arXiv subjects

Jan Benáček

Publications and source records attributed to Jan Benáček.

18 recordsLinked to original sources

arXiv2026

Fast Radio Bursts from Monster Shocks and Flares of Inspiraling Binary Neutron Stars: A Kinetic Model for Double Pulsar

The coalescence of binary neutron star systems offers unprecedented possibilities for multimessenger observations, including the detection of gravitational waves, gamma-ray bursts, kilonovae, and potentially fast radio bursts. For a detailed investigation of the latter, one requires a kinetic plasma model to describe the interacting magnetospheres of the stars. We present a three-dimensional particle-in-cell kinetic simulation of the combined magnetosphere of a binary neutron star in which the two stars physically orbit one another so that the orbital motion itself twists the magnetic loops. We find that the stellar magnetic-field intensity ratio controls the emergence of flares, while the stellar spins set the direction and modulation of the flare. We identify four spatially and dynamically distinct regions of strong electromagnetic energy release: (i) an expanding fast magnetosonic wave that steepens into a monster shock, (ii) a plasma flare being pushed by (iii) an expanding fireball and containing (iv) a reconnecting current sheet. The fast magnetosonic wave is a promising source of coherent radio emission. It is released when orbital motion cuts a closed plasma loop. The electric and magnetic wave amplitudes are similar and reach that of the background magnetic field. Our kinetic treatment yields particle spectra and plasma structures that can be used to assess coherent emission in kinetic-scale simulations. In conclusion, the stellar orbital motion constitutes a driving channel distinct from models with spin-driven magnetospheric twisting.

astro-ph.HE↗

arXiv2026

Origin of radio polarization in pulsar polar caps

It is crucial to know the polarization properties of coherent radio waves that escape from pulsar polar caps to calculate the radiative transfer through the magnetosphere and to predict observable radio properties. We describe pair cascades in the pulsar polar cap, and we determine for the first time the Stokes parameters of the escaping radio waves from first-principle kinetic simulations for a pulsar with a magnetic obliquity of $60^{\circ}$. We present 3D particle-in-cell kinetic simulations that include quantum-electrodynamic pair cascades in a charge-limited flow from the stellar surface. Our model quantitatively and qualitatively explains the observed pulsar radio powers and spectra, the pulse profiles, polarization curves, their temporal variability, the strong Stokes-$L$ and weak Stokes-$V$ polarization components, the decline in the linear polarization with frequency, and the nonexistence of a radius-to-frequency relation. The observable properties of radio emission from the polar cap can vary and include single- or double-peaked profiles. Most of the Stokes~$V$ curves from our simulations appear to be antisymmetric, but symmetric curves are also present at some viewing angles. Although the polarization-angle (PA) swing of the radiation from the polar cap fits the rotating vector model (RVM) for most viewing angles, the angles obtained from the RVM do not correspond to the dipole geometry of the magnetic field. Instead, the PA is directly related to the plasma flows in the polar cap. Our simulations demonstrate that pair discharges close to the surface of the polar cap cause the radio emission of pulsars and determine the majority of their typically observed properties. The merits of RVM for estimations of the magnetic field geometry from observations need to be reevaluated.

astro-ph.HE↗

arXiv2025

Electromagnetic field solver for QED polarization in super-strong magnetic fields of magnetar and laser plasmas

Super-strongly magnetized plasmas play a crucial role in extreme environments of magnetar and laboratory laser experiments, demanding comprehensive understanding of how quantum electrodynamic (QED) effects influence plasma behaviour. Earlier analytical and semi-analytical calculations have shown that QED effects can significantly modify the plasma polarization mode behaviour around magnetars using analytical and semi-analytical calculations. In this work, we present the first electromagnetic field solver that is valid beyond the Schwinger limit. QED vacuum polarization in super-strong magnetic fields are modeled with nonlinear Maxwell equations. We show that electromagnetic waves in simulations follow the analytical solutions well and reproduce the birefringence effects of electromagnetic wave modes between the $O$ and $X$ polarizations of perpendicular electromagnetic waves and those between $L$ and $R$ polarizations of parallel waves. This new framework can be applied to kinetic as well as in other types of computer simulations. The solver's key advantage lies in its versatility, allowing it to be used in gyro-motion, gyro-center, and gyro-kinetic simulations, which do not resolve the cyclotron motion, or in plasma studies with ground-level Landau quantization.

physics.plasm-ph↗

arXiv2024

Poynting flux transport channels formed in polar cap regions of neutron star magnetospheres

Pair cascades in polar cap regions of neutron stars are considered to be an essential process in various models of coherent radio emissions of pulsars. The cascades produce pair plasma bunch discharges in quasi-periodic spark events. The cascade properties, and therefore also the coherent radiation, depend strongly on the magnetospheric plasma properties and vary significantly across and along the polar cap. Importantly, where the radio emission emanates from in the polar cap region is still uncertain. We investigate the generation of electromagnetic waves by pair cascades and their propagation in the polar cap for three representative inclination angles of a magnetic dipole, $0^\circ$, $45^\circ$, and $90^\circ$. We use two-dimensional particle-in-cell simulations that include quantum-electrodynamic pair cascades in a charge-limited flow from the star surface. We find that the discharge properties are strongly dependent on the magnetospheric current profile in the polar cap and that transport channels for high intensity Poynting flux are formed along magnetic field lines where the magnetospheric currents approach zero and where the plasma cannot carry the magnetospheric currents. There, the parallel Poynting flux component is efficiently transported away from the star and may eventually escape the magnetosphere as coherent radio waves. The Poynting flux decreases with increasing distance from the star in regions of high magnetospheric currents. Our model shows that no process of energy conversion from particles to waves is necessary for the coherent radio wave emission. Moreover, the pulsar radio beam does not have a cone structure; rather, the radiation generated by the oscillating electric gap fields directly escapes along open magnetic field lines in which no pair creation occurs.

astro-ph.HE↗

arXiv2024

Streaming instability in neutron star magnetospheres: No indication of soliton-like waves

Coherent radiation of pulsars, magnetars, and fast radio bursts could, in theory, be interpreted as radiation from solitons and soliton-like waves. The solitons are meant to contain a large number of electric charges confined on long time-scales and may radiate strongly by coherent curvature emission. However, solitons are also known to undergo a wave collapse, which may cast doubts on the correctness of the soliton radio emission models of neutron stars. We investigate the evolution of the caviton type of solitons self-consistently formed by the relativistic streaming instability and compare 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 are studied to obtain soliton dispersion properties. We utilized 1D electrostatic and 2D electromagnetic relativistic particle-in-cell simulations at kinetic microscales. We found 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, $ω= c k$, remain. Solitons in the 1D approach are stable for $γ_\mathrm{b} \gtrsim 60$, but they disappear for low beam Lorentz factor $γ_\mathrm{b} < 6$. 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 - unless one can show that there are alternative plasma mechanisms for the soliton generation.

astro-ph.HE↗

arXiv2023

Linear acceleration emission of pulsar relativistic streaming instability and interacting plasma bunches

Linear acceleration emission is one of the mechanisms that might explain intense coherent emissions of radio pulsars. This mechanism is not well understood, however, because the effects of collective plasma response and nonlinear plasma evolution on the resulting emission power must be taken into account. In addition, details of the radio emission properties of this mechanism are unknown, which limits the observational verification of the emission model. By including collective and nonlinear plasma effects, we calculate radio emission power properties by the linear acceleration emission mechanism that occurs via the antenna principle for two instabilities in neutron star magnetospheres: 1) the relativistic streaming instability, and 2) interactions of plasma bunches. We used 1D electrostatic relativistic particle-in-cell simulations to evolve the instabilities self-consistently. From the simulations, the power properties of coherent emission were obtained by novel postprocessing of electric currents. We found that the total radio power by plasma bunch interactions exceeds the power of the streaming instability by eight orders of magnitude. The wave power generated by a plasma bunch interaction can be as large as $2.6\times10^{16}$ W. The number of bunch interactions that are required to explain the typical pulsar power, $10^{18}$-$10^{22}$ W, depends on how the coherent emissions of bunches are added up together. Although $\sim$$4\times (10^1-10^5)$ simultaneously emitting bunches are necessary for an incoherent addition of their radiation power, $\gtrsim 6-600$ bunches can explain the total pulsar power if they add up coherently. The radio spectrum of the plasma bunch is characterized by a flatter profile for low frequencies and by a power-law index up to $\approx-1.6 \pm 0.2$ for high frequencies. The plasma bunches simultaneously radiate in a wide range of frequencies.

astro-ph.HE↗

arXiv2022

Zebra stripes with high gyro-harmonic numbers

Solar radio zebras are used in the determination of the plasma density and magnetic field in solar flare plasmas. Analyzing observed zebra stripes and assuming their generation by the double-plasma resonance (DPR) instability, high values of the gyro-harmonic number are found. In some cases, they exceed one hundred, in disagreement with the DPR growth rates computed up to now, which decrease with increasing gyro-harmonic number. We address the question of how the zebras with high values of the gyro-harmonic numbers $s$ are generated. For this purpose, we compute growth rates of the DPR instability in a very broad range of $s$, considering a loss-cone $κ$-distribution of superthermal electrons and varying the loss-cone angle, electron energies, and background plasma temperature. We numerically calculated dispersion relations and growth rates of the upper-hybrid waves and found that the growth rates increase with increasing gyro-harmonic numbers if the loss-cone angles are $\sim80^\circ$. The highest growth rates for these loss-cone angles are obtained for the velocity $v_κ= 0.15\,c$. The growth rates as function of the gyro-harmonic number still show well distinct peaks, which correspond to zebra-stripe frequencies. The contrast of the growth rate peaks to surrounding growth rate levels increases as the $κ$ index increases and the background temperature decreases. Zebras with high values of $s$ can be generated in regions where loss-cone distributions of superthermal electrons with large loss-cone angles ($\sim80^\circ$) are present. Furthermore, owing to the high values of $s$, the magnetic field is relatively weak and has a small spatial gradient in such regions.

astro-ph.SR↗

arXiv2022

Wave emission of non-thermal electron beams generated by magnetic reconnection

Magnetic reconnection in solar flares can efficiently generate non-thermal electron beams. The energetic electrons can, in turn, cause radio waves through microscopic plasma instabilities as they propagate through the ambient plasma along the magnetic field lines. We aim at investigating the wave emission caused by fast moving electron beams (FEBs) with characteristic non-thermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: two-streaming EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs closer to the diffusion region. For this purpose, we utilized 2.5D fully kinetic Particle-In-Cell (PIC) code simulations in this study. We found that:(1) the two-streaming EVDFs plus the background ions are unstable to electron/ion (streaming) instabilities which cause ion acoustic waves and Langmuir waves due to the net current. This can lead to multiple harmonic plasma emission in the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs can cause multiple harmonic electromagnetic electron cyclotron waves through the electron cyclotron maser instabilities in the diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters which control magnetic reconnection in solar flares by means of radio waves observations.

astro-ph.SR↗

arXiv2021

Radio Emission by Soliton Formation in Relativistically Hot Streaming Pulsar Pair Plasmas

A number of possible pulsar radio emission mechanisms are based on streaming instabilities in relativistically hot electron-positron pair plasmas. 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 with an appropriately parameterized one-dimensional Maxwell-Jüttner velocity space particle distribution to study the evolution of the resulting streaming instability in a pulsar pair plasma. We found that strong electrostatic superluminal L-mode solitons are formed for plasmas with normalized inverse temperatures $ρ\geq 1.66$ or relative beam drift speeds with Lorentz factors $γ> 40$. The parameters of the solitons fulfill the wave emission conditions. For appropriate pulsar parameters the resulting energy densities of superluminal solitons can reach up to $1.1 \times 10^5$ erg$\cdot$cm$^{-3}$, while those of subluminal 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.

astro-ph.HE↗

arXiv2021

Bunch Expansion as a cause for Pulsar Radio Emissions

Electromagnetic waves due to electron-positron clouds (bunches), created by cascading processes in pulsar magnetospheres, have been proposed to explain the pulsar radio emission. In order to verify this hypothesis, we utilized for the first time Particle-in-Cell (PIC-) code simulations to study the nonlinear evolution of electron-positron bunches in dependence on the relative drift speeds of electrons and positrons, on the initial plasma temperature, and on the initial distance between the bunches. For this sake, we utilized the PIC-code ACRONYM with a high-order field solver and particle weighting factor, appropriate to describe relativistic pair plasmas. We found that the bunch expansion is mainly determined by the relative electron-positron drift speed. Finite drift speeds were found to cause the generation of strong electric fields that reach up to $E \sim 7.5 \times 10^{5}$ V/cm ($E / (m_\mathrm{e} c ω_\mathrm{p} e^{-1}) \sim 4.4$) and strong plasma heating. As a result, up to 15~\% of the initial kinetic energy is transformed into the electric field energy. Assuming the same electron- and positron-distributions we found that the fastest (in the bunch reference frame) particles of consecutively emitted bunches eventually overlap in the momentum (velocity) space. This overlap causes two-stream instabilities that generate (electrostatic) subluminal L-mode waves with electric field amplitudes reaching up to $E \sim 1.9\times 10^{4}$ V/cm ($E / (m_\mathrm{e} c ω_\mathrm{p} e^{-1}) \sim 0.11$). We found that the interaction of electron-position bunches leads to plasma heating, to the generation of strong electric fields and of intense superluminal L-mode waves which, in principle, can be behind the observed electromagnetic emissions of pulsars in the radio wave range.

astro-ph.HE↗

arXiv2021

Narrowband Spikes Observed during the 2013 November 7 Flare

Narrowband spikes are observed in solar flares for several decades. However, their exact origin is still discussed. To contribute to understanding of these spikes, we analyze the narrowband spikes observed in the 800-2000 MHz range during the impulsive phase of the November 7, 2013 flare. In the radio spectrum, the spikes started with typical broadband clouds of spikes, and then their distribution in frequencies changed into unique, very narrow bands having non-integer frequency ratios. We successfully fitted frequencies of these narrow spike bands by those, calculating dispersion branches and growth rates of the Bernstein modes. For comparison, we also analyzed the model, where the narrow bands of spikes are generated at the upper-hybrid frequencies. Using both models, we estimated the plasma density and magnetic field in spike sources. Then the models are discussed, and arguments in favor of the model with the Bernstein modes are presented. Analyzing frequency profiles of this spike event by the Fourier method, we found the power-law spectra with the power-law indices varying in the -0.8 -- -2.75 interval. Because at some times this power-law index was close to the Kolmogorov spectral index (-5/3), we propose that the spikes are generated through the Bernstein modes in turbulent plasma reconnection outflows or directly in the turbulent magnetic reconnection of solar flares.

astro-ph.SR↗

arXiv2021

Refining pulsar radio emission due to streaming instabilities: Linear theory and PIC simulations in a wide parameter range

Several important mechanisms that explain the coherent pulsar radio emission rely on streaming (or beam) instabilities of the relativistic pair plasma in a pulsar magnetosphere. However, it is still not clear whether a streaming instability by itself is sufficient to explain the observed coherent radio emission. Due to the relativistic conditions that are present in the pulsar magnetosphere, kinetic instabilities could be quenched. Moreover, uncertainties regarding specific model-dependent parameters impede conclusions concerning this question. We aim to constrain the possible parameter range for which a streaming instability could lead to pulsar radio emission, focusing on the transition between strong and weak beam models, beam drift speed, and temperature dependence of the beam and background plasma components. We solve a linear relativistic kinetic dispersion relation appropriate for pulsar conditions in a more general way than in previous studies, considering a wider parameter range. The analytical results are validated by comparison with relativistic kinetic particle-in-cell (PIC) numerical simulations. We obtain growth rates as a function of background and beam densities, temperatures, and streaming velocities while finding a remarkable agreement of the linear dispersion predictions and numerical simulation results in a wide parameter range. Monotonous growth is found when increasing the beam-to-background density ratio. With growing beam velocity, the growth rates firstly increase, reach a maximum and decrease again for higher beam velocities. A monotonous dependence on the plasma temperatures is found, manifesting in an asymptotic behaviour when reaching colder temperatures. We show that the generated waves are phase-coherent by calculating the fractional bandwidth. We provide an explicit parameter range of plasma conditions for efficient pulsar radio emission.

astro-ph.HE↗

arXiv2020

Expansion of Hot Plasma into Cold Plasma

The X-ray emission of coronal flare sources can be explained considering the kappa electron distribution. Motivated by this fact, we study the problem of how hot plasma with the kappa distribution of electrons is confined in these sources. For comparison, we analyze the same problem but with the Maxwellian distribution. We use a 3-D particle-in-cell code, which is large in one direction and thus effectively only one-dimensional, but describing all electromagnetic effects. In the case with the Maxwellian distribution, and in agreement with the previous studies, we show a formation of the double layer at the hot-cold transition region that suppresses the flux of hot electrons from hot plasma into the cold one. In the case with the kappa distribution, contrary to the Maxwellian case, we found that there are several fronts with the double layers in the hot-cold transition region. It is caused by a more extended tail in the kappa case than in the Maxwellian one. The electrons from the extended tail freely escape from the hot plasma into a cold one. They form a beam which generates the return current and also Langmuir turbulence, where at some locations Langmuir waves are accumulated. At these locations owing to the ponderomotive force, Langmuir waves generate density depressions, where the double layers with the thermal fronts, suppressing the hot electron flux, are formed. We also show how protons are accelerated in these processes. Finally, we compared the kappa and Maxwellian cases and discussed how these processes could be observed.

astro-ph.SR↗

arXiv2019

Growth rates of the electrostatic waves in radio zebra models

Zebras were observed not only in the solar radio emission but also in radio emissions of Jupiter and Crab Nebula pulsar. In their models, growth rates of the electrostatic waves play an important role. Considering the plasma composed from the thermal background plasma and hot and rare component with the Dory-Guest-Harris distribution, we compute the growth rates $γ$ and dispersion branches of the electrostatic waves in the $ω- k_\perp$ domain. We show complexity of the electrostatic wave branches in the upper-hybrid band. In order to compare the results, which we obtained using the kinetic theory and Particle-in-cell (PIC) simulations, we define and compute the integrated growth rate $Γ$, where the "characteristic width" of dispersion branches was considered. We found a very good agreement between the integrated growth rates and those from PIC simulations. For maximal and minimal $Γ$ we showed locations of dispersion branches in the $ω- k_\perp$ domain. We found that $Γ$ has a maximum when the dispersion branches not only cross the region with high growth rates $γ$, but when the dispersion branches in this region are sufficiently long and wide. We also mentioned the effects of changes in the background plasma and hot component temperatures.

physics.plasm-ph↗

arXiv2019

Growth Rates of the Upper-hybrid Waves for Power-law and Kappa Distributions with a Loss-cone Anisotropy

Fine structures of radio bursts play an important role in diagnostics of the solar flare plasma. Among them the zebras, which are prevalently assumed to be generated by the double plasma resonance instability, belong to the most important. In this paper we compute the growth rate of this instability for two types of the electron distribution: a) for the power-law distribution and b) for the kappa distribution, in the both cases with the loss-cone type anisotropy. We found that the growth rate of the upper-hybrid waves for the power-law momentum distribution strongly depends on the pitch-angle boundary. The maximum growth rate was found for the pitch-angle $θ_\mathrm{c} \approx$ 50$^\circ$. For small angles the growth rate profile is very flat and for high pitch-angles the wave absorption occurs. Furthermore, analyzing the growth rate of the upper hybrid waves for the kappa momentum distribution we found that a decrease of the characteristic momentum $p_κ$ shifts the maximum of the growth rate to lower values of the ratio of the electron-plasma and electron-cyclotron frequencies, and the frequency widths of the growth rate peaks are very broad. But, if we consider the kappa distribution which is isotropic up to some large momentum $p_m$ and anisotropic with loss-cone above this momentum then distinct peaks of the growth rate appear and thus distinct zebra stripes can be generated. It means that the restriction for small momenta for the anisotropic part of distributions is of principal importance for the zebra stripes generation. Finally, for the 1 August 2010 zebra stripes, the growth rates in dependence on radio frequency were computed. It was shown that in this case the growth rate peaks are more distinct than in usually presented dependencies of growth rates on the ratio of the plasma and cyclotron frequencies.

astro-ph.SR↗

arXiv2017

Double plasma resonance instability as a source of solar zebra emission

The double plasma resonance (DPR) instability plays a basic role in the generation of solar radio zebras. In the plasma, consisting of the loss-cone type distribution of hot electrons and much denser and colder background plasma, this instability generates the upper-hybrid waves, which are then transformed into the electromagnetic waves and observed as radio zebras. In the present paper we numerically study the double plasma resonance instability from the point of view of the zebra interpretation. We use a 3-dimensional electromagnetic particle-in-cell (3-D PIC) relativistic model. First using the multi-mode model, we study details of the double plasma resonance instability. We show how the distribution function of hot electrons changes during this instability. Then we show that there is a very good agreement between results obtained by the multi-mode and specific-mode models, which is caused by a dominance of the wave with the maximal growth rate. Therefore, for computations in a broad range of model parameters, we use the specific-mode model. We compute the maximal growth rates of the double plasma resonance instability. The results are compared with the analytical ones. We find a very good agreement between numerical and analytical growth rates. We also compute saturation energies of the upper-hybrid waves in a very broad range of parameters. We find that the saturation energies of the upper-hybrid waves show maxima and minima at almost the same values of $ω_\mathrm{UH}/ω_\mathrm{ce}$ as the growth rates. Furthermore, we find that the saturation energy of the upper-hybrid waves is proportional to the density of hot electrons. The maximum saturated energy can be up to one percent of the kinetic energy of hot electrons. All these findings can be used in the interpretation of solar radio zebras.

physics.plasm-ph↗

arXiv2017

Brightness Temperature of Radio Zebras and Wave Energy Densities in Their Sources

We estimated the brightness temperature of radio zebras (zebra pattern -- ZP), considering that ZPs are generated in loops having an exponential density profile in their cross-section. We took into account that when in plasma there is a source emitting in all directions, then in the escape process from the plasma the emission obtains a directional character nearly perpendicular to the constant-density profile. Owing to the high directivity of the plasma emission the region from which the emission escapes can be very small. We estimated the brightness temperature of three observed ZPs for two values of the density scale height (1 and 0.21 Mm) and two values of the loop width (1 and 2 arcsec). In all cases high brightness temperatures were obtained. For the higher value of the density scale height, the brightness temperature was estimated as 1.1 $\times$ 10$^{15}$ - 1.3 $\times$ 10$^{17}$ K, and for the lower value as 4.7 $\times$ 10$^{13}$ - 5.6 $\times$ 10$^{15}$ K. We also computed the saturation energy density of the upper-hybrid waves (which according to the double plasma resonance model are generated in the zebra source) using a 3D particle-in-cell model with the loss-cone type of distribution of hot electrons. We found that this saturated energy is proportional to the ratio of hot electron and background plasma densities. Thus, comparing the growth rate and collisional damping of the upper-hybrid waves, we estimated minimal densities of hot electrons as well as the minimal value of the saturation energy density of the upper-hybrid waves. Finally, we compared the computed energy density of the upper-hybrid waves with the energy density of the electromagnetic waves in the zebra source and thus estimated the efficiency of the wave transformation.

astro-ph.SR↗

arXiv2017

Temperature dependent growth rates of the upper-hybrid waves and solar radio zebra patterns

Context. The zebra patterns observed in solar radio emission are very important for are plasma diagnostics. The most promising model of these patterns is based on double plasma resonance instability, which generates upper-hybrid waves, which can be then transformed into the zebra emission. Aims. We aim to study in detail the double plasma resonance instability of hot electrons, together with a much denser thermal background plasma. In particular, we analyse how the growth rate of the instability depends on the temperature of both the hot plasma and background plasma components. Methods. We numerically integrated the analysed model equations, using Python and Wolfram Mathematica. Results. We found that the growth-rate maxima of the upper-hybrid waves for non-zero temperatures of both the hot and background plasma are shifted towards lower frequencies comparing to the zero temperature case. This shift increases with an increase of the harmonic number s of the electron cyclotron frequency and temperatures of both hot and background plasma components. We show how this shift changes values of the magnetic eld strength estimated from observed zebras. We confirmed that for a relatively low hot electron temperature, the dependence of growth rate vs. both the ratio of the electron plasma and electron cyclotron frequencies expresse distinct peaks, and by increasing this temperature these peaks become smoothed. We found that in some cases, the values of wave number vector components for the upper-hybrid wave for the maximal growth rate strongly deviate from their analytical estimations. We confirmed the validity of the assumptions used when deriving model equations.

astro-ph.SR↗