Tractor beams are traveling waves that transport illuminated objects in the retrograde direction relative to the direction of propagation. The theory of photokinetic effects identifies design criteria for long-range general- purpose tractor beams. These criteria distinguish first-order tractor beams that couple to induced dipole moments from higher-order tractor beams that rely on coupling to higher-order multipole moments to achieve pulling. First-order tractor beams are inherently longer-ranged and operate on a wider variety of materials. We explore the physics of first-order tractor beams in the context of a family of generalized solenoidal waves.