arXiv subjects

Deepak Gautam

Publications and source records attributed to Deepak Gautam.

3 recordsLinked to original sources

arXiv2026

Multigrid Poisson Solver for Complex Geometries Using Finite Difference Method

We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational domain through coordinate transformations, which can be applied either to the entire domain or selectively to specific boundaries inside the domain. This flexibility allows both homogeneous (Laplace equation) and inhomogeneous (Poisson equation) problems to be solved efficiently using iterative or fast direct solvers, with only the material parameters and source terms modified according to the transformation. The method is formulated within a finite difference framework, where the modified material properties are computed from the coordinate transformation equations, either analytically or numerically. This enables accurate treatment of arbitrary geometric shapes while retaining the simplicity of a uniform grid solver. Numerical experiments confirm that the method achieves second-order accuracy , and offers a straightforward pathway to integrate fast solvers such as multigrid methods on the uniform computational grid.

math.NA↗

arXiv2025

Resonantly Driven Electron Bernstein Waves in Magnetized Low-Pressure Capacitive Discharges

The physics of capacitively coupled plasma (CCP) discharges is investigated in a mildly magnetized regime, defined by $1 \le f_{ce}/f_{rf} < 2$, where $f_{ce}$ and $f_{rf}$ denote the electron cyclotron frequency and the applied radio-frequency (RF), respectively. A distinctive feature of this regime is the excitation of electron Bernstein waves (EBWs) that propagate into the bulk plasma. As the applied magnetic field increases, notable changes in the discharge characteristics occur, with EBWs observed to propagate along the plasma density gradient inside the bulk. The underlying physics of CCP operation in this regime is analyzed in detail using particle-in-cell Monte Carlo collisions (PIC-MCC) simulations.

physics.plasm-ph↗

arXiv2025

Simulation Studies of Resonant Excitation of Electron Bernstein Waves in Capacitive Discharges

The behavior of capacitive coupled plasma (CCP) discharges is investigated in a mildly magnetized regime, defined by the condition 1 $\leq$ $f_{ce}/f_{rf}$ $\lt$ 2, where $f_{ce}$ and $f_{rf}$ are the cyclotron and radio-frequencies (RF), respectively. This regime exhibits complex and distinctive plasma dynamics due to the interplay between RF fields and the externally applied magnetic field. Two prominent phenomena are observed in this regime. First, the plasma density profile becomes asymmetric across the discharge, deviating from the typical symmetric distribution seen in unmagnetized CCPs. Second, electron Bernstein waves (EBWs), high-frequency electrostatic waves, are excited and propagate within the bulk plasma, particularly along steep electron density gradients. As the strength of the magnetic field increases within this regime, the CCP discharge undergoes a transition from a symmetric configuration to an asymmetric one, and then returns to a symmetric profile at higher field strengths. Notably, the excitation and propagation of EBWs are strongly correlated with the presence of discharge asymmetry and localized density gradients. These waves play a significant role in energy transport and electron heating under mildly magnetized conditions. To gain deeper insight into the underlying physics, detailed numerical simulations are carried out using the particle-in-cell Monte Carlo collision (PIC-MCC) technique. These simulations capture the kinetic behavior of electrons and ions, including the collisionless effects and sheath dynamics essential to understanding the excitation of EBWs and the evolution of discharge symmetry. The study thus sheds light on the role of weak magnetic fields in shaping plasma behavior and highlights the importance of wave-particle interactions in magnetized CCPs.

physics.plasm-ph↗