Possible formations of sprites in the free electromagnetic field

Abstract

We derive a family of stationary and evolving Beltrami-field-like solutions from the free Maxwell equations in vacuum. The stationary electromagnetic field thus obtained is helical and/or column-like once it is represented in a suitable frame of reference. Our helical- or column-like solutions resemble those reported sprites which are brightest at about 70 km altitude. We also briefly discussed the limit of weakly Beltrami fields.