Chaos and coherence in the conservative three-mode decay interaction

Abstract

In this work we analyze the influence of chaos on the coherence of the mismatched three-wave interaction. Chaos starts to play a decisive role in the problem when adiabatic approximations leading to an integrable model for the system cease to be valid. In regular regimes where the field levels are sufficiently small, there is a characteristic value for the frequency mismatch of the triplet below which coherence and phase locking are dominant. In chaotic regimes, on the other hand, there is no such value and locking behaves in a more complicated way.

Single electron dynamics in a Hall thruster electromagnetic field profile

“…We considered a simplified three dimensional model with inhomogeneous electromagnetic fields. Using a Hamiltonian formalism and the concept of limiting curves, 19,20 we were able to determine conditions that guarantee the confinement of the electron in the acceleration channel. It was also shown that as a given parameter of the electromagnetic field is changed, the particle trajectory could transit from regular to chaotic without affecting the confinement.…”

“…Particularly, we take advantage of the concept of limiting curves. 19,20 The procedure to obtain these curves is as follows. Isolating z in the Hamiltonian (8) we can write z ¼ z(r, P r , P z ; H, P h ).…”

“…Since the magnetic field does no work on the electron, its kinetic energy is completely determined by the scalar potential as e ¼ Àe/. Using (6) and dimensionless quantities we find that e ¼ Àg e z: (19) Hence, we can express the ionization cross section in terms of the axial coordinate, r(z). Moreover, we can write dl ¼ vdt, where v is the electron speed which can be written in terms of the kinetic energy and, consequently, of the axial coordinate as v ¼ (À2g e z) 1=2 .…”

Beyond the modulational approximation in the wave triplet interaction

“…The fact is that although the high-frequency tends to be a fixed parameter for each of the interacting modes, the low-frequency associated to the modulational process grows with the amplitudes or the coupling strength of the involved waves. If at large enough amplitudes or coupling strengths the modulational frequency becomes comparable to the frequency of the carriers, the modulational approximation fails [6,7].…”

Chaotic particle heating due to an obliquely propagating wave in a magnetized plasma

“…3(c) is really bounded; a limiting curve [27] at I ≈ 0.1 acts as a barrier that completely limits the particle energy gain. On the other hand, the full system (2) is higher-dimensional and Arnold diffusion could play a role [13,22].…”