Formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive is discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase-locking with the drive yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov-Poisson simulations showing formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham's averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude avoiding the kinetic wave breaking.
When the background density in a bounded plasma is modulated in time, discrete modes become coupled. Interestingly, for appropriately chosen modulations, the average plasmon energy might be made to grow in a ladder-like manner, achieving up-conversion or down-conversion of the plasmon energy. This reversible process is identified as a classical analog of the effect known as quantum ladder climbing, so that the efficiency and the rate of this process can be written immediately by analogy to a quantum particle in a box. In the limit of densely spaced spectrum, ladder climbing transforms into con…
A modified version of the Plasma Beat-Wave Accelerator scheme is introduced and analyzed, which is based on autoresonant phase-locking of the nonlinear Langmuir wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage through resonance. This new scheme is designed to overcome some of the well-known limitations of previous approaches, namely relativistic detuning and nonlinear modulation or other non-uniformity or non-stationarity in the driven Langmuir wave amplitude, and sensitivity to frequency mismatch due to measurement uncertainties and density fluctuations an…
We demonstrate theoretically and numerically that a warm fluid model of a plasma supports space-time quasicrystalline structures. These structures are highly nonlinear, two-phase, ion acoustic waves that are excited autoresonantly when the plasma is driven by two small amplitude chirped-frequency ponderomotive drives. The waves exhibit density excursions that substantially exceed the equilibrium plasma density. Remarkably, these extremely nonlinear waves persist even when the small amplitude drives are turned off. We derive the weakly nonlinear analytical theory by applying Whitham's averaged …
Long lasting plasma density structures utilizing tailored density profiles
Chalmers University of Technology（查尔姆斯理工大学）；University of Oxford（牛津大学）；Sorbonne Université, CNRS, École Polytechnique, CEA（索邦大学、法国国家科学研究中心、巴黎综合理工学院、法国原子能和替代能源委员会）；Zhejiang University（浙江大学）；University of California, Berkeley（加州大学伯克利分校）
We present a method for constructing multiphase excitations in the generally non-integrable system of warm fluid equations describing plasma oscillations. It is based on autoresonant excitation of nonlinear electron plasma waves by phase locking with small amplitude chirped-frequency ponderomotive drives. We demonstrate the excitation of these multiphase waves by performing fully nonlinear numerical simulations of the fluid equations. We develop a simplified model based on a weakly nonlinear analytical theory by applying Whitham's averaged Lagrangian procedure. The simplified model predictions…
Excitation of large amplitude strongly nonlinear ion acoustic waves from a trivial equilibrium by a chirped frequency drive is discussed. Under certain conditions, after passage through the linear resonance in this system, the nonlinearity and the variation of parameters work in tandem to preserve the phase-locking with the driving wave via excursion of the excited ion acoustic wave in its parameter space, yielding controlled growth of the wave amplitude. We study these autoresonant waves via a fully nonlinear warm fluid model and predict formation of sharply peaked (extreme) ion acoustic exci…
The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded plasma) or continuous (boundless plasma), this phenomenon is called ladder climbing (LC) or autoresonant acceleration of plasmons. It was first proposed by Barth \textit{et al.} [PRL \textbf{115}, 075001 (2015)] based on a linear fluid model. In this paper, LC of electron plasma waves is investigated using fully nonlinear Vlasov-Poisson simulations of collisionless bounded plasma. It …
The existence of standing high frequency electromagnetic (EM) solitons in a fully degenerate overdense electron plasma is studied applying relativistic hydrodynamics and Maxwell equations. The stable soliton solutions are found in both relativistic and nonrelativistic degenerate plasmas.
Thermal fusion plasmas initiated by standing whistler waves are investigated numerically by two- and one-dimensional Particle-in-Cell simulations. When a standing whistler wave collapses due to the wave breaking of ion plasma waves, the energy of the electromagnetic waves transfers directly to the ion kinetic energy. Here we find that the ion heating by the standing whistler wave is operational even in multi-dimensional simulations of multi-ion species targets, such as deuterium-tritium (DT) ices and solid ammonia borane (H$_6$BN). The energy conversion efficiency to ions becomes as high as 15…
This paper presents a study of the two-stream instability of an electron beam propagating in a finite-size plasma placed between two electrodes. It is shown that the growth rate in such a system is much smaller than that of an infinite plasma or a finite size plasma with periodic boundary conditions. Even if the width of the plasma matches the resonance condition for a standing wave, a spatially growing wave is excited instead with the growth rate small compared to that of the standing wave in a periodic system. The approximate expression for this growth rate is $γ\approx (1/13)ω_{pe}(n_{b}/n_…
The global electrostatic mode in pair-ion plasmas is discussed for cylindric geometry and for a radially inhomogeneous equilibrium density. In the case of a Gaussian radial density profile, exact analytical eigen solutions are found in terms of the Kummer confluent hypergeometric functions. The mode is identified as a convective cell propagating in the poloidal and axial direction, having at the same time a standing wave structure in the radial direction.
We conducted experimental studies and computer simulations of standing striations in capacitive coupled plasma in Argon gas. Standing striations were observed at frequencies 3.6, 8.4 and 19.0 MHz, in a pressure range 0.05-10 Torr, tube radius R=1.1 cm, for a certain range of discharge currents (plasma densities). Numerical simulations revealed similar nature of standing striations in CCP and moving striations in DC discharges under similar discharge conditions. Comparison of computer simulations with experimental observations helped clarify the nature of these striations. The non-linear depend…
Two dimensional modelling of the interaction between electromagnetic waves and plasma-metamaterial composite structures using the particle-in-cell method
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 ra…
We present a comprehensive analysis of longitudinal particle drifting in a standing circularly polarized wave at extreme intensities when quantum radiation reaction (RR) effects should be accounted for. To get an insight into the physics of this phenomenon we made a comparative study considering the RR force in the Landau-Lifshitz or quantum-corrected form, including the case of photon emission stochasticity. It is shown that the cases of circular and linear polarization are qualitatively different. Moreover, specific features of particle dynamics have a strong impact on spatial structures of …
Efficient energy transfer from electromagnetic waves to ions has been demanded to control laboratory plasmas for various applications and could be useful to understand the nature of space and astrophysical plasmas. However, there exists a severe unsolved problem that most of the wave energy is converted quickly to electrons, but not to ions. Here, an energy conversion process to ions in overdense plasmas associated with whistler waves is investigated by numerical simulations and theoretical model. Whistler waves propagating along a magnetic field in space and laboratories often form the standi…
Langmuir probe techniques have been used to study time and spatially resolved electron densities and electron temperatures in pulse-modulated hydrogen discharges in two different planar microwave reactors (fmicrowave= 2.45 GHz, tpulse= 1 ms). The reactors are (i) a standing-wave radiative slotted waveguide reactor and (ii) a modified travelling-wave radiative slotted waveguide reactor, which generate relatively large plasmas over areas from about 350 cm^2 to 500 cm^2. The plasma properties of these reactor types are of particular interest as they have been used for basic research and for plasm…
In this article, we use the general theory derived in the companion paper [M. Tacu and D. Bénisti, Phys. Plasmas (2021)] in order to address several long-standing issues regarding nonlinear electron plasma waves (EPW's). First, we discuss the relevance, and practical usefulness, of stationary solutions to the Vlasov-Poisson system, the so-called Bernstein-Greene-Kruskal modes, to model slowly varying waves. Second, we derive an upper bound for the wave breaking limit of an EPW growing in an initially Maxwellian plasma. Moreover, we show a simple dependence of this limit as a function of $kλ_D$…
It is shown in linear approximation that in the case of one-dimensional problem of transverse electron waves in a half-infinite slab of homogeneous Maxwellian collisionless plasma with the given boundary field frequency two wave branches of solution of the dispersion equation are simultaneously realizing. These are the branch of fast forward waves determined mainly by Maxwell equations of electromagnetic field, as well as the branch of forward and backward slow waves determined in the whole by kinetic properties of electrons in the collective electrical field. The physical nature of wave movem…
A long standing puzzle in fusion research comes from experiments where a sudden peripheral electron temperature perturbation is accompanied by an almost simultaneous opposite change in central temperature, in a way incompatible with local transport models. This paper shows these experiments and similar ones are fairly well quantitatively reproduced, when induction effects are incorporated in the total plasma response, alongside standard local diffusive transport, as suggested in earlier work [V.D. Pustovitov, Plasma Phys. Control. Fusion {\bf 54}, 124036 (2012)].
The definition of magnetic shuttle is introduced to describe the magnetic space enclosed by two tandem magnetic mirrors with the same field direction and high mirror ratio. Helicon plasma immersed in such a magnetic shuttle which can provide the confinement of charged particles is modeled using an electromagnetic solver. The perpendicular structure of wave field along this shuttle is given in terms of stream vector plots, showing significant change from midplane to ending throats, and the vector field rotates and forms a circular layer that separating plasma column radially into core and edge …
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitativ…
The dynamical behaviors of electromagnetic (EM) solitons formed due to nonlinear interaction of linearly polarized intense laser light and relativistic degenerate plasmas are studied. In the slow motion approximation of relativistic dynamics, the evolution of weakly nonlinear EM envelope is described by the generalized nonlinear Schr{ö}dinger (GNLS) equation with local and nonlocal nonlinearities. Using the Vakhitov-Kolokolov criteria, the stability of an EM soliton solution of the GNLS equation is studied. Different stable and unstable regions are demonstrated with the effects of soliton velo…
The magnetic field produced by planets with active dynamos, like the Earth, can exert sufficient pressure to oppose supersonic stellar wind plasmas, leading to the formation of a standing bow shock upstream of the magnetopause, or pressure-balance surface. Scaled laboratory experiments studying the interaction of an inflowing solar wind analog with a strong, external magnetic field are a promising new way to study magnetospheric physics and to complement existing models, although reaching regimes favorable for magnetized shock formation is experimentally challenging. This paper presents experi…
The multi-fluid modelling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamics waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves…
We use particle-in-cell (PIC) simulations and simple analytic models to investigate the laser-plasma interaction known as ponderomotive steepening. When normally incident laser light reflects at the critical surface of a plasma, the resulting standing electromagnetic wave modifies the electron density profile via the ponderomotive force, which creates peaks in the electron density separated by approximately half of the laser wavelength. What is less well studied is how this charge imbalance accelerates ions towards the electron density peaks, modifying the ion density profile of the plasma. Id…
Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes $δB_{\perp}/B_{0}\gtrsim β^{\,-1/2}$ (where $β$ is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-sc…
This work, which extends Squire et al. [ApJL, 830 L25 (2016)], explores the effect of self-generated pressure anisotropy on linearly polarized shear-Alfvén fluctuations in low-collisionality plasmas. Such anisotropies lead to stringent limits on the amplitude of magnetic perturbations in high-beta plasmas, above which a fluctuation can destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, "interrupting" the wave and stopping its oscillation. These effects are explored in detail in the collisionless and weakly collisional "Braginskii" reg…
We investigate the dynamics of localized solutions of the relativistic cold fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schröndinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing…
Whistler mode wave is a fundamental perturbation of electromagnetic fields and plasmas in various environments including planetary space, laboratory and astrophysics. The origin and evolution of the waves are a long-standing question due to the limited instrumental capability in resolving highly variable plasma and electromagnetic fields. Here, we analyse data with the high time resolution from the multi-scale magnetospheric spacecraft in the weak magnetic environment (i.e., foreshock) enabling a relatively long gyro-period of whistler mode wave. Moreover, we develop a novel approach to separa…
The very long standing problem of sound waves propagation in fluids is reexamined. In particular, from the analysis of the wave damping in reacting gases following the work of Einsten \citep{Ein}, it is found that the damping due to the chemical reactions occurs nonetheless the second (bulk) viscosity introduced by Landau \& Lifshitz \citep{LL86} is zero. The simple but important case of a recombining Hydrogen plasma is examined.
The dynamics of a standing shock front in a Poynting-flux dominated relativistic flow is investigated by using a one-dimensional, relativistic, two-fluid simulation. An upstream flow containing a circularly polarized, sinusoidal magnetic shear wave is considered, mimicking a wave driven by an obliquely rotating pulsar. It is demonstrated that this wave is converted into large amplitude electromagnetic waves with superluminal phase speeds by interacting with the shock when the shock-frame frequency of the wave exceeds the proper plasma frequency. The superluminal waves propagate in the upstream…
1.5D Vlasov-Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the solar physics context. The simulations mimic the plasma emission mechanism and Larmor drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradien…
Context. Kink waves are routinely observed in coronal loops. Resonant absorption is a well-accepted mechanism that extracts energy from kink waves. Nonlinear kink waves are know to be affected by the Kelvin-Helmholtz instability. However, all previous numerical studies consider linearly polarized kink waves. Aims. We study the properties of circularly polarized kink waves on straight plasma cylinders, for both standing and propagating waves, and compare them to the properties of linearly polarized kink waves. Methods. We use the code MPI-AMRVAC to solve the full 3D Magnetohydrodynamic (MHD) eq…
1.5D PIC, relativistic, fully electromagnetic (EM) simulations are used to model EM wave emission generation in the context of solar type III radio bursts. The model studies generation of EM waves by a super-thermal, hot beam of electrons injected into a plasma thread that contains uniform longitudinal magnetic field and a parabolic density gradient. In effect, a single magnetic line connecting Sun to earth is considered, for which several cases are studied. (i) We find that the physical system without a beam is stable and only low amplitude level EM drift waves (noise) are excited. (ii) The b…
The modulation of the microwave emission intensity from a flaring loop by a standing linear sausage fast magnetoacoustic wave is considered in terms of a straight plasma slab with the perpendicular Epstein profile of the plasma density, penetrated by a magnetic field. The emission is of the gyrosynchrotron (GS) nature, and is caused by mildly relativistic electrons which occupy a layer in the oscillating slab, i.e., the emitting and oscillating volumes do not coincide. It is shown that the microwave response to the linear sausage wave is highly non-linear. The degree of the non-linearity, defi…
