TY - JOUR
T1 - Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model
AU - Lazarides, N.
AU - Kourakis, Ioannis
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2024/2
Y1 - 2024/2
N2 - The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ -distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schrödinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1 , k2) and of the spectral index κ characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ values, leads to enhance MI of the interacting wave pair. To the best of our knowledge, the dynamics of two co-propagating wavepackets in a plasma described by a fluid model with κ -distributed electrons is investigated thoroughly with respect to their MI properties as a function of κ for the first time, in the framework of an asymmetric CNLS system whose coefficients present no obvious symmetries for arbitrary k1 and k2 . Although we have focused on electrostatic wavepacket propagation in non-thermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where MI is relevant.
AB - The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ -distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schrödinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1 , k2) and of the spectral index κ characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ values, leads to enhance MI of the interacting wave pair. To the best of our knowledge, the dynamics of two co-propagating wavepackets in a plasma described by a fluid model with κ -distributed electrons is investigated thoroughly with respect to their MI properties as a function of κ for the first time, in the framework of an asymmetric CNLS system whose coefficients present no obvious symmetries for arbitrary k1 and k2 . Although we have focused on electrostatic wavepacket propagation in non-thermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where MI is relevant.
KW - Coupled nonlinear Schrödinger equations
KW - Kappa distribution
KW - Modulational instability
KW - Multiscale perturbative reduction
KW - Plasma fluid model
UR - http://www.scopus.com/inward/record.url?scp=85167330587&partnerID=8YFLogxK
U2 - 10.1007/s11071-023-09165-4
DO - 10.1007/s11071-023-09165-4
M3 - Article
AN - SCOPUS:85167330587
SN - 0924-090X
VL - 112
SP - 2795
EP - 2819
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 4
ER -