Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Zlotnik, E. Ya.

doi:10.1007/s11207-012-0151-1

Cited by 29 publications

(22 citation statements)

References 20 publications

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“…The loss-cone type of distribution of hot electrons superimposed on the distribution of much denser and colder background plasma is unstable due to the double plasma resonance instability (Zheleznyakov & Zlotnik 1975;Melrose & Dulk 1982;Zaitsev & Stepanov 1983;Winglee & Dulk 1986;Ledenev et al 2001;Zlotnik 2013;. This instability generates the upper-hybrid waves, which have their maxima close to the gyro-harmonic number s = ω UH /ω ce , where ω 2 UH = ω 2 pe + ω 2 ce and ω UH , ω pe , and ω ce are the upper-hybrid, electron-plasma, and electron-cyclotron frequency, respectively.…”

Section: Introductionmentioning

confidence: 99%

Double plasma resonance instability as a source of solar zebra emission

Benáček

Karlický

2018

A&A

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Context. 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. Aims. In the present paper we numerically study the double plasma resonance instability from the point of view of the zebra interpretation. Methods. We use a 3-dimensional electromagnetic particle-in-cell (3-D PIC) relativistic model. We use this model in two versions: a) a spatially extended "multi-mode" model and b) a spatially limited "specific-mode" model. While the multi-mode model is used for detailed computations and verifications of the results obtained by the "specific-mode" model, the specific-mode model is used for computations in a broad range of model parameters, which considerably save computational time. For an analysis of the computational results, we developed software tools in Python. Results. 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 with a dependence on the ratio between the upper-hybrid ωUH and electron-cyclotron ωce frequency. We vary temperatures of both the hot and background plasma components and study their effects on the resulting growth rates. 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 ωUH/ωce as the growth rates, but with a higher contrast between them than the growth rate maxima and minima. The contrast between saturation energy maxima and minima increases when the temperature of hot electrons increases. 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. Finally we find that the saturation energy maxima in the interval of ωUH/ωce = 3-18 decrease according to the exponential function. All these findings can be used in the interpretation of solar radio zebras.

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Section: Introductionmentioning

confidence: 99%

Double plasma resonance instability as a source of solar zebra emission

Benáček

Karlický

2018

A&A

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“…There are still questions about the generation mechanism of these ZPs. Among many proposed models (Zheleznyakov and Zlotnik, 1975;LaBelle et al, 2003;Bárta and Karlický, 2006;Kuznetsov and Tsap, 2007;Tan, 2010;Karlický, 2013), the most commonly accepted model is that based on the double-plasma resonance (DPR) (Zlotnik, 2013;Karlický and Yasnov, 2015). Based on this model, most of the observed characteristics of ZPs were explained: the frequency range, polarization, amount of stripes and their frequencies, their high-frequency limit, and their temporal changes.…”

Section: Introductionmentioning

confidence: 99%

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

2017

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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 (for emission at frequencies close to the plasma frequency) 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 × 10 15 -1.3 × 10 17 K, and for the lower value as 4.7 × 10 13 -5.6 × 10 15 K. These temperatures show that the observation probability of a burst with ZP, which is generated in the transition region with a steep gradient of the plasma density, is significantly higher than for a burst generated in a region with smoother changes of the plasma density. 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 losscone 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.

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“…Among all proposed mechanisms, the most promising one is that based on the double plasma resonance (DPR; Zheleznyakov & Zlotnik 1975;Zlotnik 2013). This model assumes that the zebra line emission is generated at locations where the upperhybrid frequency f up equals multiples of the electron-cyclotron frequency f b .…”

Section: Introductionmentioning

confidence: 99%

Determination of plasma parameters in solar zebra radio sources

Karlický

Yasnov

2015

A&A

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Aims. We present a new method for determining the magnetic field strength and plasma density in the solar zebra radio sources. Methods. Using the double plasma resonance (DPR) model of the zebra emission, we analytically derived the equations for computing the gyroharmonic number s of selected zebra lines and then solved these equations numerically. Results. The method was successfully tested on artificially generated zebras and then applied to observed ones. The magnetic field strength and plasma density in the radio sources were determined. Simultaneously, we evaluated the parameterwhere L n and L b are the characteristic scale-heights of the plasma density and magnetic field strength in the zebra source, respectively. Computations show that the maximum frequency of the low-polarized zebras is about 8 GHz, in very good agreement with observations. For the high-polarized zebras, this limit is about four times lower. Microwave zebras are preferentially generated in the regions with steep gradients of the plasma density, such as in the transition region. In models with smaller density gradients, such as those with a barometric density profile, the microwave zebras cannot be produced owing to the strong bremsstrahlung and cyclotron absorptions. We also show that our DPR model is able to explain the zebras with frequency-equidistant zebra lines.

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Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Cited by 29 publications

References 20 publications

Double plasma resonance instability as a source of solar zebra emission

Double plasma resonance instability as a source of solar zebra emission

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

Determination of plasma parameters in solar zebra radio sources

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