, the rates of pitch angle diffusion obtained using the Tsyganenko models are enhanced at all resonant pitch angles for 200 eV electrons. In contrast, for 500 eV to 10 keV electrons the rates of pitch angle scattering are enhanced at intermediate and/or high pitch angles but tend to be considerably lower near the loss cone, thus reducing the precipitation loss compared to that in a dipole field. Upper band chorus acts as the dominant cause for scattering loss of 200 eV to 2 keV electrons, while lower band chorus scattering prevails for 5–10 keV electrons, consistent with the results using the dipole model. The first-order cyclotron resonance and the Landau resonance are mainly responsible for the net scattering rates of plasma sheet electrons by oblique chorus waves and also primarily account for the differences in bounce-averaged diffusion coefficients introduced by the use of Tsyganenko models. As the geomagnetic activity increases, the differences in scattering rates compared to the dipole results increase accordingly. Nonnegligible differences also occur particularly at high pitch angles for the diffusion rates between the Tsyganenko models, showing an increase with geomagnetic activity level and a dependence on the discrepancy between the Tsyganenko model fields. The strong dependence of bounce-averaged quasi-linear scattering rates on the adopted global magnetic field model and geomagnetic activity level demonstrates that realistic magnetic field models should be incorporated into future modeling efforts to accurately quantify the role of magnetospheric chorus in driving the diffuse auroral precipitation and the formation of electron pancake distributions.

Formula omitted] transport across the polar cap

The plasma sheet, inner magnetosphere, and high-latitude magnetosphere all contain significant amounts of O + ions during active times. Singly charged oxygen ions unambiguously come from the ionosphere, making them an excellent tracer species. We test the cleft ion fountain theory, which asserts that O + ions escape from the cleft, cross the polar cap, and then enter the plasma sheet. Statistical studies of O + density in the cleft, high-altitude polar cap, and plasma sheet all indicate that the O + density increases with increasing solar wind dynamic pressure. In order to examine O + transport more directly, we use polar cap ion outflow measurements and the 2001 Tsyganenko magnetic field model driven with advanced composition explorer (ACE) solar wind parameters. We calculate the distance between the cleft and the ionospheric footpoints of magnetic field lines mapped from the polar spacecraft along the noon–midnight meridian. Using the observed outflow speed and the magnetic field line length we calculate the travel time for the ions. When we examine the distance from the cleft versus the O + travel time for individual passes, the slope of the line is consistent with the measured ionospheric convection speed across the polar cap. We conclude that O + ions emanating principally from the cleft are transported across the polar cap, and these O + ions have access to the ring current and plasma sheet.

Mass density inferred from toroidal wave frequencies and its comparison to electron density

We have estimated the magnetospheric local mass density using the frequency of the toroidal standing Alfvén waves detected with the magnetic (B) and electric (E) field experiments on the Combined Release and Radiation Effects Satellite (CRRES), which had a low‐latitude elliptical orbit (6.3 RE apogee and 18° inclination). A 73‐day period in 1991, which included several geomagnetic storms, was chosen for analysis because the spacecraft was located on the afternoon sector where toroidal waves are routinely excited. Dynamic spectra of the B and E fields were generated for each CRRES orbit for visual identification of toroidal mode ULF waves excited at a number of harmonics. The fundamental mode is the most persistent feature in the spectra, and this mode appears more clearly in the electric field than in the magnetic field. For statistical analysis we determined the fundamental frequency f1 from a separate set of electric field spectra that were computed in a moving 20‐min time window with 10‐min overlap. The frequency is in the range of 1.7–14.2 mHz. The local mass density consistent with f1 was obtained by numerically solving a magnetohydrodynamic wave equation that incorporated the Tsyganenko magnetic field model and an analytical form of field‐line mass density variation that was derived from a recent study of toroidal harmonics. We combined the estimated mass density with the local electron number density ne derived from the plasma wave spectra at CRRES to obtain the local average ion mass M (=ρ/ne). A total of 1094 M samples were obtained, with the majority (95%) coming from the plasmatrough region (ne < 100 cm−3). Our technique for the mass density is confirmed to be reliable because only 3.5% of the M samples lie outside the physically plausible range of 1 amu (all‐H+ plasma) to 16 amu (all‐O+ plasma). The average ion mass has a median value of 3.0 amu and depends on geomagnetic activity. For example, M is 2.5 amu for Dst = 0 and 4.1 amu for Dst = −60 nT. There is a similar dependence of M on Kp, but only when the Kp values are averaged over a few days. There is no strong dependence of M on the magnetic field L shell in the range L = 4 to L = 8 covered by the f1 samples, although M is significantly low (<2 amu) for the plasmaspheric regime (ne > 100 cm−3).

The dynamics of storms and substorms with the WINDMI model

WINDMI is a physics based eight-dimensional state-space model that simulates the flow of energy between the dominant global energy components in the nightside magnetosphere. The model is intrinsically three-dimensional in configuration space, and uses the basic geometry of the Tsyganenko magnetic field model to define the physical quantities. The dynamical equations satisfy the laws of energy and charge conservation for the network of branches and nodes formed by the topology of the ambient magnetic field. The model includes energy coupled by injected plasma from the plasma sheet across the Alfvén layer into the ring current. The power input into the model is the electromotive plasma dynamo derived from solar wind parameters. The output of the model is the westward Auroral Electrojet current and the energy stored in the Earth’s ring current. The prediction of the model is compared to the geomagnetic AL and D st indices. These indices measure fluctuations of the earth’s magnetic field at its surface. The model parameters have been optimized using a genetic algorithm with the Average Relative Variance (ARV) as a performance metric for five of the seven designated Geospace Environment (GEM) storms. Results for the October 3–7 2000 GEM storm and the October 20–22 2001 GEM storm are given here. The optimized models appear to give a reliable method of making predictions from the solar wind for a range of auroral and ring current activity.

The 3-dimensional characteristics of the magnetic field lines and the non-adiabatic region in the magnetosphere

In this paper, the 3-dimensional configurations of the non-adiabatic region and the magnetic field lines (MFLs) in the magnetosphere are studied based on the Tsyganenko magnetic field model. According to the parameter δ = d B/ B, the magnetosphere can be divided into the adiabatic and non-adiabatic region. A thin non-adiabatic region has been found in the near tail region, which moves toward to the Earth during the geomagnetic disturbance. Pitch angle scattering occurs when particles go through the non-adiabatic region, which is expected as the source region of the precipitating particles. Moreover, by investigating the 3-dimensional configurations of MFLs, we find that MFLs remain in the noon meridian plane if their foot prints are in the noon meridian plane; but leave the foot print plane and are swept tailward if their foot prints are not in the noon meridian plane. The characteristics of the MFLs suggest that the precipitation region is almost in the nightside region, centered near midnight.

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.

A Dynamical Model for the Coupled Inner Magnetosphere and Tail

WINDMI-RC is a family of physics-based models that range in dimensionality from low-order models of dimension d = 8, which model the flow of energy between the eight highest global energy components of the tail, to high-order models with dimension d /spl sim/ 100 or more, for models that resolve the nonlinear dynamics of the system into different latitude zones. The models are intrinsically three-dimensional in configuration space and use the basic geometry of the Tsyganenko magnetic field model to define the geometrical quantities. The models satisfy the constraints of the conservations laws of energy and electrical charge in their network of nodes and branches that follow from the structure of the system. These models describe the injection of plasma from the plasma sheet and across the Alfve/spl acute/n layer into the inner ring current. The transport uses the storm-time solar wind dynamo electric field as the driver for the network model coupled to the inner magnetospheric corotation electric field.

Ring current ion motion in the disturbed magnetosphere with non-equipotential magnetic field lines

Transport of ring current ions during the main phase of the geomagnetic storm is modeled. Particle trajectories are simulated by the Lorentz equation for dipole and Tsyganenko magnetic field models. The convection electric field is described by variations on the K p dependent Volland–Stern model structure in the equatorial plane. Out of that plane the electric field is assumed to be the same as in the equatorial plane at least at the low latitudes. This consideration implies the possibility of non-equipotentiality of geomagnetic field lines at least for L⩾6 during strong magnetic storms. In our modeling energetic protons, typically of several tens of keV, start on the night side at L=4 or at L=7, and move initially under gradient magnetospheric drift largely confined to the equatorial plane. However, soon after crossing the noon–night meridian, the protons rather abruptly depart from the equatorial plane and deviate towards high latitude regions. This latter motion is essentially confined to a plane perpendicular to the equator, and it is characterized by finite periodic motion. The calculations indicate a slow violation of the first adiabatic invariant at the point of ion departure from the equatorial region, with slower non-adiabatic variation later along the orbit. The greater the convection electric field, the higher is the energy of the protons participating in this off equatorial divergent flow. The more energetic ions, of hundreds of keV and higher, however, rather continue their magnetic drift around the Earth uninterruptedly and these ions form the symmetric ring current ion population. The numerical calculations described herein explicitly indicate that the perpendicular divergent ion flow can contribute to the morning–evening component of the magnetic field perturbation during magnetic storm conditions, and can result in populating the high latitude and tail regions by the energetic protons.

The electric field model of the earth's magnetotail

The electric field in the Earth's magnetosphere is the main driving force of plasma motion there. The magnetospheric electric field is now generally taken to be a uniform dawn-dusk field or a projected field. In this work it is assumed that magnetic field lines are the equipotential lines of electric field, and that the electric field of the terrestrial ionosphere is taken to be the magnetospheric electric field projected along magnetic field lines. By using Tsyganenko's magnetic field model (T89), the ionospheric electric field is projected to the magnetotail, so obtaining a new model of magnetospheric electric field. In this paper a comparison between the bipolar magnetic field and the projection of the T89 model is made. A break of the restriction to bipolar magnetic fields has been achieved, which has a large range of application for the magnetosphere.

Interpretation of the He II (304 Å) EUV image of the inner magnetosphere by using empirical models

The visualization of the inner magnetosphere is a long‐cherished goal in magnetospheric physics. This goal was recently achieved with the He II (304 Å) image of the inner magnetosphere by using the EUV scanner on board the Planet‐B spacecraft (Nakamura et al., 2000). However, our understanding of the inner magnetosphere in relation to these images has not been assessed. The two‐dimensional (2‐D) EUV image is difficult to interpret, as it is necessary to infer the three‐dimensional (3‐D) spatial information of the inner magnetosphere from the 2‐D remote sensing data. We examine our present knowledge of the inner magnetosphere and compare simulated 2‐D images with the real EUV image. We conclude that an empirical model that assumes conventional E × B flows and combines the diffusive equilibrium model of Chiu et al. (1979) and the Weimer (1995) electric potential and Tsyganenko (1989) magnetic field models is in good agreement with the EUV image only within the Earth‐dominated flow regime. Furthermore, the model gives a better fit to the EUV image data, by assuming the convection‐dominated flow regime to be filled with ionospheric He+ at a filling rate of 1.2·(6.6/L)−3.0 (He+ ions cm−3 d−1), instead of the well‐known L−4 density dependence on flux tube volume.

Distortion of the nightside boundary of the "firmly-closed" region in the 1996 Tsyganenko magnetic field model

Distortion of the nightside boundary of the "firmly-closed" region in the 1996 Tsyganenko magnetic field model

Testing electric and magnetic field models of the storm‐time inner magnetosphere

We calculate the equipotential contours, drift trajectories, and predicted proton energy spectra in the inner magnetosphere using combinations of dipole or Tsyganenko magnetic field models and Volland‐Stern or Weimer electric fields models. We compare the results with observations of proton energy spectra at L=4–5 over a range of local times from the Active Magnetospheric Particle Tracer Explorers/charge‐energy‐mass instrument. We find that the trajectories, and in particular the source location in the tail and the exit location on the dayside, depend significantly on both the electric and magnetic field models. However, the predicted energy spectra in the inner magnetosphere depended almost entirely on the choice of electric field. Using the Weimer electric field gives less loss along the trajectories, which is usually in better agreement with the observed energy spectra.

Investigation of the conjugacy between auroral breakup and energetic electron injection

Auroral TV observations at Loparskaya, Kola Peninsula, and CRRES energetic electron and proton measurements during a moderate isolated substorm at 2000–2100 UT on February 13, 1991, are compared. The CRRES was at the apogee of orbit 494 in the outer radiation belt near the magnetic equator. CRRES footprint projection estimated by using a Tsyganenko magnetic field model was situated at the same latitudes several degrees eastward of active aurora during the substorm breakup or the intensification. The intensification consists of several activations of 1‐min duration, and this fine spatial and temporal structure is important for the conjugacy investigations. It is shown that injected energetic electrons have been accelerated at the same time as one of the auroral activations at the same latitude and approximately the same azimuthal extended region. The lack of enhanced electrons during other activations suggests that the acceleration region has a sharp equatorial boundary.

Evaluation of the tail current contribution to Dst

The Dst index is produced using low‐latitude ground magnetic field measurements and frequently is used as an estimate of the energy density of the ring current carried mainly by energetic (∼ 10 – 200 keV) ions relatively close to the Earth. However, other magnetospheric current systems can cause field perturbations at the Earth's surface: for example, dayside magnetopause currents are known to contribute to the Dst index. It has also been suggested that the nightside tail current sheet can significantly affect the Dst index during high magnetic activity periods when the currents are intense and flow relatively close to the Earth. In this study, several disturbed periods are input into Tsyganenko magnetic field models. From the time series of the external and internal fields an artificial Dst index is computed using the same procedure followed in the actual Dst calculation. A tail region in the magnetosphere is explicitly defined and the T96 and T89 models are used to calculate the effect of current within this tail region on ground measurements and therefore on Dst. The results are then compared with the measured Dst to determine the tail current contribution to Dst. It is found that for a geomagnetic storm and a storm‐time substorm with Dst of ∼ 80 nT the tail current contribution is between 22 and 26 nT. The same analysis is also applied to several isolated non‐storm‐time substorms, yielding a nearly linear relationship between Dst and the tail current contribution. This contribution is approximately one quarter of Dst.

Distortion of the outer boundary of the closed region in the Tsyganenko magnetic field model

Distortion of the outer boundary of the closed region in the Tsyganenko magnetic field model

The magnetostatic equilibrium in high latitude magnetosphere and the selection of coordinate system for high latitude processes description

The coordinate system employing isosurfaces of magnetic flux tube volume as the coordinate surfaces was used for the reconstruction of azimuthal magnetospheric plasma pressure gradients on a basis of the data of large scale field aligned currents distribution and the Tsyganenko magnetic field models. The integral plasma pressure changes are compared with the satellite measurements of plasma pressure. It was shown that Region I and Region II currents can be maintained by azimuthal hot plasma pressure gradients. The localization of the Region I currents in the inner magnetosphere creates the mechanism of dawn-dusk electric field formation which does not require the reconnection or viscous interaction of the solar wind with the magnetosphere.