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We provide exact analytical solutions for the magnetic field produced by prescribed current distributions located inside a toroidal filament of finite thickness. The solutions are expressed in terms of toroidal functions, which are modifications of the Legendre functions. In application to the MHD equilibrium of a twisted toroidal current loop in the solar corona, the Grad–Shafranov equation is decomposed into an analytic solution describing an equilibrium configuration against the pinch-effect from its own current and an approximate solution for an external strapping field to balance the hoop force. Our solutions can be employed in numerical simulations of coronal mass ejections (CMEs). When superimposed on the background solar coronal magnetic field, the excess magnetic energy of the twisted current loop configuration can be made unstable by applying flux cancellation to reduce the strapping field. Such loss of stability accompanied by the formation of an expanding flux rope is typical for the Titov & Démoulin eruptive event generator. The main new features of the proposed model are as follows: the filament is filled with finiteβplasma with finite mass and energy, the model describes an equilibrium solution that will spontaneously erupt due to magnetic reconnection of the strapping magnetic field arcade, and there are analytic expressions connecting the model parameters to the asymptotic velocity and total mass of the resulting CME, providing a way to connect the simulated CME properties to multipoint coronograph observations.

 

We describe our first attempt to systematically simulate the solar wind during different phases of the last solar cycle with the Alfvén Wave Solar atmosphere Model (AWSoM) developed at the University of Michigan. Key to this study is the determination of the optimal values of one of the most important input parameters of the model, the Poynting flux parameter, which prescribes the energy flux passing through the chromospheric boundary of the model in the form of Alfvén wave turbulence. It is found that the optimal value of the Poynting flux parameter is correlated with the area of the open magnetic field regions with the Spearman’s correlation coefficient of 0.96 and anticorrelated with the average unsigned radial component of the magnetic field with the Spearman’s correlation coefficient of −0.91. Moreover, the Poynting flux in the open field regions is approximately constant in the last solar cycle, which needs to be validated with observations and can shed light on how Alfvén wave turbulence accelerates the solar wind during different phases of the solar cycle. Our results can also be used to set the Poynting flux parameter for real-time solar wind simulations with AWSoM.

 

We present a reduced magnetohydrodynamic (MHD) mathematical model describing the dynamical behavior of highly conducting plasmas with frozen-in magnetic fields, constrained by the assumption that there exists a frame of reference, where the magnetic field vector, B, is aligned with the plasma velocity vector, u, at each point. We call this solution “stream-aligned MHD” (SA-MHD). Within the framework of this model, the electric field, E = − u × B ≡ 0, in the induction equation vanishes identically and so does the electromagnetic energy flux (Poynting flux), E × B ≡ 0, in the energy equation. At the same time, the force effect from the magnetic field on the plasma motion (the Ampère force) is fully taken into account in the momentum equation. Any steady-state solution of the proposed model is a legitimate solution of the full MHD system of equations. However, the converse statement is not true: in an arbitrary steady-state magnetic field, the electric field does not have to vanish identically (its curl has to, though). Specifically, realistic three-dimensional solutions for the steady-state (“ambient”) solar atmosphere in the form of so-called Parker spirals can be efficiently generated within the stream aligned MHD (SA-MHD) with no loss in generality. 

A versatile suite of computational models, already used to forecast magnetic storms and potential power grid and telecommunications disruptions, is preparing to welcome a larger group of users. 

The heating near the coronal hole boundary is included into the AWSoM model via the Alfven wave interaction with the boundary between the closed and open field lines. Although the excessive heating on the Alfven surface wave is possible (Evans et al 2012), we chose to parameterize the surface effect in terms of excessive nonlinear reflection proportional to the transverse gradient of density. The efficiency of such reflection is derived analytically and compared with the solar wind observation data at 1 AU. 

To simulate solar coronal mass ejections (CMEs) and predict their time of arrival and geomagnetic impact, it is important to accurately model the background solar wind conditions in which CMEs propagate. We use the Alfvén Wave Solar atmosphere Model (AWSoM) within the the Space Weather Modeling Framework to simulate solar maximum conditions during two Carrington rotations and produce solar wind background conditions comparable to the observations. We describe the inner boundary conditions for AWSoM using the ADAPT global magnetic maps and validate the simulated results with EUV observations in the low corona and measured plasma parameters at L1 as well as at the position of the Solar Terrestrial Relations Observatory spacecraft. This work complements our prior AWSoM validation study for solar minimum conditions and shows that during periods of higher magnetic activity, AWSoM can reproduce the solar plasma conditions (using properly adjusted photospheric Poynting flux) suitable for providing proper initial conditions for launching CMEs.

 

MHD-based global space weather models have mostly been developed and maintained at academic institutions. While the ``free spirit'' approach of academia enables the rapid emergence and testing of new ideas and methods, the lack of long-term stability and support makes this arrangement very challenging. This paper describes a successful example of a university-based group, the Center of Space Environment Modeling (CSEM) at the University of Michigan that developed and maintained the Space Weather Modeling Framework (SWMF) and its core element, the BATS-R-US extended MHD code. It took a quarter of a century to develop this capability and reach its present level of maturity that makes it suitable for research use by the space physics community through the Community Coordinated Modeling Center (CCMC) as well as operational use by the NOAA Space Weather Prediction Center (SWPC).