J. Plasma Physics (1989), vol. 41, part 2, pp. 281-287 281 Printed in (treat Britain Ion- and electron-acoustic waves in sheet plasmas By M. B. CHAUDHRY AND M. D. TAHIR Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan (Received 1 September 1987 and in revised form 4 October 1988) Ion-acoustic waves in sheet plasmas, which are of thickness of order of the ion Larmor radius p it have been investigated numerically. The frequency range considered is less than the ion cyclotron frequency OJ C( . An integral equation in wavenumber space is derived from the linearized Vlasov-Poisson equations and analysed numerically. Eigenfrequencies and eigenfunctions of the wave have been studied systematically by varying the plasma thickness, plasma density, electron-to-ion temperature ratio and parallel wavenumber. Electron- acoustic waves are found when the parallel wavenumber is very small (e.g. £j p i = 0-005) and the electron and ion temperatures are comparable. 1. Introduction Experimental studies of the RF confinement of plasma (Miyake et al. 1971; Hatori & Watanabe 1972; Hatori et al. 1974) in the RFC-XX have shown that a sheet plasma of thickness of order of the ion Larmor radius p t is created in the line cusp region. In addition, Yatsu, Sadamoto & Miyoshi (1977) and Sadamoto, Yatsu & Miyoshi (1980) have shown that a sheet plasma can be produced at one end of a minimum-B magnetic field configuration. In these experiments an ambipolar electric field is often observed inside the sheet plasma. Experimental studies of electrostatic ion cyclotron waves (Sato et al. 1982) and of ion Bernstein waves (Kumazawa et al. 1982) in the sheet plasma have also been carried out. In previous work, Chaudhry, Watanabe & Nishikawa (1982a, b) and Chaudhry & Watanabe (1985) analysed these modes in sheet plasmas (with and without an ambipolar field) analytically and numerically, using an integral equation in wavenumber space. These studies were carried out in the frequency range greater than or equal to the ion cyclotron frequency w ci . In this paper we restrict ourselves to the frequency range less than the ion cyclotron frequency where ion-acoustic waves can be excited. Eigenfrequencies and eigenfunctions of the ion-acoustic waves have been studied numerically by varying the plasma thickness, plasma density, parallel wavenumber and clectron-to-ion temperature ratio. In the case where the parallel wavenumber is very small (e.g. k^p t = 0-005) and T t « T e , an electron-acoustic wave is found (here T t and T e are the ion and electron temperatures respectively). In §2 we describe the model of the sheet plasma and the basic equations. The numerical results are presented in §3. Finally, in §4 we summarize the results and make some concluding remarks.