Dynamics of a spherical obstacle

¹ Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, 140 00 Praha 4, Czech Republic
² Lamar University, Department of Physics, PO Box 10046 Beaumont, TX 77010, USA
³ Space Weather National Laboratory, Instituto de Geofisica, Universidad Nacional Autonoma de Mexico, Morelia, Mexico
⁴ CONAHCYT Fellowship, Instituto de Geofisica, Unidad Michoacan, Universidad Nacional Autnonoma de Mexico, Morelia, Mexico

^⋆ Corresponding authors; vandas@asu.cas.cz; eromashets@lamar.edu; p.coronaromero@igeofisica.unam.mx

Received: 5 August 2024
Accepted: 30 January 2025

Abstract

Context. A magnetized plasma cloud acts as a magnetic obstacle to an external plasma flow. We used an analytical approach to examine forces acting on a spherical static obstacle, which can be applied to the kinematic analysis of the obstacle’s motion.

Aims. We aimed to determine the magnetic field in the sheath region around a spherical obstacle for cases when the background magnetic field is perpendicular, parallel, or at an arbitrary angle to the plasma flow direction. Additionally, we calculated the diagmagnetic force exerted by the magnetic field on the obstacle.

Methods. We applied a potential field method, under the conditions that the normal component of the magnetic field is conserved on the bow shock and is zero at the obstacle. We analytically determined the modification of the background magnetic field by a supersonic obstacle. Results were compared with the field modification by a slow, subsonic obstacle. Uniform and nonuniform background magnetic fields were considered and the diamagnetic force acting on an obstacle was calculated.

Results. The diamagnetic force on the slow obstacle in the ambient field is zero, while the supersonic obstacle experiences a decelerating diamagnetic force in the uniform background field. The magnetic field with a gradient produces an accelerating diamagnetic force on a subsonic obstacle, pushing it away from a stronger magnetic field. The diamagnetic force on the supersonic obstacle from the nonuniform background field is much weaker.