Fast and optimal solution to the “Rankine‐Hugoniot problem”

Abstract

A new, definitive, reliable and fast iterative method is described for determining the geometrical properties of a shock (i.e., θ Bn , n , V s and M A ), the conservation constants and the self‐consistent asymptotic magnetofluid variables using the Rankine‐Hugoniot conservation equations. The technique uses the three dimensional magnetic field and plasma observations. The method is well conditioned and reliable at all θ Bn angles regardless of the shock strength or geometry. Explicit proof of “uniqueness” of the shock geometry solution by either analytical or graphical methods is given. The method is applied to synthetic and real interplanetary shocks, including a bow shock event and the results are then compared with those determined by preaveraging methods and other iterative schemes. A complete analysis of the confidence region and error bounds of the solution is also presented.