7 May 2001 Physics Letters A 283 (2001) 37–43 www.elsevier.nl/locate/pla Electron dynamics in circularly-polarized laser and uniform electric fields: acceleration in vacuum Yousef I. Salamin a,b a Theoretische Quantendynamik, Fakultät für Physik, Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany b Physics Department, Birzeit University, P.O. Box 14, Birzeit, West Bank, Palestine Received 13 January 2001; received in revised form 7 March 2001; accepted 28 March 2001 Communicated by P.R. Holland Abstract We solve exactly analytically the relativistic equation of motion of a single electron injected initially at an angle to the direction of propagation of a circularly-polarized plane-wave laser field, of arbitrary intensity, and a uniform electric field. It is shown, in principle, that the electron may be accelerated to high energies in this environment.  2001 Elsevier Science B.V. All rights reserved. PACS: 42.65.-k; 52.40.Nk; 42.50.Vk; 52.75.Di 1. Introduction Analytic work on the dynamics of electrons in elec- tromagnetic plane waves has been around many years now [1–6]. Most of the solutions, however, have been restricted to cases where the electron is initially at rest or has a vanishing average velocity. Analytic solutions addressing the general situations of initial motion at relativistic speeds and at an arbitrary direction with re- spect to the wave propagation direction have recently been given [7–11]. The problem becomes more intri- cate analytically with the addition of an extra elec- tric or magnetic field. The case of an added uniform magnetic field has been considered in the past [12] and has led to the introduction of the auto-resonance laser accelerator (ALA) scheme [13–15]. This prob- lem has also been revisited lately [11,16] with empha- E-mail address: salamin@tqd1.physik.uni-freiburg.de (Y.I. Salamin). sis placed on the acceleration of the electron to high energies and the associated radiation aspects. The case of a sin 2 pulse and a uniform axial magnetic field has also been done more recently [17]. The subject of the present Letter is the dynamics of an electron injected in vacuum at some arbitrary angles to (a) the direction of a uniform electric field of strength E s , and (b) the propagation direction of a circularly-polarized plane-wave laser field of arbitrary intensity (see Fig. 1 for a schematic). To the best of our knowledge, an exact analytic solution to this problem has not been done before. This solution is important for the understanding of issues related to particle ac- celeration [18,19], electron motion following ioniza- tion, and the scattering of radiation and, possibly, gen- eration of harmonics in the presence of the added elec- tric field [20,21]. While the plane-wave-based analytic solution may model a laboratory situation only approximately, we believe that it represents a good first step towards the analysis of a realistic scheme. It leads to better insights 0375-9601/01/$ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0375-9601(01)00228-6