Relativistic motion in parallel electric and magnetic fields
= Relativistic motion in parallel electric and magnetic fields
When uniform $\mathbf E$ and $\mathbf B$ are parallel, the <relativistic Lorentz force> splits into independent hyperbolic motion along the fields and circular motion in the perpendicular plane. The circle is periodic in <proper time>, while electric acceleration makes the helix's longitudinal pitch grow exponentially from one proper-time cyclotron period to the next.