- Letter
- Open Access
Linking the Langevin equation to scaling properties of space plasma turbulence at sub-ion scales
Phys. Rev. Research 5, L042014 – Published 19 October, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L042014
Abstract
Current understanding of the kinetic-scale turbulence in weakly collisional plasmas still remains elusive. We employ a general framework in which the turbulent energy transfer is envisioned as a scale-to-scale Langevin process. Fluctuations in the sub-ion range show a global scale invariance, thus suggesting a homogeneous energy repartition. In this Letter, we interpret such a feature by linking the drift term of the Langevin equation to scaling properties of fluctuations. Theoretical expectations are verified on solar wind observations and numerical simulations, thus giving relevance to the proposed framework for understanding kinetic-scale turbulence in space plasmas.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (61)
- R. Bruno and V. Carbone, The Solar Wind as a Turbulence Laboratory, Living Rev. Sol. Phys. 10, 2 (2013).
- A. Chasapis, W. H. Matthaeus, T. N. Parashar, S. A. Fuselier, B. A. Maruca, T. D. Phan, J. L. Burch, T. E. Moore, C. J. Pollock, D. J. Gershman, R. B. Torbert, C. T. Russell, and R. J. Strangeway, High-resolution statistics of solar wind turbulence at kinetic scales using the magnetospheric multiscale mission, Astrophys. J. Lett. 844, L9 (2017).
- P. A. Cassak, M. H. Barbhuiya, H. Liang, and M. R. Argall, Quantifying energy conversion in higher-order phase space density moments in plasmas, Phys. Rev. Lett. 130, 085201 (2023).
- O. Alexandrova, V. Carbone, P. Veltri, and L. Sorriso-Valvo, Small-scale energy cascade of the solar wind turbulence, Astrophys. J. 674, 1153 (2008).
- F. Sahraoui, M. L. Goldstein, P. Robert, and Y. V. Khotyaintsev, Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale, Phys. Rev. Lett. 102, 231102 (2009).
- C. H. K. Chen, T. S. Horbury, A. A. Schekochihin, R. T. Wicks, O. Alexandrova, and J. Mitchell, Anisotropy of solar wind turbulence between ion and electron scales, Phys. Rev. Lett. 104, 255002 (2010).
- C. H. K. Chen, S. Boldyrev, Q. Xia, and J. C. Perez, Nature of subproton scale turbulence in the solar wind, Phys. Rev. Lett. 110, 225002 (2013).
- L. Matteini, P. Hellinger, S. Landi, P. M. Trávníček, and M. Velli, Ion kinetics in the solar wind: Coupling global expansion to local microphysics, Space Sci. Rev. 172, 373 (2012).
- S. Zenitani, M. Hesse, A. Klimas, and M. Kuznetsova, New measure of the dissipation region in collisionless magnetic reconnection, Phys. Rev. Lett. 106, 195003 (2011).
- M. Wan, W. H. Matthaeus, V. Roytershteyn, H. Karimabadi, T. Parashar, P. Wu, and M. Shay, Intermittent dissipation and heating in 3D kinetic plasma turbulence, Phys. Rev. Lett. 114, 175002 (2015).
- R. Bandyopadhyay, W. H. Matthaeus, T. N. Parashar, Y. Yang, A. Chasapis, B. L. Giles, D. J. Gershman, C. J. Pollock, C. T. Russell, R. J. Strangeway, R. B. Torbert, T. E. Moore, and J. L. Burch, Statistics of kinetic dissipation in the earth's magnetosheath: MMS observations, Phys. Rev. Lett. 124, 255101 (2020).
- C. H. K. Chen, K. G. Klein, and G. G. Howes, Evidence for electron Landau damping in space plasma turbulence, Nat. Commun. 10, 740 (2019).
- D. Verscharen, K. G. Klein, and B. A. Maruca, The multi-scale nature of the solar wind, Living Rev. Sol. Phys. 16, 5 (2019).
- W. H. Matthaeus, S. Oughton, K. T. Osman, S. Servidio, M. Wan, S. P. Gary, M. A. Shay, F. Valentini, V. Roytershteyn, H. Karimabadi, and S. C. Chapman, Nonlinear and linear timescales near kinetic scales in solar wind turbulence, Astrophys. J. 790, 155 (2014).
- K. Sekimoto, Stochastic Energetics (Springer-Verlag Berlin Heidelberg, 2010).
- D. Faranda, Y. Sato, B. Saint-Michel, C. Wiertel, V. Padilla, B. Dubrulle, and F. Daviaud, Stochastic chaos in a turbulent swirling flow, Phys. Rev. Lett. 119, 014502 (2017).
- B. Dubrulle, Beyond Kolmogorov cascades, J. Fluid Mech. 867, P1 (2019).
- T. Alberti, F. Daviaud, R. V. Donner, B. Dubrulle, D. Faranda, and V. Lucarini, Chameleon attractors in turbulent flows, Chaos, Solitons Fractals 168, 113195 (2023).
- R. Friedrich and J. Peinke, Description of a turbulent cascade by a Fokker-Planck equation, Phys. Rev. Lett. 78, 863 (1997).
- J. Davoudi and M. R. R. Tabar, Theoretical model for the kramers-moyal description of turbulence cascades, Phys. Rev. Lett. 82, 1680 (1999).
- C. Renner, J. Peinke, and R. Friedrich, Evidence of markov properties of high frequency exchange rate data, Physica A 298, 499 (2001).
- P. Milan, M. Wächter, and J. Peinke, Turbulent character of wind energy, Phys. Rev. Lett. 110, 138701 (2013).
- D. Nickelsen and A. Engel, Probing small-scale intermittency with a fluctuation theorem, Phys. Rev. Lett. 110, 214501 (2013).
- A. Fuchs, C. Herbert, J. Rolland, M. Wächter, F. Bouchet, and J. Peinke, Instantons and the path to intermittency in turbulent flows, Phys. Rev. Lett. 129, 034502 (2022).
- M. Strumik and W. M. Macek, Testing for markovian character and modeling of intermittency in solar wind turbulence, Phys. Rev. E 78, 026414 (2008).
- S. Benella, M. Stumpo, G. Consolini, T. Alberti, V. Carbone, and M. Laurenza, Markovian features of the solar wind at subproton scales, Astrophys. J. Lett. 928, L21 (2022).
- S. Benella, M. Stumpo, G. Consolini, T. Alberti, M. Laurenza, and E. Yordanova, Kramers-Moyal analysis of interplanetary magnetic field fluctuations at sub-ion scales, Rend. Fis. Acc. Lincei 33, 721 (2022).
- W. M. Macek, D. Wójcik, and J. L. Burch, Magnetospheric multiscale observations of markov turbulence on kinetic scales, Astrophys. J. 943, 152 (2023).
- K. H. Kiyani, S. C. Chapman, Y. V. Khotyaintsev, M. W. Dunlop, and F. Sahraoui, Global scale-invariant dissipation in collisionless plasma turbulence, Phys. Rev. Lett. 103, 075006 (2009).
- K. T. Osman, K. H. Kiyani, W. H. Matthaeus, B. Hnat, S. C. Chapman, and Y. V. Khotyaintsev, Multi-spacecraft measurement of turbulence within a magnetic reconnection jet, Astrophys. J. Lett. 815, L24 (2015).
- U. Frisch, Turbulence: The legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995).
- G. H. Hardy, Weierstrass's non-differentiable function, T. Am. Math. Soc. 17, 301 (1916).
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics: Course of Theoretical Physics (Pergamon, London, 1959), Vol. 6.
- P. Flandrin, On the spectrum of fractional brownian motions, IEEE Trans. Inf. Theory 35, 197 (1989).
- R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, Extended self-similarity in turbulent flows, Phys. Rev. E 48, R29 (1993).
- C. Renner, J. Peinke, and R. Friedrich, Experimental indications for markov properties of small-scale turbulence, J. Fluid Mech. 433, 383 (2001).
- A. Arnèodo, R. Benzi, J. Berg, L. Biferale, E. Bodenschatz, A. Busse, E. Calzavarini, B. Castaing, M. Cencini, L. Chevillard, R. T. Fisher, R. Grauer, H. Homann, D. Lamb, A. S. Lanotte, E. Lévèque, B. Lüthi, J. Mann, N. Mordant, W. C. Müller, et al., Universal intermittent properties of particle trajectories in highly turbulent flows, Phys. Rev. Lett. 100, 254504 (2008).
- N. Reinke, A. Fuchs, D. Nickelsen, and J. Peinke, On universal features of the turbulent cascade in terms of non-equilibrium thermodynamics, J. Fluid Mech. 848, 117 (2018).
- H. Risken, The Fokker-Planck Equation (Springer Berlin, Heidelberg, 1996), pp. 63–95.
- R. Chhiber, W. H. Matthaeus, T. A. Bowen, and S. D. Bale, Subproton-scale intermittency in near-sun solar wind turbulence observed by the parker solar probe, Astrophys. J. Lett. 911, L7 (2021).
- T. Alberti, G. Consolini, V. Carbone, E. Yordanova, M. Marcucci, and P. De Michelis, Multifractal and chaotic properties of solar wind at MHD and kinetic domains: An empirical mode decomposition approach, Entropy 21, 320 (2019).
- O. Pezzi, D. Perrone, S. Servidio, F. Valentini, L. Sorriso-Valvo, and P. Veltri, Proton-proton collisions in the turbulent solar wind: Hybrid boltzmann-maxwell simulations, Astrophys. J. 887, 208 (2019).
- O. Pezzi, H. Liang, J. L. Juno, P. A. Cassak, C. L. Vásconez, L. Sorriso-Valvo, D. Perrone, S. Servidio, V. Roytershteyn, J. M. TenBarge, and W. H. Matthaeus, Dissipation measures in weakly collisional plasmas, Mon. Not. R. Astron. Soc. 505, 4857 (2021).
- S. Servidio, F. Valentini, D. Perrone, A. Greco, F. Califano, W. H. Matthaeus, and P. Veltri, A kinetic model of plasma turbulence, J. Plasma Phys. 81, 325810107 (2015).
- S. S. Cerri, S. Servidio, and F. Califano, Kinetic cascade in solar-wind turbulence: 3d3v hybrid-kinetic simulations with electron inertia, Astrophys. J. 846, L18 (2017).
- L. Franci, S. Landi, A. Verdini, L. Matteini, and P. Hellinger, Solar wind turbulent cascade from MHD to sub-ion scales: Large-size 3d hybrid particle-in-cell simulations, Astrophys. J. 853, 26 (2018).
- E. Leonardis, L. Sorriso-Valvo, F. Valentini, S. Servidio, F. Carbone, and P. Veltri, Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence, Phys. Plasmas 23, 022307 (2016).
- Y. Narita, K. H. Glassmeier, U. Motschmann, and M. Wilczek, Doppler shift and broadening in solar wind turbulence, Earth, Planets and Space 65, e5 (2013).
- R. Chhiber, A. V. Usmanov, W. H. Matthaeus, T. N. Parashar, and M. L. Goldstein, Contextual predictions for parker solar probe. II. Turbulence properties and taylor hypothesis, Astrophys J. Suppl. S. 242, 12 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L042014 for details about data samples used in the analysis, hybrid Vlasov-Maxwell simulation setup, test of the Markov condition on data sample obtained from numerical simulations and fit of the structure functions used to derive the scaling laws.
- J. V. Shebalin, W. H. Matthaeus, and D. Montgomery, Anisotropy in mhd turbulence due to a mean magnetic field, J. Plasma Phys. 29, 525 (1983).
- W. H. Matthaeus, S. Ghosh, S. Oughton, and D. A. Roberts, Anisotropic three-dimensional mhd turbulence, J. Geophys Res-Space 101, 7619 (1996).
- M. K. Verma, Statistical theory of magnetohydrodynamic turbulence: Recent results, Phys. Rep. 401, 229 (2004).
- W. H. Matthaeus, S. Servidio, P. Dmitruk, V. Carbone, S. Oughton, M. Wan, and K. T. Osman, Local anisotropy, higher order statistics, and turbulence spectra, Astrophys. J. 750, 103 (2012).
- F. Sahraoui, S. Y. Huang, G. Belmont, M. L. Goldstein, A. Rétino, P. Robert, and J. De Patoul, Scaling of the electron dissipation range of solar wind turbulence, Astrophys. J. 777, 15 (2013).
- V. Carbone, D. Telloni, F. Lepreti, and A. Vecchio, High-frequency magnetic fluctuations in space plasmas and the role of electron landau damping, Astrophys. J. Lett. 924, L26 (2022).
- F. Nguyen, J.-P. Laval, and B. Dubrulle, Characterizing most irregular small-scale structures in turbulence using local hölder exponents, Phys. Rev. E 102, 063105 (2020).
- C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985), Vol. 3.
- N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 2007).
- https://spdf.gsfc.nasa.gov/index.html.
- https://github.com/irfu/irfu-matlab.