A nonlinear single-mode structure in a plasma with anisotropic temperature

An exact solution is derived to the equations of vortex electron anisotropic hydrodynamics for a plasma that is unstable against the Weibel instability driven by the electron temperature anisotropy. This solution describes saturation of the Weibel instability in the single-mode regime with an arbitrary wavelength and corresponds to a standing helical wave of magnetic perturbations in which the amplitude of the generated magnetic field varies periodically over time. The longitudinal and transverse (with respect to the rotating anisotropy axis) plasma temperatures are subject to the same periodic variations. In this case, the maximum magnetic field energy can be on the order of the plasma thermal energy.