Characterizing Magnetic Reconnection Regions Using Gaussian Mixture Models on Particle Velocity Distributions

We present a method based on unsupervised machine learning to identify regions of interest using particle velocity distributions as a signature pattern. An automatic density estimation technique is applied to particle distributions provided by PIC simulations to study magnetic reconnection. The key components of the method involve: i) a Gaussian mixture model determining the presence of a given number of subpopulations within an overall population, and ii) a model selection technique with Bayesian Information Criterion to estimate the appropriate number of subpopulations. Thus, this method identifies automatically the presence of complex distributions, such as beams or other non-Maxwellian features, and can be used as a detection algorithm able to identify reconnection regions. The approach is demonstrated for specific double Harris sheet simulations but it can in principle be applied to any other type of simulation and observational data on the particle distribution function.

[1]  David G. Sibeck,et al.  On the electron diffusion region in planar, asymmetric, systems , 2014 .

[2]  René Pellat,et al.  Stability of a thick two‐dimensional quasineutral sheet , 1982 .

[3]  E. Priest,et al.  Magnetohydrodynamic evolution of magnetic skeletons , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4]  V. Titov,et al.  Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona , 2007, astro-ph/0703671.

[5]  S. Sheather Density Estimation , 2004 .

[6]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[7]  E. G. Harris On a plasma sheath separating regions of oppositely directed magnetic field , 1962 .

[8]  G. Lapenta,et al.  Ion reflection and acceleration near magnetotail dipolarization fronts associated with magnetic reconnection , 2015 .

[9]  Enrico Camporeale,et al.  RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE , 2013, 1304.1444.

[10]  H. Karimabadi,et al.  Fundamental Concepts Associated with Magnetic Reconnection , 2016 .

[11]  B. Ishak,et al.  Statistics, data mining, and machine learning in astronomy: a practical Python guide for the analysis of survey data, by Željko Ivezić, Andrew J. Connolly, Jacob T. VanderPlas and Alexander Gray , 2017 .

[12]  E. Priest,et al.  Magnetic reconnection at three-dimensional null points , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  V. Vasyliūnas,et al.  A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3. , 1968 .

[14]  S. M. Shaaban,et al.  Temperature anisotropy instabilities stimulated by the interplay of the core and halo electrons in space plasmas , 2018 .

[15]  M. Hesse,et al.  The Diffusion Region in Collisionless Magnetic Reconnection , 1999 .

[16]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[17]  Richard M. Thorne,et al.  Variability of the pitch angle distribution of radiation belt ultrarelativistic electrons during and following intense geomagnetic storms: Van Allen Probes observations , 2015 .

[18]  V. Vasyliūnas Theoretical models of magnetic field line merging , 1975 .

[19]  R. Torbert,et al.  Highly structured electron anisotropy in collisionless reconnection exhausts , 2014 .

[20]  A. Klimas,et al.  New measure of the dissipation region in collisionless magnetic reconnection. , 2011, Physical review letters.

[21]  Stefano Markidis,et al.  Multi-scale simulations of plasma with iPIC3D , 2010, Math. Comput. Simul..

[22]  M. Shay,et al.  Energy partition in magnetic reconnection in Earth's magnetotail. , 2013, Physical review letters.

[23]  N. Bessho,et al.  Electron distribution functions in the diffusion region of asymmetric magnetic reconnection , 2016 .

[24]  W. Newcomb Motion of magnetic lines of force , 1958 .

[25]  Adam Szabo,et al.  Physics-based Tests to Identify the Accuracy of Solar Wind Ion Measurements: A Case Study with the Wind Faraday Cups , 2006 .

[26]  Thomas E. Moore,et al.  Magnetospheric Multiscale Overview and Science Objectives , 2016 .

[27]  J. Finn,et al.  Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines , 1990 .

[28]  Eric Ronald Priest,et al.  Reconnection of magnetic fields : magnetohydrodynamics and collisionless theory and observations , 2007 .

[29]  M. Shay,et al.  Effect of inflow density on ion diffusion region of magnetic reconnection: Particle-in-cell simulations , 2011 .

[30]  L. Fazendeiro,et al.  Viriato: A Fourier-Hermite spectral code for strongly magnetized fluid-kinetic plasma dynamics , 2015, Comput. Phys. Commun..

[31]  N. Buzulukova,et al.  Spontaneous formation of dipolarization fronts and reconnection onset in the magnetotail , 2013 .

[32]  Michael Hesse,et al.  Electron nongyrotropy in the context of collisionless magnetic reconnection , 2013 .

[33]  M. Hellberg,et al.  Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution , 2002 .

[34]  M. Lazar,et al.  Kappa Distributions: Theory and Applications in Space Plasmas , 2010, 1003.3532.

[35]  Eli Upfal,et al.  Machine Learning in High Energy Physics Community White Paper , 2018, Journal of Physics: Conference Series.

[36]  W. Dorland,et al.  Fluidization of collisionless plasma turbulence , 2018, Proceedings of the National Academy of Sciences.

[37]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[38]  C. Russell,et al.  Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory. , 2017, Physical review letters.

[39]  D. Mccomas,et al.  Characterizing the dayside magnetosheath using energetic neutral atoms: IBEX and THEMIS observations , 2013 .

[40]  Nils-Bastian Heidenreich,et al.  Bandwidth selection for kernel density estimation: a review of fully automatic selectors , 2013, AStA Advances in Statistical Analysis.

[41]  S. Schwartz,et al.  Electron Energy Partition across Interplanetary Shocks. I. Methodology and Data Product , 2019, The Astrophysical journal. Supplement series.

[42]  Verena Heidrich-Meisner,et al.  Solar Wind Classification Via k-Means Clustering Algorithm , 2018 .

[43]  G. Lapenta,et al.  On the origin of the crescent‐shaped distributions observed by MMS at the magnetopause , 2017, 1702.03550.

[44]  Richard M. Thorne,et al.  The modified plasma dispersion function , 1991 .

[45]  M. Swisdak,et al.  Quantifying gyrotropy in magnetic reconnection , 2015, 1509.00787.

[46]  M. Hesse,et al.  A theoretical foundation of general magnetic reconnection , 1988 .

[47]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[48]  M. Desai,et al.  Generation of Kappa Distributions in Solar Wind at 1 au , 2018 .

[49]  J. B. Blake,et al.  Electron-scale measurements of magnetic reconnection in space , 2016, Science.

[50]  Stefano Markidis,et al.  On the electron agyrotropy during rapid asymmetric magnetic island coalescence in presence of a guide field , 2016, 1608.00725.

[51]  P. Cassak,et al.  Spacecraft Observations and Analytic Theory of Crescent-Shaped Electron Distributions in Asymmetric Magnetic Reconnection. , 2016, Physical review letters.

[52]  R. Torbert,et al.  Spatiotemporal evolution of electron characteristics in the electron diffusion region of magnetic reconnection: Implications for acceleration and heating , 2015 .

[53]  G. Lapenta,et al.  What Can We Learn about Magnetotail Reconnection from 2D PIC Harris-Sheet Simulations? , 2016 .

[54]  Andrew J. Connolly,et al.  Statistics, Data Mining, and Machine Learning in Astronomy , 2014 .

[55]  Daniel N. Baker,et al.  Classification of Magnetospheric Particle Distributions Via Neural Networks , 2018 .

[56]  J. Scudder,et al.  Electron diffusion region and thermal demagnetization , 2008 .

[57]  D. Mccomas,et al.  Understanding Kappa Distributions: A Toolbox for Space Science and Astrophysics , 2013 .

[58]  G. Lapenta,et al.  Multiscale study of electron energization during unsteady reconnection events , 2015 .

[59]  Stefano Markidis,et al.  Automated Classification of Plasma Regions Using 3D Particle Energy Distributions , 2019, Journal of Geophysical Research: Space Physics.

[60]  H. Ji,et al.  Conversion of magnetic energy in the magnetic reconnection layer of a laboratory plasma , 2014, Nature Communications.

[61]  Stefano Markidis,et al.  Progress towards physics-based space weather forecasting with exascale computing , 2017, Adv. Eng. Softw..

[62]  Michael Hesse,et al.  Geospace Environmental Modeling (GEM) magnetic reconnection challenge , 2001 .

[63]  M. Gruntman Anisotropy of the energetic neutral atom flux in the heliosphere , 1992 .