Physics

A charged particle in a magnetic field splits its motion into two independent parts: the component parallel to the field (which experiences no force) and the component perpendicular to it (which curves in a circle). As you tilt your launch angle $\alpha$ away from the field direction, you're redistributing the proton's fixed speed between these two components—more perpendicular means tighter spiraling, more parallel means faster forward progress. The key is recognizing that the magnetic force only cares about the perpendicular component, while the parallel component determines how quickly the helix advances along the field.

A charged particle in a magnetic field splits its motion into two independent parts: the component parallel to the field (which experiences no force) and the component perpendicular to it (which curves in a circle). As you tilt your launch angle $\alpha$ away from the field direction, you're redistributing the proton's fixed speed between these two components—more perpendicular means tighter spiraling, more parallel means faster forward progress. The key is recognizing that the magnetic force only cares about the perpendicular component, while the parallel component determines how quickly the helix advances along the field.