Instability of a Relativistically Strong Electromagnetic Wave of Circular Polarization

We demonstrate that a circularly polarized electromagnetic wave propagating through a cold plasma and strong enough to make electrons relativistic (${\nu }_0\equiv \frac{e{E}_0}{m_{e}c{\omega }_0}\gtrsim 1$) is subject to a new pinching type of instability. The linearized equations are solved exactly, without the necessity of introducing an infinite determinant. This allows our results to describe the transition from nonrelativistic to extreme-relativistic electron motion. In the relativistic limit, the growth rates are as high as $0.47{\omega }_0$.