Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas
One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics labor...
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MDPI AG
2021-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/4/470 |
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| author | Belén Acosta-Tripailao Denisse Pastén Pablo S. Moya |
| author_facet | Belén Acosta-Tripailao Denisse Pastén Pablo S. Moya |
| author_sort | Belén Acosta-Tripailao |
| collection | DOAJ |
| description | One of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here, we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback–Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell–Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium. |
| first_indexed | 2024-03-10T12:16:50Z |
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| language | English |
| last_indexed | 2024-03-10T12:16:50Z |
| publishDate | 2021-04-01 |
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| record_format | Article |
| series | Entropy |
| spelling | doaj.art-d735566619b143d08d3bf56feb2bcf142023-11-21T15:48:42ZengMDPI AGEntropy1099-43002021-04-0123447010.3390/e23040470Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal PlasmasBelén Acosta-Tripailao0Denisse Pastén1Pablo S. Moya2Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago 837.0415, ChileDepartamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago 837.0415, ChileDepartamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago 837.0415, ChileOne of the fundamental open questions in plasma physics is the role of non-thermal particles distributions in poorly collisional plasma environments, a system that is commonly found throughout the Universe, e.g., the solar wind and the Earth’s magnetosphere correspond to natural plasma physics laboratories in which turbulent phenomena can be studied. Our study perspective is born from the method of Horizontal Visibility Graph (HVG) that has been developed in the last years to analyze time series avoiding the tedium and the high computational cost that other methods offer. Here, we build a complex network based on directed HVG technique applied to magnetic field fluctuations time series obtained from Particle In Cell (PIC) simulations of a magnetized collisionless plasma to distinguish the degree distributions and calculate the Kullback–Leibler Divergence (KLD) as a measure of relative entropy of data sets produced by processes that are not in equilibrium. First, we analyze the connectivity probability distribution for the undirected version of HVG finding how the Kappa distribution for low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> tends to be an uncorrelated time series, while the Maxwell–Boltzmann distribution shows a correlated stochastic processes behavior. Subsequently, we investigate the degree of temporary irreversibility of magnetic fluctuations that are self-generated by the plasma, comparing the case of a thermal plasma (described by a Maxwell–Botzmann velocity distribution function) with non-thermal Kappa distributions. We have shown that the KLD associated to the HVG is able to distinguish the level of reversibility that is associated to the thermal equilibrium in the plasma, because the dissipative degree of the system increases as the value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> parameter decreases and the distribution function departs from the Maxwell–Boltzmann equilibrium.https://www.mdpi.com/1099-4300/23/4/470electromagnetic turbulencenon-thermal plasmasKappa distributionshorizontal visibility graphentropyirreversibility |
| spellingShingle | Belén Acosta-Tripailao Denisse Pastén Pablo S. Moya Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas Entropy electromagnetic turbulence non-thermal plasmas Kappa distributions horizontal visibility graph entropy irreversibility |
| title | Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas |
| title_full | Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas |
| title_fullStr | Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas |
| title_full_unstemmed | Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas |
| title_short | Applying the Horizontal Visibility Graph Method to Study Irreversibility of Electromagnetic Turbulence in Non-Thermal Plasmas |
| title_sort | applying the horizontal visibility graph method to study irreversibility of electromagnetic turbulence in non thermal plasmas |
| topic | electromagnetic turbulence non-thermal plasmas Kappa distributions horizontal visibility graph entropy irreversibility |
| url | https://www.mdpi.com/1099-4300/23/4/470 |
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