In this week, I started to move to Potential Field Source Surface (PFSS) models. I am going to make an introduction to these models in this post.
PFSS models are aiming to solve the magnetic field satisfying
∇ × B = 0, ∇ · B = 0
in a spherical region with appropriate boundary conditions. Therefore, this model could be easily implemented to extrapolate global solar magnetic field. As mentioned in previous posts, solarbextrapolation is limited to the Cartesian coordinate system and a small active region. By adding support to PFSS models, we are going to expand its compatibility with different coordinate systems and regions.
Generally, the model would solve the equations in the spherical coordinate system. Note that the grid would be converted to a rectilinear grid that is equally spaced in ρ, s, and φ, where
ρ = ln(r), s = cos(θ), φ = φ
and (r, θ, φ) are spherical coordinates. The models were initially developed by Altschuler and Newkirk . Recently, Anthony Yeates  provided codes to solve this model numerically, but the major object to store the data in his code would be numpy.ndarray.
Therefore, the major tasks of this part would be:
- Replicate the code of Anthony Yeates
- Replace the major data object in the function by NDCube
Right now, I am editing the interfaces of input and output to add compatibility with NDCube. Next step would be modifying codes of numerical schemes to make the whole function compatible with NDCube. Hope I could show some results of PFSS solver with NDCube in the next few weeks!
 Altschuler, M.D. and G. Newkirk, Magnetic fields and structure of solar corona .I. Methods of calculating coronal fields, Solar Physics 9, 131, 1969.
 Anthony Yeates. (2018, October 26). antyeates1983/pfss: First release of pfss code. (Version v1.0). Zenodo. http://doi.org/10.5281/zenodo.1472183