Noncoplanar magnetic fields, shock potentials, and ion deflection

A puzzling aspect of the structure of collisionless shock waves concerns the existence of a component of magnetic field that lies out of the coplanarity plane in the transition layer. We show that the existence of this component may be understood and its value calculated from a simple expression derived from first principles. The value of this field component may be derived without reference to the transformation properties of the fields or the changes in energy that the ions and electrons undergo on traversing the electrostatic potential of the shock interface. In fact, the derivation does not depend on the particular value that this potential jump may be observed to have in any particular reference frame and relies solely on Maxwell's equations and the Rankine‐Hugoniot jump conditions. Our results, however, are consistent with previously published work that links these two notions and hence may be considered as an independent verification of this work.