Marinelli, A., Hemsing, E. and Rosenzweig, B. (2012) Three-Dimensional Analysis of Longitudinal Plasma Oscillations in a Thermal Relativistic Electron Beam: Application to an Initial Value Problem. Physics of Plasmas, 19, Article ID: 063108.
https://doi.org/10.1063/1.4714639

has been cited by the following article:

• TITLE: On the Relativistic Harmonic Oscillator

  AUTHORS: Yair Zarmi

  KEYWORDS: Relativistic Harmonic Oscillator, Weak-Relativistic Limit, Extreme-Relativistic Limit

  JOURNAL NAME: Applied Mathematics, Vol.14 No.1, January 10, 2023

  ABSTRACT: The relativistic harmonic oscillator represents a unique energy-conserving oscillatory system. The detailed characteristics of the solution of this oscillator are displayed in both weak- and extreme-relativistic limits using different expansion procedures, for each limit. In the weak-relativistic limit, a Normal Form expansion is developed, which yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures. In the extreme-relativistic limit, an expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) → 1 yields an excellent approximation for the solution throughout the whole period of oscillations. The variation of the coefficients of the Fourier expansion of the solution from the weak- to the extreme-relativistic limits is displayed.