Relativistic Two-stream Instability Research Articles

A relativistic two-stream instability in an extremely low-density plasma

A linear analysis based on two-fluid equations in the approximation of a cold plasma, wherein the plasma temperature is assumed to be zero, demonstrates that a two-stream instability occurs in all cases. However, if this were true, the drift motion of electrons in an electric current over a wire would become unstable, inducing an oscillation in an electric circuit with ions bounded around specific positions. To avoid this peculiar outcome, we must assume a warm plasma with a finite temperature when discussing the criterion of instability. The two-stream instability in warm plasmas has typically been analyzed using the kinetic theory to provide a general formula for the instability criterion from the distribution function of the plasma. However, the criteria based on the kinetic theory do not have an easily applicable form. Here, we provide an easily applicable criterion for the instability based on the two-fluid model at finite temperatures, extensionally in the framework of special relativity. This criterion is relevant for analyzing two-stream instabilities in low-density plasmas in the universe and in Earth-based experimental devices.

A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations

Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in the light-wave modes. This can lead to intolerable simulation errors where accurate light propagation is needed (e.g. in laser-plasma interactions). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce an exactly energy- and charge-conserving relativistic electromagnetic PIC algorithm. Specifically, we employ the leap-frog method for Maxwell's equations, and the Crank-Nicolson method for the particle equations. The semi-implicit formulation still features a timestep CFL, but facilitates exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm employs a new particle pusher designed to maximize efficiency and minimize wall-clock-time impact vs. the explicit alternative. It has been implemented in a code named iVPIC, based on the Los Alamos National Laboratory VPIC code (https://github.com/losalamos/vpic). We present numerical results that demonstrate the properties of the scheme with sample test problems: relativistic two-stream instability, Weibel instability, and laser-plasma instabilities.

Quadratic conservative scheme for relativistic Vlasov–Maxwell system

For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solved the first-principle equations of kinetic plasmas, such as the relativistic Vlasov–Maxwell system. This fatal problem is brought by the fact that both the Vlasov and Maxwell equations are indirectly associated with the conservation laws by means of some mathematical manipulations. Here we propose a quadratic conservative scheme, which can strictly maintain the conservation laws by discretizing the relativistic Vlasov–Maxwell system. A discrete product rule and summation-by-parts are the key players in the construction of the quadratic conservative scheme. Numerical experiments of the relativistic two-stream instability and relativistic Weibel instability prove the validity of our computational theory, and the proposed strategy will open the doors to the first-principle studies of mesoscopic and macroscopic plasma physics.

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.

The nonlinear development of the relativistic two-stream instability

The two-stream instability has been mooted as an explanation for a range of astrophysical applications from GRBs and pulsar glitches to cosmology. Using the first nonlinear numerical simulations of relativistic multi-species hydrodynamics we show that the onset and initial growth of the instability are very well described by linear perturbation theory. In the later stages the linear and nonlinear description match only qualitatively, and the instability does not saturate even in the nonlinear case by purely ideal hydrodynamic effects.

Using the Relativistic Two-Stream Instability for the Generation of Soft-X-Ray Attosecond Radiation Pulses

In this Letter we discuss a novel method for generating ultrashort radiation pulses using a broadband two-stream instability in an intense relativistic electron beam. This method relies on an electron beam having two distinct two-energy bands. The use of this new high brightness electron beam scenario, in combination with ultrashort soft x-ray pulses from high harmonic generation in gas, allows the production of high power attosecond pulses for ultrafast pump and probe experiments.

Relativistic two-stream instability

We study the (local) propagation of plane waves in a relativistic, non- dissipative, two-fluid system, allowing for a relative velocity in the “background” configuration. The main aim is to analyze relativistic two-stream instability. This instability requires a relative flow—either across an interface or when two or more fluids interpenetrate—and can be triggered, for example, when one-dimensional plane-waves appear to be left-moving with respect to one fluid, but right-moving with respect to another. The dispersion relation of the two-fluid system is studied for different two-fluid equations of state: (i) the “free” (where there is no direct coupling between the fluid densities), (ii) coupled, and (iii) entrained (where the fluid momenta are linear combinations of the velocities) cases are considered in a frame-independent fashion (e.g.no restriction to the rest-frame of either fluid). As a by-product of our analysis we determine the necessary conditions for a two-fluid system to be causal and absolutely stable and establish a new constraint on the entrainment.

Relativistic collisional current-filamentation instability and two-stream instability in dense plasma

The collisional effects on the current-filamentation instability (CFI) and the two-stream instability (TSI), which appear as a relativistic intense electron beam penetrating into a cold dense plasma, are investigated. It is shown that the growth rate of the CFI mode is first attenuated and then enhanced by the collisional effects as the density ratio of the background plasma to the beam increases. Meanwhile, the maximum CFI growth rate is shifted to the long-wavelength region due to both the bulk plasma density increase and the collisional effects, resulting in larger filaments formation. On the other hand, collisional effects mainly attenuate the TSI and finally stabilize it. Numerical solutions under parameters close to the fast ignition scenario (FIS) are given, which show that the CFI growth rate can be enhanced by 2 orders of magnitude instead of being suppressed in the dense region. Therefore, the CFI-induced electron filaments formation and the resultant kinetic anomalous heating are potentially significant for the target heating in the FIS.

Channeled blast wave behavior based on longitudinal instabilities

To address the important issue of how kinetic energy of collimated blast waves is converted into radiation, Pohl & Schlickeiser (2000) have recently investigated the relativistic two-stream instability of electromagnetic turbulence. They have shown that swept-up matter is quickly isotropized in the blast wave, which provides relativistic particles and, as a result, radiation. Here we present new calculations for the electrostatic instability in such systems. It is shown that the electrostatic instability is faster than the electromagnetic instability for highly relativistic beams. However, even after relaxation of the beam via the faster electrostatic turbulence, the beam is still unstable with respect to the electromagnetic waves, thus providing the isotropization required for efficient production of radiation. While the emission spectra in the model of Pohl and Schlickeiser have to be modified, the basic characteristics persist.

Generation of Magnetic Fields in the Relativistic Shock of Gamma‐Ray Burst Sources

We show that the relativistic two-stream instability can naturally generate strong magnetic fields with 10-5-10-1 of the equipartition energy density, in the collisionless shocks of gamma-ray burst (GRB) sources. The generated fields are parallel to the shock front and fluctuate on the very short scale of the plasma skin depth. The synchrotron radiation emitted from the limb-brightened source image is linearly polarized in the radial direction relative to the source center. Although the net polarization vanishes under circular symmetry, GRB sources should exhibit polarization scintillations as their radio afterglow radiation gets scattered by the Galactic interstellar medium. Detection of polarization scintillations could therefore test the above mechanism for magnetic field generation.

Lattice of Langmuir solitons in the pulsar magnetosphere

From the study of the nonlinear evolution of the relativistic two-stream instability in the physical conditions of the pulsar magnetosphere, that gives rise to strong Langmuir turbulence, we conclude to the probable existence of a lattice of stable Langmuir soliton-like solutions, called "Langmuir microstructures". Such microstructures are associated to three different types of radiation mechanisms. The first mechanism is direct radiation of the microstructures. The second one is curvature radiation of the microstructures moving along the dipolar pulsar magnetic field lines. The third one is related to the acceleration of beam particles in interaction with the lattice of Langmuir microstructures. It can be extremely efficient when some coherence is maintained between the phases of beam particles, for instance by a modulation of the beam. The conditions in which one or the other of these three radiation mechanisms can account for observed pulsar radio luminosities are given.

Microtexture in the pulsar radio emission zone

This paper completes an analysis of a non-linear mechanism for pulsar radio radiation. This non-linear process results from the evolution of relativistic two-stream instability in the pulsar magnetosphere, which gives rise to strong Langmuir turbulence. There are stable Langmuir soliton-like solutions, called Langmuir microstructures, which may form a lattice in the magnetosphere. These Langmuir microstructures naturally produce three different types of radiation. The first is direct radiation of the microstructures themselves when perturbed in a direction perpendicular to the magnetic field lines

Effect of electron-ion collisions on the nonlinear state of the relativistic two-stream instability

The analysis outlines conditions for the hydrodynamic interaction, including foil scattering and beam self-magnetic field effects. For the hydrodynamic interaction, the oblique coupling coefficient model is extended to include the effect of a finite electron-ion collision rate on the nonlinear state. Partial numerical simulation results are found to be in agreement with the model. Limitations due to temperature inhomogeneity along the deposition length and to increased deposition length are also discussed. It is found that an intense relativistic electron beam can couple its energy via the two-stream instability to a high density 1017–1020 cm−3 plasma. It is required that the plasma be fully ionized, with an initial electron temperature of ≳10 eV for 1017 cm−3, 10–20 eV for 1018 cm−3, 15–50 eV for 1019 cm−3, and ∼100 eV for 1020 cm−3.

Plasma heating by relativistic electron beams. II. Return current interaction

The combined interactions of the relativistic two-stream instability and return current driven Buneman/ion sound instability are investigated by numerical simulation for a beam-to-plasma density ratio ≈10−1 and γ=2−8. In this regime the evolution of the two-stream instability is relatively unaffected by the return current instability. The growth rate of the Buneman instability drops sharply when trapping of plasma electrons by the unstable Buneman waves occurs, but wave growth continues at a much reduced rate until other processes, e.g.,ion acceleration, wave scattering, and nonlinear Landau damping set in. Ions are heated by the return current and this heating is almost independent of the initial beam γ for constant return current. The bulk of the electron distribution is heated, whereas in the absence of a return current the two-stream instability primarily produces only energetic tails. The total plasma electron energy after several hundred plasma periods is proportional to the beam energy. The effective collision frequency of the plasma electrons due to microturbulence is typically 0.2?0.4 ωi, where ωi is the ion plasma frequency. In the strong turbulence created by the electron beam and the return current, the wave energy spectrum scales as ‖Ek‖2≈k−2.

Saturation of the relativistic two-stream instability by electron trapping

The single-wave weak cold relativistic two-stream instability has been studied in one dimension by numerical integration of the equations of motion, energy conservation, and Poisson’s equation. The dynamics is shown to depend only on the single parameter S = β02γ0(nb/2np)1/3. The nondimensionalized wave energy at initial saturation due to beam trapping, W1 = 〈E2〉/8πnbmc2γ0, reaches a maximum W1 = 0.09 at S = 0.4 and then decreases with S, but if S≳0.5 the wave energy is larger at subsequent bounces of the trapped particles, so that Wmax increases roughly monotonically with S, reaching 0.11 at S = 3. The drop-off of W1(S) is due to a relativistic tendency of beam electrons to bunch in the part of the orbit where the beam electron energy is largest. The self-consistent nonlinear shifts in wave frequency and amplitude are shown to play an essential role in extracting energy from the beam.

Ion Acceleration by the Relativistic Two-Stream Instability

Through theoretical analysis and computer simulation, one finds that a pinched relativistic electron beam in a plasma interacts strongly with plasma ions by means of the two-stream instability. Due both to the low phase velocity of the unstable waves and to their subsequent non-linear collapse, ions are accelerated to very high energies. This process is suggested as a possible explanation for experimentally observed collective ion acceleration by electron beams. (auth)