Envelope equations and conservation laws describing wakefield generation and electron acceleration

R. A. Cairns, A. Reitsma, R. Bingham

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Previous authors have proposed various envelope equations to describe the behavior of an electromagnetic pulse generating a wakefield. In general these retain second-order derivatives, the reason being that the eikonal contains the initial wave frequency. Here it is shown that if the evolution of the wave frequency is followed using ray-tracing equations, a first-order evolution equation is obtained. It can be shown with this formalism that wave action is conserved and the energy lost from the electromagnetic wave can be explicitly accounted for in terms of energy gained by the plasma. The energy balance equations suggest that an electron bunch which will extract energy efficiently from a wakefield can be at least as efficiently accelerated by direct interaction with the electromagnetic pulse.
Original languageEnglish
Pages (from-to)766-770
Number of pages5
JournalPhysics of Plasmas
Issue number2
Early online date20 Jan 2004
Publication statusPublished - Feb 2004


  • plasma waves
  • electromagnetic interactions
  • plasma electromagnetic waves
  • carrier generation
  • conservation laws


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