Waves in Plasmas: Lecture notes

Space Science Reviews, 1985

Journal of Plasma Physics, 1992

We develop an (r, k) phase-space description of waves in plasmas by introducing Gaussian window functions to separate short-scale oscillations from long-scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation in an inhomogeneous and time-varying background plasma, we first discuss the proper form of the current response function. In analogy with the particle distribution function f(v, r, t), we introduce a wave density N(k, r, t) on phase space. This function is proved to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible.

2006

It is certified that work contained in this dissertation is based on theoretical investigation carried out by Mushtaq Ahmad under my supervision. He has fulfilled all the requirements and is eligible to submit the associated thesis for the degree of Doctor of Philosophy in Physics.

This is a short introduction on waves in a non-relativistic plasma. We will consider a plasma of electrons and protons which is fully ionized, nonrelativistic and homogeneous.

1975

Journal of Physics: Conference Series, 2009

A symposium in honor of Professor Allan N. Kaufman's 80 th year was held at the University of California at Berkeley on October 5-7, 2007. The meeting celebrated Allan's contributions to plasma physics as well as his friendship and guidance. The present paper very briefly summarizes the talks presented.

Physics of Plasmas, 2013

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in Valentini et al. [Phys. Plasmas 19, 092103 (2012)]. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in Schamel [Phys. Plasmas 20, 034701 ]. V C 2013 American Institute of Physics.

2014

The work presented in this thesis is about a study of some linear and nonlinear plasma waves. Firstly, a kinetic-theoretical approach is used to study ion Bernstein waves in an electron-proton plasma with a kappa velocity distribution. The effects of the parameter kappa on the dispersion relation of ion Bernstein waves are discussed in detail, considering various values of the ratio of the ion plasma frequency to the ion cyclotron frequency, ωpi/ωci, allowing application of the results to various space environments. For a fixed value of ωpi/ωci, we have found that the dispersion relation depends significantly on the parameter kappa of the ions, κi, but is independent of the electron kappa. Over all cyclotron harmonics, the dispersion curves are shifted to higher wavenumbers (k) if κi is reduced. When the value of ωpi/ωci is increased, the fall-off of the wave frequency, ω, at large k is smaller for lower κi, and curves are shifted towards larger wavenumbers. For large values of ωpi/...

Journal of Physics: Conference Series, 2009

A brief review is presented of the contributions of Allan Kaufman to the theory of plasma waves. These contributions have been rich and various, characterized by high quality and a sense of what makes a problem both interesting and important. We include a brief summary of work prior to the mid-1980's, but the primary emphasis will be on more recent work concerning the use of phase space methods in the theory of linear plasma waves and mode conversion. One goal of the paper is to place Allan's contributions in the wider context of semi-classical methods. We will emphasize the underlying intuitions rather than providing a detailed mathematical exposition which can be found in the literature cited.

The electrostatic ion waves are studied for non-Maxwellian or Lorentzian distributed unmagnetized pair-ion plasmas. The Vlasov equation is solved and damping rates are calculated for electrostatic waves in Lorentzian pair-ion plasmas. The damping rates of the electrostatic ion waves are studied for the equal and different ion temperatures of pair-ion species. It is found that the Landau damping rate of the ion plasma wave is increased in Lorentzian plasmas in comparison with Maxwellian pair-ion plasmas. The numerical results are also presented for illustration by taking into account the parameters reported in fullerene pair-ion plasma experiments. During this decade, theoretical study of pair-ion PI plasma has gained attraction due to stable production of fullerene ion plasmas in the laboratory experiments. 1–3 The dynamics of symmetric or PI plasma is different from the usual electron-ion plasma in which both fast and slow time scales occur due to difference in masses of ions and electrons. The collective behavior of fullerene PI plasmas has also been studied and three types of electrostatic waves, i.e., ion acoustic wave IAW, intermediate frequency wave IFW, and ion plasma wave IPW have been observed in the direction parallel to the magnetic field. The observed frequency ranges for IAW, IFW, and IPW are / 2 12 kHz, 12 / 2 20 kHz, and / 2 20 kHz, respectively , and the ion cyclotron frequency is c / 2 = 4.3 kHz at B = 0.2 T. A lot of theoretical research work has already been published on linear and nonlinear electrostatic waves in PI plasmas. Mostly two fluid plasma theory is used to study the dynamics of PI plasmas. 4–14 In PI plasmas, IPW and IAW can be derived from linear theory of two fluid plasma dynamics provided the temperature difference between the same mass ion species exist. In the experiments, it has been reported that a difference in temperature exists between two fullerene ion species which occurs due to different charging processes, i.e., the electron impact ionization and attachment for the production of both positive and negative of fullerene ions in PI plasmas. 2 The third mode IFW cannot be obtained from linear theory using two fluid model in homogeneous PI plasmas 2,7 and its theoretical understanding is still not clear. The surface ion waves in PI plasmas has been studied by Hasegawa and Shukla. 4 Schamel and Luque 15 investigated electrostatic waves in PI plasmas with the inclusion of trapped ions in the potential troughs in their model. Recently, the arbitrary amplitude solitary waves in PI plasma have been study by Dubinov et al. 8 They studied that elec-trostatic solitary waves are formed only when there exist a small difference of temperatures between PI species. The low amplitude solitons and shocks have been studied in PI plasma using reductive perturbation method. 10–12 It has been reported the nonlinear compressive and rarefactive electro-static structures are formed only when a little difference of temperature occurs between the PI species. Recently, a criterion for pure PI has been studied for its production in laboratory experiments. 16 The electrostatic modes parallel to magnetic field in PI plasmas have been studied by Vranjes and Poedts 17 for same temperature PI species. They studied the resonant damping of longitudinal electrostatic waves in PI plasma using the kinetic model for Maxwellian distributed PI plasmas. However , it has been mentioned by the authors that the choice of Maxwellian plasmas in their study is not a good assumption because ions collected from the exciter hole may not have completely followed the Maxwellian distribution in PI fullerene plasma experiment. 2 The non-Maxwellian velocity distributed plasmas have been observed in space and as-trophysical plasma situations. The observed particles are found to have distribution of quasi-Maxwellian up to mean thermal velocities with non-Maxwellian suprathermal tails at high velocities and energies. 18 The nonthermal plasmas are found to exist in the magnetospheres of the Earth and in planets and also in the solar wind. 19–21 In general, the observed non-Maxwellian plasma distributed particles are well fitted with the generalized Lorentzian or kappa distribution, which contains both thermal as well as suprathermal parts of the observed velocity spectra. The kappa distributions have been used by a number of authors to study the damping rates of the electrostatic and electromagnetic waves in plasmas. Therefore, it will be interesting to study longitudinal waves in PI plasma with kappa distribution function, so that the PI species are assumed to be nonthermal in the laboratory experiment. The kappa distribution function approaches to Maxwellian when the spectral index kappa approaches to infinity. Recently, the damping rate for Langmuir, dust ion acoustic, and dust acoustic waves are studied in generalized Lorentzian multicomponent plasmas. 22,23 In this brief communication, we study the electrostatic longitudinal waves in the presence of non-Maxwellian distributed generalized Lorentzian or kappa distribution pure PI plasma containing positive and negative fullerene C 60