Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T00:16:31.742Z Has data issue: false hasContentIssue false
  • English
  • Français

ViDA: a Vlasov–DArwin solver for plasma physics at electron scales

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  09 October 2019

Oreste Pezzi Open the ORCID record for Oreste Pezzi [Opens in a new window] ,
Giulia Cozzani Open the ORCID record for Giulia Cozzani [Opens in a new window] ,
Francesco Califano Open the ORCID record for Francesco Califano [Opens in a new window] ,
Francesco Valentini Open the ORCID record for Francesco Valentini [Opens in a new window] ,
Massimiliano Guarrasi Open the ORCID record for Massimiliano Guarrasi [Opens in a new window] ,
Enrico Camporeale Open the ORCID record for Enrico Camporeale [Opens in a new window] ,
Gianfranco Brunetti Open the ORCID record for Gianfranco Brunetti [Opens in a new window] ,
Alessandro Retinò Open the ORCID record for Alessandro Retinò [Opens in a new window]  and
Pierluigi Veltri Open the ORCID record for Pierluigi Veltri [Opens in a new window]
Oreste Pezzi*
Affiliation:
Gran Sasso Science Institute, Viale F. Crispi 7, I-67100 LAquila, Italy INFN/Laboratori Nazionali del Gran Sasso, Via G. Acitelli 22, I-67100 Assergi (AQ), Italy Dipartimento di Fisica, Università della Calabria, Via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
Giulia Cozzani
Affiliation:
Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy Laboratoire de Physique des Plasmas, CNRS/École Polytechnique/Sorbonne Université, Université Paris Sud, Observatoire de Paris, 91128 Palaiseau, France
Francesco Califano
Affiliation:
Dipartimento di Fisica ‘E. Fermi’, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
Francesco Valentini
Affiliation:
Dipartimento di Fisica, Università della Calabria, Via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
Massimiliano Guarrasi
Affiliation:
CINECA Interuniversity Consortium, Via Magnanelli 6/3, 40033 Casalecchio di Reno, Italy
Enrico Camporeale
Affiliation:
CIRES, University of Colorado, Boulder, CO, USA Center for Mathematics and Computer Science (CWI), 1090 GB Amsterdam, The Netherlands
Gianfranco Brunetti
Affiliation:
Dipartimento di Fisica, Università della Calabria, Via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
Alessandro Retinò
Affiliation:
Laboratoire de Physique des Plasmas, CNRS/École Polytechnique/Sorbonne Université, Université Paris Sud, Observatoire de Paris, 91128 Palaiseau, France
Pierluigi Veltri
Affiliation:
Dipartimento di Fisica, Università della Calabria, Via P. Bucci, I-87036 Arcavacata di Rende (CS), Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a Vlasov–DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the nonlinear regime to guarantee a clean description of the plasma dynamics at fine spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to the Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations of a non-relativistic fully kinetic collisionless plasma and it is expected to provide relevant insights into important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region.

Keywords

space plasma physicsplasma simulationplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 5 , October 2019 , 905850506
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barnes, A. 1966 Collisionless damping of hydromagnetic waves. Phys. Fluids 9 (8), 1483–1495.Google Scholar
Birdsall, C. K. & Langdon, A. B. 2004 Plasma Physics Via Computer Simulation. CRC press.Google Scholar
Birn, J., Drake, J., Shay, M., Rogers, B., Denton, R., Hesse, M., Kuznetsova, M., Ma, Z., Bhattacharjee, A., Otto, A. et al. 2001 Geospace environmental modeling (GEM) magnetic reconnection challenge. J. Geophys. Res. 106 (A3), 3715–3719.Google Scholar
Breuillard, H., Matteini, L., Argall, M. R., Sahraoui, F., Andriopoulou, M., Contel, O. L., Retinò, A., Mirioni, L., Huang, S. Y., Gershman, D. J. et al. 2018 New insights into the nature of turbulence in the Earth’s magnetosheath using magnetospheric MultiScale mission data. Astrophys. J. 859 (2), 127.Google Scholar
Brunetti, M., Califano, F. & Pegoraro, F. 2000 Asymptotic evolution of nonlinear Landau damping. Phys. Rev. E 62, 4109–4114.Google Scholar
Bruno, R. & Carbone, V. 2016 Turbulence in the Solar Wind. Springer.Google Scholar
Burch, J. L., Moore, T. E., Torbert, R. B. & Giles, B. L. 2016a Magnetospheric multiscale overview and science objectives. Space Sci. Rev. 199, 5–21.Google Scholar
Burch, J. L., Torbert, R. B., Phan, T. D., Chen, L.-J., Moore, T. E., Ergun, R. E., Eastwood, J. P., Gershman, D. J., Cassak, P. A., Argall, M. R. et al. 2016b Electron-scale measurements of magnetic reconnection in space. Science 352 (6290), aaf2939.Google Scholar
Califano, F., Cerri, S., Faganello, M., Laveder, D. & Kunz, M.2018 Electron-only magnetic reconnection in plasma turbulence, Preprint, arXiv:1810.03957.Google Scholar
Califano, F., Faganello, M. & Pegoraro, F. 2007 Collisionless magnetic reconnection. Plasma Phys. Control. Fusion 49 (12B), B439–B446.Google Scholar
Califano, F., Hellinger, P., Kuznetsov, E., Passot, T., Sulem, P. L. & Trvnek, P. M. 2008 Nonlinear mirror mode dynamics: simulations and modeling. J. Geophys. Res. 113 (A8), A08219.Google Scholar
Califano, F. & Mangeney, A. 2008 A one dimensional, electrostatic Vlasov model for the generation of suprathermal electron tails in solar wind conditions. J. Geophys. Res. 113 (A6), A06103.Google Scholar
Camporeale, E. & Burgess, D. 2011 The dissipation of solar wind turbulent fluctuations at electron scales. Astrophys. J. 730 (2), 114.Google Scholar
Camporeale, E. & Burgess, D. 2017 Comparison of linear modes in kinetic plasma models. J. Plasma Phys. 83 (2), 535830201.Google Scholar
Camporeale, E. & Zimbardo, G. 2015 Wave–particle interactions with parallel whistler waves: nonlinear and time-dependent effects revealed by particle-in-cell simulations. Phys. Plasmas 22 (9), 092104.Google Scholar
Cerri, S. S. & Califano, F. 2017 Reconnection and small-scale fields in 2D–3V hybrid-kinetic driven turbulence simulations. New J. Phys. 19 (2), 025007.Google Scholar
Cerri, S. S., Kunz, M. W. & Califano, F. 2018 Dual phase-space cascades in 3D hybrid-Vlasov–Maxwell turbulence. Astrophys. J. 856 (1), L13.Google Scholar
Cerri, S. S., Servidio, S. & Califano, F. 2017 Kinetic cascade in solar–wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia. Astrophys. J. 846 (2), L18.Google Scholar
Chasapis, A., Matthaeus, W. H., Parashar, T. N., Wan, M., Haggerty, C. C., Pollock, C. J., Giles, B. L., Paterson, W. R., Dorelli, J., Gershman, D. J. et al. 2018 In situ observation of intermittent dissipation at kinetic scales in the Earth’s magnetosheath. Astrophys. J. 856 (1), L19.Google Scholar
Chen, G. & Chacón, L. 2014 An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D–3V Vlasov–Darwin particle-in-cell algorithm. Comput. Phys. Commun. 185 (10), 2391–2402.Google Scholar
Chen, G. & Chacón, L. 2015 A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm. Comput. Phys. Commun. 197, 73–87.Google Scholar
Cheng, C.-Z. & Knorr, G. 1976 The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22 (3), 330–351.Google Scholar
Cozzani, G., Retinò, A., Califano, F., Alexandrova, A., Le Contel, O., Khotyaintsev, Y., Vaivads, A., Fu, H. S., Catapano, F., Breuillard, H. et al. 2019 In situ spacecraft observations of a structured electron diffusion region during magnetopause reconnection. Phys. Rev. E 99, 043204.Google Scholar
Daughton, W., Roytershteyn, V., Karimabadi, H., Yin, L., Albright, B., Bergen, B. & Bowers, K. 2011 Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas. Nat. Phys. 7 (7), 539–542.Google Scholar
Delzanno, G. 2015 Multi-dimensional, fully-implicit, spectral method for the Vlasov–Maxwell equations with exact conservation laws in discrete form. J. Comput. Phys. 301, 338–356.Google Scholar
Divin, A., Khotyaintsev, Y. V., Vaivads, A., Andr, M., Markidis, S. & Lapenta, G. 2015 Evolution of the lower hybrid drift instability at reconnection jet front. J. Geophys. Res. 120 (4), 2675–2690.Google Scholar
Falchetto, G. L., Scott, B. D., Angelino, P., Bottino, A., Dannert, T., Grandgirard, V., Janhunen, S., Jenko, F., Jolliet, S., Kendl, A. et al. 2008 The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas. Plasma Phys. Control. Fusion 50 (12), 124015.Google Scholar
Franci, L., Landi, S., Matteini, L., Verdini, A. & Hellinger, P. 2016 Plasma beta dependence of the ion-scale spectral break of solar wind turbulence: high-resolution 2D hybrid simulations. Astrophys. J. 833 (1), 91.Google Scholar
Franci, L., Landi, S., Verdini, A., Matteini, L. & Hellinger, P. 2018 Solar wind turbulent cascade from MHD to sub-ion scales: large-size 3D hybrid particle-in-cell simulations. Astrophys. J. 853 (1), 26.Google Scholar
Franci, L., Verdini, A., Matteini, L., Landi, S. & Hellinger, P. 2015 Solar wind turbulence from MHD to sub-ion scales: high-resolution hybrid simulations. Astrophys. J. Lett. 804, L39.Google Scholar
Fuselier, S. A., Lewis, W. S., Schiff, C., Ergun, R., Burch, J. L., Petrinec, S. M. & Trattner, K. J. 2016 Magnetospheric multiscale science mission profile and operations. Space Sci. Rev. 199 (1), 77–103.Google Scholar
Galeotti, L. & Califano, F. 2005 Asymptotic evolution of weakly collisional Vlasov–Poisson plasmas. Phys. Rev. Lett. 95, 015002.Google Scholar
Galeotti, L., Califano, F. & Pegoraro, F. 2006 Echography of Vlasov codes. Phys. Lett. A 355 (4), 381–385.Google Scholar
Gary, S. P. & Karimabadi, H. 2006 Linear theory of electron temperature anisotropy instabilities: whistler, mirror, and Weibel. J. Geophys. Res. Space Phys. 111 (A11), A11224.Google Scholar
Genestreti, K. J., Varsani, A., Burch, J. L., Cassak, P. A., Torbert, R. B., Nakamura, R., Ergun, R. E., Phan, T.-D., Toledo-Redondo, S., Hesse, M. et al. 2018 Mms observation of asymmetric reconnection supported by 3-D electron pressure divergence. J. Geophys. Res. 123 (3), 1806–1821.Google Scholar
Ghizzo, A., Sarrat, M. & Del Sarto, D. 2017 Vlasov models for kinetic Weibel-type instabilities. J. Plasma Phys. 83 (1), 705830101.Google Scholar
González, C. A., Parashar, T. N., Gomez, D., Matthaeus, W. H. & Dmitruk, P. 2019 Turbulent electromagnetic fields at sub-proton scales: two-fluid and full-kinetic plasma simulations. Phys. Plasmas 26 (1), 012306.Google Scholar
Griffiths, D. J. 1962 Introduction to Electrodynamics. Prentice Hall.Google Scholar
Grošelj, D., Cerri, S. S., Navarro, A. B., Willmott, C., Told, D., Loureiro, N. F., Califano, F. & Jenko, F. 2017 Fully kinetic versus reduced-kinetic modeling of collisionless plasma turbulence. Astrophys. J. 847 (1), 28.Google Scholar
Haggerty, C. C., Parashar, T. N., Matthaeus, W. H., Shay, M. A., Yang, Y., Wan, M., Wu, P. & Servidio, S. 2017 Exploring the statistics of magnetic reconnection $x$ -points in kinetic particle-in-cell turbulence. Phys. Plasmas 24 (10), 102308.Google Scholar
Harris, E. G. 1962 On a plasma sheath separating regions of oppositely directed magnetic field. Il Nuovo Cimento 23 (1), 115–121.Google Scholar
Helander, P., Eriksson, L.-G. & Andersson, F. 2002 Runaway acceleration during magnetic reconnection in tokamaks. Plasma Phys. Control. Fusion 44 (12B), B247–B262.Google Scholar
Hesse, M., Aunai, N., Birn, J., Cassak, P., Denton, R. E., Drake, J. F., Gombosi, T., Hoshino, M., Matthaeus, W., Sibeck, D. et al. 2016 Theory and modeling for the magnetospheric multiscale mission. Space Sci. Rev. 199 (1), 577–630.Google Scholar
Hoilijoki, S., Palmroth, M., Walsh, B. M., Pfau-Kempf, Y., von Alfthan, S., Ganse, U., Hannuksela, O. & Vainio, R. 2016 Mirror modes in the Earth’s magnetosheath: results from a global hybrid-Vlasov simulation. J. Geophys. Res. Space Phys. 121 (5), 4191–4204.Google Scholar
Howes, G., Dorland, W., Cowley, S., Hammett, G., Quataert, E., Schekochihin, A. & Tatsuno, T. 2008a Kinetic simulations of magnetized turbulence in astrophysical plasmas. Phys. Rev. Lett. 100 (6), 065004.Google Scholar
Howes, G. G. 2016 The dynamical generation of current sheets in astrophysical plasma turbulence. Astrophys. J. Lett. 827 (2), L28.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. A. 2008b A model of turbulence in magnetized plasmas: implications for the dissipation range in the solar wind. J. Geophys. Res. 113 (A5), A05103.Google Scholar
Howes, G. G., Cowley, S. C., Dorland, W., Hammett, G. W., Quataert, E. & Schekochihin, A. e A. 2006 Astrophysical gyrokinetics: basic equations and linear theory. Astrophys. J. 651 (1), 590–614.Google Scholar
Howes, G. G., Tenbarge, J. M., Dorland, W., Quataert, E., Schekochihin, A. A., Numata, R. & Tatsuno, T. 2011 Gyrokinetic simulations of solar wind turbulence from ion to electron scales. Phys. Rev. Lett. 107 (3), 035004.Google Scholar
Juno, J., Hakim, A., TenBarge, J., Shi, E. & Dorland, W. 2018 Discontinuous galerkin algorithms for fully kinetic plasmas. J. Comput. Phys. 353, 110–147.Google Scholar
Karimabadi, H., Roytershteyn, V., Wan, M., Matthaeus, W. H., Daughton, W., Wu, P., Shay, M., Loring, B., Borovsky, J. & Leonardis, E. 2013 Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas. Phys. Plasmas 20 (1), 012303.Google Scholar
Kaufman, A. N. & Rostler, P. S. 1971 The Darwin model as a tool for electromagnetic plasma simulation. Phys. Fluids 14 (2), 446–448.Google Scholar
Kempf, Y., Pokhotelov, D., von Alfthan, S., Vaivads, A., Palmroth, M. & Koskinen, H. E. J. 2013 Wave dispersion in the hybrid-Vlasov model: verification of Vlasiator. Phys. Plasmas 20 (11), 112114.Google Scholar
Kobayashi, S., Sahraoui, F., Passot, T., Laveder, D., Sulem, P. L., Huang, S. Y., Henri, P. & Smets, R. 2017 Three-dimensional simulations and spacecraft observations of sub-ion scale turbulence in the solar wind: influence of Landau damping. Astrophys. J. 839 (2), 122.Google Scholar
Krall, N. A. & Trivelpiece, A. W. 1973 Principles of plasma physics. Am. J. Phys. 41 (12), 1380–1381.Google Scholar
Kulsrud, R. M. 2005 Plasma Physics for Astrophysics. Princeton University Press.Google Scholar
Landau, L. 1946 On the vibration of the electronic plasma. Zh. Eksp. Teor. Fiz. 16, 574.Google Scholar
Lapenta, G., Markidis, S., Goldman, M. V. & Newman, D. L. 2015 Secondary reconnection sites in reconnection-generated flux ropes and reconnection fronts. Nat. Phys. 11 (8), 690–695.Google Scholar
Lapenta, G., Pucci, F., Goldman, M. V. & Newman, D. L.2019 A violin sonata for reconnection, Preprint, arXiv:1904.02094.Google Scholar
Le Contel, O., Retinò, A., Breuillard, H., Mirioni, L., Robert, P., Chasapis, A., Lavraud, B., Chust, T., Rezeau, L., Wilder, F. D. et al. 2016 Whistler mode waves and Hall fields detected by mms during a dayside magnetopause crossing. Geophys. Res. Lett. 43 (12), 5943–5952.Google Scholar
Leonardis, E., Chapman, S. C., Daughton, W., Roytershteyn, V. & Karimabadi, H. 2013 Identification of intermittent multifractal turbulence in fully kinetic simulations of magnetic reconnection. Phys. Rev. Lett. 110 (20), 205002.Google Scholar
Lyutikov, M. 2003 Explosive reconnection in magnetars. Mon. Not. R. Astron. Soc. 346 (2), 540–554.Google Scholar
Mandt, M. E., Denton, R. E. & Drake, J. F. 1994 Transition to whistler mediated magnetic reconnection. Geophys. Res. Lett. 21 (1), 73–76.Google Scholar
Mangeney, A., Califano, F., Cavazzoni, C. & Travnicek, P. 2002 A numerical scheme for the integration of the Vlasov–Maxwell system of equations. J. Comput. Phys. 179 (2), 495–538.Google Scholar
Markidis, S., Lapenta, G. & Rizwan-uddin 2010 Multi-scale simulations of plasma with ipic3d. Maths Comput. Simul. 80 (7), 1509–1519; Multiscale modeling of moving interfaces in materials.Google Scholar
Marsch, E. 2006 Kinetic physics of the solar corona and solar wind. Living Rev. Solar Phys. 3 (1), 1.Google Scholar
Navarro, A. B. n, Teaca, B., Told, D., Groselj, D., Crandall, P. & Jenko, F. 2016 Structure of plasma heating in gyrokinetic Alfvénic turbulence. Phys. Rev. Lett. 117, 245101.Google Scholar
O’Neil, T. 1965 Collisionless damping of nonlinear plasma oscillations. Phys. Fluids 8 (12), 2255–2262.Google Scholar
Palmroth, M., Ganse, U., Pfau-Kempf, Y., Battarbee, M., Turc, L., Brito, T., Grand in, M., Hoilijoki, S., Sandroos, A. & von Alfthan, S. 2018 Vlasov methods in space physics and astrophysics. Living Rev. Comput. Astrophys. 4 (1), 1.Google Scholar
Palmroth, M., Honkonen, I., Sandroos, A., Kempf, Y., von Alfthan, S. & Pokhotelov, D. 2013 Preliminary testing of global hybrid-Vlasov simulation: magnetosheath and cusps under northward interplanetary magnetic field. J. Atmos. Sol. Terr. Phys. 99, 41–46.Google Scholar
Palodhi, L., Califano, F. & Pegoraro, F. 2009 Nonlinear kinetic development of the Weibel instability and the generation of electrostatic coherent structures. Plasma Phys. Control. Fusion 51 (12), 125006.Google Scholar
Palodhi, L., Califano, F. & Pegoraro, F. 2010 On the transition between the Weibel and the whistler instabilities. Plasma Phys. Control. Fusion 52 (9), 095007.Google Scholar
Parashar, T. N., Matthaeus, W. H. & Shay, M. A. 2018 Dependence of kinetic plasma turbulence on plasma  $\unicode[STIX]{x1D6FD}$ . Astrophys. J. 864 (1), L21.Google Scholar
Parashar, T. N., Shay, M. A., Cassak, P. A. & Matthaeus, W. H. 2009 Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma. Phys. Plasmas 16 (3), 032310.Google Scholar
Passot, T. & Sulem, P. L. 2007 Collisionless magnetohydrodynamics with gyrokinetic effects. Phys. Plasmas 14 (8), 082502.Google Scholar
Perrone, D., Passot, T., Laveder, D., Valentini, F., Sulem, P. L., Zouganelis, I., Veltri, P. & Servidio, S. 2018 Fluid simulations of plasma turbulence at ion scales: comparison with Vlasov–Maxwell simulations. Phys. Plasmas 25 (5), 052302.Google Scholar
Peyret, R. & Taylor, T. D. 1986 Computational Methods for Fluid Flow, Springer Series in Computational Physics. Springer.Google Scholar
Pezzi, O., Parashar, T. N., Servidio, S., Valentini, F., Vásconez, C. L., Yang, Y., Malara, F., Matthaeus, W. H. & Veltri, P. 2017a Colliding Alfvénic wave packets in magnetohydrodynamics, Hall and kineticsimulations. J. Plasma Phys. 83 (1), 705830108.Google Scholar
Pezzi, O., Parashar, T. N., Servidio, S., Valentini, F., Vásconez, C. L., Yang, Y., Malara, F., Matthaeus, W. H. & Veltri, P. 2017b Revisiting a classic: the parkermoffatt problem. Astrophys. J. 834 (2), 166.Google Scholar
Pezzi, O., Perrone, D., Servidio, S., Valentini, F., Sorriso-Valvo, L. & Veltri, P.2019 Proton–proton collisions in the turbulent solar wind: hybrid Boltzmann–Maxwell simulations, Preprint, arXiv:1903.03398.Google Scholar
Pezzi, O., Servidio, S., Perrone, D., Valentini, F., Sorriso-Valvo, L., Greco, A., Matthaeus, W. H. & Veltri, P. 2018 Velocity-space cascade in magnetized plasmas: numerical simulations. Phys. Plasmas 25 (6), 060704.Google Scholar
Pezzi, O., Valentini, F. & Veltri, P. 2016 Collisional relaxation of fine velocity structures in plasmas. Phys. Rev. Lett. 116 (14), 145001.Google Scholar
Pfau-Kempf, Y., Battarbee, M., Ganse, U., Hoilijoki, S., Turc, L., von Alfthan, S., Vainio, R. & Palmroth, M. 2018 On the importance of spatial and velocity resolution in the hybrid-Vlasov modeling of collisionless shocks. Front. Phys. 6, 44.Google Scholar
Phan, T., Eastwood, J. P., Shay, M., Drake, J., Sonnerup, B. Ö, Fujimoto, M., Cassak, P., Øieroset, M., Burch, J., Torbert, R. et al. 2018 Electron magnetic reconnection without ion coupling in Earths turbulent magnetosheath. Nature 557 (7704), 202.Google Scholar
Pokhotelov, D., von Alfthan, S., Kempf, Y., Vainio, R., Koskinen, H. E. J. & Palmroth, M. 2013 Ion distributions upstream and downstream of the Earth’s bow shock: first results from Vlasiator. Ann. Geophys. 31 (12), 2207–2212.Google Scholar
Pritchett, P. 2008 Collisionless magnetic reconnection in an asymmetric current sheet. J. Geophys. Res. 113 (A6), A06210.Google Scholar
Pritchett, P. L. 2001 Geospace environment modeling magnetic reconnection challenge: simulations with a full particle electromagnetic code. J. Geophys. Res. 106, 3783–3798.Google Scholar
Pucci, F., Matthaeus, W. H., Chasapis, A., Servidio, S., Sorriso-Valvo, L., Olshevsky, V., Newman, D. L., Goldman, M. V. & Lapenta, G. 2018 Generation of turbulence in colliding reconnection jets. Astrophys. J. 867 (1), 10.Google Scholar
Pucci, F., Servidio, S., Sorriso-Valvo, L., Olshevsky, V., Matthaeus, W. H., Malara, F., Goldman, M. V., Newman, D. L. & Lapenta, G. 2017 Properties of turbulence in the reconnection exhaust: numerical simulations compared with observations. Astrophys. J. 841 (1), 60.Google Scholar
Retinò, A., Sundkvist, D., Vaivads, A., Mozer, F., André, M. & Owen, C. J. 2007 In situ evidence of magnetic reconnection in turbulent plasma. Nat. Phys. 3, 236–238.Google Scholar
Rincon, F., Califano, F., Schekochihin, A. A. & Valentini, F. 2016 Turbulent dynamo in a collisionless plasma. Proc. Natl Acad. Sci. USA 113 (15), 3950–3953.Google Scholar
Roytershteyn, V., Boldyrev, S., Delzanno, G. L., Chen, C. H. K., Grošelj, D. & Loureiro, N. F. 2019 Numerical study of inertial kinetic-Alfvén turbulence. Astrophys. J. 870 (2), 103.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Plunk, G. G., Quataert, E. & Tatsuno, T. 2008 Gyrokinetic turbulence: a nonlinear route to dissipation through phase space. Plasma Phys. Control. Fusion 50 (12), 124024.Google Scholar
Schmitz, H. & Grauer, R. 2006a Darwin–Vlasov simulations of magnetised plasmas. J. Comput. Phys. 214 (2), 738–756.Google Scholar
Schmitz, H. & Grauer, R. 2006b Kinetic Vlasov simulations of collisionless magnetic reconnection. Phys. Plasmas 13 (9), 092309.Google Scholar
Servidio, S., Chasapis, A., Matthaeus, W. H., Perrone, D., Valentini, F., Parashar, T. N., Veltri, P., Gershman, D., Russell, C. T., Giles, B. et al. 2017 Magnetospheric multiscale observation of plasma velocity-space cascade: Hermite representation and theory. Phys. Rev. Lett. 119, 205101.Google Scholar
Servidio, S., Matthaeus, W. H., Shay, M. A., Cassak, P. A. & Dmitruk, P. 2009 Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 102 (11), 115003.Google Scholar
Servidio, S., Matthaeus, W. H., Shay, M. A., Dmitruk, P., Cassak, P. A. & Wan, M. 2010 Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 17 (3), 032315.Google Scholar
Servidio, S., Valentini, F., Califano, F. & Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108 (4), 045001.Google Scholar
Servidio, S., Valentini, F., Perrone, D., Greco, A., Califano, F., Matthaeus, W. H. & Veltri, P. 2015 A kinetic model of plasma turbulence. J. Plasma Phys. 81 (1), 325810107.Google Scholar
Shay, M. A., Drake, J. F., Rogers, B. N. & Denton, R. E. 2001 Alfvénic collisionless magnetic reconnection and the Hall term. J. Geophys. Res. 106 (A3), 3759–3772.Google Scholar
Shay, M. A., Haggerty, C. C., Matthaeus, W. H., Parashar, T. N., Wan, M. & Wu, P. 2018 Turbulent heating due to magnetic reconnection. Phys. Plasmas 25 (1), 012304.Google Scholar
Skoutnev, V., Hakim, A., Juno, J. & TenBarge, J. M. 2019 Temperature-dependent saturation of Weibel-type instabilities in counter-streaming plasmas. Astrophys. J. Lett. 872 (2), L28.Google Scholar
Sorriso-Valvo, L., Carbone, F., Perri, S., Greco, A., Marino, R. & Bruno, R. 2018a On the statistical properties of turbulent energy transfer rate in the inner heliosphere. Solar Phys. 293 (1), 10.Google Scholar
Sorriso-Valvo, L., Catapano, F., Retinò, A., Le Contel, O., Perrone, D., Roberts, O. W., Coburn, J. T., Panebianco, V., Valentini, F., Perri, S. et al. 2019 Turbulence-driven ion beams in the magnetospheric Kelvin–Helmholtz instability. Phys. Rev. Lett. 122, 035102.Google Scholar
Sorriso-Valvo, L., Perrone, D., Pezzi, O., Valentini, F., Servidio, S., Zouganelis, I. & Veltri, P. 2018b Local energy transfer rate and kinetic processes: the fate of turbulent energy in two-dimensional hybrid Vlasov–Maxwell numerical simulations. J. Plasma Phys. 84 (2), 725840201.Google Scholar
Sulem, P. L. & Passot, T. 2015 Landau fluid closures with nonlinear large-scale finite Larmor radius corrections for collisionless plasmas. J. Plasma Phys. 81 (1), 325810103.Google Scholar
Sulem, P. L., Passot, T., Laveder, D. & Borgogno, D. 2016 Influence of the nonlinearity parameter on the solar wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations. Astrophys. J. 818 (1), 66.Google Scholar
Tanabe, H., Yamada, T., Watanabe, T., Gi, K., Kadowaki, K., Inomoto, M., Imazawa, R., Gryaznevich, M., Michael, C., Crowley, B. et al. 2015 Electron and ion heating characteristics during magnetic reconnection in the mast spherical tokamak. Phys. Rev. Lett. 115, 215004.Google Scholar
Tatsuno, T., Dorland, W., Schekochihin, A. A., Plunk, G. G., Barnes, M., Cowley, S. C. & Howes, G. G. 2009 Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence. Phys. Rev. Lett. 103 (1), 015003.Google Scholar
TenBarge, J. M., Howes, G. G. & Dorland, W. 2013 Collisionless damping at electron scales in solar wind turbulence. Astrophys. J. 774 (2), 139.Google Scholar
Told, D., Jenko, F., TenBarge, J. M., Howes, G. G. & Hammett, G. W. 2015 Multiscale nature of the dissipation range in gyrokinetic simulations of Alfvénic turbulence. Phys. Rev. Lett. 115 (2), 025003.Google Scholar
Torbert, R. B., Burch, J. L., Giles, B. L., Gershman, D., Pollock, C. J., Dorelli, J., Avanov, L., Argall, M. R., Shuster, J., Strangeway, R. J. et al. 2016 Estimates of terms in Ohm’s law during an encounter with an electron diffusion region. Geophys. Res. Lett. 43 (12), 5918–5925.Google Scholar
Torbert, R. B., Burch, J. L., Phan, T. D., Hesse, M., Argall, M. R., Shuster, J., Ergun, R. E., Alm, L., Nakamura, R., Genestreti, K. J. et al. 2018 Electron-scale dynamics of the diffusion region during symmetric magnetic reconnection in space. Science 362 (6421), 1391–1395.Google Scholar
Tronci, C. & Camporeale, E. 2015 Neutral Vlasov kinetic theory of magnetized plasmas. Phys. Plasmas 22 (2), 020704.Google Scholar
Umeda, T., Miwa, J.-i, Matsumoto, Y., Nakamura, T. K. M., Togano, K., Fukazawa, K. & Shinohara, I. 2010 Full electromagnetic Vlasov code simulation of the Kelvin–Helmholtz instability. Phys. Plasmas 17 (5), 052311.Google Scholar
Umeda, T., Togano, K. & Ogino, T. 2009 Two-dimensional full-electromagnetic Vlasov code with conservative scheme and its application to magnetic reconnection. Comput. Phys. Commun. 180 (3), 365–374.Google Scholar
Umeda, T. & Wada, Y. 2016 Secondary instabilities in the collisionless Rayleigh–Taylor instability: full kinetic simulation. Phys. Plasmas 23 (11), 112117.Google Scholar
Umeda, T. & Wada, Y. 2017 Non-MHD effects in the nonlinear development of the MHD-scale Rayleigh–Taylor instability. Phys. Plasmas 24 (7), 072307.Google Scholar
Uzdensky, D. A. 2011 Magnetic reconnection in extreme astrophysical environments. Space Sci. Rev. 160 (1), 45–71.Google Scholar
Uzdensky, D. A. & Kulsrud, R. M. 2006 Physical origin of the quadrupole out-of-plane magnetic field in Hall-magnetohydrodynamic reconnection. Phys. Plasmas 13 (6), 062305.Google Scholar
Vaivads, A., Retinò, A., Soucek, J., Khotyaintsev, Y. V., Valentini, F., Escoubet, C. P., Alexandrova, O., André, M., Bale, S. D., Balikhin, M. et al. 2016 Turbulence heating observer satellite mission proposal. J. Plasma Phys. 82 (5), 905820501.Google Scholar
Valentini, F., Califano, F. & Veltri, P. 2010 Two-dimensional kinetic turbulence in the solar wind. Phys. Rev. Lett. 104, 205002.Google Scholar
Valentini, F., Carbone, V., Veltri, P. & Mangeney, A. 2005 Self-consistent Lagrangian study of nonlinear Landau damping. Phys. Rev. E 71 (1), 017402.Google Scholar
Valentini, F., Perrone, D., Stabile, S., Pezzi, O., Servidio, S., Marco, R. D., Marcucci, F., Bruno, R., Lavraud, B., Keyser, J. D. et al. 2016 Differential kinetic dynamics and heating of ions in the turbulent solar wind. New J. Phys. 18 (12), 125001.Google Scholar
Valentini, F., Trávníček, P., Califano, F., Hellinger, P. & Mangeney, A. 2007 A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma. J. Comput. Phys. 225 (1), 753–770.Google Scholar
Valentini, F., Vásconez, C. L., Pezzi, O., Servidio, S., Malara, F. & Pucci, F. 2017 Transition to kinetic turbulence at proton scales driven by large-amplitude kinetic Alfvén fluctuations. Astron. Astrophys. 599, A8.Google Scholar
Vàsconez, C. L., Valentini, F., Camporeale, E. & Veltri, P. 2014 Vlasov simulations of kinetic Alfvén waves at proton kinetic scales. Phys. Plasmas 21 (11), 112107.Google Scholar
Von Alfthan, S., Pokhotelov, D., Kempf, Y., Hoilijoki, S., Honkonen, I., Sandroos, A. & Palmroth, M. 2014 Vlasiator: first global hybrid-Vlasov simulations of Earth’s foreshock and magnetosheath. J. Atmos. Sol.-Terr. Phys. 120, 24–35.Google Scholar
Wan, M., Matthaeus, W. H., Roytershteyn, V., Karimabadi, H., Parashar, T., Wu, P. & Shay, M. 2015 Intermittent dissipation and heating in 3D kinetic plasma turbulence. Phys. Rev. Lett. 114 (17), 175002.Google Scholar
Weibel, E. S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83–84.Google Scholar
Yang, Y., Matthaeus, W. H., Parashar, T. N., Haggerty, C. C., Roytershteyn, V., Daughton, W., Wan, M., Shi, Y. & Chen, S. 2017 Energy transfer, pressure tensor, and heating of kinetic plasma. Phys. Plasmas 24 (7), 072306.Google Scholar
Zeiler, A., Biskamp, D., Drake, J. F., Rogers, B. N., Shay, M. A. & Scholer, M. 2002 Three-dimensional particle simulations of collisionless magnetic reconnection. J. Geophys. Res. 107 (A9), SMP 6-1–SMP 6-9.Google Scholar