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Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave mo...
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Context 1
... the case ρ = 1 shown in figure 7, relativistic effects are important. Comparing the dispersion curves in figure 7 with those in figure 6, an obvious difference is the cutoff frequency ω x = ω L (∞), which is only marginally below ω = ω p for ρ = 20, and is significantly below ω = ω p for ρ = 1. ...
Context 2
... the case ρ = 1 shown in figure 7, relativistic effects are important. Comparing the dispersion curves in figure 7 with those in figure 6, an obvious difference is the cutoff frequency ω x = ω L (∞), which is only marginally below ω = ω p for ρ = 20, and is significantly below ω = ω p for ρ = 1. Another notable difference is the frequency ω 1 = ω L (1) at which the dispersion curve for the L mode crosses the light line: this is marginally above ω = ω p for ρ = 20, and significantly above ω = ω p for ρ = 1. ...
Context 3
... turnover branch of the Alfvén mode for z A > z m and ρ 1 is dominated by the peak in z 2 W(z). For the case ρ = 1 shown in figure 7, the Alfvén mode consists of a thin loop, with the higher-frequency and lower-frequency portions joining at a turnover that corresponds to the peak at z = z m in the RPDF. The maximum frequency of the Alfvén mode decreases with increasing θ approximately along the line z = z m . ...
Context 4
... the case ρ = 1 shown in figure 7, relativistic effects are important. Comparing the dispersion curves in figure 7 with those in figure 6, an obvious difference is the cutoff frequency ω x = ω L (∞), which is only marginally below ω = ω p for ρ = 20, and is significantly below ω = ω p for ρ = 1. ...
Context 5
... the case ρ = 1 shown in figure 7, relativistic effects are important. Comparing the dispersion curves in figure 7 with those in figure 6, an obvious difference is the cutoff frequency ω x = ω L (∞), which is only marginally below ω = ω p for ρ = 20, and is significantly below ω = ω p for ρ = 1. Another notable difference is the frequency ω 1 = ω L (1) at which the dispersion curve for the L mode crosses the light line: this is marginally above ω = ω p for ρ = 20, and significantly above ω = ω p for ρ = 1. ...
Context 6
... turnover branch of the Alfvén mode for z A > z m and ρ 1 is dominated by the peak in z 2 W(z). For the case ρ = 1 shown in figure 7, the Alfvén mode consists of a thin loop, with the higher-frequency and lower-frequency portions joining at a turnover that corresponds to the peak at z = z m in the RPDF. The maximum frequency of the Alfvén mode decreases with increasing θ approximately along the line z = z m . ...
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Citations
... Finally, Fig 8 shows the total (generations I and II) distributions of the secondary particles as a function of their longitudinal 4-velocity u ′ in the plasma rest frame (< v ′ > = 0) for two values x0 = 0.5 and 0.8. Curve lines correspond to Jüttner distributions (Rafat et al. 2019) ...
A detailed study of the refraction of an ordinary wave in the magnetosphere of radio pulsars was carried out. For this, a consistent theory of the generation of secondary particles was constructed, which essentially takes into account the dependence of the number density and the energy spectrum of secondary particles on the distance from the magnetic axis. This made it possible to determine with high accuracy the refraction of the ordinary O-mode in the central region of the outflowing plasma, which makes it possible to explain the central peak of three-humped mean radio profiles. As shown by detailed numerical calculations, in most cases it is possible to reproduce quite well the observed mean profiles of radio pulsars.
... We found that this frequency corresponds to the maximum frequency ω max of superluminal waves in the simulation. ω max is determined by the point in the ω − k domain, where the L-mode branch crosses the light line, i.e., it goes from superluminal to subluminal mode (Rafat et al. 2019;Manthei et al. 2021). Higher frequency wave modes (ω > ω max ) are subluminal, they do not generate electromagnetic waves in the 1D limit. ...
... Contrary, at least 3 × (10 5 − 10 9 ) such emitting regions would be necessary to account for the observed emission power by a streaming instability. The total emission flux depends on the properties of the plasma instabilities and on the intensities of the electrostatic superluminal L-mode waves, the solutions of permittivity tensor component Λ 33 = 0, see Rafat et al. (2019). For the streaming instability, the emission power depends on the formation of soliton-like superluminous waves, which are generated for inverse temper-atures ρ ≥ 1.66 and Lorentz factors γ s > 40 (Benáček et al. 2021b). ...
Linear acceleration emission is one of the mechanisms proposed to explain the intense pulsar radio emissions. This mechanism is however not well understood due to a lack of its proper mathematical analyses, e.g., of the collective plasma response and the resulting emission power. We utilize 1D relativistic particle-in-cell simulations to derive the emission properties of two instabilities in neutron star magnetospheres, relativistic beam instability and interactions of plasma bunches/clouds. We found that the emission power by plasma bunch interactions exceeds emission due to streaming instability by seven orders of magnitude. The wave power generated by a plasma bunch interaction can be obtained as large as $3.4\times10^{19}$ W. It alone can account for the total radio power emitted by typical pulsars ($10^{18}-10^{22}$ W). The emission of the plasma bunch has a number of features of the observed pulsar radiation. Its spectrum is characterized by an almost flat profile for lower frequencies and a power-law with an index $\approx-2.5$ for higher frequencies. The angular width of the radiation decreases with increasing frequency. The generated wave power depends on the pulsar rotation angle. It can cause fine structures in the observed intensity as it fluctuates between positive and negative wave interference as a function of the emission angle.
... We have observed that E oscillations inductively driven in the inclined pair production bursts can act as a source for coherent electromagnetic waves. Although the initial oscillations in E is longitudinal, the induced waves are oblique and electromagnetic in nature, which makes them distinct from the L mode waves discussed in previous works (Rafat et al. 2019;Melrose et al. 2020). Moreover, the electromagnetic modes observed in our simulations are naturally produced in the oblique pair production fronts, and do not require the production of intermediary modes such as the L modes suggested by Melrose et al. (2020). ...
Pulsar magnetospheres are thought to be filled with electron-positron plasma generated in pair cascades. The driving mechanism of these cascades is the emission of gamma-ray photons and their conversion into pairs via Quantum Electrodynamics (QED) processes. In this work, we present 2D particle-in-cell simulations of pair cascades in pulsar polar caps with realistic magnetic field geometry that include the relevant QED processes from first principles. Our results show that, due to variation of magnetic field curvature across the polar cap, pair production bursts self-consistently develop an inclination with respect to the local magnetic field that favors the generation of coherent electromagnetic modes with properties consistent with pulsar radio emission. We show that this emission is peaked along the magnetic axis and close to the polar cap edge and may thus offer an explanation for the core and conal components of pulsar radio emission.
... As we are dealing with the dispersion properties of waves modes in relativistic plasmas, the naming convention of waves and properties is slightly different from that used in nonrelativistic plasmas, where "classical" Langmuir waves are present (Rafat et al. 2019c). In the context of this paper, we distinguish between subluminal waves, subluminal solitons, superluminal waves, and superluminal solitons. ...
... They define the properties of the parallel Alfvén mode (A-mode, Λ 11 = 0), parallel X-mode (Λ 22 = 0), and parallel longitudinal mode (L-mode, Λ 33 = 0). As only longitudinal waves are present in our simulations, we are interested in the solutions to the latter equation, Λ 33 = 0, with Λ 33 defined as (Rafat et al. 2019a(Rafat et al. , 2019c In order to account for the relativistic pulsar conditions, a Maxwell-Jüttner distribution is suited to model the velocity distribution function for both the background and beam plasma (Equations (2) and (3)). These distribution functions, labeled g α (u) (α = 0, 1 as subscripts for background and beam, respectively) define the respective relativistic plasma dispersion functions W α (z): ...
A number of possible pulsar radio emission mechanisms is based on instabilities of the relative streaming and beams in their relativistic electron-positron pair plasma. At saturation the unstable waves can form, in principle, stable solitary waves which could emit the observed intense radio signals. We searched for the proper plasma parameters which would lead to the formation of solitons, investigated their properties and dynamics as well as the resulting oscillations of electrons and positrons possibly leading to radio wave emission. We utilized a one-dimensional version of the relativistic Particle-in-Cell code Acronym, initialized an appropriately parameterized one-dimensional Maxwell-J\"uttner velocity space particle distribution and studied the evolution of the resulting streaming instability in the strong pulsar magnetic fields. We found that for plasmas with inverse temperatures $\rho \geq 1.66$ or relative electron-positron drift speeds with Lorentz factors $\gamma > 40$, strong electrostatic solitons form associated with L- and A-mode plasma waves. The parameters of the solitons fulfill the wave emission conditions. For appropriate pulsar parameters the resulting energy densities of L-mode solitons can reach up to $1.1 \times 10^5$ erg$\cdot$cm$^{-3}$ while those of A-mode solitons reach only up to $1.2 \times 10^4$ erg$\cdot$cm$^{-3}$. Estimated energy densities of up to $7 \times 10^{12}$ erg$\cdot$cm$^{-3}$ suffice to explain pulsar nanoshots.
... Wave dispersion in a pulsar plasma plays an important role in our discussion of possible radio emission mechanisms. In three recent papers, referred to here as RMM1 (Rafat et al. 2019a), RMM2 (Rafat et al. 2019b) and RMM3 (Rafat et al. 2019c) we discussed aspects of the plasma physics relevant to a pulsar plasma in detail. In RMM1 we discussed wave dispersion in the rest frame of a pulsar plasma. ...
We consider critically the three most widely favored pulsar radio emission mechanisms: coherent curvature emission (CCE), beam-driven relativistic plasma emission (RPE) and anomalous Doppler emission (ADE). We assume that the pulsar plasma is one dimensional (1D), streaming outward with a bulk Lorentz factor γs ≫ 〈γ〉 − 1 ≳ 1, where 〈γ〉 is the intrinsic spread in the rest frame of the plasma. We argue that the formation of beams in a multi-cloud model is ineffective in the intrinsically relativistic case for plausible parameters, because the overtaking takes too long. We argue that the default choice for the particle distribution in the rest frame is a Jüttner distribution and that relativistic streaming should be included by applying a Lorentz transformation to the rest-frame distribution, rather than the widely assumed relativistically streaming Gaussian distribution. We find that beam-driven wave growth is severely restricted by (a) the wave properties in pulsar plasma, (b) a separation condition between beam and background, and (c) the inhomogeneity of the plasma in the pulsar frame. The growth rate for the kinetic instability is much smaller and the bandwidth of the growing waves is much larger for a Jüttner distribution than for a relativistically streaming Gaussian distribution. No reactive instability occurs at all for a Jüttner distribution. We conclude that none of CCE, RPE and ADE in tenable as the generic pulsar radio emission mechanism for “plausible” assumptions about the pulsar plasma.
... Wave dispersion in a pulsar plasma plays an important role in our discussion of possible radio emission mechanisms. In three recent papers, referred to here as RMM1 (Rafat et al. 2019a), RMM2 (Rafat et al. 2019b) and RMM3 (Rafat et al. 2019c) we discussed aspects of the plasma physics relevant to a pulsar plasma in detail. In RMM1 we discussed wave dispersion in the rest frame of a pulsar plasma. ...
We consider critically the three most widely favored pulsar radio emission mechanisms: coherent curvature emission (CCE), beam-driven relativistic plasma emission (RPE) and anomalous Doppler emission (ADE). We assume that the pulsar plasma is one dimensional (1D), streaming outward with a bulk Lorentz factor $\gamma_{\rm s} \gg \langle\gamma\rangle -1 \gtrsim 1$, where $\langle\gamma\rangle$ is the intrinsic spread in the rest frame of the plasma. We argue that the formation of beams in a multi-cloud model is ineffective in the intrinsically relativistic case for plausible parameters, because the overtaking takes too long. We argue that the default choice for the particle distribution in the rest frame is a J{\"u}ttner distribution and that relativistic streaming should be included by applying a Lorentz transformation to the rest-frame distribution, rather than the widely assumed relativistically streaming Gaussian distribution. We find that beam-driven wave growth is severely restricted by (a) the wave properties in pulsar plasma, (b) a separation condition between beam and background, and (c) the inhomogeneity of the plasma in the pulsar frame. The growth rate for the kinetic instability is much smaller and the bandwidth of the growing waves is much larger for a J{\"u}ttner distribution than for a relativistically streaming Gaussian distribution. No reactive instability occurs at all for a J{\"u}ttner distribution. We conclude that none of CCE, RPE and ADE in tenable as the generic pulsar radio emission mechanism for ``plausible'' assumptions about the pulsar plasma.
Fast radio bursts (FRBs) can present a variety of polarization properties and some of them are characterized by narrow spectra. In this work, we study spectral properties from the perspective of intrinsic radiation mechanisms and absorption through the waves propagating in the magnetosphere. The intrinsic radiation mechanisms are considered by invoking quasi-periodic bunch distribution and perturbations on charged bunches moving on curved trajectories. The narrowband emission is likely to reflect some quasi-periodic structure on the bulk of bunches, which may be due to quasi-periodically sparking in a ``gap'' or quasi-monochromatic Langmuir waves. A sharp spike would appear in the spectrum if the perturbations were to induce a monochromatic oscillation of bunches; however, it is difficult to create a narrow spectrum because the Lorentz factor has large fluctuations, so the spike disappears. Both the bunching mechanism and perturbations scenarios share the same polarization properties, with a uniformly distributed bulk of bunches. We investigated the absorption effects, including Landau damping and curvature self-absorption in the magnetosphere, which are significant at low frequencies. Subluminous O-mode photons cannot escape from the magnetosphere due to the Landau damping, leading to a height-dependent lower frequency cut-off. The spectra can be narrow when the frequency cut-off is close to the characteristic frequency of curvature radiation, however, such conditions cannot always be met. The spectral index is 5/3 at low-frequency bands due to the curvature self-absorption are not as steep as what is seen in observations. The intrinsic radiation mechanisms are more likely to generate the observed narrow spectra of FRBs, rather than the absorption effects.
Context. Coherent radiation of pulsars, magnetars, and fast radio bursts could, in theory, be interpreted as radiation from solitons and soliton-like waves. Solitons are meant to contain a large number of electric charges confined on long timescales and can radiate strongly via coherent curvature emission. However, solitons are also known to undergo a wave collapse, which casts doubts on the correctness of the soliton radio emission models of neutron stars.
Aims. We investigated the evolution of the caviton type of solitons self-consistently formed by the relativistic streaming instability and compared their apparent stability in 1D calculations with more generic 2D cases, in which the solitons are seen to collapse. Three representative cases of beam Lorentz factors and plasma temperatures were studied to obtain soliton dispersion properties.
Methods. We utilized 1D electrostatic and 2D electromagnetic relativistic particle-in-cell simulations at kinetic microscales.
Results. We find that no solitons are generated by the streaming instability in the 2D simulations. Only superluminal L -mode (relativistic Langmuir) waves are produced during the saturation of the instability, but these waves have smaller amplitudes than the waves in the 1D simulations. The amplitudes tend to decrease after the instability has saturated, and only waves close to the light line, ω = ck , remain. Solitons in the 1D approach are stable for γ b ≳ 60, but they disappear for low beam Lorentz factors, γ b < 6.
Conclusions. Our examples show that the superluminal soliton branch that is formed in 1D simulations will not be generated by the relativistic streaming instability when more dimensional degrees of freedom are present. The soliton model cannot, therefore, be used to explain the coherent radiation of pulsars, magnetars, and fast radio bursts – unless one can show that there are alternative plasma mechanisms for the soliton generation.
Context. The microwave radio dynamic spectra of the Crab pulsar interpulse contain fine structures represented via narrowband quasiharmonic stripes. The pattern significantly constrains any potential emission mechanism. Similar to the zebra patterns observed, for example, in type IV solar radio bursts or decameter and kilometer Jupiter radio emission, the double plasma resonance (DPR) effect of the cyclotron maser instability may allow for interpretion of observations of pulsar radio zebras.
Aims. We provide insight at kinetic microscales of the zebra structures in pulsar radio emissions originating close to or beyond the light cylinder.
Methods. We present electromagnetic relativistic particle-in-cell (PIC) simulations of the electron–positron cyclotron maser for cyclotron frequency smaller than the plasma frequency. In four distinct simulation cycles, we focused on the effects of varying the plasma parameters on the instability growth rate and saturation energy. The physical parameters were the ratio between the plasma and cyclotron frequency, the density ratio of the “hot” loss-cone to the “cold” background plasma, the loss-cone characteristic velocity, and comparison with electron–proton plasma.
Results. In contrast to the results obtained from electron–proton plasma simulations (for example, in solar system plasmas), we find that the pulsar electron–positron maser instability does not generate distinguishable X and Z modes. On the contrary, a singular electromagnetic XZ mode was generated in all studied configurations close to or above the plasma frequency. The highest instability growth rates were obtained for the simulations with integer plasma-to-cyclotron frequency ratios. The instability is most efficient for plasma with characteristic loss-cone velocity in the range v th = 0.2 − 0.3 c . For low density ratios, the highest peak of the XZ mode is at double the frequency of the highest peak of the Bernstein modes, indicating that the radio emission is produced by a coalescence of two Bernstein modes with the same frequency and opposite wave numbers. Our estimate of the radiative flux generated from the simulation is up to ∼30 mJy from an area of 100 km ² for an observer at 1 kpc distance without the inclusion of relativistic beaming effects, which may account for multiple orders of magnitude.
A detailed study of the refraction of an ordinary wave in the magnetosphere of radio pulsars was carried out. For this, a consistent theory of the generation of secondary particles was constructed, which essentially takes into account the dependence of the number density and the energy spectrum of secondary particles on the distance from the magnetic axis. This made it possible to determine with high accuracy the refraction of the ordinary O-mode in the central region of the outflowing plasma, which makes it possible to explain the central peak of three-humped mean radio profiles. As shown by detailed numerical calculations, in most cases it is possible to reproduce quite well the observed mean profiles of radio pulsars.
