Tsyganenko Magnetic Field Model

[Geneva Andreotti]

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Data-based (or empirical) modeling of the geomagnetic field started as a disciplineas early as in the first half of XIX century, when Gauss developed mathematical foundations of themodeling of Earth's main magnetic field and obtained first estimates of its spherical harmonic coefficients, using thenavailable ground-based data. That approach, based on the potential (current-free) nature of themain field outside Earth, is still at the core of modernIGRF models.With the advent of space era and understanding the crucial role of the geomagneticfield in the dynamics of the Earth's upper atmosphere and radiation belts, a needwas realized to extend the models from low to high altitudes, eventually including theentire magnetosphere, an integral part of our space environment. Modeling the magnetic field inthat region is much more difficult, mostly because the magnetic field from external sources(currents in the magnetospheric plasma) rapidly outweighs the main field with growing distancefrom Earth. The external field is not current-free and, hence, it is no longer possibleto conveniently represent it by a scalar potential, uniquely defined by observationsat a surface, as was the case with the main field. Rather, vector measurements of themagnetic field should now be made throughout the entire 3D modeling region, making it necessaryto accumulate large amounts of space magnetometer data taken in a wide range of geocentricdistances.This task turns out to be even more complicated due to the fact that, unlike the maingeomagnetic field that varies on a timescale of thousands of years, the Earth's magnetosphereis a very dynamical system, whose configuration depends on many internal and external factors.The first factor is orientation of the Earth's magnetic axis with respect to the directionof the incoming solar wind flow, which varies with time because of (i) Earth's diurnal rotation andits yearly orbital motion around Sun, and (ii) frequent "side gusts" of the solar wind. Theanimation on the left below shows how the magnetospheric field varies in response to the diurnalwobbling of the geodipole. The background color coding displays the distribution of thescalar difference DB between the total model magnetic field and that of the Earth's dipolealone. Yellow and red colors correspond to the negative values of DB (depressed fieldinside the ring current, in the dayside polar cusps, and in the plasma sheetof the magnetotail). Black and blue colors indicate a compressed field(in the subsolar region on the dayside and in the magnetotail lobes on thenightside). Another important factor is the state of the solar wind, in particular, theorientation and strength of the interplanetary magnetic field (IMF),"carried" to the Earth's orbit from Sun due to the high electricalconductivity of the solar wind plasma. Interaction between the terrestrialand interplanetary fields becomes much more effective when the interplanetarymagnetic field turns antiparallel to the Earth's field on the dayside boundaryof the magnetosphere. In this case, geomagnetic and interplanetary field linesconnect across the magnetospheric boundary, which greatly enhances the transferof the solar wind mass, energy, and electric field inside the magnetosphere.As a result, the magnetospheric field and plasma become involved in a convection,as illustrated in the second animation below(right): In actuality, that kind of steady convection is rarely realized. The solar windis far from being a stationary flow: periods with a stable ram pressure are often interrupted bystrong "gusts"; in addition, the interplanetary magnetic field often fluctuates both inmagnitude and orientation. This results in dramatic dynamical changes of theentire magnetospheric configuration, which culminate in magnetosphericstorms, accompanied by an explosive conversion of large amounts of thesolar wind energy into the kinetic energy of charged particles in thenear-Earth space, manifested in polar auroral phenomena and ionosphericdisturbances.The third animation below (left panel) illustrates the dynamical changes of the global magneticfield in the course of a disturbance: a temporary compression of themagnetosphere by enhanced flow of the solar wind is followed by a tailwardstretching of the field lines. Eventually, the increase of the tailmagnetic field results in a sudden collapse of the nightside field(a substorm ) and a gradual recovery of the magnetosphere to itspre-storm configuration. Space weatherSpace weather is a modern field of space research, focused on the solar activity and its impact upon thenear-Earth environment, spacecraft hardware, and humans. It includes investigation and prediction of solarflares, coronal mass ejections (CME), sunspots, magnetic storms, particle precipitation into the Earth atmosphere, and associatedionospheric phenomena. The flow of plasma from the Sun, known as the solar wind, is the principal factor determining thespace weather in our planetary system. This is why it is very important to know in advance its principal characteristics: particle density,bulk velocity, the strength and direction of the Interplanetary Magnetic Field (IMF). The NASA Advanced Composition Explorer (ACE)satellite (operating since 1997) and the recently (2015) launched Deep Space Climate Ovservatory (DSCOVR) mission reside at the L1 libration point(1,500,000 km sunward from Earth) and provide continuous flow of information about the solar wind state nearly one hour in advance.Their real-time data are provided online by theNational Oceanic and Atmospheric Administration (NOAA) Space Weather Prediction Center (SWPC).The orientation of the IMF vector is a crucial factor that determines the state of the near-Earth space environment.Southward IMF (Bz

The Tsyganenko models are semi-empirical best-fit representations for the magnetic field, based on a large number of satellite observations (IMP, HEOS, ISEE, POLAR, Geotail, GOES, etc). The models include the contributions from major external magnetospheric sources: ring current, magnetotail current system, magnetopause currents, and large-scale system of field-aligned currents.

The T89 model was primarily developed as a simple empirical approximation for the global magnetosphere, binned into several intervals of the disturbance index Kp. The T96 model has an explicitly defined realistic magnetopause, large-scale Region 1 and 2 Birkeland current systems, and IMF penetration across the boundary. The model was parameterized by the solar wind ram pressure, Dst-index, and transverse components (By and Bz) of the IMF. The T01 model represents the variable configuration of the inner and near magnetosphere for different interplanetary conditions and ground disturbance levels. It also takes into account the observed dawn-dusk asymmetry of the inner magnetosphere due to the partial ring current that develops during magnetospheric disturbances. The TS05 model is a dynamical model of the storm-time geomagnetic field in the inner magnetosphere, based on space magnetometer data taken during 37 major events in 1996-2000 and concurrent observations of the solar wind and IMF.

The Tsyganenko model suite also includes GEOPACK library with 20 FORTRAN subroutines. The GEOPACK-2008 library includes subroutines for the current (IGRF) and past (DGRF) internal geomagnetic field models, a group of subroutines for transformations between various coordinate systems, a field line tracer, and two magnetopause model codes.

The model returns magnetic field for an instance of solar wind and geomagnetic indices.In addition, the TS05 model uses parameters based on time integrals of solar wind data that create an appearance of physical transitions between the magnetic fields returned for each time step.

When using the web interface for instantaneous calculation of external and internal geomagnetic field along a field line and at the specified point the user sets the date and time (year, day of the year, UT hour, minute, and second).

The T89 model was primarily developed as a simple empirical approximation for the global magnetosphere, binned into several intervals of the disturbance index Kp. The T96 model has an explicitly defined realistic magnetopause, large-scale Region 1 and 2 Birkeland current systems, and IMF penetration across the boundary. The model was parameterized by the solar wind ram pressure, Dst-index, and transverse components (By and Bz) of the IMF. The T02 model represents the variable configuration of the inner and near magnetosphere for different interplanetary conditions and ground disturbance levels. It also takes into account the observed dawn-dusk asymmetry of the inner magnetosphere due to the partial ring current that develops during magnetospheric disturbances. The TS05 model is a dynamical model of the storm-time geomagnetic field in the inner magnetosphere, based on space magnetometer data taken during 37 major events in 1996-2000 and concurrent observations of the solar wind and IMF.

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