Magnetic Field Magnitude Modification for a Force-free Magnetic Cloud Model

A scheme was developed by Lepping, Berdichevsky, and Wu ( Solar Phys. 292 , 27, 2017 ) [called the LBW article here] to approximate the average magnetic field magnitude ( B -) profile of a typical magnetic cloud (MC) at/near 1 AU. It was based on actual Wind MC data, taken over 21 years, that were used to modify a time-shifted Bessel function (force-free) magnetic field, where shifted refers to a field that was adjusted for typical MC self-similar expansion. This was developed in the context of the Lepping, Jones, and Burlaga ( J. Geophys. Res. 95 , 11957, 1990 ) [called LJB here] MC parameter fitting model and should provide more realistic future representations of the MC B -profile in most cases. In the LBW article, we showed through testing that in about 80% of the MC cases (but this varies according to the actual closest approach distances of the spacecraft) on average, the MC B -profile of the modified model is expected to significantly improve when this scheme is used. We describe how this scheme can be employed practically to modify the LJB MC fitting model, and we test a new and slightly better (and less unwieldy) version of the scheme, the non-shifted (of Bessel functions) version, which is indeed used in the LJB model modification. The new scheme is based on slightly more accurate modification formulae compared to the old scheme, and it is expected to improve the B -profile in approximately 83% of the cases on average. The schemes are applicable for use with data originating only at/near 1 AU, since the magnetic field and plasma data used in the development of the associated formulae were taken only from the Wind spacecraft, which was and is at 1 AU.