Using a variational method, we show that an effective attractive force exists between two Gaussian laser beams in a plasma because of a mutual coupling from relativistic mass corrections. The effective force can be generalized to other nonlinearities. This force can cause two laser beams to spiral around each other with a rotation period that is proportional to the Rayleigh length. These orbits are stable if the ratio of the orbit diameter to the laser spot size $d_0{/W}_0\le \sqrt{2}$. Three-dimensional particle-in-cell simulations are presented which confirm the mutual attraction.

• Received 18 April 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.2124