HIGH-CURRENT RELATIVISTIC ELECTRON BEAM FOCUSING IN PLASMA

The analysis of the envelope equation for high-current relativistic electron beam propagation in plasma in an external uniform magnetic field is presented. The envelope equation is obtained in a Hamiltonian form with an effective potential, which depends from electron beam and plasma parameters, and external magnetic field. Hamiltonian aproach allows fully analyze the behavior of the beam envelope as a function of the beam current, beam energy, plasma density and conductivity, as well as on the external magnetic field and the initial beam angular momentum.

On the phase dependence of the soliton collisions in the Dyachenko–Zakharov envelope equation

We study soliton collisions in the Dyachenko–Zakharov equation for the envelope of gravity waves in deep water. The numerical simulations of the soliton interactions revealed several fundamentally different effects when compared to analytical two-soliton solutions of the nonlinear Schrodinger equation. The relative phase of the solitons is shown to be the key parameter determining the dynamics of the interaction. We find that the maximum of the wave field can significantly exceed the sum of the soliton amplitudes. The solitons lose up to a few percent of their energy during the collisions due to radiation of incoherent waves and in addition exchange energy with each other. The level of the energy loss increases with certain synchronization of soliton phases. Each of the solitons can gain or lose the energy after collision, resulting in increase or decrease in the amplitude. The magnitude of the space shifts that solitons acquire after collisions depends on the relative phase and can be either positive or negative.