On force-free magnetic fields and beltrami flows

Solenoidal vector fields, which satisfy the condition that the field rector everywhere parallels to its curl, have complex topological structures, and usually show chaotic behaviors. In this paper, analytical solutions for vector fields with constant proportional factor in three basic coordinate systems are presented and it is pointed out that a Beltrami flow can sustain a steady force-free magnetic field in a perfectly conducting fluid, provided the magnetic field is parallel to the velocity everywhere.