Effect of Ion Temperature Anisotropy on Modulated Electrostatic Waves and Envelope Solitons in a Magnetized Plasma

Abstract

The modulational instability (MI) of electrostatic waves, i.e., slow and fast electrostatic modes, is investigated in a magnetized plasma in the presence ion pressure anisotropy. The anisotropic ion pressure is defined using the double adiabatic Chew–Goldberger–Low (CGL) theory. The nonlinear Schrödinger equation (NLSE) is derived to study the amplitude modulation of obliquely propagating electrostatic waves in a magnetized plasma using the Krylov-Bogoliubov–Mitropolsky (KBM) method. The dispersive and nonlinear coefficients, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> , respectively, of NLSE are obtained which depends on system parameters such as plasma density, the magnetic field intensity, wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> , and ion parallel and perpendicular temperatures (anisotropy effects), respectively. The modulationally unstable regions ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PQ&gt;0$ </tex-math></inline-formula> ) of modulated slow [or ion-acoustic wave (IAW)] and fast [or ion-cyclotron wave (ICW)] electrostatic modes are investigated numerically in a magnetized plasma with ion temperature anisotropy, and the contour plots of product <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$PQ&gt;0$ </tex-math></inline-formula> with wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> and critical wave numbers are also presented. It is found that the unstable regions for modulated IAW and ICW are extended to large wave propagation angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> and its corresponding critical wave numbers in the presence of ion temperature anisotropy in comparison to cold ions’ case. The existence of magnetized plasma with ion pressure anisotropy in different space plasma regions and in the laboratory experiments is also pointed out.