arXiv subjects

Sudip Sengupta

Publications and source records attributed to Sudip Sengupta.

At least 19 recordsLinked to original sources

arXiv2026

Revisiting Electron Heating in Capacitively Coupled Plasma (CCP) Discharges: A Nonlinear Dynamics Perspective

Despite decades of research, the electron heating mechanisms in capacitively coupled plasma (CCP) discharges over a wide range of operating conditions is not fully understood. Although stochastic heating is generally regarded as the dominant collisionless heating mechanism at low pressures, the inherently nonlinear electron dynamics responsible for this process have not been fully quantified. These nonlinear interactions drive stochastic heating, a mechanism considered crucial for energy transfer in CCPs, yet its quantitative impact on plasma parameters remains insufficiently explored. In this work, we investigate electron dynamics in steady-state CCP discharges and demonstrate that electron motion in the plasma bulk exhibits intrinsically chaotic behavior. The onset of chaos is identified using Poincare sections and quantified through Lyapunov exponent analysis. To further quantify this behavior, we map the spatial distribution of the Lyapunov exponent-normalized by the electron-neutral collision frequency-across the plasma bulk for different pressures and RF voltages. The normalized Lyapunov exponent increases systematically with decreasing pressure and increasing RF voltage, indicating enhanced stochasticity and a stronger sensitivity of electron trajectories to initial conditions. These results establish the Lyapunov exponent as a quantitative measure of effective stochastic scattering in collisionless CCPs and provide a direct comparison with the classical stochastic collision frequency proposed by Popov and Godyak [Journal of Applied Physics 57, 53-58 (1985)]. The present analysis offers a unified nonlinear dynamical framework for understanding stochastic electron heating in low-pressure RF plasmas.

physics.plasm-ph↗

arXiv2026

Collisionless Bulk Electron Heating in Resonant Low-Voltage Capacitively Coupled Plasmas

We investigate collisionless power absorption in resonant, low$-$pressure capacitively coupled plasmas (CCPs). In these radio-frequency (RF) discharges, the sheath capacitance almost exactly balances the plasma inductance, driving the total RF discharge voltage down to just a few volts. However, plasma persists not only in this ultra$-$low$-$voltage regime; it also generates ions that strike the electrodes with kinetic energies substantially exceeding the amplitude of the applied RF voltage. This counterintuitive behavior arises from the presence of a pronounced electrostatic potential well of approximately 40 V within the plasma bulk, which confines electrons while simultaneously accelerating ions toward the electrodes. We show that, under these resonant conditions, collisionless electron heating exhibits a fundamentally different behavior from the conventional paradigm of stochastic sheath heating mediated by electron$-$sheath interactions. Instead, the predominant energy transfer mechanism is bulk electron heating in RF electric fields via a primarily collisionless process that emerges from the synergistic action of: (i) a strongly amplified RF electric field within the plasma bulk, (ii) electron oscillatory motion (bouncing) within the plasma potential well, and (iii) electron scattering resulting from collisions with neutral atoms. Collectively, these phenomena give rise to a pronounced high$-$energy tail in the electron energy distribution function and thereby lead to a substantial enhancement of the ionization rates. As the gas pressure rises, the resonance is disrupted. At the same time, the region of maximum power absorption moves from the plasma core toward the edges and the sheath, which is accompanied by the disappearance of the high$-$energy electron population and a corresponding decrease in ionization rates

physics.plasm-ph↗

arXiv2024

Sheet model description of spatio-temporal evolution of upper-hybrid oscillations in an inhomogeneous magnetic field

Spatio-temporal evolution of large amplitude upper hybrid oscillations in a cold homogeneous plasma in the presence of an inhomogeneous magnetic field is studied analytically and numerically using the Dawson sheet model. It is observed that the inhomogeneity in magnetic field which causes the upper hybrid frequency to acquire a spatial dependence, results in phase mixing and subsequent breaking of the upper hybrid oscillations at arbitrarily low amplitudes. This result is in sharp contrast to the usual upper hybrid oscillations in a homogeneous magnetic field where the oscillations break within a fraction of a period when the amplitude exceeds a certain critical value. Our perturbative calculations show that the phase mixing (wave breaking) time scales inversely with the amplitude of magnetic field inhomogeneity ($Δ$) and amplitude of imposed density perturbation ($δ$), and scales directly with the ratio of magnetic field inhomogeneity scale length to imposed density perturbation scale length ($(α/k_L)^{-1}$ ) as $ω_{pe}τ_{mix} \sim \left( 1+β^2 \right) ^{3/2}k_L/(β^2δΔα)$, where $β$ is the ratio of electron cyclotron frequency to electron plasma frequency. Further phase mixing time measured in simulations, performed using a 1-1/2 D code based on Dawson sheet model, shows good agreement with the above mentioned scaling. This result may be of relevance to plasma based particle acceleration experiments in the presence of a transverse inhomogeneous magnetic field.

physics.plasm-ph↗

arXiv2023

Charged particle dynamics in an elliptically polarized electromagnetic wave and a uniform axial magnetic field

An analytical study of the charged particle dynamics in the presence of an elliptically polarized electromagnetic wave and a uniform axial magnetic field, is presented. It is found that for $gω_{0}/ ω' = \pm 1$, maximum energy gain occurs respectively for linear and circular polarization; $ω_{0}$ and $ω'$ respectively being the cyclotron frequency of the charged particle in the external magnetic field and Doppler-shifted frequency of the wave seen by the particle, and $g =\pm 1$ respectively correspond to left and right-handedness of the polarization. An explicit solution of the governing equation is presented in terms of particle position or laboratory time, for the specific case of resonant energy gain in a circularly polarized electromagnetic wave. These explicit position- or time-dependent expressions are useful for better insight into various phenomena, viz., cosmic ray generation, microwave generation, plasma heating, and particle acceleration, etc.

physics.plasm-ph↗

arXiv2022

Investigating the effects of electron bounce-cyclotron resonance on plasma dynamics in capacitive discharges operated in the presence of a weak transverse magnetic field

Recently, S Patil et al. have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio-frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their Particle-in-Cell (PIC) simulations show, that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied RF frequency for a given fixed voltage. In the present work we take a detailed look at this phenomenon and further delineate the effect of this "electron bounce cyclotron resonance (EBCR)" on the electron and ion dynamics of the system. We find that the ionization collision rate and stochastic heating is maximum under resonance condition. The electron energy distribution function also indicates that the population of tail end electrons is highest for the case where EBCR is maximum. Formation of electric field transients in the bulk plasma region are also seen at lower values of applied magnetic field. Finally, we demonstrate that the EBCR induced effect is a low pressure phenomenon and weakens as the neutral gas pressure increases. The potential utility of this effect to advance the operational performance of CCP devices for industrial purposes is discussed.

physics.plasm-ph↗

arXiv2021

Effect of radiation-reaction on charged particle dynamics in a focused electromagnetic wave

Effect of radiation-reaction force on the dynamics of a charged particle in an intense focused light wave is investigated using the physically appealing Hartemann-Luhmann equation of motion. It is found that, irrespective of the choice of initial conditions, radiation reaction force causes the charge particle to cross the focal region, thereby enhancing the forward energy gained by the particle from the intense light wave. This result is in sharp contrast to the well known result, derived in the absence of radiation reaction forces, where for certain initial conditions the particle reflects from the high intensity region of the focused light wave, thereby losing forward energy. These results, which are of relevance to the present day direct laser acceleration schemes of charge particle, also agrees with that obtained using the well known Landau-Lifshitz equation of motion.

physics.plasm-ph↗

arXiv2021

Excitation of Electrostatic Standing Wave in the Superposition of Two Counter Propagating Relativistic Whistler Waves

The problem of standing wave formation by superposing two counter-propagating whistler waves in an overdense plasma, studied recently by Sano et al. (Phys. Rev. E 100, 053205 (2019) and Phys. Rev. E 101, 013206 (2020)), has been revisited in the relativistic limit. A detailed theory along with simulation has been performed to study the standing wave formation in the interaction of two counter propagating relativistically intense whistler waves. The relativistic theory explains such interaction process more precisely and predicts correct field amplitudes of the standing wave for a much wider range of physical parameters of the problem as compared to its non-relativistic counterpart. The analytical results are compared with 1-D Particle-in-Cell (PIC) simulation results, performed using OSIRIS 4.0. The results are of relevance to ion heating and fast ignition scheme of inertial confinement fusion.

physics.plasm-ph↗

arXiv2021

Effect of Ion Motion on Breaking of Longitudinal Relativistically Strong Plasma Waves: Khachatryan mode revisited

Effect of ion motion on the spatio-temporal evolution of a relativistically strong space charge wave, is studied using a 1-D fluid simulation code. In our simulation, these waves are excited in the wake of a rigid electron beam propagating through a cold homogeneous plasma with a speed close to the speed of light. It is observed that the excited wave is a mode as described by Khachatryan [Phys. Rev. E 58, 7799 (1998)] whose profile gradually sharpens and the wave eventually breaks after several plasma periods exhibiting explosive behaviour. It is found that breaking occurs at amplitudes, which is far below the breaking limit analytically derived by Khachatryan [Phys. Rev. E 58, 7799 (1998)]. This phenomenon of wave breaking, at amplitudes well below the breaking limit, is understood in terms of phase mixing of the excited wave. It is further found that the phase mixing time (wave breaking time) scales inversely with the energy density of the wave.

physics.plasm-ph↗

arXiv2020

Exact Solution of Hartemann-Luhmann Equation of Motion for a Charged Particle interacting with an Intense Electromagnetic Wave/Pulse

We report an exact solution of the Hartemann-Luhmann equation of motion for a charged particle interacting with an intense electromagnetic wave/pulse. It is found that the radiation reaction force has a significant affect on the charged particle dynamics and the particle shows, on average, a net energy gain over a period of time. Further, using a MATHEMATICA based single particle code, the net energy gained by the particle is compared with that obtained using Landau-Lifshitz and Ford-O'connell equation of motion, for different polarizations of the electromagnetic wave. It is found that the average energy gain is independent of both the chosen model equation and polarization of the electromagnetic wave. Our results thus show, that the simpler and hence analytically tractable Hartemann-Luhmann equation of motion ( as compared to Landau-Lifshitz and Ford-O'connell equation of motion) is adequate for calculations of practical use (for e.g. energy calculation).

physics.plasm-ph↗

arXiv2020

An enhanced operating regime for high frequency capacitive discharges

We report the existence of an enhanced operating regime for a high-frequency, low-pressure capacitively coupled plasma (CCP) discharge in the presence of a weak magnetic field applied parallel to the electrodes. Our PIC-MCC simulations show that the plasma density and ion flux values exhibit a sharp peak when the electron cyclotron frequency equals half of the applied RF frequency. The physical mechanism responsible for this behaviour is traced to a synchronization between the oscillatory motion of the electrode sheath edge and the motion of a set of electrons reflected by this sheath. These electrons gain a substantial amount of energy that causes a concomitant higher ionisation leading to a peak in the ion flux. Our theoretical findings should be easy to verify experimentally in present day CCP devices and could provide useful guidelines for enhancing the operational performance of CCP devices in industrial applications.

physics.plasm-ph↗

arXiv2020

Wavebreaking amplitudes in warm, inhomogeneous plasmas revisited

The effect of electron temperature on the space-time evolution of nonlinear plasma oscillations in an inhomogeneous plasma is studied using a one-dimensional particle-in-cell (PIC) code. In contrast to the conventional wisdom, it is found that for an inhomogeneous plasma, there exists a critical value of electron temperature beyond which wave breaking does not occur. This novel result, which is of relevance to present day laser plasma experiments, has been explained on the basis of interplay between electron thermal pressure and background inhomogeneity.

physics.plasm-ph↗

arXiv2020

Wave Breaking limit in Arbitrary Mass Ratio Warm Plasmas

The maximum sustainable amplitude, so-called wave breaking limit, of a nonlinear plasma wave in arbitrary mass ratio warm plasmas is obtained in the non-relativistic regime. Using the method of Sagdeev potential a general wave breaking formula is derived by taking into account the dynamics of both the species having finite temperature. It is found, that the maximum amplitude of the plasma wave decreases monotonically with the increase in temperature and mildly increases with increase in mass ratio.

physics.plasm-ph↗

arXiv2020

Excitation of plasma wakefields by proton beam

A stationary wave solution is obtained for the proton driven plasma wake field accelerator (PDPWFA). The wake field excitation by trains of equidistant proton microbunches produced due to self modulational instability has been discussed. Also, considering the necessity of the external magnetic field to control focusing of the beam, studies on the effect of magnetic field on the wake field structures have been done.

physics.plasm-ph↗

arXiv2020

Excitation of plasma wakefields by intense ultra-relativistic proton beam

We report here an exact analytical travelling wave solution for nonlinear electron plasma wave excited by an intense ultra-relativistic proton beam. It brings out the underlying physics of longitudinal electric field characteristics of the excited wake wave formed behind the drive beam. The results are further supplemented by a fully relativistic particle in cell (PIC) code OSIRIS in 2D geometry. The plasma and beam parameters in the simulation are chosen in conformity with experimental work and it provides us the anticipated axial and transverse electric field profiles. The investigation is further extended by providing an analytical description of the wake wave excited by equi-spaced train of small proton bunches with the inclusion of the non-relativistic plasma ion dynamics. Our results show that the amplitude of the wake field does not grow indefinitely with the increase in the number of proton bunches. On the contrary, it saturates to a definitive limit.

physics.plasm-ph↗

arXiv2020

Excitation and breaking of relativistic electron beam driven longitudinal electron-ion modes in a cold plasma

The excitation and breaking of relativistically intense electron-ion modes in a cold plasma is studied using 1D-fluid simulation techniques. To excite the mode, we have used a relativistic rigid homogeneous electron beam propagating inside a plasma with a velocity close to the speed of light. It is observed that the wake wave excited by the electron beam is identical to the corresponding Khachatryan mode, a relativistic electron-ion mode in a cold plasma. It is also seen in the simulation that the numerical profile of the excited electron-ion mode gradually modifies with time and eventually breaks after several plasma periods exhibiting explosive behavior in the density profile. This is an well known phenomena, known as wave breaking. It is found that the numerical wave breaking limit of these modes lies much below than their analytical breaking limit. The discrepancy between the numerical and analytical wave breaking limit has been understood in terms of phase-mixing process of the mode. The phase mixing time (or wave breaking time) obtained from the simulations has also been scaled as a function of beam parameters and found to follow the analytical scaling.

physics.plasm-ph↗

arXiv2019

Effect of Transverse Beam Size on the Wakefields and Driver Beam Dynamics in Electron Beam Driven Plasma Wakefield Acceleration

In this paper, wakefields driven by a relativistic electron beam in a cold homogeneous plasma is studied using 2-D fluid simulation techniques. It has been shown that in the limit when the transverse size of a rigid beam is greater than the longitudinal extension, the wake wave acquires purely an electrostatic form and the simulation results show a good agreement with the 1-D results given by Ratan et al. [Phys. Plasmas, 22, 073109 (2015)]. In the other limit, when the transverse dimensions are equal or smaller than the longitudinal extension, the wake waves are electromagnetic in nature. Furthermore, a linear theoretical analysis of 2-D wakefields for a rigid bi-parabolic beam has also been done and compared with the simulations. It has also been shown that the transformer ratio which a key parameter that measures the efficiency in the process of acceleration, becomes higher for a 2-D system (i.e. for a beam having a smaller transverse extension compared to longitudinal length) than the 1-D system (beam having larger transverse extension compared to longitudinal length). Furthermore, including the self-consistent evolution of the driver beam in the simulation, we have seen that the beam propagating inside the plasma undergoes the transverse pinching which occurs much earlier than the longitudinal modification. Due to the presence of transverse dimensions in the system the 1-D rigidity limit given by Tsiklauri et al. [Phys. Plasmas, 25, 032114 (2018)] gets modified. We have also demonstrated the modified rigidity limit for the driver beam in a 2-D beam-plasma system.

physics.plasm-ph↗

arXiv2019

Stationary Bernstein-Greene-Kruskal structures in a current carrying relativistic cold plasma

Nonlinear stationary structures formed in a cold plasma with immobile ions in the presence of a relativistic electron current beam have been investigated analytically in the collisionless limit. These are cold plasma version of the relativistic Berstein-Greene-Kruskal (BGK) waves. The structure profile is governed by the ratio of maximum electrostatic field energy density to the relativistic kinetic energy density of the electron beam, {\it i.e.}, $κ_{R} = E_{m}/ (8 πn_{0} (γ_{0}-1)m_{0} c^{2})^{1/2}$, where $E_{m}$ is the maximum electric field associated with the nonlinear structure and $γ_{0}$ is the Lorentz factor associated with the beam velocity. It is found that, in the linear limit, {\it i.e.}, $κ_{R} \ll 1/\sqrt{γ_{0}}$, the fluid variables, {\it viz}, density, electric field, and velocity vary harmonically in space. In the range $0 < κ_{R} \leq 1/\sqrt{γ_{0}}$, the fluid variables exhibit an-harmonic behavior. For values of $κ_{R} > 1/\sqrt{γ_{0}}$, the electric field shows finite discontinuities at specific spatial locations indicating the formation of negatively charged planes at these locations.

physics.plasm-ph↗

arXiv2018

Nonlinear Dynamics of Relativistically Intense Cylindrical and Spherical Plasma Waves

Spatio-temporal evolution and breaking of relativistically intense cylindrical and spherical space charge oscillations in a homogeneous cold plasma is studied analytically and numerically using Dawson Sheet Model [J.M. Dawson, Phys. Rev.113, 383(1959)]. It is found that cylindrical and spherical space charge oscillations break via the process of phase mixing at an arbitrarily small amplitude due to anharmonicity introduced by geometry and relativistic mass variation effects. A general expression for phase mixing time (wave breaking time) has been derived and it is shown that for both cases, it scales inversely with the cube of the initial wave amplitude. Finally this analytically obtained scaling is verified by using a numerical code based on Dawson Sheet Model.

physics.plasm-ph↗