Nonlinear Plasma Research Articles

Bernstein–Greene–Kruskal and Case–Van Kampen Modes for the Landau–Vlasov Equation

The one-dimensional Landau–Vlasov equation describing ultracold dilute bosonic gases in the mean-field collisionless regime under strong transverse confinement is analyzed using traditional methods of plasma physics. Time-independent, stationary solutions are found using a similar approach as for the Bernstein–Greene–Kruskal nonlinear plasma modes. Linear stationary waves similar to the Case–Van Kampen plasma normal modes are also shown to be available. The new bosonic solutions have no decaying or growth properties, in the same sense as the analog plasma solutions. The results are applied for real ultracold bosonic gases accessible in contemporary laboratory experiments.

A Study on Second Harmonic Excitation in Electron Beam–Plasma Instability

The electron beam–plasma interaction is a fundamental nonlinear plasma process that is frequently taking place in space and laboratory plasmas. Such an interaction is found to generate electromagnetic waves observed in space plasmas. Using the two-dimensional electromagnetic particle in cell simulations, we investigated the second harmonic excitation in the electron beam–plasma instability. Results showed that, first, the Langmuir waves are excited in the system; then at longer time scales, following the excitation of ion acoustic waves, the second harmonic electromagnetic waves are excited. We found that in the case of background pair plasmas, where the masses are the same, there is no signature of waves in the second harmonic, which is a direct verification of the three-wave coupling mechanism for the generation of electromagnetic waves in the second harmonic.

Ion dynamics driven by a strongly nonlinear plasma wake

In plasma wakefield accelerators, the wave excited in the plasma eventually breaks and leaves behind slowly changing fields and currents that perturb the ion density background. We study this process numerically using the example of a Facility for Advanced aCcelerator Experimental Tests (FACET) experiment where the wave is excited by an electron bunch in the bubble regime in a radially bounded plasma. Four physical effects underlie the dynamics of ions: (1) attraction of ions toward the axis by the fields of the driver and the wave, resulting in formation of a density peak, (2) generation of ion-acoustic solitons following the decay of the density peak, (3) positive plasma charging after wave breaking, leading to acceleration of some ions in the radial direction, and (4) plasma pinching by the current generated during the wave-breaking. The interplay of these effects results in the formation of various radial density profiles, which are difficult to produce in any other way.

Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions

This research aims to investigate a generalized fifth-order nonlinear partial differential equation for the Sawada-Kotera (SK), Lax, and Caudrey-Dodd-Gibbon (CDG) equations to study the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasma physics, and other nonlinear sciences. The Painlevé analysis is used to determine the integrability of the equation, and the simplified Hirota technique is applied to construct multiple soliton solutions with an investigation of the dispersion relation and phase shift of the equation. We utilize a linear combination approach to construct a system of equations to obtain a general logarithmic transformation for the dependent variable. We generate one-soliton, two-soliton, and three-soliton wave solutions using the simplified Hirota method and showcase the dynamics of these solutions graphically through interaction between one, two, and three solitons. We investigate the impact of the system’s parameters on the solitons and periodic waves. The SK, Lax, and CDG equations have a wide range of applications in nonlinear dynamics, plasma physics, oceanography, soliton theory, fluid dynamics, and other sciences.

Physiologically-based pharmacokinetic model for 2,4-dinitrophenol.

New approaches in drug development are needed to address the growing epidemic of obesity as the prevalence of obesity increases worldwide. 2,4-Dinitrophenol (DNP) is an oxidative phosphorylation uncoupling agent that was widely used in the early 1930s for weight loss but was quickly banned by the FDA due to the severe toxicities associated with the compound. One of the limitations leading to the demise of DNP as a pharmaceutical was a lack of understanding about the pharmacokinetic-pharmacodynamic relationship. The purpose of this study was to investigate whole body disposition of DNP in order to understand the relationship between the pharmacokinetics, efficacy and toxicity in the C57BL/6J diet induced obese mouse model. Following intravenous administration of 1mg/kg, and intraperitoneal administration of 5mg/kg and 15mg/kg of DNP, we found limited DNP distribution to tissues. Experimentally measured partition coefficients were found to be less than 1 for all analyzed tissues. In addition, DNP exhibits significant nonlinear pharmacokinetics, which we have attributed to nonlinear plasma protein binding and nonlinear partitioning into liver and kidney. By enhancing our understanding of the PK-PD relationship, we can develop new approaches to leverage oxidative phosphorylation uncoupling as a weight loss strategy.

Generation of topologically complex three-dimensional electron beams in a plasma photocathode

Laser-triggered ionization injection is a promising way of generating controllable high-quality electrons in plasma-based acceleration. We show that ionization injection of electrons into a fully nonlinear plasma wave wake using a laser pulse comprising of one or more Laguerre-Gaussian modes with combinations of spin and orbital angular momentum can generate exotic three-dimensional spatial distributions of high-quality relativistic electrons. The phase dependent residual momenta and initial positions of the ionized electrons are encoded into their final phase space distributions, leading to complex spatiotemporal structures. The structures are formed as a result of the transverse (betatron) and longitudinal (phase slippage and energy gain) dynamics of the electrons in the wake immediately after the electrons are injected. Theoretical analysis and three-dimensional simulations verify this mapping process leads to the generation of these complex topological beams. These beams may trigger novel beam-plasma interactions as well as produce coherent radiation with orbital angular momentum when sent through a resonant undulator.

Electromagnetic wave propagation characteristics of oblique incidence nonlinear ionospheric Langmuir disturbance

Based on the generalized Zakharov model, a numerical model of electromagnetic wave propagating in the ionosphere at different angles is established by combining the finite difference time domain (FDTD) method of obliquely incident plasma with the double hydrodynamics equation and through equivalently transforming the two-dimensional Maxwell equation into one-dimensional Maxwell equation and the plasma hydrodynamics equation. In this paper. the dominant equation of Z-wave in obliquely incident nonlinear ionospheric plasma having been analyzed and deduced, the FDTD algorithm suitable for calculating the propagation characteristics of ionospheric electromagnetic wave is deduced. The simulation results prove the accuracy and effectiveness of this method for the Langmuir disturbance caused by electromagnetic wave heating the ionosphere at a small inclination angle. The results show that under small angle incidence, the high-power high-frequency electromagnetic wave excites the Langmuir wave near the O-wave reflection point in the ionospheric plasma. At the same time, the wave particle interaction causes the O-wave to convert into Z-wave and propagate into the higher region of the ionosphere. In this work, the electromagnetic wave propagation characteristics are further studied based on ionospheric plasma, which is helpful in laying the foundation of numerical algorithm for comprehensively and in depth analyzing the influence of ionospheric Langmuir disturbance on ionospheric radio wave propagation characteristics.

Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+1)-dimensions with gas bubbles in hydrodynamics and fluids

Nonlinear evolution equations (NLEEs) are frequently employed to determine the fundamental principles of natural phenomena. Nonlinear equations are studied extensively in nonlinear sciences, ocean physics, fluid dynamics, plasma physics, scientific applications, and marine engineering. The generalized exponential rational function (GERF) technique is used in this article to seek several closed-form wave solutions and the evolving dynamics of different wave profiles to the generalized nonlinear wave equation in (3+1) dimensions, which explains several more nonlinear phenomena in liquids, including gas bubbles. A large number of closed-form wave solutions are generated, including trigonometric function solutions, hyperbolic trigonometric function solutions, and exponential rational functional solutions. In the dynamics of distinct solitary waves, a variety of soliton solutions are obtained, including single soliton, multi-wave structure soliton, kink-type soliton, combo singular soliton, and singularity-form wave profiles. These determined solutions have never previously been published. The dynamical wave structures of some analytical solutions are graphically demonstrated using three-dimensional graphics by providing suitable values to free parameters. This technique can also be used to obtain the soliton solutions of other well-known equations in engineering physics, fluid dynamics, and other fields of nonlinear sciences.

A simulation chain for reflectometry and non-linear MHD: type-I ELM case

A complete chain from a non-linear MHD plasma model simulation through full-wave code simulations implementing synthetic conventional reflectometry is established. For this purpose, the two-dimensional full-wave code REFMUL is employed together with MHD descriptions obtained from the JOREK code. First results of the integrated modeling are presented here where a type-I ELM crash, leading to a fast collapse of the H-mode pedestal, was taken as case-study. The REFMUL simulations were customized to implement synthetic reflectometry in conventional set-up using fixed frequency probing with O-mode waves. Posing challenging conditions for reflectometry, the type-I ELM crash reveals some of the merits and caveats of the diagnostic technique. This work also opens up the possibility to extend modeling to other MHD or ELM studies and provide support to experimental observations with reflectometry.

Plasma scale length and quantum electrodynamics effects on particle acceleration at extreme laser plasmas

In this work, simulations of multipetawatt lasers at irradiances ${\sim }10^{23} \ \mathrm {W}\ \mathrm {cm}^{-2}$ , striking solid targets and implementing two-dimensional particle-in-cell code was used to study particle acceleration. Preformed plasma at the front surface of a solid target increases both the efficiency of particle acceleration and the reached maximum energy by the accelerated charged particles via nonlinear plasma processes. Here, we have investigated the preformed plasma scale length effects on particle acceleration in the presence and absence of nonlinear quantum electrodynamic (QED) effects, including quantum radiation reaction and multiphoton Breit–Wheeler pair production, which become important at irradiances ${\sim } 10^{23}\ \mathrm {W}\ \mathrm {cm}^{-2}$ . Our results show that QED effects help particles gain higher energies with the presence of preformed plasma. In the results for all cases, preplasma leads to more efficient laser absorption and produces more energetic charged particles, as expected. In the case where QED is included, however, physical mechanisms changed and generated secondary particles ( $\gamma$ -rays and positrons) reversing this trend. That is, the hot electrons cool down due to QED effects, while ions gain more energy due to different acceleration methods. It is found that more energetic $\gamma$ -rays and positrons are created with increasing scale length due to high laser conversion efficiency ( ${\sim }$ 24 % for $\gamma$ -rays and $\sim$ 4 % for positrons at $L = 7\ \mathrm {\mu }\textrm {m}$ scale length), which affects the ion and electron acceleration mechanisms. It is also observed that the QED effect reduces the collimation of angular distribution of accelerated ions because the dominant ion acceleration mechanism is changing when QED is involved in the process.

Edge harmonic oscillations in plasmas with a separatrix and the effect of edge magnetic shear

This work presents an extension of exfernal mode theory, where the effects of edge magnetic shear and plasma separatrix are investigated and applied to edge harmonic oscillations (EHOs). Linear analytical modelling is performed on a large aspect ratio tokamak with circular cross section, from which a set of three coupled differential equations describing the dispersion relation are derived. To correctly assess the effect of edge shear on exfernal modes, higher order corrections need to be retained in the expansion of the safety factor around the rational surface. The equations are solved numerically for equilibrium pressure and safety factor profiles containing the key features for the excitation of exfernal modes, including a model of a plasma separatrix. The current-driven branch of the instability is significantly reduced by the inclusion of the separatrix, but the mode remains unstable through coupling with the pressure-driven infernal drive. The obtained parameter space for the instability without the effect of the separatrix is compared with the growth rates calculated using the KINX code, and with the nonlinear plasma displacement calculated using the VMEC free-boundary code. From the comparison it was found that the edge shear can be of order unity and still excite exfernal modes, implying that EHOs can be excited even with weak flattening of the local safety factor at the edge, which is in line with some current experimental observations, but contrary to previous simpler analytic theory.

Riemann–Hilbert problem and interactions of solitons in the ‐component nonlinear Schrödinger equations

AbstractIn this work, we systematically investigate the general‐component nonlinear Schrödinger equations by using the Riemann–Hilbert method. Starting from the Lax pair associated with anmatrix spectral problem, we construct a Riemann–Hilbert problem and obtain the compact‐soliton solutions formula expressed by determinants. Taking two‐components nonlinear Schrödinger equations as an example, this work detailedly analyzes its multisoliton solutions by means of parameters modulation. Many interesting new phenomena are displayed including elastic collision, soliton reflection, parallel propagation, time‐periodic propagation and (space, time)‐periodic propagation. In addition, the interactions between solitons from weak to strong are presented. Finally, some conjectures about the dynamical behaviors of‐soliton solutions are proposed. We hope that the present analysis would be useful for a better understanding of soliton interactions in related fields such as nonlinear optics, plasma physics, oceanography, and Bose–Einstein condensates.

Even and odd nonautonomous NLSE hierarchy and reversible transformations

Under investigation are the nonautonomous Nonlinear Schrödinger equation (NLSE) hierarchies. We have presented the soliton solution of the hierarchy in the most generalized form, namely in terms of the spectral parameter of nonautonomous NLSE spectral problem. We analysed crucial differences between the even order hierarchies and the odd order hierarchies and the corresponding solutions. We have also presented the generalized reversible transformations, which transform the nonautonomous NLSE hierarchy into variable coefficient autonomous NLSE hierarchy. We found that the reversible coordinate transformations are monotonic for odd order hierarchies but not strictly monotonic for even order hierarchies or for a combination of the both. The Jacobian of the transformation is, however, unity in all the transformations. We have identified a set of constraints among the dispersion and the nonlinear coefficients of the general nonautonomous NLSE hierarchy, which are preserved under the transformations. We hope that our analysis provides a universal mathematical platform to study diverse physical systems in nonlinear optics, plasma physics, atomic physics and climate physics.

Optical Bistability of 1-D Photonic Crystals Containing of Nonlinear Plasma

In this article, a novel nonlinear model is proposed to describe the permittivity of the plasma, and the nonlinear optical bistable phenomenon of the 1-D photonic crystals, which is composed of a nonlinear plasma defect layer, is theoretically investigated by the conventional transfer matrix method (TMM) under TM wave. It is figured out that the permittivity of nonlinear plasma exists in bistable state. Then, the tuning effects of the number of the photonic crystals’ (PCs) periodic layers, the incident frequency, the thicknesses of the nonlinear plasma layer, and the incident angle on the optical bistability (OB) have been emphatically studied. Additionally, the transmission and the reflectance under the influences of this bistable tuning are further proposed. The calculated results show that the adjustment of the OB can be achieved without changing the multi-layer material geometry. This multi-composite nonlinear plasma defect structure with the tunable bistable phenomenon can be applied to numerous valuable optical devices, such as novel optical power threshold devices, logic gates, and optical information memory.

Optical nonreciprocal bistable absorption in a one-dimensional asymmetric layered structure composed of nonlinear plasmas and general-function photonic crystals

In this paper, a one-dimensional asymmetric layered structure combining general-function photonic crystals and nonlinear plasmas is proposed. The novel structure is theoretically investigated using the conventional transfer matrix method. Using these two special nonlinear materials, the optical nonreciprocity of the bistable absorption caused by forward and backward propagation is comprehensively studied. It is found that due to the asymmetry of the spatial distribution and the nonlinear properties of the nonlinear materials, the absorption, reflection, and transmission of light in two different directions, forward and backward, have apparent optical nonreciprocity. It is notable that when the light is traveling in the forward direction, the position of the working interval of the bistable absorption is significantly higher than that of the backward direction, and that the magnitudes of the absorptances corresponding to the forward and backward directions are also evidently different. Meanwhile, the sensitivity properties of the incident frequency and the angle under this optical nonreciprocity are further analyzed, and the reason for this extraordinary nonreciprocity phenomenon is explicated by the electric and magnetic field distributions of the proposed structure.

Abundant closed-form wave solutions and dynamical structures of soliton solutions to the (3+1)-dimensional BLMP equation in mathematical physics

The physical principles of natural occurrences are frequently examined using nonlinear evolution equations (NLEEs). Nonlinear equations are intensively investigated in mathematical physics, ocean physics, scientific applications, and marine engineering. This paper investigates the Boiti-Leon-Manna-Pempinelli (BLMP) equation in (3+1)-dimensions, which describes fluid propagation and can be considered as a nonlinear complex physical model for incompressible fluids in plasma physics. This four-dimensional BLMP equation is certainly a dynamical nonlinear evolution equation in real-world applications. Here, we implement the generalized exponential rational function (GERF) method and the generalized Kudryashov method to obtain the exact closed-form solutions of the considered BLMP equation and construct novel solitary wave solutions, including hyperbolic and trigonometric functions, and exponential rational functions with arbitrary constant parameters. These two efficient methods are applied to extracting solitary wave solutions, dark-bright solitons, singular solitons, combo singular solitons, periodic wave solutions, singular bell-shaped solitons, kink-shaped solitons, and rational form solutions. Some three-dimensional graphics of obtained exact analytic solutions are presented by considering the suitable choice of involved free parameters. Eventually, the established results verify the capability, efficiency, and trustworthiness of the implemented methods. The techniques are effective, authentic, and straightforward mathematical tools for obtaining closed-form solutions to nonlinear partial differential equations (NLPDEs) arising in nonlinear sciences, plasma physics, and fluid dynamics.

Koopman Autoencoder Architecture for Current Density Modeling in Kinetic Plasma Simulations

We present a reduced-order model (ROM) based on Koopman autoencoder architecture for prediction of current density in kinetic plasma simulations. We apply the proposed method to forecast the time evolution of the current density derived from high-fidelity electromagnetic particle-in-cell (EMPIC) simulation based on the Maxwell- Vlasov system of equations. We test the Koopman auto encoder architecture for a two-dimensional oscillating electron beam inside a square cavity. Such analysis can be crucial in modeling of complex nonlinear plasma system as well as expediting time-consuming particle-in-cell simulations.

Inverse ray tracing on icosahedral tetrahedron grids for non-linear laser plasma interaction coupled to 3D radiation hydrodynamics

A novel approach to efficiently model 3-D laser plasma interactions at fluid scales is presented. This method, implemented in the IFRIIT propagation code developed at CELIA, relies on inverse ray tracing to compute laser fields at arbitrary locations in a plasma. This enables to describe the fields at high order in space compared to standard forward ray tracing approaches. In addition, inverse ray tracing enables the use of etalon integral methods to reconstruct caustic fields and greatly speeds up calculations of cross-beam energy transfer by decoupling the ray amplitude and ray phase calculations. A comparison of the inverse and forward methods for 3-D calculations of fields in presence or not of cross-beam energy transfer illustrates the significant advantages of the inverse method. Conversely, while the inverse method is well suited to most spherical plasma profiles, it currently cannot treat concave profiles or target holders. The coupling of IFRIIT with the 3-D ASTER radiative hydrodynamics code developed at the Laboratory for Laser Energetics is then presented. ASTER and IFRIIT resolve their respective equations on separate grids which communicate through interpolation. As such, IFRIIT uses a dedicated laser grid adapted to the computations at play, which also allows to use different parallelization methods for both codes: block decomposition for the hydrodynamics versus domain duplication for the laser. Applications to direct-drive implosions for inertial confinement fusion are presented, for which a geodesic icosahedron grid is implemented in IFRIIT. The performances of the ASTER/IFRIIT coupling are demonstrated by conducting simulations of cryogenic implosions performed on the OMEGA laser system, in presence of various sources of 3-D effects; laser port geometry, cross-beam energy transfer, beam imbalance and target mis-alignment. Comparison with neutron data, measured through bang-time, for a cryogenic implosion experiment shows an excellent agreement for the laser-plasma coupling.

Excitation of strongly nonlinear plasma wakefield by electron bunches

We propose a new method for analytical self-consistent description of the excitation of a strongly nonlinear wakefield (a bubble) excited by an electron bunch. This method makes it possible to calculate the shape of the bubble and the distribution of the electric field in it based only on the properties of the driver, without relying on any additional parameters. The analytical results are verified by particle-in-cell simulations and show good correspondence. A complete analytical solution for cylindrical drivers and scaling laws for the properties of the bubble and other plasma accelerator parameters depending on the bunch charge and length are derived.

Restructuring of rotating spokes in response to changes in the radial electric field and the neutral pressure of a cylindrical magnetron plasma

Nonlinear plasma structures in the partially magnetized E×B plasma of a cylindrical magnetron are investigated using 2D3V particle-in-cell Monte Carlo collision simulations. In the early phase of the discharge, plasma gradients and radial electric fields excite a lower hybrid type instability that forms long wavelength rotating density spokes. As the discharge grows in density by ionization and the cathode gets shielded by the formation of an ion sheath, radial electric fields diminish in the quasineutral region of the discharge. This induces a transition of the spokes into short-scale spoke-on-spoke modes. The short wavelength structures can be reversed back into a long spiral spoke by lowering the neutral pressure, which revives the radial electric fields via a turbulent plasma expansion. Plasma phenomena connected to the rotating spoke include the anomalous radial transport and loss of electrons through the spoke, azimuthal dragging of ions by the spoke’s field, plasma temperature modulations by the spoke structure, and formation of electron vortices around equipotential islands, in some cases with opposing rotations to the underlying E×B drift. Electron scattering from non-ionizing collisions with neutrals also has a minor influence on the instability.