Ion-acoustic cnoidal wave and associated non-linear ion flux in dusty plasma

Abstract

Using reductive perturbation method with appropriate boundary conditions, coupled evolution equations for first and second order potentials are derived for ion-acoustic waves in a collisionless, un-magnetized plasma consisting of hot isothermal electrons, cold ions, and massive mobile charged dust grains. The boundary conditions give rise to renormalization term, which enable us to eliminate secular contribution in higher order terms. Determining the non secular solution of these coupled equations, expressions for wave phase velocity and averaged non-linear ion flux associated with ion-acoustic cnoidal wave are obtained. Variation of the wave phase velocity and averaged non-linear ion flux as a function of modulus (k2) dependent wave amplitude are numerically examined for different values of dust concentration, charge on dust grains, and mass ratio of dust grains with plasma ions. It is found that for a given amplitude, the presence of positively (negatively) charged dust grains in plasma decreases (increases) the wave phase velocity. This behavior is more pronounced with increase in dust concentrations or increase in charge on dust grains or decrease in mass ratio of dust grains. The averaged non-linear ion flux associated with wave is positive (negative) for negatively (positively) charged dust grains in the plasma and increases (decreases) with modulus (k2) dependent wave amplitude. For given amplitude, it increases (decreases) as dust concentration or charge of negatively (positively) charged dust grains increases in the plasma.

The separation of ions and fluxes in nonlinear ion-acoustic waves

“…A similar dependence of the sign of the nonlinear wave-induced ion flux on the wave amplitude was obtained in Ref. 4, while in Ref. 3 the flux was found to be always positive.…”

“…Periodic stationary cnoidal ion-acoustic waves in a collisionless electron-ion plasma (ei-plasma) with cold ions are well known to carry a non-zero ion flux averaged over the wave period 1 . In the follow up works 2-6, cnoidal ionacoustic waves were considered for other models of collisionless plasma, and average ion fluxes associated with the wave were calculated: in an ei-plasma with warm ions 2 , and in a dusty eid-plasma with warm and cold ions [3][4][5][6] . The presence of ion fluxes in electrostatic waves implies not only the transport of ions along the direction of the wave propagation, but also the induction of the ion flux-caused magnetic field.…”

Experimental observation of cnoidal waveform of nonlinear dust acoustic waves

“…This has been predicted theoretically for nonlinear waves in various physical systems [34][35][36][37][38][39]. Theories have also been developed specifically for dusty plasmas [40][41][42][43][44][45][46], under various assumptions, predicting cnoidal solutions for nonlinear waves. For example, Yadav et al [40,41] derived a theory predicting a cnoidal solution for dust acoustic waves under an assumption that included Boltzmann electrons and ions and cold dust with fluctuating charges.…”

Effect of Pressure Anisotropy on Nonlinear Periodic Waves in a Magnetized Superthermal Electron-Positron-Ion Plasma

“…The propagation of compressive ion-acoustic cnoidal waves in dusty plasma has been studied in Ref [11]. The effects of critical dust density have been highlighted in the work of Prudskikh [11], which is extended by Jain et al, considering the nonlinear ion flux with the associated periodic waves [12]. The ion-acoustic, dust-ion-acoustic solitary waves, and periodic waves were studied in nonthermal electronpositron-ion plasma [13][14][15][16].…”