Cold Pair Plasma Research Articles

Waves in a warm pair plasma: a relativistically complete two-fluid analysis

We present an ideal two-fluid wave mode analysis for a pair plasma, extending an earlier study for cold conditions to the warm pair plasma case. Starting from the completely symmetrized means for writing the governing linearized equations in the pair fluid rest frame, we discuss the governing dispersion relation containing all six pairs of forward and backward propagating modes, which are conveniently labelled as S, A, F, M, O and X. These relate to the slow (S), Alfvén (A) and fast (F) magnetohydrodynamic waves, include a modified (M) electrostatic mode, as well as the electromagnetic O and X branches. In the dispersion relation, only two parameters appear, which define the pair plasma magnetization$E^{2}\in [0,\infty ]$and the squared pair plasma sound speed $v^{2}$, measured in units of the light speed $c$. The description is valid also in the highly relativistic regime, where either a high magnetization and/or a relativistic temperature (hence sound speed) is reached. We recover the exact relativistic single-fluid magnetohydrodynamic expressions for the S, A and F families in the low wavenumber–frequency regime, which can be obtained for any choice of the equation of state. We argue that, as in a cold pair plasma, purely parallel or purely perpendicular propagation with respect to the magnetic field vector$\boldsymbol{B}$is special, and near-parallel or near-perpendicular orientations demonstrate avoided crossings of branches at computable wavenumbers and frequencies. The complete six-mode phase and group diagram views are provided as well, visually demonstrating the intricate anisotropies in all wave modes, as well as their transformations. Analytic expressions for all six wave group speeds at both small and large wavenumbers complement the analysis.

The synchrotron maser emission from relativistic shocks in Fast Radio Bursts: 1D PIC simulations of cold pair plasmas

ABSTRACT The emission process of Fast Radio Bursts (FRBs) remains unknown. We investigate whether the synchrotron maser emission from relativistic shocks in a magnetar wind can explain the observed FRB properties. We perform particle-in-cell (PIC) simulations of perpendicular shocks in cold pair plasmas, checking our results for consistency among three PIC codes. We confirm that a linearly polarized X-mode wave is self-consistently generated by the shock and propagates back upstream as a precursor wave. We find that at magnetizations σ ≳ 1 (i.e. ratio of Poynting flux to particle energy flux of the pre-shock flow) the shock converts a fraction $f_\xi ^{\prime } \approx 7 \times 10^{-4}/\sigma ^2$ of the total incoming energy into the precursor wave, as measured in the shock frame. The wave spectrum is narrow-band (fractional width ≲1−3), with apparent but not dominant line-like features as many resonances concurrently contribute. The peak frequency in the pre-shock (observer) frame is $\omega ^{\prime \prime }_{\rm peak} \approx 3 \gamma _{\rm s | u} \omega _{\rm p}$, where γs|u is the shock Lorentz factor in the upstream frame and ωp the plasma frequency. At σ ≳ 1, where our estimated $\omega ^{\prime \prime }_{\rm peak}$ differs from previous works, the shock structure presents two solitons separated by a cavity, and the peak frequency corresponds to an eigenmode of the cavity. Our results provide physically grounded inputs for FRB emission models within the magnetar scenario.

Wave modes in a cold pair plasma: the complete phase and group diagram point of view

We present a complete analysis of all wave modes in a cold pair plasma, significantly extending standard textbook treatments. Instead of identifying the maximal number of two propagating waves at fixed frequency $\unicode[STIX]{x1D714}$, we introduce a unique labelling of all 5 mode pairs described by the general dispersion relation $\unicode[STIX]{x1D714}(k)$, starting from their natural ordering at small wavenumber $k$. There, the 5 pairs start off as Alfvén (A), fast magnetosonic (F), modified electrostatic (M) and electromagnetic O and X branches, and each $\unicode[STIX]{x1D714}(k)$ branch smoothly connects to large wavenumber resonances or limits. For cold pair plasmas, these 5 branches show avoided crossings, which become true crossings at exactly parallel or perpendicular orientation. Only for those orientations, we find a changed connectivity between small and large wavenumber behaviour. Analysing phase and group diagrams for all 5 wave modes, distinctly different from the Clemmow–Mullaly–Allis representation, reveals the true anisotropy of the A, M and O branches.

Kinetic inhibition of magnetohydrodynamics shocks in the vicinity of a parallel magnetic field

According to magnetohydrodynamics (MHD), the encounter of two collisional magnetized plasmas at high velocity gives rise to shock waves. Investigations conducted so far have found that the same conclusion still holds in the case of collisionless plasmas. For the case of a flow-aligned field, MHD stipulates that the field and the fluid are disconnected, so that the shock produced is independent of the field. We present a violation of this MHD prediction when considering the encounter of two cold pair plasmas along a flow-aligned magnetic field. As the guiding magnetic field grows, isotropization is progressively suppressed, resulting in a strong influence of the field on the resulting structure. A micro-physics analysis allows us to understand the mechanisms at work. Particle-in-cell simulations also support our conclusions and show that the results are not restricted to a strictly parallel field.

Simulation study of the formation of a non-relativistic pair shock

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed $c/5$, where $c$ is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.

The Alfvén resonance in pair plasmas

Waves propagating obliquely in a magnetized cold pair plasma experience an approximate resonance in the wavevector component perpendicular to the magnetic field, which is the analogue of the Alfvén resonance in normal electron-ion plasmas. Wave absorption at the resonance can take place via mode conversion to the analogue of the short wavelength inertial Alfvén wave. The Alfvén resonance could play a role in wave propagation in the pulsar magnetosphere leading to pulsar radio emission. Ducting of waves in strong plasma gradients may occur in the pulsar magnetosphere, which leads to the consideration of Alfvén surface waves, whose energy is concentrated in the region of strong gradients.

Relativistic collisionless shocks formation in pair plasmas

AbstractCollisionless shocks are ubiquitous in astrophysics and in the laboratory. Recent numerical simulations and experiments have shown how these can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step toward a microscopic understanding of the process, we here analyze in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two unmagnetized, symmetric, and initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω=0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.

Collisionless shock formation, spontaneous electromagnetic fluctuations, and streaming instabilities

Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic Particle-In-Cell simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.

Theoretical aspects of the Fireball scenario

Collisionless shocks are a key ingredient of the Fireball scenario. Yet, their formation from the encounter of two collisionless plasma shells is not understood from first principles. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in details the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω = 0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.

Alfvén resonance absorption in electron-positron plasmas

AbstractWaves propagating obliquely in a magnetized cold pair plasma experience an approximate resonance in the wavevector component perpendicular to the magnetic field, which is the analogue of the Alfvén resonance in normal electron-ion plasmas. Wave absorption at the resonance can take place via mode conversion to the analogue of the short wavelength inertial Alfvén wave. The Alfvén resonance could play a role in wave propagation in the pulsar magnetosphere leading to pulsar radio emission. Ducting of waves in strong plasma gradients may occur in the pulsar magnetosphere, which leads to the consideration of Alfvén surface waves, whose energy is concentrated in the region of strong gradients.

The Alfvén resonance in pair plasmas

The absorption of wave energy in a magnetized cold pair plasma at the analog of the Alfvén resonance is considered. Splitting of the parallel propagating wave modes due to imbalance of pair species densities is discussed. For oblique propagation of the waves, it is shown that, if the wave frequency is much less than the plasma frequency, there is an approximate resonance in the wave vector component perpendicular to the magnetic field, which may be identified as the analog of the Alfvén resonance in normal electron-ion plasmas. The wave differential equations for a nonuniform plasma also exhibit the resonance. The pair species charge imbalance plays a similar role in the Alfvén resonance process to the Hall term (or finite ion cyclotron frequency effect) in electron-ion plasmas. Wave absorption at the resonance can take place via mode conversion to the analog of the short wavelength inertial Alfvén wave, whose properties are discussed.

Numerical construction of magnetosphere with relativistic two-fluid plasma flows

We present a numerical model in which a cold pair plasma is ejected with relativistic speed through a polar cap region and flows almost radially outside the light cylinder. Stationary axisymmetric structures of electromagnetic fields and plasma flows are self-consistently calculated. In our model, motions of positively and negatively charged particles are assumed to be determined by electromagnetic forces and inertial terms, without pair creation and annihilation or radiation loss. The global electromagnetic fields are calculated by the Maxwell's equations for the plasma density and velocity, without using ideal MHD condition. Numerical result demonstrates the acceleration and deceleration of plasma due to parallel component of the electric fields. Numerical model is successfully constructed for weak magnetic fields or highly relativistic fluid velocity, i.e, kinetic energy dominated outflow. It is found that appropriate choices of boundary conditions and plasma injection model at the polar cap should be explored in order to extend present method to more realistic pulsar magnetosphere, in which the Poynting flux is dominated.