Self-generated Electromagnetic Field Research Articles

The effect of collisions on the multi-fluid plasma Richtmyer–Meshkov instability

The Richtmyer–Meshkov instability (RMI) results from the impulsive acceleration of a density interface where the RMI itself or the acceleration is perturbed. The RMI is ubiquitous in shock environments and may arise due to an interface of fluid species, isotopes, temperature, or more. The plasma RMI can be significantly influenced by electromagnetic effects and can be modeled more accurately by a multi-fluid plasma (MFP) model rather than conventional magnetohydrodynamics, though with increased computational expense. MFP modeling of the plasma RMI has revealed many phenomena but has only been completed within the ideal regime. Modeling the effects of elastic collisions is vital for understanding the behavior of the instability in a dense plasma. The Braginskii transport coefficients provide theoretically based relations modeling thermal equilibration, inter-species drag, viscous momentum- and energy-transfers, and thermal conductivity. Our numerical simulations of the MFP RMI with these relations show that the key changes from the ideal case are (1) reduction of relative motion between the ion and electron fluids (consequently affecting the self-generated electromagnetic fields), (2) introduction of anisotropy in momentum and energy via transport coefficients, and (3) damping of high frequency electromagnetic waves and plasma waves. Under the conditions studied, the net effect is a reduction in the MFP RMI amplitude width and the growth rate to levels approaching the neutral fluid instability, as well as a reduction in large scale perturbations along the ion fluid density interface, a positive for inertial confinement fusion efforts. There are, however, two important caveats: small-scale density interface perturbations remain, and the conditions simulated are a few relevant points in a large parameter space that requires further investigation.

Confinement of intense proton beams by an applied axial magnetic field in large-scale plasma

Stable and efficient transport of particle beams through plasma is a frequent topic in particle–matter interactions. In plasma, intense ion beams can focus and flap because of the self-generated electromagnetic fields and soon diverge if no restrictions are imposed. In this study, the transport of a slab beam in large-scale plasma with a uniform applied axial magnetic field is simulated and analyzed using a newly developed kinetic particle-in-cell code. The simulation results show that the applied axial magnetic field intensifies the Lorentz force acting on the beams and is effective at preventing ion-beam divergence. This confinement effect from the external magnetic field influences the beam flapping more than it does the focusing, and with increasing applied magnetic field, more beam particles converge and more energy is transferred into the transverse direction in the flapping region. In the present scenario, the beam behavior is affected synthetically by both the self-generated electromagnetic field and the external axial magnetic field. Also shown is that the applied field exerts little control over the total beam energy, which the present theoretical analysis explains well. Beam confinement by an external magnetic field is likely to have a major impact on nuclear fusion, astrophysics, and beam control.

Self-generated magnetic field in plasma reconstructed by using inverse Abel transformation in proton radiography

The magnetic fields generated in plasmas have extensive influences on many processes of the inertial confinement fusion and the astrophysics. Therefore, the quantitative diagnosis of the magnetic field is quite essential. Proton radiography is a widely used experimental technique to diagnose the electric field or magnetic field in high-energy-density plasma. The effective explanation of the results of proton radiography depends on the reliability and availability of the inversion method. Traditional inversion methods can only provide one- or two-dimensional structure of the self-generated magnetic field. In this study, it is found that there is an Abel transformation relationship between the deflection velocity and the magnetic field with column symmetry, which allows us to reconstruct the three-dimensional structure of the magnetic field for the first time. We theoretically deduce the process of reconstructing the cylindrical magnetic field through proton radiography with the Abel inversion algorithm. The feasibility of this method is verified by numerical simulation as well. Based on this inversion method, we reanalyze the proton radiography experimental results of Li et al. (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.1038/ncomms13081">2016 <i>Nat. Commun.</i> <b>7</b> 13081</ext-link>) on the self-generated magnetic field of plasma jets. The inversion results show that the maximum magnetic field intensity is about 1.9 times the traditional inversion results. We discuss a new proton radiography inversion method for the existence of magnetic fields with cylindrical symmetry in thiswork, which will contributes to an intensive understanding of the self-generated electromagnetic field and its spatiotemporal evolution related to the laser fusion and the laboratory astrophysics.

Ion kinetic effects on the evolution of Richtmyer–Meshkov instability and interfacial mix

Plasma effects, such as the multi-component kinetic diffusion and self-generated electromagnetic fields, are recognized as a pivotal key to understanding the physics of interface evolution in inertial confinement fusion and supernova remnants. In this work, a two-dimensional hybrid fluid-PIC code is used to investigate the ion kinetic effects of the single-mode Richtmyer–Meshkov instability (RMI) at the interface between hydrogen plasma and carbon plasma. After an electrostatic shockwave passing through the perturbed interface, the RMI, which reshapes the interface, grows via the vorticity depositing as well as the self-generated magnetic field. After scaling the growth of the interfacial mix region with time, the density transition layer has been found to exceed the disturbance wavelength and lead to a suppression of the instability evolution finally.

Hybrid fluid–particle modeling of shock-driven hydrodynamic instabilities in a plasma

Shock-driven hydrodynamic instabilities in a plasma usually lead to interfacial mixing and the generation of electromagnetic fields, which are nonequilibrium processes coupling kinetics with meso- and macroscopic dynamics. The understanding and modeling of these physical processes are very challenging tasks for single-fluid hydrodynamic codes. This work presents a new framework that incorporates both kinetics and hydrodynamics to simulate shock waves and hydrodynamic instabilities in high-density plasmas. In this hybrid code, ions are modeled using the standard particle-in-cell method together with a Monte Carlo description of collisions while electrons are modeled as a massless fluid, with the electron heat flux and fluid–particle energy exchange being considered in the electron pressure equation. In high-density plasmas, Maxwell’s equations are solved using Ohm’s law instead of Ampère’s law. This hybrid algorithm retains ion kinetic effects and their consequences for plasma interpenetration, shock wave propagation, and hydrodynamic instability. Furthermore, we investigate the shock-induced (or gravity-induced) turbulent mixing between a light and a heavy plasma, where hydrodynamic instabilities are initiated by a shock wave (or gravity). This study reveals that self-generated electromagnetic fields play a role in the formation of baroclinic vorticity along the interface and in late-time mixing of the plasmas. Our results confirm the ability of the proposed method to describe shock-driven hydrodynamic instabilities in a plasma, in particular, nonequilibrium processes that involve mixing and electromagnetic fields at the interface.

Richtmyer-Meshkov instability of an imploding flow with a two-fluid plasma model

The two-fluid (ions and electrons) plasma Richtmyer-Meshkov instability of a cylindrical light/heavy density interface is numerically investigated without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. When the coupling becomes strong, the electrons are restricted to co-move with the ions and the resulting evolution is similar to the hydrodynamic neutral fluid case. The charge separation that occurs between the electrons and ions results in self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling between the electrons and ions is weak. In addition to the Rayleigh-Tayler stabilization effect during flow deceleration, the interfaces are accelerated by the induced spatio-temporally varying Lorentz force. As a consequence, the perturbations develop into the Rayleigh-Taylor instability, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case.

Numerical investigation on relativistic electron scattering by a plasma density gradient

A Monte-Carlo code based on a single scattering model is developed for numerical investigations on relativistic electron scattering by a plasma density gradient in electron radiography. A relativistic electron beam is taken to side-on radiograph a steep density gradient region in a fully ionized polystyrene foil target and the beam’s kinetic energy is chosen to be much higher than its energy loss in the target. The beam profile of the transmitted electrons on the radiograph shows a modulation of peak-to-trough structure due to electron scattering from the density gradient region. For a 30 μm thick target made up of densities from 1 g cm−3 to 3 g cm−3 across the gradient region, a maximum modulation contrast of about 13% could be produced. The influence of beam energy and spread, density gradient width, detection distance, and plasma self-generated electromagnetic fields are investigated. In an approximation of multiple scattering, an analytical model is introduced to assist in the interpretation of the scattering characteristics resulting from the density gradient. The modulation features and their relations to the gradient width may be applied to diagnose a steep density gradient region of width 1 μm in dense plasma.

Time Global Finite-Energy Weak Solutions to the Many-Body Maxwell–Pauli Equations

We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the electrons and their self-generated electromagnetic field is referred to as the many-body Maxwell-Pauli equations. Here we construct time global, finite-energy, weak solutions to the many-body Maxwell-Pauli equations under the assumption that the fine structure constant $\alpha$ and the atomic numbers are not too large. The particular assumptions on the size of $\alpha$ and the atomic numbers ensure that we have energetic stability of the many-body Pauli Hamiltonian, i.e., the ground state energy is finite and uniformly bounded below with lower bound independent of the magnetic field and the positions of the nuclei. This work serves as an initial step towards understanding the connection between the energetic stability of matter and the wellposedness of the corresponding dynamical equations.

Physics of the laser-plasma interface in the relativistic regime of interaction

The reflection of intense laser radiation from solids appears as a result of relativistic dynamics of the electrons driven by both incoming and self-generated electromagnetic fields at the periphery of the emerging dense plasma. In the case of highly relativistic motion, electrons tend to form a thin oscillating layer, which makes it possible to model the interaction and obtain the temporal structure of the reflected radiation. The modeling reveals the possibility and conditions for producing singularly intense and short extreme ultraviolet (XUV) bursts of radiation, which are interesting for many applications. However, the intensity and duration of the XUV bursts, as well as the high-energy end of the harmonic spectrum, depend on the thickness of the layer and its internal structure which are not assessed by such macroscopic modeling. Here, we analyze the microscopic physics of this layer and clarify how its parameters are bound and how this controls the outlined properties of XUV bursts.

Ground State for the Relativistic One Electron Atom in a Self-Generated Electromagnetic Field

We study the Dirac--Maxwell system coupled with an external potential of Coulomb type. We prove the existence of a “ground state" solution using the Foldy--Wouthuysen (unitary) transformation of the Dirac operator and its realization as an elliptic problem in the 4-dim half space $\mathbb{R}^4_{+}$ with a Neumann boundary condition.

Kinetic physics in ICF: present understanding and future directions

Kinetic physics has the potential to impact the performance of indirect-drive inertial confinement fusion (ICF) experiments. Systematic anomalies in the National Ignition Facility implosion dataset have been identified in which kinetic physics may play a role, including inferred missing energy in the hohlraum, drive asymmetry in near-vacuum hohlraums, low areal density and high burn-averaged ion temperatures (〈Ti〉) compared with mainline simulations, and low ratios of the DD-neutron and DT-neutron yields and inferred 〈Ti〉. Several components of ICF implosions are likely to be influenced or dominated by kinetic physics: laser-plasma interactions in the LEH and hohlraum interior; the hohlraum wall blowoff, blowoff/gas and blowoff/ablator interfaces; the ablator and ablator/ice interface; and the DT fuel all present conditions in which kinetic physics can significantly affect the dynamics. This review presents the assembled experimental data and simulation results to date, which indicate that the effects of long mean-free-path plasma phenomena and self-generated electromagnetic fields may have a significant impact in ICF targets. Simulation and experimental efforts are proposed to definitively quantify the importance of these effects at ignition-relevant conditions, including priorities for ongoing study.

Gamma-ray generation from laser-driven electron resonant acceleration: In the non-QED and the QED regimes

Electron acceleration and γ-ray emission by circularly polarized laser pulses interacting with near-critical-density plasmas are systematically investigated for both the non-quantum-electrodynamic (non-QED) and QED regimes. In the non-QED regime, since electron density in the plasma channel is small and the self-generated electromagnetic fields are weak, only a few electrons can achieve the resonant acceleration, leading to weak γ-ray emission. However, when it comes to the QED regime, the radiation recoil force significantly affects the electron dynamics, which helps in not only the trapping of electrons, but also the relaxing of the condition for electrons to hit the resonance with laser fields, resulting in the formation of an ultradense helical electron bunch under resonant acceleration in the plasma channel. Therefore, an intense γ-ray pulse with unprecedented flux can be generated. Theoretical analysis and three-dimensional particle-in-cell simulations are carried out to compare the dynamics in two different regimes.

Deuteron-deuteron fusion in laser-driven counter-streaming collisionless plasmas

Nuclear fusion reactions are the most important processes in nature to power stars and produce new elements, and lie at the center of the understanding of nucleosynthesis in the universe. It is critically important to study the reactions in full plasma environments that are close to true astrophysical conditions. By using laser-driven counter-streaming collisionless plasmas, we studied the fusion D$+$D$\rightarrow n +^3$He in a Gamow-like window around 27 keV. The results show that astrophysical nuclear reaction yield can be modulated significantly by the self-generated electromagnetic fields and the collective motion of the plasma. This plasma-version mini-collider may provide a novel tool for studies of astrophysics-interested nuclear reactions in plasma with tunable energies in earth-based laboratories.

The quantum charged particle self-interaction problem within the Fock many temporal and Feynman proper time paradigms

A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.

A reduced model for relativistic electron beam transport in solids and dense plasmas

A hybrid reduced model for relativistic electron beam transport based on the angular moments of the relativistic kinetic equation with a special closure is presented. It takes into account collective effects with the self-generated electromagnetic fields as well as collisional effects with the slowing down of the relativistic electrons by plasmons, bound and free electrons and their angular scattering on both ions and electrons. This model allows for fast computations of relativistic electron beam transport while describing their energy distribution evolution. Despite the loss of information concerning the angular distribution of the electron beam, the model reproduces analytical estimates in the academic case of a monodirectional and monoenergetic electron beam propagating through a warm and dense plasma and hybrid particle-in-cell simulation results in a realistic laser-generated electron beam transport case.

Stationary solutions of non-autonomous Maxwell–Dirac systems

The Maxwell–Dirac system describes the interaction of a particle with its self-generated electromagnetic field. In this paper, we study the existence of least energy stationary solutions for non-autonomous Maxwell–Dirac system with a nonlinear term in (3+1)-Minkowski space–time via variational methods. This problem is strongly indefinite and presents a lack of compactness. To overcome these difficulties, we will use the linking and concentration compactness arguments.

Scott Correction for Large Atoms and Molecules in a Self-Generated Magnetic Field

We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that $Z\al^2\le \kappa_0$ for a sufficiently small $\kappa_0$, where $\al$ denotes the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, $\al\to 0$ such that $\kappa =Z\al^2$ is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.

Numerical Techniques for the Analysis of Charge Transport and Electrodynamics in Graphene Nanoribbons

In this paper, we report on multiphysics full-wave techniques in the frequency (energy)-domain and the time-domain, aimed at the investigation of the combined electromagnetic-coherent transport problem in carbon based on nano-structured materials and devices, e.g., graphene nanoribbons. The frequency-domain approach is introduced in order to describe a Poisson/Schrödinger system in a quasi static framework. An example of the self-consistent solution of laterally coupled graphene nanoribbons is shown. The time-domain approach deals with the solution of the combined Maxwell/Schrödinger system of equations. The propagation of a charge wavepacket is reported, showing the effect of the self-generated electromagnetic field that affects the dynamics of the charge wavepacket.

Angular distribution of emitted electrons due to intense p-polarized laser foil interaction

The angular distribution of electrons emitting from a foil surface illuminated by p-polarized laser pulses is studied using particle-in-cell simulation for incident angles of θ1=22.5°, 45°, 67.5° and laser amplitudes of a=0.5, 1, 2. Theoretical prediction of the emission direction, based on canonical momentum conservation along the target surface, is verified. Surface ablation, the Alfvén current limit, as well as self-generated electromagnetic fields on the surface are numerically investigated and found to play important roles in the modulation of the angular distribution of the emitted electrons. The emitted electrons of higher energy are found to be directly accelerated to near the polarization direction of the incident laser light. The simulation results agree very well with the recent experimental results from Al targets irradiated by a 60 fs, 180 mJ laser pulse.

Ground State Energy of Large Atoms in a Self-Generated Magnetic Field

We consider a large atom with nuclear charge $Z$ described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous $Z\to \infty$, $\al\to 0$ limit if $Z\al^2\leq \kappa$ for some universal $\kappa$, where $\al$ is the fine structure constant.