New Eulerian methods for nonlinear wave equations: computing multi-valued solutions in a Traveling Wave Tube
Abstract
It is well known that solutions to nonlinear hyperbolic wave equations can exhibit ``steepening,'' and can ``break'' in a finite time. Most commonly the physical situations being modeled dictate that shock formation occurs at the breaking point. However, it has long been acknowledged that another interpretation of the breaking event is the formation of ``multi-valued'' solutions [1]. In fact, in electron beam devices Lagrangian methods are commonly used to compute solutions when the electron beam velocity and density becomes multi-valued. Recently an Eulerian technique for computing multi-valued solutions was developed in the context of geometrical optics [2]. In [3] this technique is applied to the Euler-Poisson equations which may be used to model, among other systems, nonlinear electron beam evolution in Klystron amplifiers. In this paper we apply the technique to the Traveling Wave Tube (TWT). The moment formulation used in the technique provides insights into spectral mixing in the electron beam at the onset of TWT saturation and beyond; such insights are not available in a conventional Lagrangian model. We discuss the numerical technique, and the insights it has generated into TWT physics. [1] G.B. Whitham. Linear and Nonlinear Waves, Wiley 1974. [2] S. Jin and X.T. Li. Physica D 182, 46--85 (2003). [3] X.T. Li, J.G. Wöhlbier, et al. Phys. Rev. E 70, 016502 (2004).
- Publication:
-
APS Division of Plasma Physics Meeting Abstracts
- Pub Date:
- November 2004
- Bibcode:
- 2004APS..DPPFP1139W