Sudip Sengupta

Nonlinear electron magnetohydrodynamic simulations of sausage-like instability of current channels

The stability of current channels to fast electron magnetohydrodynamic modes is a topic of great interest in several frontier areas of plasma research, e.g., fast ignitor concept of laser fusion, fast Z pinches, plasma opening switches, current channels at the center of fast magnetic reconnection region, etc. This paper deals with a detailed fluid simulation study of linear and nonlinear aspects of the velocity shear modes in electron current channels in a two dimensional geometry. Simulation results clearly show the development of sausage-like structures (kink structures, which are intrinsically three-dimensional excitations, are ruled out in the present simulations) which grow linearly and eventually saturate by nonlinear effects. An analytic understanding of the nonlinear saturation mechanism is also provided.

Stability of nonlinear one-dimensional laser pulse solitons in a plasma

In a recent one-dimensional numerical fluid simulation study [Saxena et al., Phys. Plasmas 13, 032309 (2006)], it was found that an instability is associated with a special class of one-dimensional nonlinear solutions for modulated light pulses coupled to electron plasma waves in a relativistic cold plasma model. It is shown here that the instability can be understood on the basis of the stimulated Raman scattering phenomenon and the occurrence of density bursts in the trailing edge of the modulated structures are a manifestation of an explosive instability arising from a nonlinear phase mixing mechanism.

Phase mixing/wave breaking studies of large amplitude oscillations in a cold homogeneous unmagnetized plasma

The subject of phase mixing/wave breaking serves as a useful paradigm to illustrate the physics of many plasma-based phenomena in the laboratory and astrophysical situations where nonlinear oscillations/waves are excited. Phase mixing leads to wave breaking and occurs whenever the characteristic frequency acquires a spatial dependence. In this paper, we review our investigations done in the area of phase mixing/wave breaking of large amplitude oscillation and waves in cold homogeneous unmagnetized plasma.

Nonlinear evolution of an arbitrary density perturbation in a cold homogeneous unmagnetized plasma

An exact and general analytical solution describing the nonlinear evolution of a large amplitude plasma oscillation initiated by an arbitrary density perturbation which can be expressed as a Fourier series in x is found. This general solution is first used to reproduce the earlier results of R. C. Davidson and P. P. Schram [Nucl. Fusion 8, 183 (1968)] and J. M. Dawson [Phys. Rev. 113, 383 (1959)] using appropriate initial conditions and later applied to derive the space time evolution for a square wave and a triangular wave. It is found that the addition of a second harmonic increases the wave breaking limit of the fundamental mode. Analytical results pertaining to this two mode case have been verified using one-dimensional particle-in-cell simulation.

Nonlinear lower-hybrid oscillations in cold plasma

In a fluid description nonlinear lower-hybrid oscillation have been studied in a cold quasineutral magnetized plasma using Lagrangian variables. An exact analytical solution with nontrivial space and time dependence is obtained. The solution demonstrates that under well defined initial and boundary conditions the amplitude of the oscillations increases due to nonlinearity and then comes back to its initial condition again. These solutions indicate a class of nonlinear transient structures in magnetized plasma.

Nonlinear interaction of electron plasma waves with electron acoustic waves in plasmas

An analysis of interaction between two temperature electron species in the presence of static neutralizing ion background is presented. It is shown that electron plasma waves can nonlinearly interact with electron acoustic wave in a time scale much longer than ωp−1, where ωp is electron plasma frequency. A set of coupled nonlinear differential equations is shown to exist in such a scenario. Propagating soliton solutions are demonstrated from these equations.

Particle-in-cell simulation of large amplitude ion-acoustic solitons

The propagation of large amplitude ion-acoustic solitons is studied in the laboratory frame (x, t) using a 1-D particle-in-cell code that evolves the ion dynamics by treating them as particles but assumes the electrons to follow the usual Boltzmann distribution. It is observed that for very low Mach numbers the simulation results closely match the Korteweg-de Vries soliton solutions, obtained in the wave frame, and which propagate without distortion. The collision of two such profiles is observed to exhibit the usual solitonic behaviour. As the Mach number is increased, the given profile initially evolves and then settles down to the exact solution of the full non-linear Poisson equation, which then subsequently propagates without distortion. The fractional change in amplitude is found to increase linearly with Mach number. It is further observed that initial profiles satisfying k2λde2<1 break up into a series of solitons.

Anomalous energy dissipation of electron current pulses propagating through an inhomogeneous collisionless plasma medium

The evolution of fast rising electron current pulses propagating through an inhomogeneous plasma has been studied through electron magnetohydrodynamic fluid simulations. A novel process of anomalous energy dissipation and stopping of the electron pulse in the presence of plasma density inhomogeneity is demonstrated. The electron current essentially dissipates its energy through the process of electromagnetic shock formation in the presence of density inhomogeneity. A direct relevance of this rapid energy dissipation process to the fast ignition concept of laser fusion is shown.

Sausage instabilities in the electron current layer and its role in the concept of fast ignition

The fast ignition concept of laser fusion utilizes hot electrons produced at the surface of the target by an incident intense laser pulse for the creation of the hot spot for ignition. As the hot electrons move inwards to the core of the precompressed target, the electrons from the background plasma provide a return shielding current. Three-dimensional PIC simulations have shown that intense Weibel, tearing and coalescence instabilities take place which organize the current distribution into a few current filaments. In each of these filaments the central core region constitutes a current due to the fast electrons propagating inwards towards the pellet core, while the outer cylindrical shell region carries the return shielding current. The presence of instabilities and their subsequent nonlinear development can hinder the propagation of fast electrons towards the core influencing the location of the hot spot for ignition. Earlier studies showing the existence of sausage-like modes were carried out in the non-relativistic limit and under the assumption of equal electron densities of the fast and the cold electrons. The fast electron density, in general, differs considerably from the background plasma density as it is dependent on the incident laser intensity. This paper incorporates relativistic effects and also studies the dependence of the growth rate on the fast electron density. Finally, nonlinear saturation of the instability and its impact on the stopping of the fast electron motion towards the core have also been investigated using numerical simulations. The simulations have, however, currently been carried out for non-relativistic dynamics. The results show that the sheared velocity profile of the channel gets flattened, causing an effective drop in the inward moving current.

Relativistic effects on nonlinear lower hybrid oscillations in cold plasma

Nonlinear lower hybrid mode in a quasineutral magnetized plasma is analyzed in one space dimension using Lagrangian coordinates. In a cold fluid, we treat electron fluid relativistically, whereas ion fluid nonrelativistically. The homotopy perturbation method is employed to obtain the nonlinear solution which also finds the frequency-amplitude relationship for the lower hybrid mode. The solution indicates that the amplitude of oscillation increases due to the weak relativistic effects. The appearance of density spikes is not ruled out in a magnetized plasma.