A. V. Usmanov

Determination of the magnetospheric current system parameters and development of experimental geomagnetic field models based on data from IMP and HEOS satellites

Abstract An elaborate analytical model representation of the magnetospheric magnetic field has been developed based on the merged IMP-HEOS experimental data set. As distinct from the approach of Mead and Fairfield (1975), our model incorporates separate mathematical description of the ring current, the magnetotail current sheet and the magnetopause contributions to the total magnetic field. Model formulae for the magnetic field components contain in total 28 input parameters (21 linear coefficients and 7 non-linear parameters) obtained by means of an iterative minimization procedure, which fits the model to the experimental data sets corresponding to different levels of geomagnetic activity, as well as to different conditions in the solar wind.

A global MHD solar wind model with WKB Alfvén waves: Comparison with Ulysses data

We use a steady state global axisymmetric MHD model to reproduce quantitatively the Ulysses observations during its first fast latitude traversal in 1994–1995. In particular, we are able to account for the transformation of a surface dipole magnetic field near the Sun into the configuration observed at large heliocentric distances. The MHD equations are solved by combining a time relaxation numerical technique with a marching-along-radius method. We assume that Alfven waves, propagating outward from the Sun, provide additional heating and acceleration to the flow. Only solutions with waves reproduce the plasma parameters observed in the high-latitude fast solar wind. We show that the meridional distribution of solar wind plasma and magnetic field parameters is dominated by two processes. First, inside ∼24 R⊙ both the plasma velocity and magnetic field relax toward a latitude-independent profile outside the equatorial current sheet (where magnetic forces dominate over thermal and wave gradient forces). Second, outside ∼24 R⊙ there is another meridional redistribution due to a poleward thermal pressure gradient that produces a slight poleward gradient in the radial velocity and an equatorward gradient in the radial component of the magnetic field. We reproduce the observed bimodal structure and morphology of both fast and slow wind and show that computed parameters are generally in agreement with both in situ data and conditions inferred to be characteristic of the solar corona.

A global numerical 3-D MHD model of the solar wind

A fully three-dimensional, steady-state global model of the solar corona and the solar wind is developed. A numerical, self-consistent solution for 3-D MHD equations is constructed for the region between the solar photosphere and the Earths orbit. Boundary conditions are provided by the solar magnetic field observations. A steady-state solution is sought as a temporal relaxation to the dynamic equilibrium in the region of transonic flow near the Sun and then traced to the orbit of the Earth in supersonic flow region. The unique features of the proposed model are: (a) uniform coverage and self-consistent treatment of the regions of subsonic/sub-Alfvénic and supersonic/super-Alfvénic flows, (b) inferring the global structure of the interplanetary medium between the solar photosphere and 1 AU based on large-scale solar magnetic field data. As an experimental test for the proposed technique, photospheric magnetic field data for CR 1682 are used to prescribe boundary condition near the Sun and results of a simulation are compared with spacecraft measurements at 1 AU. The comparison demonstrates a qualitative agreement between computed and observed parameters. While the difference in densities is still significant, the 3-D model better reproduces variations of the solar wind velocity than does the 2-D model presented earlier (Usmanov, 1993).

Solar Wind Modeling with Turbulence Transport and Heating

We have developed an axisymmetric steady-state solar wind model that describes properties of the large-scale solar wind, interplanetary magnetic field, and turbulence throughout the heliosphere from 0.3 AU to 100 AU. The model is based on numerical solutions of large-scale Reynolds-averaged magnetohydrodynamic equations coupled with a set of small-scale transport equations for the turbulence energy, normalized cross helicity, and correlation scale. The combined set of time-dependent equations is solved in the frame of reference corotating with the Sun using a time-relaxation method. We use the model to study the self-consistent interaction between the large-scale solar wind and smaller-scale turbulence and the role of the turbulence in the large-scale structure and temperature distribution in the solar wind. To illuminate the roles of the turbulent cascade and the pickup protons in heating the solar wind depending on the heliocentric distance, we compare the model results with and without turbulence/pickup protons. The variations of plasma temperature in the outer heliosphere are compared with Ulysses and Voyager 2 observations.

A global 3-D simulation of interplanetary dynamics in June 1991

The global dynamics of the solar wind and interplanetary magnetic field in June 1991 is simulated based on a fully three-dimensional, time-dependent numerical MHD model. The numerical simulation includes eight transient disturbances associated with the major solar flares of June 1991. The unique features of the present simulation are: (i) the disturbances are originated at the coronal base (1Rs) and their propagation through inhomogeneous ambient solar wind is simulated out to 1.5 AU; (ii) as a background for the transients, the global steady-state solar wind structure inferred from the 3-D steady-state model (Usmanov, 1993c) is used. The parameters of the initial pulses are prescribed in terms of the near-Sun shock velocities (as inferred from the metric Type II radio burst observations) relative to the preshock steady-state flow parameters at the flare sites. The computed parameters at the Earths location for the period 1–18 June, 1991 are compared with the available observations of the interplanetary magnetic field, solar wind velocity, density, and with variation of the geomagnetic activityKpindex.

TRANSPORT EQUATION FOR MHD TURBULENCE: APPLICATION TO PARTICLE ACCELERATION AT INTERPLANETARY SHOCKS

The aim of the present paper is to unify the various transport equations for turbulent waves that are used in different areas of space physics. Here, we mostly focus on the magnetohydrodynamic turbulence, in particular the Alfvturbulence. The applied methods, however, are general and can be extended to other forms of turbulence, for example the acoustic turbulence, or Langmuir plasma waves. With minor modifications, the derivations followed here can be extended for relativistic motions, thus making it possible to apply them to the wave transport in astrophysical objects with high plasma speeds (radiojets), or strong gravity (black hole surroundings).

A view of the inner heliosphere during the May 10–11, 1999 low density anomaly

On May 10 and 11, 1999, near-Earth spacecraft observed the solar wind density drop to below 0.1 particles cm−3. Using those data, we have mapped solar wind parameters back to the Sun from 1 AU using two techniques. The first assumed constant-velocity trajectories plus corotation, while the second employed MHD-derived magnetofluid parameters. This inverse tracing creates a view of the inner heliosphere useful for identifying the source location on the Sun of the density anomaly. We compare the two methods and show that the source location of the anomaly predicted by MHD is mapped ∼20° eastward of the constant-velocity result. The coronal magnetic field maps indicate that the low density event occurred as the polar coronal magnetic field began reversing. We suggest that the event was initiated by a latitudinal excursion of the low velocity heliospheric current sheet toward the helioequator. The emergence of this slow flow into the preexisting faster wind produced strong rarefaction and anomalously low densities.

RECONSTRUCTING THE SOLAR WIND FROM ITS EARLY HISTORY TO CURRENT EPOCH

Stellar winds from active solar type stars can play a crucial role in removal of stellar angular momentum and erosion of planetary atmospheres. However, major wind properties except for mass loss rates cannot be directly derived from observations. We employed a three dimensional magnetohydrodynamic Alfven wave driven solar wind model, ALF3D, to reconstruct the solar wind parameters including the mass loss rate, terminal velocity and wind temperature at 0.7, 2 and 4.65 Gyr. Our model treats the wind thermal electrons, protons and pickup protons as separate fluids and incorporates turbulence transport, eddy viscosity, turbulent resistivity, and turbulent heating to properly describe proton and electron temperatures of the solar wind. To study the evolution of the solar wind, we specified three input model parameters, the plasma density, Alfven wave amplitude and the strength of the dipole magnetic field at the wind base for each of three solar wind evolution models that are consistent with observational constrains. Our model results show that the velocity of the paleo solar wind was twice as fast, about 50 times denser and 2 times hotter at 1 AU in the Suns early history at 0.7 Gyr. The theoretical calculations of mass loss rate appear to be in agreement with the empirically derived values for stars of various ages. These results can provide constraints for wind dynamic pressures on magnetospheres of (exo)planets around the young Sun and other active stars, which is crucial in realistic assessment of the Joule heating of their ionospheres and corresponding effects of atmospheric erosion.

The global structure of the solar wind in June 1991

A numerical simulation of the global solar wind structure for Carrington rotation 1843 (31 May–28 June, 1991) is performed based on a fully three-dimensional, steady-state MHD model of the solar wind (Usmanov, 1993b). A self-consistent solution for 3-D MHD equations is constructed for the spherical shell extending from the solar photosphere up to 10 AU. Solar magnetic field observations are used to prescribe boundary conditions. The computed distribution of the magnetic field is compared with coronal hole observations and with the IMF measurements made by IMP-8 spacecraft at the Earths orbit.

Interplanetary magnetic field structure and solar wind parameters as inferred from solar magnetic field observations and by using a numerical 2-D MHD model

An attempt is made to infer parameters of the solar corona and the solar wind by means of a numerical, self-consistent MHD simulation. Boundary conditions for the magnetic field are given from the observations of the large-scale magnetic field at the Sun. A two-region, planar (the ecliptic plane is assumed) model for the solar wind flow is considered. Region I of transonic flow is assumed to cover the distances from the solar surface up to 10RS (RS is the radius of the Sun). Region II of supersonic, super-Alfvénic flow extends between 10RS and the Earths orbit. Treatment for region I is that for a mixed initial-boundary value problem. The solution procedure is similar to that discussed by Endler (1971) and Steinolfson, Suess, and Wu (1982): a steady-state solution is sought as a relaxation to the dynamic equilibrium of an initial state. To obtain a solution to the initial value problem in region II with the initial distribution of dependent variables at 10RS (deduced from the solution for region I), a numerical scheme similar to that used by Pizzo (1978, 1982) is applied. Solar rotation is taken into account for region II; hence, the interaction between fast and slow solar wind streams is self-consistently treated. As a test example for the proposed formulation and numerical technique, a solution for the problem similar to that discussed by Steinolfson, Suess, and Wu (1982) is obtained. To demonstrate the applicability of our scheme to experimental data, solar magnetic field observations at Stanford University for Carrington rotation 1682 are used to prescribe boundary conditions for the magnetic field at the solar surface. The steady-state solution appropriate for the given boundary conditions was obtained for region I and then traced to the Earths orbit through region II. We compare the calculated and spacecraft-observed solar wind velocity, radial magnetic field, and number density and find that general trends during the solar rotation are reproduced fairly well although the magnitudes of the density in comparison are vastly different.