Conformally-mapped planetary magnetosheath model

A high-precision model of steady-state plasma flow and magnetic field in the planetary magnetosheath region is proposed by introducing the concept of conformal mapping and transforming the Kobel-Flueckiger scalar potential (the exact solution of Laplace equation) from the parabolic boundaries (bow shock and magnetopause) into arbitrary shape of boundaries. While the statistically-confirmed bow shock and magnetopause models can often be extended to the complex plane by analytic contiuation, construction of conformal mapping in a general magnetosheath case turns out be a mathematical challenge. The reason for this is that the analytic continuation of the bow shock shape does not necessarily meet the analytic contination of the magnetopause shape in general. We overcome this problem and construct a numerical conformal mapping method for the magnetosheath with arbitrary bow shock and magnetopause shapes by (1) modeling shell-like envelopes that smoothly change vary between the two boundaries (the v-variables), (2) imposing the orthogonality condition to find normal directions to the envelopes (the u-variables), and (3) applying the u and v variables to the Kobel-Flueckiger potential. Our conformal mapping method serves as a reference model of magnetosheath, which is numerically inexpensive and is easily implemented. Analysis of in-situ measurement data and numerical simulations of the planetary magnetosheath region will significantly benefit from the conformal mapping method. Moreover, our method can be used to derive the upstream conditions (flow speed and magnetic field) using the magnetosheath data.