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 $\omega_\mathrm{UH}/\omega_\mathrm{ce}$ 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.Comment: 8 pages, 12 figure

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 radio emissions of radio pulsars. This mechanism is, however, not well understood 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) a relativistic streaming instability and 2) interactions of plasma bunches/clouds. We utilize 1D electrostatic relativistic particle-in-cell simulations to evolve the instabilities self-consistently. From the simulations, the power properties of coherent emission are obtained by novel post-processing 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. Therefore, $\sim$$4\times (10^1-10^5)$ simultaneously interacting plasma bunches may account for the total observed radio power of typical pulsars ($10^{18}$-$10^{22}$~W). The radio spectrum of the plasma bunch is characterized by a flatter profile for lower frequencies and a power-law index up to $\approx-1.6 \pm 0.2$ for higher frequencies. The plasma bunches radiate in a wide range of frequencies simultaneously, fulfilling no specific relation between emission frequency and height in the magnetosphere. The power of the streaming instability is more narrowband than that of the interacting bunches.Comment: 17 pages, 13 figures, 1 tabl

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.Comment: 15 pages, 7 figures. An abridged version of the abstract is shown here. Accepted in A&

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-J\"uttner 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 $\rho \geq 1.66$ or relative beam drift speeds with Lorentz factors $\gamma > 40$. 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.Comment: 20 pages, 15 figures, 1 tabl

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 ($E / (m_\mathrm{e} c \omega_\mathrm{p} e^{-1}) \sim 4.4$) 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 ($E / (m_\mathrm{e} c \omega_\mathrm{p} e^{-1}) \sim 0.11$). 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.Comment: 18 pages, 13 figure

Determining Factors of the Czech Foreign Trade Balance:Structural Issues in Trade Creation

Using panel data for 29 industries, the study tests alternative specifications of Czech export and import functions. The balance of trade is primarily influenced by the real exchange rate, aggregate demand and tariff changes. Reduced growth of the Czech economy after 1996 was an important factor that has kept the balance of trade at a sustainable level in the medium-term, contributing even to the appreciation of the real exchange rate