A new class of Ion-acoustic solitons that can exist below critical Mach number

Abstract

It is commonly believed that ion-acoustic solitons can only exist above the critical Mach number in a plasma system. A new class of ion-acoustic solitons that can exist below the critical Mach number is reported for the first time in a three-component plasma consisting of hot Maxwellian electrons, and two counterstreaming ion beams. The analysis is based on the Sagdeev pseudopotential technique, and considers a simple case of two counterstreaming proton beams with equal density and streaming velocity. Linear stability analysis shows that the slow ion-acoustic modes become unstable due to ion beam instability when the beam velocity normalized with the ion acoustic speed, U0, is in the range of 0.55 ≤ U0 ≤ 1.14. It is shown that when the normalized streaming velocity is below or at a threshold value, Uth = 1.14, only the regular solitons having Mach numbers greater than critical Mach number can exist. However, when the streaming velocity exceeds the threshold value (all modes are stable), both regular and the new class of ion-acoustic solitons can exist. A special case of unequal ion densities and unequal streaming velocities of the counterstreaming beams is considered in , and similar effects are found. Hence, the new class of slow ion-acoustic solitons can exist in the parametric regime where the system is stable to counterstreaming ion beams instability. The results could be useful in the interpretation of slow electrostatic solitary waves (ESWs) observed in the magnetosphere.

On the Existence of Subsonic Solitary Waves Associated with Reconnection Jets in Earth’s Magnetotail

“…The existence of fast and slow ion-acoustic modes has been established in multi-warm ion plasma models based on linear wave theory, followed by fascinating nonlinear analyses of plasmas permeated by two counterstreaming ion beams (Lakhina et al 2020;Verheest & Hellberg 2021). Recent plasma studies, adopting a plasma-fluid formalism, have revealed that beam-permeated plasmas may not only support the conventional supersonic (superacoustic) electrostatic structures (solitary waves, SWs) but also a subsonic (subacoustic) ion-acoustic nonlinear mode propagating at a speed below the sound speed but above a certain Mach number threshold (M min ; Lakhina et al 2020;Verheest & Hellberg 2021). Interestingly, Papadopoulos et al (1971) studied the heating of counterpropagating ion beams propagating across an ambient field, based on linear theory in combination with computer simulations.…”

“…A plasma-fluid model consisting of two hot counterstreaming ion beams and Maxwellian electrons was adopted by Lakhina et al (2021Lakhina et al ( , 2020, who were the first to show that SWs may exist below critical Mach number, provided that certain conditions are met. Verheest & Hellberg (2021) subsequently revisited the same model by neglecting thermal ion effects and pinpointed the crucial role played by the beam speed(s)-rather than thermal effects-in subsonic solitary wave formation.…”

“…However, slow (subacoustic) solitary waves were reportedly detected in satellite observations, and a theoretical framework for these was so far lacking in the literature. Our work was based on the surprising, and arguably pioneering, recent prediction furnished by Lakhina et al (2021Lakhina et al ( , 2020, and later refined by Verheest & Hellberg (2021), that subsonic electrostatic soliton may, in fact, exist in a beam-permeated plasma.…”

Electrostatic Solitary Waves in the Venusian Ionosphere Pervaded by the Solar Wind: A Theoretical Perspective

“…As the background electrons follow Maxwellian distribution, their number density in the presence of electrostatic waves with potential, f is given as (Lakhina et al 2014(Lakhina et al , 2020)…”

“…Equation (7) represents the motion of a pseudoparticle of unit mass in a pseudopotential, S(f,M), with f and ξ, respectively depicting pseudo-displacement from the equilibrium and pseudo-time (Lakhina et al 2009;Rubia et al 2017;Lakhina et al 2020). The Sagdeev pseudopotential, S(f,M), is given by Equation ( 8) is represented in an allegorical form where the operation of a square root on a squared expression results in the same expression, e.g., ( )…”