J. Plasma Physics (2015), vol. 81, 905810204 c  Cambridge University Press 2014 doi:10.1017/S0022377814000853 1 Effect of electron beam on the properties of electron-acoustic rogue waves E. K. El-Shewy 1,2 †, S. A. Elwakil 2 , A. M. El-Hanbaly 2 and A. I. Kassem 2 1 Department of Physics, Taibah University, Al-Madinah Al-Munawarrah, Kingdom of Saudi Arabia 2 Theoretical Physics Group, Faculty of Science, Mansoura University, Mansoura, Egypt (Received 28 June 2014; revised 17 August 2014; accepted 1 September 2014; first published online 3 December 2014) The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, Maxwellian hot electrons, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles and the associated electric field on the carrier wave number, normalized density of hot electron and electron beam, relative cold electron temperature and relative beam temperature are discussed. The results of the present investigation may be applicable in auroral zone plasma. 1. Introduction In many physical situations electron-acoustic (EA) waves appear in plasmas containing two various groups of electrons, referred to as hot and cold electrons (Ikezawa and Nakamura 1981). Electron-acoustic soliton has been observed in different regions of Earth magnetosphere by various satellites, e.g. Viking, FAST etc (Dubouloz et al. 1993; Cattell et al. 1998; Ergun et al. 1999; Pottelette et al. 1999 and Miyake et al. 2000). It has been found under the conditions that the hot to cold electron temperature ratio is greater than 10 and cold electrons represent a significant fraction of plasma (more than 10%) (Tokar and Gary 1985a, 1985b; Mace and Hellberg 1990a and Mace et al. 1999b). It is known that the linear and nonlinear properties of the plasma depend on the velocity distribution functions of the plasma particles. The most commonly used distribution in a collisionless plasma is the Maxwellian velocity distribution, which is a distribution that is in the thermal equilibrium. Many of partial differential equations are used to describe the nonlinear plasma waves that depending on the medium where they propagate. Some of these equations are the nonlinear schr¨ odinger (NLS) equation (Sulem and Sulem 1999) and the Korteweg-de-Vries (KdV) equation (Drazin and Johnson 1989). The NLS equation describes the dynamics of a modulated wave packet in which nonlinearities are balanced by the dispersion effect. The stationary solution of the NLS equation leads to an envelope structure, called an envelope soliton. Recently, several studies were made to explain electron-acoustic solitary waves. For instance, Mace et al. (1991) inspected the electron-acoustic solitary (EAS) waves in an unmagnetized plasma model where the ions and the cold electron fluid are of finite temperature. They appeared the existence of negative potential solitary structures associated with a compression † Email address for correspondence: e k el shewy@mans.edu.eg, emadshewy@yahoo.com