Hausdorf dimension of typical very low frequency chorus emissions and verification of their excitation mechanism

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Abstract

A quantitative study of the degree of complexity of electromagnetic VLF chorus emissions in the region of their excitation near the local minimum of the magnetic field outside the plasmasphere was carried out using modern mathematical tools. From the vast observational data collected during the Van Allen Probe mission, typical examples of chorus have been selected for which high-resolution digitized data are available. The original program was used to calculate the Hausdorff dimension of long numerical sequences. In all cases, the dimension turned out to be non-integer, which indicates the complex dynamics of the system. During the calculations, jumps in dimension were noted, including its decrease by about a factor of two for a fragment of a burst of chorus. The obtained results are important for confirming the mechanism of excitation of chorus by amplifying short noise pulses and for substantiating the possibility of automatic identification of electromagnetic radiation of different types.

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P. A. Bespalov

Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences; Higher School of Economics National Research University

Author for correspondence.
Email: PBespalov@mail.ru
Russian Federation, Nizhny Novgorod; Nizhny Novgorod

O. N. Savina

Higher School of Economics National Research University

Email: PBespalov@mail.ru
Russian Federation, Nizhny Novgorod

G. M. Neshchetkin

Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences; Higher School of Economics National Research University

Email: PBespalov@mail.ru
Russian Federation, Nizhny Novgorod; Nizhny Novgorod

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2. Fig. 1. Analysis of the chorus burst recorded by the Van Allen Probe spacecraft on 2018-11-01 at 10:37:43 UT: the middle panel on the left shows the low-resolution dynamic spectrum, where the white line shows the value of half of the local electron gyrofrequency and the arrow shows the time of registration of the chorus burst; the middle panel on the right shows the dynamic spectrum of the choruses from the high-resolution data; the top panel on the left shows the results of the calculation of |log(C(m, r))| from |log(r)|; the top right panel shows the line segment, whose tangent of the slope angle is used to determine the dimensionality value; the bottom two panels show the results of the dimensionality calculation for Fr

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3. Fig. 2. Analysis of the chorus burst recorded by the Van Allen Probe spacecraft 2014-02-20 at 22:08:42 UT, presented similarly to Fig. 1

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