Abstract:
A nonlinear evolution equation for Alfvén waves, propagating in streaming plasmas with nonuniform densities and inhomogeneous magnetic fields, is obtained by using the reductive perturbation technique. The governing equation is a modified derivative nonlinear Schrödinger (MDNLS) equation. The numerical solution of this equation shows that inhomogeneities exhibit their presence as an effective dissipation. The spatiotemporal evolution of long-wavelength Alfvénic fluctuations shows that the wave steepens as it propagates. High-frequency radiation is also observed in our simulations. Unlike coherent Alfvén waves in homogeneous plasmas, which can become noncoherent/chaotic only in the presence of a driver, MDNLS evolves into noncoherent/turbulent state without any driver simply because of inhomogeneities. This clearly indicates that the integrability property of the derivative nonlinear Schrödinger equation, which allows coherent solitary solutions, is destroyed by inhomogeneities.
