Weak turbulence theory for reactive instability

Yoon, P. H.
November 2010
Physics of Plasmas;Nov2010, Vol. 17 Issue 11, p112316
Academic Journal
In the present paper, the customary weak turbulence theory is generalized to include reactive instabilities. For the sake of simplicity, the formalism assumes electrostatic perturbation propagating in one-dimensional uniform unmagnetized plasmas. By weak turbulence theory it is meant as the perturbative nonlinear theory based upon Vlasov equation, truncated at the second (or up to third) order nonlinearity and ensemble averaged. By reactive instability it is meant as the plasma instability whose growth rate is not necessarily exceedingly small. The traditional weak turbulence theory found in the literature is applicable only to weakly growing plasma instabilities whose real frequency ωk can be determined from the real part of the dispersion relation, Re ε(k,ωk)=0, while the growth rate may be determined by the Landau formula, γk=-Im ε(k,ωk)[∂ Re ε(k,ωk)/∂ωk]-1. This implies the assumption that |γk|<ωk. On the other hand, for reactive instabilities for which γk/ωk is not necessarily small, the real frequency and growth/damping rate must be determined from the complex roots of the dispersion relation, ε(k,ωk+iγk)=0. The present paper extends the textbook weak turbulence theory to deal with such a situation.


Related Articles

  • Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams. Logan, Nikolas C.; Davidson, Ronald C. // Physics of Plasmas;Jul2012, Vol. 19 Issue 7, p073113 

    This paper places a lowest upper bound on the field energy in electrostatic perturbations in single-species charged particle beams with initial temperature anisotropy (T∥/T⊥<1). The result applies to all electrostatic perturbations driven by the natural anisotropies that develop in...

  • Renormalized non-modal theory of the kinetic drift instability of plasma shear flows. Mikhailenko, V. S.; Mikhailenko, V. V.; Stepanov, K. N. // Physics of Plasmas;Jun2011, Vol. 18 Issue 6, p062103 

    The linear and renormalized nonlinear kinetic theory of drift instability of plasma shear flow across the magnetic field, which has the Kelvin's method of shearing modes or the so-called non-modal approach as its foundation, is developed. The developed theory proves that the time-dependent...

  • Impact of resonant magnetic perturbations on nonlinearly driven modes in drift-wave turbulence. Leconte, M.; Diamond, P. H. // Physics of Plasmas;May2012, Vol. 19 Issue 5, p055903 

    In this work, we study the effects of resonant magnetic perturbations (RMPs) on turbulence, flows, and confinement in the framework of resistive drift wave turbulence. We extend the Hasegawa-Wakatani model to include RMP fields. The effect of the RMPs is to induce a linear coupling between the...

  • Overview of nonlinear kinetic instabilities. Berk, H. L. // AIP Conference Proceedings;9/24/2012, Vol. 1478 Issue 1, p29 

    The saturation of shear Alfvén-like waves by alpha particles is presented from the general viewpoint of determining the saturation mechanisms of basic waves in a plasma destabilized by a perturbing source of free energy. The formalism is reviewed and then followed by analyses of isolated mode...

  • Quasistationary wake plasma wave excited by a comoving charged pulse. Wang, Youmei; Yu, M. Y. // Physics of Plasmas;Nov2010, Vol. 17 Issue 11, p112116 

    Fully nonlinear quasistationary wake plasma waves excited by and comoving with a charged pulses are investigated. The characteristics of the excited plasma wave depend on a (nonlinear) resonance between the wave and the pulse. With two comoving driver pulses, localized wake structures without...

  • Cylindrical effects on Richtmyer-Meshkov instability for arbitrary Atwood numbers in weakly nonlinear regime. Liu, W. H.; He, X. T.; Yu, C. P. // Physics of Plasmas;Jul2012, Vol. 19 Issue 7, p072108 

    When an incident shock collides with a corrugated interface separating two fluids of different densities, the interface is prone to Richtmyer-Meshkov instability (RMI). Based on the formal perturbation expansion method as well as the potential flow theory, we present a simple method to...

  • Modulational instability of ion acoustic waves in e-p-i plasmas with electrons and positrons following a q-nonextensive distribution. Eslami, Parvin; Mottaghizadeh, Marzieh; Pakzad, Hamid Reza // Physics of Plasmas;Oct2011, Vol. 18 Issue 10, p102313 

    The propagation of ion acoustic waves (IAWs) in plasmas composed of ions and nonextensive electrons and positrons is investigated. By means of the reduction perturbation technique, a nonlinear Schrödinger equation is derived and the modulation instability (MI) of ion acoustic waves is...

  • Asymptotic growth in the linear Richtmyer--Meshkov instability. Wouchuk, Juan Gustavo; Nishihara, Katsunobu // Physics of Plasmas;Apr97, Vol. 4 Issue 4, p1028 

    Presents an analytic model for the asymptotic growth in the linear Richtmyer-Meshkov instability. Formulation of an analytical formula for interface velocity; Role of the bulk vorticity in lowering the velocity predicted by the irrotational approximation; Consideration of perturbation...

  • Influence of profile shape on the diocotron instability in a non-neutral plasma column. Davidson, Ronald C.; Felice, Gian Marco // Physics of Plasmas;Oct98, Vol. 5 Issue 10, p3497 

    Examines the influence of density profile shape on the diocotron instability in a cylindrical electron plasma column. Confinement of the column radially by a uniform axial magnetic field; Assumption of electrostatic flute perturbations for axisymmetric equilibrium density profile analysis;...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics