arXiv subjects

Sanjeev Kumar Pandey

Publications and source records attributed to Sanjeev Kumar Pandey.

11 recordsLinked to original sources

arXiv2026

Dynamics of phase space vortices in Vlasov plasmas with ion scale inhomogeneity : I Constant frequency drive study

Formation dynamics and stability starting from various phase space vortex (PSV) or Bernstein-Greene-Kruskal (BGK) structures i.e electron acoustic wave (EAW), Langmuir (LAN) waves is investigated in the presence of a quasi-stationary ion scale (QSIS) inhomogeneity using high resolution Vlasov-Poisson simulations with VPPM-OMP 1.0 solver. In a one dimensional, collisionless, periodic, unmagnetized plasma with kinetic ions and kinetic electrons, we first create a QSIS inhomogeneity using low amplitude electric field drive at ion acoustic (IA) frequency with k eq = mk min [where m = 2 is the mode number, k min corresponds to the longest scale in the system]. While creating QSIS inhomogeneity, we have demonstrated the existence of ion trapped particle instability (ITPI) which saturates as the amplitude of sideband modes become comparable to that of the primary nonlinear mode (quite analogous to the trapped particle instability in large amplitude electron plasma waves). Also, mode transition from m = 2 to m = 1 is observed during relaxation period due to the energy cascading process. Finally, an electron acoustic (EA) perturbation of scale k p = k min [m = 1] is applied on top of the QSIS inhomogeneity to determine its response in the presence of background ion scale inhomogeneity. Some key observations such as formation of transient PSV, wave-wave mode coupling interaction and various frequency generation alongwith comparative investigation with EA perturbation launched in the absence of ion scale inhomogeneity is also reported.

physics.plasm-ph↗

arXiv2026

Dynamics of phase space vortices in Vlasov plasmas with ion scale inhomogeneity : II Chirped frequency drive study

In Part I of the companion paper [Ref Part I], we have extensively discussed about the creation of quasi-stationary ion scale (QSIS) inhomogeneity using a constant frequency external drive at ion-acoustic time scales, resulting in ion trapped particle instability (ITPI), wave-wave mode coupling interaction and energy cascading. QSIS thus formed is perturbed by applying small amplitude electron acoustic (EA) mode leading to the several key plasma response features. In this Part II, using electrostatic, unbounded, OpenMP Vlasov-Poisson solver i.e VPPM-OMP 1.0, we have investigated the formation of various phase space vortices (PSV) (generated using two step or one step time dependent downward frequency chirping drives) in the presence of background QSIS inhomogeneity obtained in Part I. In addition, we have also performed one to one comparison of individual cases with their homogeneous counterparts with exact simulation parameters. In presence of QSIS inhomogeneity, we have observed interesting phenomenon such as early onset of Langmuir (LAN) mode, suppression of PSV sizes, omission of PSVs when compared to the homogeneous cases. Also, for different two step or one step downward chirp perturbation cases, particle trapping or untrapping fractions and its response to the increasing chirp intervals are respectively reported.

physics.plasm-ph↗

arXiv2026

Thermal Effects on Buneman Instability: A Vlasov-Poisson Study

Buneman instability has been extensively studied, and related aspects, namely anomalous resistivity, have been explored in detail using analytical theory as well as numerical simulations based on Particle-in-Cell and Vlasov solvers. Most numerical studies have focused on understanding the nonlinear evolution of the instability. In the present study, the growth rate of the Buneman instability in the presence of thermal effects of the constituent species (i.e., ions and electrons) is investigated. It is observed that the growth rate differs significantly from that obtained using fluid models (both cold and warm) as well as from linearized kinetic models. While the well-known result of $(m/M)^{1/3}$ dependence of the maximum growth rate is recovered, it is shown that the maximum growth rate is essentially independent of the temperature ratio of the constituent species. It is further demonstrated numerically that the amplitude of ion density inhomogeneity self-consistently controls the transfer of electron beam energy into the bulk plasma temperature. In particular, as one moves from the cold to the warm plasma limit, the decrease in ion density inhomogeneity reduces the generation of sidebands and thus lowers the transfer efficiency.

physics.plasm-ph↗

arXiv2025

Multiphysics Simulation and First Prototype Development of a Microwave Plasma System for Chemical Vapour Deposition (CVD) Applications

With the aid of COMSOL multiphysics simulations, a compact microwave plasma reactor operated at 2.45 GHz frequency has been designed for diamond film deposition. The reactor consists of a cylindrical cavity that resonates in the fundamental mode $TM_{01p}$ with a longitudinal field variation (p = 1). Investigations on microwave electric field and hydrogen $(H_{2})$ plasma characteristics inside the microwave plasma cavity have been carried out, which assisted in the resonant cavity optimizations. The new reactor design includes a unique antenna structure which facilitates better thermal management and gas inlet arrangement. Parametric analysis of the effect of increase in microwave power, gas pressure and synergistic effects of power and pressure variations on the $H_{2}$ plasma characteristics such as electron density, gas temperature, and atomic hydrogen density have been performed computationally to estimate the optimize reactor operating conditions. Observations from our simulations indicate that the cavity design is able to operate within a range of microwave power and gas pressure upto $P_{in}=6$ kW and $p_{0}=30$ kPa respectively. Preliminary experimental validation which includes vacuum integrity and $H_{2}$ plasma ignition tests inside the cavity are also reported.

physics.plasm-ph↗

arXiv2024

Dualizing involutions on the $n$-fold metaplectic cover of $\GL(2)$

Let $F$ be a non-Archimedean local field of characteristic zero and $G=\GL(2,F)$. Let $n\geq 2$ be a positive integer and $\widetilde{G}=\widetilde{\GL}(2,F)$ be the $n$-fold metaplectic cover of $G$. Let $\pi$ be an irreducible smooth representation of $G$ and $\pi^{\vee}$ be the contragredient of $\pi$. Let $\tau$ be an involutive anti-automorphism of $G$ satisfying $\pi^{\tau}\simeq \pi^{\vee}$. In this case, we say that $\tau$ is a dualizing involution. A well known theorem of Gelfand and Kazhdan says that the standard involution $\tau$ on $G$ is a dualizing involution. In this paper, we show that any lift of the standard involution to $\widetilde{G}$ is a dualizing involution if and only if $n=2$.

math.RT↗

arXiv2024

Demonstrating Remote Synchronization: An Experimental Approach with Nonlinear Oscillators

This study investigates remote synchronization in arbitrary network clusters of coupled nonlinear oscillators, a phenomenon inspired by neural synchronization in the brain. Employing a multi-faceted approach encompassing analytical, numerical, and experimental methodologies, we leverage the Master Stability Function (MSF) to analyze network stability. We provide experimental evidence of remote synchronization between two clusters of nonlinear oscillators, where oscillators within each cluster are also remotely connected. This observation parallels the thalamus-mediated synchronization of neuronal populations in the brain. An electronic circuit testbed, supported by nonlinear ODE modeling and LT Spice simulation, was developed to validate our theoretical predictions. Future work will extend this investigation to encompass diverse network topologies and explore potential applications in neuroscience, communication networks, and power systems.

eess.SY↗

arXiv2024

Experimental Demonstration of Remote Synchronization in Coupled Nonlinear Oscillator

This study investigates remote synchronization in scale-free networks of coupled nonlinear oscillators inspired by synchronization observed in the brain's cortical regions and power grid. We employ the Master Stability Function (MSF) approach to analyze network stability across various oscillator models. Synchronization results are obtained for a star network using linearization techniques and extended to arbitrary networks with benchmark oscillators, verifying consistent behavior. Stable synchronous solutions emerge as the Floquet multiplier decreases and the MSF becomes negative. Additionally, we demonstrate remote synchronization in a star network, where peripheral oscillators communicate exclusively through a central hub, drawing parallels to neuronal synchronization in the brain. Experimental validation is achieved through an electronic circuit testbed, supported by nonlinear ODE modeling and LTspice simulation. Future work will extend the investigation to arbitrary network topologies, further elucidating synchronization dynamics in complex systems.

eess.SY↗

arXiv2024

Interaction of driven "cold" electron plasma wave with thermal bulk mediated by spatial ion inhomogeneity

Using high resolution Vlasov - Poisson simulations, evolution of driven ``cold" electron plasma wave (EPW) in the presence of stationary inhomogeneous background of ions is studied. Mode coupling dynamics between ``cold'' EPW with phase velocity $v_ϕ$ greater than thermal velocity i.e $v_ϕ \gg v_{thermal}$ and its inhomogeneity induced sidebands is illustrated as an initial value problem. In driven cases, formation of BGK like phase space structures corresponding to sideband modes due to energy exchange from primary mode to bulk particles via wave-wave and wave-particle interactions leading to particle trapping is demonstrated for inhomogeneous plasma. Qualitative comparison studies between initial value perturbation and driven problem is presented, which examines the relative difference in energy transfer time between the interacting modes. Effect of variation in background ion inhomogeneity amplitude as well as ion inhomogeneity scale length on the driven EPWs is reported.

physics.plasm-ph↗

arXiv2024

A Necessary and Sufficient Condition for Local Synchronization in Nonlinear Oscillator Networks

Determining conditions on the coupling strength for the synchronization in networks of interconnected oscillators is a challenging problem in nonlinear dynamics. While sophisticated mathematical methods have been used to derive conditions, these conditions are usually only sufficient and/ or based on numerical methods. We addressed the gap between the sufficient coupling strength and numerically observations using the Lyapunov-Floquet Theory and the Master Stability Function framework. We showed that a positive coupling strength is a necessary and sufficient condition for local synchronization in a network of identical oscillators coupled linearly and in full state fashion. For partial state coupling, we showed that a positive coupling constant results in an asymptotic contraction of the trajectories in the state space, which results in synchronisation for two-dimensional oscillators. We extended the results to networks with non-identical coupling over directed graphs and showed that positive coupling constants is a sufficient condition for synchronisation. These theoretical results are validated using numerical simulations and experimental implementations. Our results contribute to bridging the gap between the theoretically derived sufficient coupling strengths and the numerically observed ones.

eess.SY↗

arXiv2024

Structure of Twisted Jacquet Modules of principal series representations of $Sp_{4}(F)$

Let $F$ be a non-archimedean local field. For the symplectic group $Sp_{4}(F),$ let $P$ and $Q$ denote respectively its Siegel and Klingen parabolic subgroups with respective Levi decompositions $P=MN$ and $Q=LU.$ For a non-trivial character $ψ$ of the unipotent radical $N$ of $P,$ let $M_ψ$ denote the stabilizer of the character $ψ$ in $M$ under the conjugation action of $M$ on characters of $N.$ For an irreducible representation of the Levi subgroups $M$ or $L,$ let $π$ denote the respective representation of $Sp_{4}(F)$ parabolically induced either from $P$ or from $Q.$ Let $ψ$ be a character of the group $N$ given by a rank one quadratic form. In this article, we determine the structure of the twisted Jacquet module $r_{N,ψ}(π)$ as an $M_ψ$-module. We also deduce the analogous results in the case where $F$ is a finite field of order $q.$

math.RT↗

arXiv2022

Coupling of "cold" electron plasma wave via stationary ion inhomogeneity to the plasma bulk

Using high resolution kinetic (VPPM-OMP 1.0) and fluid (BOUT++) solvers, evolution of long-wavelength electron plasma wave (EPW) in the presence of stationary periodic ion background non-uniformity is investigated. Mode coupling dynamics between long-wavelength EPW mode of scale k and ion inhomogeneity of scale $k_{0}$ is illustrated. Validity of well known Bessel function $J_{n}(x)$ scaling in the cold plasma approximation (i.e., when phase velocity $ω/k >> v_{thermal}$) along-with the effect of ion inhomogeneity amplitude (A) on temporal evolution of energy density in the long-wavelength EPW mode is investigated. Effect of finite system sizes on the Bessel $J_{n}(x)$ scaling is examined and scaling law for $τ_{FM}$ i.e the time required to attain first minimum of energy density of the corresponding perturbed mode (also called phase mixing time for $k \sim 0$ modes) versus ion inhomogeneity amplitude A obtained from both kinetic and fluid solutions for each of the cases studied, along-with some major differences in $τ_{FM}$ scaling for small system sizes is also reported.

physics.plasm-ph↗