1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
f
Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas
Rent:
Rent this article for
Access full text Article
/content/aip/journal/pop/20/1/10.1063/1.4773205
1.
1. P. Goldreich and S. Sridhar, Astrophys. J. 438, 763 (1995).
http://dx.doi.org/10.1086/175121
2.
2. G. Zank and W. H. Matthaeus, Phys. Fluids A 5, 257 (1993).
http://dx.doi.org/10.1063/1.858780
3.
3. A. Lazarian and J. Cho, Phys. Scr., T 116, 32 (2005).
http://dx.doi.org/10.1238/Physica.Topical.116a00032
4.
4. P. Dmitruk and W. Matthaeus, Phys. Plasmas 13, 042307 (2006).
http://dx.doi.org/10.1063/1.2192757
5.
5. A. Beresnyak, Phys. Rev. Lett. 106, 075001 (2011).
http://dx.doi.org/10.1103/PhysRevLett.106.075001
6.
6. P. Diamond, S.-I. Itoh, and K. Itoh, Relaxation Dynamics in Laboratory and Astrophysical Plasmas, Vol. 1: Biennial Reviews of the Theory of Magnetized Plasmas, edited by P. G. Patrick, H. Diamond, X. Garbet, and Y. Sarazin (World Scientific, 2009), pp. 117150.
7.
7. A. V. Usmanov, M. L. Goldstein, and W. H. Matthaeus, Astrophys. J. 754(1), 40 (2012).
http://dx.doi.org/10.1088/0004-637X/754/1/40
8.
8. E. Lee, M. E. Brachet, A. Pouquet, P. D. Mininni, and D. Rosenberg, Phys. Rev. E 81, 016318 (2010).
http://dx.doi.org/10.1103/PhysRevE.81.016318
9.
9. T. N. Parashar, M. A. Shay, P. A. Cassak, and W. H. Matthaeus, Phys. Plasmas 16, 032310 (2009).
http://dx.doi.org/10.1063/1.3094062
10.
10. G. G. Howes, J. M. TenBarge, W. Dorland, E. Quataert, A. A. Schekochihin, R. Numata, and T. Tatsuno, Phys. Rev. Lett. 107, 035004 (2011).
http://dx.doi.org/10.1103/PhysRevLett.107.035004
11.
11. O. Chang, S. P. Gary, and J. Wang, Geophys. Res. Lett. 38, L22102, doi:10.1029/2011GL049827 (2011).
http://dx.doi.org/10.1029/2011GL049827
12.
12. D. Verscharen, E. Marsch, U. Motschmann, and J. Muller, Phys. Plasmas 19, 022305 (2012).
http://dx.doi.org/10.1063/1.3682960
13.
13. S. Servidio, F. Valentini, F. Califano, and P. Veltri, Phys. Rev. Lett. 108, 045001 (2012).
http://dx.doi.org/10.1103/PhysRevLett.108.045001
14.
14. S. Boldyrev and J. C. Perez, “Spectrum of kinetic-Alfven turbulence,” Astrophys. J. Lett. 758, L44 (2012).
http://dx.doi.org/10.1088/2041-8205/758/2/L44
15.
15. L. Rudakov, M. Mithaiwala, G. Ganguli, and C. Crabtree, Phys. Plasmas 18, 012307 (2011).
http://dx.doi.org/10.1063/1.3532819
16.
16. L. Rudakov, C. Crabtree, G. Ganguli, and M. Mithaiwala, Phys. Plasmas 19, 042704 (2012).
http://dx.doi.org/10.1063/1.3698407
17.
17. R. Numata, G. G. Howes, T. Tatsuno, M. Barnes, and W. Dorland, J. Comput. Phys. 229(24), 9347 (2010).
http://dx.doi.org/10.1016/j.jcp.2010.09.006
18.
18. M. Wan, W. Matthaeus, H. Karimabadi, V. Roytershteyn, M. A. Shay, P. Wu, W. Daughton, B. Loring, and S. C. Chapman, Phys. Rev. Lett. 109, 195001 (2012).
http://dx.doi.org/10.1103/PhysRevLett.109.195001
19.
19. K. J. Bowers, B. J. Albright, L. Yin, B. Bergen, and T. J. T. Kwan, Phys. Plasmas 15, 7 (2008).
http://dx.doi.org/10.1063/1.2840133
20.
20. T. A. Yousef, T. Heinemann, A. A. Schekochihin, N. Kleeorin, I. Rogachevskii, A. B. Iskakov, S. C. Cowley, and J. C. McWilliams, Phys. Rev. Lett. 100, 184501 (2008).
http://dx.doi.org/10.1103/PhysRevLett.100.184501
21.
21. K. Julien and E. Knobloch, Philos. Trans. R. Soc. London 368, 1607 (2010).
http://dx.doi.org/10.1098/rsta.2009.0251
22.
22. F. Sahraoui, M. L. Goldstein, P. Robert, and Y. V. Khotyaintsev, Phys. Rev. Lett. 102, 231102 (2009).
http://dx.doi.org/10.1103/PhysRevLett.102.231102
23.
23. O. Alexandrova, V. Carbone, P. Veltri, and L. Sorriso-Valvo, Astrophys. J. 674, 1153 (2008).
http://dx.doi.org/10.1086/524056
24.
24. B. A. Maruca, J. C. Kasper, and S. D. Bale, Phys. Rev. Lett. 107, 201101 (2011).
http://dx.doi.org/10.1103/PhysRevLett.107.201101
25.
25. N. P. Korzhov, V. V. Mishin, and V. M. Tomozov, Planet. Space Sci. 32, 1169 (1984).
http://dx.doi.org/10.1016/0032-0633(84)90142-9
26.
26. D. A. Roberts, M. L. Goldstein, W. H. Matthaeus, and S. Ghosh, J. Geophys. Res., [Space Phys.] 97, 17115, doi:10.1029/92JA01144 (1992).
http://dx.doi.org/10.1029/92JA01144
27.
27. G. P. Zank, W. H. Matthaeus, and C. W. Smith, J. Geophys. Res., [Space Phys.] 101, 17093, doi:10.1029/96JA01275 (1996).
http://dx.doi.org/10.1029/96JA01275
28.
28. B. Breech, W. H. Matthaeus, J. Minnie, J. W. Bieber, S. Oughton, C. W. Smith, and P. A. Isenberg, J. Geophys. Res., [Space Phys.] 113, A08105, doi:10.1029/2007JA012711 (2008).
http://dx.doi.org/10.1029/2007JA012711
29.
29. J. E. Borovsky, J. Geophys. Res. 117, A06224, doi:10.1029/2012JA017623 (2012).
http://dx.doi.org/10.1029/2012JA017623
30.
30. M. J. Lighthill, Proc. R. Soc. London 211, 564 (1952).
http://dx.doi.org/10.1098/rspa.1952.0060
31.
31. A. Miura and P. L. Pritchett, J. Geophys. Res., [Space Phys.] 87, 7431, doi: 10.1029/JA087iA09p07431 (1982).
http://dx.doi.org/10.1029/JA087iA09p07431
32.
32. K. Nykyri and A. Otto, Geophys. Res. Lett. 28, 3565, doi:10.1029/2001GL013239 (2001).
http://dx.doi.org/10.1029/2001GL013239
33.
33. T. K. M. Nakamura, M. Fujimoto, and A. Otto, J. Geophys. Res., [Space Phys.] 113, A09204, doi:10.1029/2007JA012803 (2008).
http://dx.doi.org/10.1029/2007JA012803
34.
34. M. Faganello, F. Califano, and F. Pegoraro, Phys. Rev. Lett. 101, 105001 (2008).
http://dx.doi.org/10.1103/PhysRevLett.101.105001
35.
35. P. Dmitruk, W. Matthaeus, and N. Seenu, Astrophys. J. 617, 667 (2004).
http://dx.doi.org/10.1086/425301
36.
36. A. Monin and A. Yaglom, Statistical Fluid Mechanics, CTR Monograph (MIT, 1971 and 1975), Vol. 1 and 2, no. v. 1, pt. 2.
37.
37. S. Bourouaine, O. Alexandrova, E. Marsch, and M. Maksimovic, Astrophys. J. 749, 102 (2012).
http://dx.doi.org/10.1088/0004-637X/749/2/102
38.
38. F. Anselmet, Y. Gagne, E. J. Hopfinger, and R. A. Antonia, J. Fluid Mech. 140, 63 (1984).
http://dx.doi.org/10.1017/S0022112084000513
39.
39. A. N. Kolmogorov, J. Fluid Mech. 13, 82 (1962).
http://dx.doi.org/10.1017/S0022112062000518
40.
40. A. M. Obukhov, J. Geophys. Res. 67, 3011, doi:10.1029/JZ067i008p03011 (1962).
http://dx.doi.org/10.1029/JZ067i008p03011
41.
41. K. R. Sreenivasan and R. A. Antonia, Annu. Rev. Fluid Mech. 29, 435 (1997).
http://dx.doi.org/10.1146/annurev.fluid.29.1.435
42.
42. S. Servidio, M. Wan, W. Matthaeus, and V. Carbone, Phys. Fluids 22, 125107 (2010).
http://dx.doi.org/10.1063/1.3526760
43.
43. B. Cabral and L. Leedom, in Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, ACM New York, NY, 1993, pp. 263270.
44.
44. J. Egedal, W. Daughton, and A. Le, Nat. Phys. 8, 321 (2012).
http://dx.doi.org/10.1038/nphys2249
45.
45. E. Marsch, Living Rev. Solar Phys. 3, 1 (2006).
46.
46. B. J. Vasquez, C. W. Smith, K. Hamilton, B. T. MacBride, and R. J. Leamon, J. Geophys. Res. 112, A07101, doi:10.1029/2007JA012305 (2007).
http://dx.doi.org/10.1029/2007JA012305
47.
47. K. T. Osman, W. H. Matthaeus, A. Greco, and S. Servidio, Astrophys. J. Lett. 727, L11 (2011).
http://dx.doi.org/10.1088/2041-8205/727/1/L11
48.
48. V. Roytershteyn, W. Daughton, H. Karimabadi, and F. S. Mozer, Phys. Rev. Lett. 108, 185001 (2012).
http://dx.doi.org/10.1103/PhysRevLett.108.185001
49.
49. D. Sundkvist, A. Retino, A. Vaivads, and S. D. Bale, Phys. Rev. Lett. 99, 025004 (2007).
http://dx.doi.org/10.1103/PhysRevLett.99.025004
50.
50. A. A. Schekochihin, S. C. Cowley, W. Dorland, G. W. Hammett, G. G. Howes, E. Quataert, and T. Tatsuno, Astrophys. J. 182, 310 (2009).
http://dx.doi.org/10.1088/0067-0049/182/1/310
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/1/10.1063/1.4773205
Loading
View: Figures

Figures

Image of FIG. 1.

Click to view

FIG. 1.

Development of turbulence in physical space. (a) Formation of current sheets on the edge of the vortex. Current is normalized to . (b) Wrapping of current sheets inside the vortex and continuation of secondary instabilities. (c) Full development of turbulence. (d) Hierarchy of coherent structures as seen in close up of a region marked with a rectangle in (c). The size of each minor tick mark in Fig. 7(d) corresponds to .

Image of FIG. 2.

Click to view

FIG. 2.

(a) and (b) Omnidirectional energy (per unit mass) spectra of magnetic field and ion velocity field (Units not equated). Vertical dashed lines correspond to , , and Debye length , respectively. The magnetic spectra above show several point spectral features.

Image of FIG. 3.

Click to view

FIG. 3.

Generation of secondary tearing instabilities. (a) Plot of showing the formation of chains of tearing islands at . (b) Plot of highlighting the fact that tearing modes are formed in regions where the in-plane magnetic field is weak. Our linear tearing analysis was conducted for the two current sheets associated with these two chains of islands. Also shown are contours of vector potential . (c) Plot of showing the formation of chains of tearing islands well into the turbulent phase at and (d) corresponding plot of .

Image of FIG. 4.

Click to view

FIG. 4.

Wave excitation. (a) Plot of illustrating the launch of waves into the ambient plasma. (b) Zoomed-in region marked with a box in (a).

Image of FIG. 5.

Click to view

FIG. 5.

Wave diagnostics. (a) Frequency vs ky spectrum of magnetic fluctuations computed at the edge of the simulation away from the vortex. Superimposed on the spectrum are lines corresponding to dispersion of compressional and shear Alfven modes . (b) Compressibility diagnostic showing association of magnetosonic modes with high compressibility and shear Alfven modes with low compressibility as expected from the linear properties of these modes.

Image of FIG. 6.

Click to view

FIG. 6.

Normalized PDF of magnetic field increments, where , and is its variance. The increments are computed at spatial lag , and as is decreased beginning with large (energy containing) scales, moving through inertial range scales, and into dissipative scales, the PDFs of velocity increments are found to become increasingly non-Gaussian, acquiring “extended tails” associated with enhanced occurrence of large nearly discontinuous jumps. This phenomenon is viewed as diagnostic of intermittency or burstiness of dissipation.

Image of FIG. 7.

Click to view

FIG. 7.
Image of FIG. 8.

Click to view

FIG. 8.

is defined to be the change in the energy for each component from its initial value. (a) Time evolution of changes from their initial value of energy of the electron thermal energy, ion thermal energy, in-plane magnetic field energy, and ion flow energy. (b) Comparison of change in ion flow energy for runs that are identical except for the presence ( ) or absence ( is ) of an initial in-plane field.

Image of FIG. 9.

Click to view

FIG. 9.

Characterization of electron energization. (a) Electron distribution function in coordinates at and . Electrons are heated preferentially in the direction along the imposed magnetic field. (b) Electron energy distribution. The dashed line is drawn at times the electron thermal energy as a way to define high energy portion of the distribution function.

Image of FIG. 10.

Click to view

FIG. 10.

Dissipation in localized structures. Filamentary structure of turbulence as may be seen by spacecraft. (a) Plot of electron temperature anisotropy and a 1D cut mimicking of what a spacecraft may see in crossing such regions. (b) Density of electrons with energy in the range of where is the initial electron temperature. Energy band diagnostic consists of calculating the density of particles in each computational grid with energies in a pre-selected range of energy bands. (c) Ion temperature anisotropy.

Image of FIG. 11.

Click to view

FIG. 11.

Plot of the volume filling factor of coherent structures as measured by the volume of space that has exceeding a given threshold value on the x-axis. The x-axis is normalized to the noise level, i.e., standard deviation of in the quiet region of the simulation.

Image of FIG. 12.

Click to view

FIG. 12.

(a) Threshold plot of where values below 5 times noise level value are set to 0 (black) and those above are set to 1. (b) Plot of . (c) Overlay of the two panels, showing a close association of with intense current sheets. Bandpass filter was used to remove grid-scale noise.

Image of FIG. 13.

Click to view

FIG. 13.

3D effects. Comparison of 2D and 3D simulations of shear driven turbulence at . Intensity plot of the total current density in (a) 2D and (b) 3D. (c) Spectrum of the total magnetic energy in 2D (red) and 3D (blue), showing similar spectral index of ∼3.1. The 2D result has been re-scaled to match total magnetic energy in 3D.

Loading

Article metrics loading...

/content/aip/journal/pop/20/1/10.1063/1.4773205
2013-01-16
2014-04-24

Abstract

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

Loading

Full text loading...

/deliver/fulltext/aip/journal/pop/20/1/1.4773205.html;jsessionid=4ncrd7lrojsk3.x-aip-live-02?itemId=/content/aip/journal/pop/20/1/10.1063/1.4773205&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/pop
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Coherent structures, intermittent turbulence, and dissipation in high-temperature plasmas
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/1/10.1063/1.4773205
10.1063/1.4773205
SEARCH_EXPAND_ITEM