Swarniv Chandra

We investigate the formation and evolution of nonlinear electrostatic structures in a collisionless, unmagnetized plasma comprising Cairns-Gurevich distributed electrons, accounting for both energetic populations and trapped particles. Utilizing the reductive perturbation technique (RPT), a nonplanar Schamel-type evolution equation is derived and analytically solved via the weighted residual method (WRM). To validate and extend the analytical insights, numerical simulations are performed in planar, cylindrical, and spherical geometries using the newly developed FORKET simulation code. The study also incorporates real-space observational data from the MMS-1 spacecraft on 2 November 2024, where precise ephemeris information facilitated modeling of plasma dynamics in the outer magnetosphere under realistic conditions. The spatiotemporal behavior of solitons is analyzed in relation to physical parameters such as the nonthermal and trapping factors, as well as initial wave speeds. The results demonstrate significant differences in soliton profiles between planar and nonplanar geometries, with important implications for understanding plasma behavior in both space environments and laboratory settings where electron trapping is significant.

The solar storms of May 2024 represented one of the most significant space weather events of the 21st century, producing multiple X-class solar flares, a rare "cannibal" coronal mass ejection (CME), and G5-class geomagnetic storms that rivaled historical events like the Halloween Storms of 2003. This comprehensive analysis examines the underlying physics, technological impacts, societal consequences, and historical context of these extraordinary solar phenomena, while exploring their implications for our increasingly technology-dependent civilization.

In this article, we consider a dense astrophysical plasma consisting of predominantly electrons, positrons, and ions under the action of the magnetic field of a star or planet. We have derived the Korteweg-de Vries-Burgers (KdV)-Burgers equations using the Poincaré-Lighthill-Kuo (PLK) method and obtained shock and solitary wave solutions for magnetoacoustic waves. We have further studied the mutual interaction of such stationary formations and the breakdown mechanism. The possibility of a rogue wave-like structure is also discussed. We have used a newly designed code to study the time evolution of wave–wave interaction and the breakdown mechanism. The results will be helpful to interpret magnetoacoustic wave formations in solar corona, or other stellar entities and can help in understanding the study of inhomogeneous plasmas in laboratory and fusion reactors.

We have examined collisional degenerate plasma composed of charged state of heavy positive ion and light positive as well as negative ion. Employing the reductive perturbation method, we derived the damped Korteweg-de Vries-Burgers (dKdV-B) equation and by using its standard solution we analyze the characteristics of the solitary-shock profile under varying parameters. Furthermore, with the application of planar dynamical systems bifurcation theory, the phase portraits have been analyzed. This dynamical system analysis allowed us to extract important information on the stability of these structures as represented by the dKdV-B equation.

The study explores a model called Relativistic Degenerate Magneto-Rotating Quantum Plasma (RDMRQP), which comprises a static heavy nucleus, an inertial non-degenerate light nucleus, and warm non-relativistic or ultra-relativistic electrons. The focus is on observing the emergence of Nucleus-Acoustic Envelope Solitons (NAESs). Using the reductive perturbation method, a Nonlinear Schrödinger equation (NLSE) is derived to characterize the properties of NAESs. We have analysed the Peregrine breather soliton solution. The investigation reveals that the temperature of warm degenerate species, plasma system’s rotational speed, and the presence of heavy nucleus species can alter the fundamental features (height and width) of NAESs in the WDMRQP system. The study emphasizes the existence of only positive NA wave potential. Additionally, a phase plane analysis is conducted to gain a deeper understanding of the parametric dependencies. Through detailed mathematical and numerical analysis, the study avoids overloading with complex mathematics while demonstrating parametric dependence via phase portrait analysis. The research augments the envelop soliton model with breather mode solutions and discusses modulation instability using the Benjamin-Feir Index, highlighting the significance of solitons in star formation. Envelop solitons, stable waves within stars and proto-stars, influence energy transport and stellar evolution, playing a crucial role in the accretion process and formation of stable structures. Key findings include the effects of various parameters on NAESs’ generation and propagation in which non-relativistic and ultra-relativistic electrons support NAESs, with amplitude and width influenced by temperature, rotational frequency, inclination angle, and the presence of a static heavy nucleus. The research is applicable to hot white dwarfs and neutron stars, suggesting further exploration of quantum effects and non-planar or arbitrary amplitude NAESs.

The dust-ion collisional effect is investigated for dust ion acoustic waves (DIAWs) in the spherical and cylindrical geometry. Using the reductive perturbation technique (RPT), the evolution equation is derived with an additional damping term. An approximate analytical time-dependent solitary wave solution is obtained for the evolution equation in nonplaner geometry. It is seen that dust ion collisional frequency plays an important role in the existence region of the solitary wave structure in the nonplanar geometry. It is also seen that dust-ion collisional frequency and spectral index $\kappa$ have a significant role in the amplitude and width of the solitary wave. Additionally, we have numerically investigated the parametric influence on the solitonic evolution mechanism which will help understand the process better.