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Зайцев, В. В.; Kislyakov, A. G.; Urpo, S.; Shkelev, E. I.

doi:10.1023/a:1013059009379

Cited by 9 publications

(31 citation statements)

References 7 publications

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“…In this subsection we consider an equation for the equivalent electric circuit of a coronal magnetic loop, which was derived and studied by Zaitsev et al (1998Zaitsev et al ( , 2001). Here we will not repeat the whole procedure of this derivation, but just consider its final result.…”

Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

“…Here we will not repeat the whole procedure of this derivation, but just consider its final result. The LCR-circuit equation of the loop is obtained by the integration of the generalized Ohm's law (Zaitsev & Stepanov 1992;Khodachenko & Zaitsev 2002) across and along the loop (Zaitsev et al , 2001. By this, two basic regions are distinguished inside the loop: Region 1, or the dynamo region, located in the photospheric footpoints of the loop, influenced by the converging supergranulation flows of the partially ionized photospheric plasma, and Region 2, corresponding to the coronal part of the loop.…”

Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

“…After the whole course of integration Zaitsev et al (2001) obtain an equation for the relative variation y = (I z − I z0 )/I z0 of the oscillating longitudinal current about its equilibrium value I z0 in the equivalent electric circuit of the magnetic loop. In the case of a small amplitude of the electric current oscillations (|y| 1) this equation transforms to the equation of a linear oscillator…”

Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

“…Therefore it is natural to expect that such structural complexity of a flaring region will manifest itself in peculiarities of the emitted radiation. In particular, the dynamic spectra of the LF oscillations modulating the microwave radiation from the solar active regions quite often contain several spectral tracks demonstrating a similar or slightly different temporal behaviour (Zaitsev et al 2001(Zaitsev et al , 2003. We consider these multi-track features as an indication that the detected microwave radiation is produced within a system of a few separate, but closely located, magnetic loops having slightly different parameters, and involved in a kind of common global dynamic process.…”

Section: Introductionmentioning

confidence: 99%

“…It usually involves simplified geometry assumptions and is obtained by integrating an appropriate form of Ohm's law for plasma over a circuit (Spicer 1982;Melrose 1995;Zaitsev et al 1998Zaitsev et al , 2001. A simple circuit model ignores the fact that changes of the magnetic field propagate in plasma at the Alfvén speed.…”

Section: Introductionmentioning

confidence: 99%

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Low-frequency modulations in the solar microwave radiation as a possible indicator of inductive interaction of coronal magnetic loops

Khodachenko

Зайцев²,

Kislyakov³

et al. 2005

A&A

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Abstract. Low-frequency (LF) modulations of 37 GHz microwave radiation during solar flares, recorded at the Metsähovi Radio Observatory, are considered. A fast Fourier transformation with a sliding window is used to obtain the dynamic spectra of the LF pulsations. We pay attention to the LF dynamic spectra having a specific multi-track structure, which is supposed to be an indication of a complex multi-loop composition of a flaring region. Application of the equivalent electric circuit models of the loops including the effects of electromagnetic inductive interaction in groups of slowly growing current-carrying magnetic loops allows us to explain and reproduce the main dynamical features of the observed LF modulation dynamic spectra. Each loop is considered as an equivalent electric circuit with variable parameters (resistance, capacitance and inductive coefficients) which depend on shape, scale, position of the loop with respect to other loops, as well as on the plasma parameters and value of the total longitudinal current in the magnetic tube.

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Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

Section: Lcr-circuit Analog Of a Current-carrying Magnetic Loopmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-frequency modulations in the solar microwave radiation as a possible indicator of inductive interaction of coronal magnetic loops

Khodachenko

Зайцев²,

Kislyakov³

et al. 2005

A&A

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Spectral-time analysis with the use of cross Wigner–Ville transform

Shkelev

Zemnyukov

2010

Radiophys Quantum El

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We consider the possibility of obtaining frequency-time distributions of signals by means of the cross Wigner-Ville transform in which the reference (test) signal is designed in accordance with the structure of the studied signal. It is shown that because of the complex nature of the WignerVille distributions (WVDs) P (t, ω), information on the frequency-time characteristics of studied signals can be obtained by analyzing the modulus of the distribution |P (t, ω)|, as well as by the real Re[P (t, ω)] and imaginary Im[P (t, ω)] parts of the WVD. Their analysis by the method of selected sections permits one to disclose in more detail the spectral-time content of processed signals and thereby increase the frequency-time resolution. The efficiency of the proposed technique was verified by numerical modeling and in work with acoustic signals received by a mobile receiver from a fixed transmitter.When the problems related to determining the spectral content of the time-varied signals are considered, the methods based on obtaining cross frequency-time distributions offer the best accuracy. The problem of choosing the method is complicated by the fact that the obtained distributions differ in form, and each distribution has unique properties [1,2]. Despite the differences, the methods of obtaining frequencytime distributions are similar in that they reveal the correlation of the studied signal u(t) with either the signal itself having a modifed dependence on time t and frequency ω via a shift or inversion or with an additional reference signal. The method of obtaining cross frequency-time distributions considered in this paper is based on the Wigner-Ville transform [1, 3]which can be treated as a two-dimensional (t and ω) cross correlation function between the direct and time-inverted signals. In Eq. (1), the studied signal u(t) is represented as an analytical signal and generally contains a useful component s(t) and noise n(t), namely, u(t) = s(t) + n(t), and the symbol * denotes complex conjugation. Due to the use of the time-inverted signal u(t), the Wigner-Ville transform yields an absolute distribution in time and frequency, which stipulates its high frequency-time resolution confirmed by the results obtained in processing of experimental data (see, e.g., [4][5][6]). The Wigner-Ville transform is nonlinear and features cross-modulation distortions, such that the part corresponding to the useful signal s(t) in the distribution calculated using Eq. (1) may become indiscernible against their background [7]. Hence, during estimation of the parameters of the signal s(t), especially in the

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On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

et al. 2006

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Dynamic spectra of low-frequency modulation of microwave emission from solar flares are obtained. Data of 15 bursts observed in 1989-2000 with Metsähovi radio telescope at 37 GHz have been used. During 13 bursts a 5-min modulation of the microwave emission intensity was detected with the frequency of ν I = 3.2 ± 0.24 (1σ ) mHz. Five bursts revealed a 5-min wave superimposed on a ∼1 Hz, linear frequency modulated signal generated, presumably, by coronal magnetic loop, this wave frequency is ν fm = 3.38 ± 0.37 (1σ ) mHz. Both intensity and frequency modulations detected are in good agreement with the data on 5-min global oscillations of photosphere and with the data on the umbral velocity oscillations observed in the vicinity of sunspots. Possible role of p-mode photospheric oscillations in modulation of microwave burst emission is discussed.

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Cited by 9 publications

References 7 publications

Low-frequency modulations in the solar microwave radiation as a possible indicator of inductive interaction of coronal magnetic loops

Low-frequency modulations in the solar microwave radiation as a possible indicator of inductive interaction of coronal magnetic loops

Spectral-time analysis with the use of cross Wigner–Ville transform

On the Possible Connection between Photospheric 5-Min Oscillation and Solar Flare Microwave Emission

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