The set of space-weather tools are developed for the purpose of improving techniques employed in space-weather forecasting. They consist of different models of the evolution of magnetic flux ropes (HELIO-XM), the background solar wind and solar energetic particles.

This tool was defined and developed by STORMS and CDPP staff through a subcontract with GFI informatique and CNES financial support and with the great help of Michael Lavarra (intern), Valbona Kunkel (post-doc), and Anthony Bourdelle (intern).

At this stage, only HELIO-XM is operational, it is an interface that allows users to compute the forces acting on a magnetic flux rope embedded in a background coronal magnetic field. For a given set of initial parameters the tool propagates the magnetic flux rope to any spacecraft or planet situated in the inner heliosphere. It computes the 3-D vector components of the magnetic field measured by a probe flying through the flux rope for any flux rope orientation specified near the Sun. The model reproduces well the statistical properties of magnetic clouds measured near 1AU.

Background on HELIO-XM

Bending a cylindrical screw pinch into a torus generates a set of toroidal forces (hoop, tire-tube and 1/R forces) directed outwardly along the major radius of the toroid. Xue and Chen (1983) and Chen (1989) proposed that these toroidal forces to overcome the confining tension force of the background coronal field as well as the effect of the gravitational force. In this model, these toroidal forces act to accelerate CMEs to high speeds in the solar corona. For the sake of mathematical simplicity, the geometries used by Chen (1989) and following workers assumed either an exponential or else linear rise of the variation of minor-axis length from the footpoint to the apex of the varying cross-sectional area of the toroid. For a circular toroidal current axis, this leads to discontinuities in the variation of the flux surfaces near the apex of the CME. To obtain topologically realistic 3-D magnetic field lines, we modified the geometry used in previous studies and derived a new analytical formulation of both the inductance and the 3-D magnetic field.

Force balance

We model the forces acting on the flux rope erupting in the corona: they include the toroidal forces, the effect of the confining field, the gravitational force and the drag force. As CMEs erupt in the corona they sweep up coronal material and their mass increases, we included this ‘snow-plow’ effect by using a simple analytical formulation based on the observational study of Feng et al. (2015). Like Chen (1989), we inject poloidal magnetic field that we convert into toroidal current (to compute the toroidal forces) using the inductance approach (Shafranov 1966).

Reconstruction of the 3-D magnetic topology

With our new geometry we can solve analytically for the 3-D topology of the embedded magnetic field transported by the erupting flux rope. To satisfy Maxwell’s equations, we abandoned the symmetrical description of the poloidal field proposed by Chen (1989, 1996). Our new representation of the field is asymmetric (along the central cross section of the CME) such as the solution proposed by Romashets and Vandas (Figure 2b). We also conserve the average toroidal magnetic field strength from apex to footpoints.

Conservation of helicity

After the flux rope has formed in the corona, the total helicity (number of turns plus writhe) of the magnetic field must be conserved (Torok et al. 2012). Our model does not include writhing, therefore total helicity is directly related with the total number of turns in each flux surface inside the propagating flux rope. We conserved this quantity after the injection phase of the poloidal magnetic field inside the structure. Using lists of magnetic cloud fittings, Démoulin et al. (2015) show that the number of turns per unit length does not vary between the apex and mid-way down the legs of the flux rope, this behaviour is reproduced in the present model.

References

Bateman, MHD instabilities, Cambridge, Mass., MIT Press, 1978. 270 p., 1978,

Chen J.,  Effects of toroidal forces in current loops embedded in a background plasma, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 338, March 1, 1989, p. 453-470, 1989,

Chen, J. Theory of prominence eruption and propagation : Interplanetary consequences, Journal of geophysical research, 1996,

Démoulin, P., Janvier, M., Dasso, S., Magnetic Flux and Helicity of Magnetic Clouds, submitted, 2015,

Feng, L. et al., Why Does the Apparent Mass of a Coronal Mass Ejection Increase?, The Astrophysical Journal, Volume 812, Issue 1, article id. 70, 12, 2015, 

Janvier, Démoulin & Dasso, Global axis shape of magnetic clouds deduced from the distribution of their local axis orientation, A&A, 2013,

Lepping, Berdichevsky, Ferguson, Estimated errors in magnetic cloud model fit parameters withforce-free cylindrically symmetric assumptions, Journal of Geophysical Research, 2003,

Török, Berger & Kliem, The writhe of helical structures in the solar corona, A&A, 2012,

Romashets & Vandas, Free-force field inside a toroidal magnetic cloud, Geophysical Research Letters, 2003,

Shafranov, V.D., Plasma Equilibrium in a Magnetic Field, Reviews of Plasma Physics, Volume 2. Authorized translation from the Russian by Herbert Lashinsky, University of Maryland, USA. Edited by M. A. Leontovich. Published by Consultants Bureau, New York, 1966, 103,