Counterstreaming Plasmas Research Articles

Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas.

Electromagnetic turbulence and ion kinetics in counterstreaming plasmas hold great significance in laboratory astrophysics, such as turbulence field amplification and particle energization. Here, we quantitatively demonstrate for the first time how electromagnetic turbulence affects ion kinetics under achievable laboratory conditions (millimeter-scale interpenetrating plasmas with initial velocity of 2000 km/s, density of 4×10^{19} cm^{-3}, and temperature of 100eV) utilizing a recently developed high-order implicit particle-in-cell code without scaling transformation. It is found that the electromagnetic turbulence is driven by ion two-stream and filamentation instabilities. For the magnetized scenarios where an applied magnetic field of tens of Tesla is perpendicular to plasma flows, the growth rates of instabilities increase with the strengthening of applied magnetic field, which therefore leads to a significant enhancement of turbulence fields. Under the competition between the stochastic acceleration due to electromagnetic turbulence and collisional thermalization, ion distribution function shows a distinct super-Gaussian shape, and the ion kinetics are manifested in neutron yields and spectra. Our results have well explained the recent unmagnetized experimental observations, and the findings of magnetized scenario can be verified by current astrophysical experiments.

Deuterium–deuterium fusion in nanowire plasma driven with a nanosecond high-energy laser

Investigating the enhancement of the interaction between laser and plasma is crucial for fundamental and applied physics research studies based on laser-induced acceleration and nuclear reactions. The improvement of energy conversion efficiency resulting in increasing reaction yields has been extensively studied by the interaction of femtosecond (fs) or picosecond (ps) lasers with nanowire targets. However, the effects of nanosecond (ns) lasers interacting with nanowire targets on energy absorption and production yield remain unknown. To address this issue, we conducted a deuterium–deuterium fusion experiment based on the collision of two plasmas induced by the interaction of the kilo-Joule-level nanosecond laser with nanowire targets. The experimental results of neutron detection indicate that the yields of nanowire targets remain at the same level as those of planar targets. We have used the counter-streaming collisionless plasma model to perform a numerical analysis of the output of nuclear reaction products at the center-of-mass energy (Ec.m.) values between 10 and 30 keV, and the calculation results are in good agreement with the experimental results. In addition, a magneto-hydrodynamic numerical simulation was also performed. It shows that the critical density of the target’s surface, which forms on the picosecond time scale, blocks the absorption of laser energy with nanosecond pulse length. Consequently, both our experimental and simulation results indicate that the enhancement factor is limited when a target with a spatial period less than µm is used in conjunction with a ns laser. Therefore, additional research is highly desirable to develop a target structure that can improve the efficiency of energy conversion between the laser and the target.

Experimental evidence of early-time saturation of the ion-Weibel instability in counterstreaming plasmas of CH, Al, and Cu.

The collisionless ion-Weibel instability is a leading candidate mechanism for the formation of collisionless shocks in many astrophysical systems, where the typical distance between particle collisions is much larger than the system size. Multiple laboratory experiments aimed at studying this process utilize laser-driven (I≳10^{15} W/cm^{2}), counterstreaming plasma flows (V≲2000km/s) to create conditions unstable to Weibel-filamentation and growth. This technique intrinsically produces temporally varying plasma conditions at the midplane of the interaction where Weibel-driven B fields are generated and studied. Experiments discussed herein demonstrate robust formation of Weibel-driven B fields under multiple plasma conditions using CH, Al, and Cu plasmas. Linear theory based on benchmarked radiation-hydrodynamic FLASH calculations is compared with Fourier analyses of proton images taken ∼5-6 linear growth times into the evolution. The new analyses presented here indicate that the low-density, high-velocity plasma-conditions present during the first linear-growth time (∼300-500ps) sets the spectral characteristics of Weibel filaments during the entire evolution. It is shown that the dominant wavelength (∼300μm) at saturation persists well into the nonlinear phase, consistent with theory under these experimental conditions. However, estimates of B-field strength, while difficult to determine accurately due to the path-integrated nature of proton imaging, are shown to be in the ∼10-30T range, an order of magnitude above the expected saturation limit in homogenous plamas but consistent with enhanced B fields in the midplane due to temporally varying plasma conditions in experiments.

Evolution of Kelvin–Helmholtz Instability in the Fan-spine Topology

Abstract We use multiwavelength imaging observations from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory to study the evolution of the Kelvin–Helmholtz (K–H) instability in a fan-spine magnetic field configuration. This magnetic topology exists near an active region AR12297 and is rooted in a nearby sunspot. In this magnetic configuration, two layers of cool plasma flow in parallel and interact with each other inside an elongated spine. The slower plasma flow (5 km s−1) is the reflected stream along the spine’s field lines from the top, which interacts with the impulsive plasma upflows (114–144 km s−1) from below. This process generates a shear motion and subsequent evolution of the K–H instability. The amplitude and characteristic wavelength of the K–H unstable vortices increase, satisfying the criterion of the fastest-growing mode of this instability. We also describe how the velocity difference between two layers and the velocity of K–H unstable vortices are greater than the Alfvén speed in the second denser layer, which also satisfies the criterion of the growth of the K–H instability. In the presence of the magnetic field and sheared counterstreaming plasma as observed in the fan-spine topology, we estimate the parametric constant Λ ≥ 1, which confirms the dominance of velocity shear and the evolution of the linear phase of the K–H instability. This observation indicates that in the presence of complex magnetic field structuring and flows, the fan-spine configuration may evolve into rapid heating, while the connectivity changes due to the fragmentation via the K–H instability.

Efficient generation of turbulent collisionless shocks in laser-ablated counter-streaming plasmas

Laser-ablated high-energy-density (HED) plasmas offer a promising route to study astrophysically relevant processes underlying collisionless shock formation, magnetic field amplification, and particle acceleration in the laboratory. Using large-scale, multi-dimensional particle-in-cell simulations, we explore the interpenetration of laser-ablated counter-streaming plasmas for realistic experimental flow profiles. We find that the shock formation and its structure are substantially different from those of more idealized and commonly considered uniform flows: shock formation can be up to 10 times faster due to the transition from small-angle scattering to magnetic reflection and the shock front develops strong corrugations at the ion gyroradius scale. These findings have important consequences for current experimental programs and open exciting prospects for studying the microphysics of turbulent collisionless shocks with currently available high-energy laser systems.

Momentum transfer driven by fluctuations in relativistic counter-propagating electron beams

A semi-Lagrangian relativistic Vlasov–Maxwell solver is used to describe the non-linear momentum transfer between electron beams, which is driven by spontaneous fluctuations in the oblique filamentation instability (a type of Weibel mode) in two-dimensional plasmas. For counter-streaming plasmas, these filamentation instabilities may strengthen the generation of a fine structure of the distribution function in phase space. Properties of such counter-streaming beams are investigated using full-kinetic simulations and a Hamiltonian reduction technique based on the invariance of the transverse canonical momentum, the so-called multi-stream model. In the regime where , being the wavevector and d e the electron skin depth, a momentum transfer takes place when a mesoscale current filamentation mode couples with microscopic phase-space fluctuations. This regime is characterized by the appearance of filamentation modes with large wavenumbers and large amplitude fluctuations, which induce variations of the L 2-norm of the plasma in link with the self-organization of counter-streaming electron beams. We also discuss some theoretical aspects of information theory that highlight the role of the (reversible) entropy production in momentum transfer, thus by clarifying the connections between (microscopic) fluctuations of the distribution function and the fundamental aspects of the filamentation in Vlasov theory. The momentum transfer between beams is quantitatively analyzed by means of both theoretical estimations and numerical experiments.

Low- and high-frequency nature of oblique filamentation modes. I. Linear theory

The solution of the linear dispersion relation of electromagnetic oblique instabilities, for two counterstreaming electron beams, is investigated by using an extended fluid approach that includes the full dynamics of the pressure tensor. Numerical solutions of the simplified polynomial formulation so obtained are analyzed and compared to full kinetic solutions. They correspond to two classes of eigenmodes: low- and high-frequency oblique modes of resonant character. Coexistence of several oblique modes in neighboring regions of the wave vector plane, having close growth-rates, leads to the possibility of a transition starting from a low wave number mode to an oblique mode of high values in wave numbers. For such counterstreaming plasmas, the oblique instability may strengthen and amplify the filamentation process of the distribution function in velocity space, a property of the Vlasov equation. In addition to its simplicity, useful for solving the dispersion relation in the linear regime and for identifying kinetic solutions difficult to calculate otherwise, this extended fluid model is helpful in gaining insight into the fundamental properties of Vlasov theory, which are possibly relevant to kinetic heating processes.

Numerical simulation on the formation and merging of ablation plasma in two exploding aluminum wires

In this paper, computational results characterizing the formation and merging of counter-streaming interpenetrating plasma flows formed in exploding double parallel aluminum wires are presented. A radial magnetohydrodynamic computation is carried out first to obtain the parameters of core-corona structure in individual wires, providing an initial condition for the planar magnetohydrodynamic model in a multi-species fluids scheme with two-temperature treatment of plasma. In the XY plane, two aluminum plasma clouds are surrounded by extremely thin air, which represents a vacuum environment. A long-lasting compressed layer of extremely thin air in the central region of the inter-wire gap is formed before the merger of aluminum plasma flows. The accordance between the increasing mass fraction of aluminum plasma species in the central slit and the enhancement in self-emission light demonstrates that the real physical characteristics of extremely low-density vacuum environment plays an important role in merger of aluminum plasma flows. Current density is concentrated in the central column during the merging process of counter-streaming interpenetrating aluminum plasma flows, evolving from a structure of bifurcated current sheets into a single narrow sheet. Efficient numerical investigation on the interaction between counter-streaming plasma flows requires the incorporation of surrounding fluid species of extremely thin air.

On the local measurement of electric currents and magnetic fields using Thomson scattering in Weibel-unstable plasmas

We demonstrate the capability of the Thomson Scattering (TS) diagnostic to measure locally the microscopic electron and ion currents in counter-streaming plasmas unstable to the Weibel or current-filamentation instability. Synthetic TS spectra are calculated with particle distribution functions obtained from particle-in-cell simulations and used to accurately reproduce the simulated currents. We show that this technique allows accurate local measurements of the magnetic field, thus opening the way for the complete experimental characterization of the growth rate, saturation, and nonlinear dynamics of electromagnetic instabilities in plasmas. We illustrate the application of this diagnostic to experimental TS data, which yields local measurements of the magnetic field in Weibel-unstable plasmas and indicates that the magnetic energy density reaches ∼1% of the kinetic energy density of the flows, in agreement with previous numerical studies.

Plasma Collision in a Gas Atmosphere.

We present a study on the impact of a gas atmosphere on the collision of two counterpropagating plasmas (gold and carbon). Imaging optical Thomson scattering data of the plasma collision with and without helium in between have been obtained at the Omega laser facility. Without gas, we observed large scale mixing of colliding gold and carbon ions. Once ambient helium is added, the two plasmas remain separated. The difference in ionic temperature is consistent with a reduction of the maximum Mach number of the flow from M=7 to M=4. It results in a reduction of a factor ∼10 of the counterstreaming ion-ion mean free path. By adding a low-density ambient gas, it is possible to control the collision of two high-velocity counterstreaming plasma, transitioning from an interpenetrating regime to a regime in agreement with a hydrodynamic description.

Calibration of CR-39 solid state track detectors with monoenergetic protons from 0.3 MeV to 2.5 MeV

The2H(d,p)3H reaction is one of the most crucial reactions in the Big Bang nucleosynthesis (BBN). It is of particular interest to investigate this kind of reactions in plasma environments, generated by high intensity lasers, which are similar to real astrophysical conditions. We have experimentally investigated the2H(d,p)3H reaction using laser-driven counter-streaming collisionless plasmas at the Shenguang-II laser facility. CR-39 track detectors are widely employed as the main diagnostics in such experiments and laser-driven ion acceleration. In this work, we performed calibration of CR-39 track detectors with monoenergetic protons from the tandem accelerator, and then presented their track diameters for proton energies ranging from 300 keV to 2.5 MeV and for etching times between 4 and 28 hours. In addition, we recommended the optimal etching time at the typical etching conditions, which will be very useful for the following massive data analysis from the CR-39 detectors.

Distinguishing and diagnosing the spontaneous electric and magnetic fields of Weibel instability through proton radiography

The Weibel instability, a subject of relevance to many fields of physics ranging from inertial confinement fusion to some astrophysical scenarios, is usually probed with side-on proton radiography. In order to diagnose the strength and wavelength of the spontaneous fields, two concerns that must be settled are how to distinguish the coexisting electric and magnetic fields, and how to overcome the counteracting of deflections in radiographing the filamentary structured fields. In this paper, proton radiography of the Weibel instability in two counterstreaming plasma flows is studied by simulation. It suggests that the electric field dominates the deflection of probe protons, whereas the contribution from the magnetic field is negligible. To resolve the deflection-counteracting problem, the spatial spectrum of the electric field energy is found to be related to the deflection velocity of the probe beam by theoretical analyses. The strength and wavelength of the electric field are then obtainable from the proton flux on the detection plane, whereas the strength and wavelength of the magnetic field can be deduced through the equilibrium between the electric field and the magnetic field pressure gradient after the linear growth stage of the instability. Both numerical and experimental verifications suggest that our method performs well in extracting the strength and wavelength of the spontaneous electric and magnetic fields of the Weibel instability from proton radiography.

Characterizing filamentary magnetic structures in counter-streaming plasmas by Fourier analysis of proton images

Proton imaging is a powerful tool for probing electromagnetic fields in a plasma, providing a path-integrated map of the field topology. However, in cases where the field structure is highly inhomogeneous, inferring spatial properties of the underlying field from proton images can be difficult. This problem is exemplified by recent experiments, which used proton imaging to probe the filamentary magnetic field structures produced by the Weibel instability in collisionless counterstreaming plasmas. In this paper, we perform analytical and numerical analyses of proton images of systems containing many magnetic filaments. We find that, in general, the features observed on proton images do not directly correspond to the spacing between magnetic filaments (the magnetic wavelength) as has previously been assumed and that they instead correspond to the filament size. We demonstrate this result by Fourier analysis of synthetic proton images for many randomized configurations of magnetic filaments. Our results help guide the interpretation of experimental proton images of filamentary magnetic structures in plasmas.

Direct measurements of counter-streaming flows in a low-shear stellarator magnetic island topology

We report on the first experimental verification of theoretically predicted multiple bundles of counter-streaming plasma flows in the island-divertor scrape-off layer (SOL) of the stellarator Wendelstein 7-X. In the standard toroidal field direction (counter-clockwise when looking from the top) experiments, the overall structure of the SOL flows, such as flow directions, the number of flow bundles and the magnitude of the flow velocities, are consistent with numerical predictions obtained with EMC3-EIRENE. However, the modelling does not predict changes of the flow patterns with reversal of the magnetic field direction, which are experimentally observed. This indicates that additional relevant physics, such as particle drifts, will need to be incorporated into the numerical model to better describe the whole stellarator scrape-off layer behaviour.

A multispecies, multifluid model for laser–induced counterstreaming plasma simulations

The interpenetration of counterstreaming plasmas is an important phenomenon in several application areas, such as astrophysical flows, design of controlled fusion devices, and laser–induced plasma experiments. Multispecies “single-fluid” codes are unable to model this phenomenon due to the single velocity representation for all the species/fluids. Kinetic codes, though capable of modeling interpenetration, are computationally prohibitive for at-scale simulations. In this paper, we propose a multifluid model that solves the fluid equations for each ion fluid or stream. This allows distinct flows that interact with each other through electrostatic and collisional forces. We introduce and describe our code, EUCLID, that uses a conservative finite-difference formulation to discretize the governing equations in space. The 5th-order Monotonicity-Preserving WENO scheme is used for the upwind approximation of the hyperbolic flux, and the explicit 4th-order Runge–Kutta scheme is used for time integration. The code is verified for several benchmark cases and manufactured solutions. We simulate one- and two-dimensional interactions of counterstreaming plasmas in vacuum as well as in the presence of gas fill, where the setups are representative of laser-induced plasma experiments.

Temperature-dependent Saturation of Weibel-type Instabilities in Counter-streaming Plasmas

Abstract We present the first 2X2V continuum Vlasov–Maxwell simulations of interpenetrating, unmagnetized plasmas to study the competition between two-stream, Oblique, and filamentation modes in the weakly relativistic regime. We find that after nonlinear saturation of the fastest-growing two-stream and Oblique modes, the effective temperature anisotropy, which drives current filament formation via the secular Weibel instability, has a strong dependence on the internal temperature of the counter-streaming plasmas. The effective temperature anisotropy is significantly more reduced in colder than in hotter plasmas, leading to orders of magnitude lower magnetization for colder plasmas. A strong dependence of the energy conversion efficiency of Weibel-type instabilities on internal beam temperature has implications for determining their contribution to the observed magnetization of many astrophysical and laboratory plasmas.

Deflection effect of electromagnetic field generated byWeibel instability on proton probe

<sec> The electric and magnetic fields generated by the Weibel instability, most of which have a tube-like structure, are of importance for many relevant physical processes in the astrophysics and the inertial confinement fusion. Experimentally, proton radiography is a commonly used method to diagnose the Weibel instability, where the proton deflection introduced from the self-generated electric field is usually ignored. This assumption, however, is in conflict with the experimental observations by Quinn, Fox and Huntington, et al. because the magnetic field with a tube-like structure cannot introduce parallel flux striations on the deflection plane in the proton radiography.</sec><sec> In this paper, we re-examine the nature of the proton radiography of the Weibel instability numerically. Two symmetric counterstreaming plasma flows are used to generate the electron Weibel instability with the three-dimensional particle-in-cell simulations. The proton radiography of the Weibel instability generated electric and magnetic fields are calculated with the ray tracing method. Three cases are considered andcompared: only the self-generated electric field <i>E</i> is included, only the self-generated magnetic field <i>B</i> is included, both the electric field <i>E</i> and magnetic field <i>B</i> are included.</sec><sec> It is shown that when only <i>E</i> is included, the probe proton flux density perturbation on the detection plane, i.e., δ<i>n</i>/<i>n</i><sub>0</sub>, is much larger than that when only <i>B</i> is included. Also, when both <i>E</i> and <i>B</i> are included, δ<i>n</i>/<i>n</i><sub>0</sub> is almost the same as that when only <i>E</i> is included. This suggests that in the proton radiography of the Weibel instability generated electric and magnetic fields, the deflection from the electric field dominates the radiography, whereas the magnetic field has an ignorable influence. Our conclusion is quite different from that obtained on the traditional assumption that the electric field is ignorable in the radiography. This mainly comes from the spatial structure of the Weibel instability generated magnetic field, which is tube-like and points to the azimuthal direction around the current filaments. When the probe protons pass through the field region, the deflection from the azimuthal magnetic field can be compensated for completely by itself along the passing trajectories especially if the deflection distance inside the field region is small. Whereas for the electric field, which is in the radial direction, the deflection to the probe protons will not be totally compensated for and will finally introduce an evident flux density perturbation into the detection plane. This understanding can beconducive to the comprehension of the experimental results about the proton radiography of the Weibel instability.</sec>

Maxwell-Jüttner distributed counterstreaming magnetoplasmas—Parallel propagation

Counterstreaming beams of charged particles are frequently observed in the laboratory and space plasma systems, and they are responsible for supplying the free energy of the system in the absence of temperature anisotropies. Such systems are unstable and give rise to excitation of various electrostatic and electromagnetic plasma waves. This work is intended as a supplement to the previous investigations of the Maxwell-Jüttner distributed counterstreaming plasmas on the basis of the covariant (fully relativistic) formulation. Here, we aim to find analytical solutions of the dispersion relations and investigate the properties of the growth rate for the electrostatic and electromagnetic modes propagating parallel to the background magnetic field. The influences of the important parameters of the beam, namely, velocity, temperature, the relative intensity of the two streams, and the strength of the stationary magnetic field, on the growth rates of the longitudinal and transverse modes are compared. The analytical evaluation of the parallel modes reveals several interesting results. First, for all investigated modes, the growth rate is minimum only if the particle distribution function is exactly symmetric. Second, the behavior of the electrostatic and electromagnetic instabilities by varying the beam temperature is totally opposite. Third, increasing the drift velocity, the growth rate exhibits a maximum at a certain velocity; however, beyond that, wave damping occurs. Finally, under the same conditions, the external magnetic field has a destabilizing (stabilizing) effect on the left (right)-hand branch of the transverse modes.

Stability analysis of a periodic system of relativistic current filaments

The nonlinear evolution of current filaments generated by the Weibel-type filamentation instability is a topic of prime interest in space and laboratory plasma physics. In this paper, we investigate the stability of a stationary periodic chain of nonlinear current filaments in counterstreaming pair plasmas. We make use of a relativistic four-fluid model and apply the Floquet theory to compute the two-dimensional unstable eigenmodes of the spatially periodic system. We examine three different cases, characterized by various levels of nonlinearity and asymmetry between the plasma streams: a weakly nonlinear symmetric system, prone to purely transverse merging modes; a strongly nonlinear symmetric system, dominated by coherent drift-kink modes whose transverse periodicity is equal to, or an integer fraction of the unperturbed filaments; a moderately nonlinear asymmetric system, subject to a mix of kink and bunching-type perturbations. The growth rates and profiles of the numerically computed eigenmodes agree with particle-in-cell simulation results. In addition, we derive an analytic criterion for the transition between dominant filament-merging and drift-kink instabilities in symmetric two-beam systems.

Disruption of Current Filaments and Isotropization of the Magnetic Field in Counterstreaming Plasmas.

We study the stability of current filaments produced by the Weibel, or current filamentation, instability in weakly magnetized counterstreaming plasmas. It is shown that a resonance exists between the current-carrying ions and a longitudinal drift-kink mode that strongly deforms and eventually breaks the current filaments. Analytical estimates of the wavelength, growth rate, and saturation level of the resonant mode are derived and validated by three-dimensional particle-in-cell simulations. Furthermore, self-consistent simulations of counterstreaming plasmas indicate that this drift-kink mode is dominant in the slow down of the flows and in the isotropization of the magnetic field, playing an important role in the formation of collisionless shocks.