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Driving magnetic turbulence using flux ropes in a moderate guide field linear system

  • Matthew I. Brookhart (a1), Aaron Stemo (a1) (a2), Roger Waleffe (a1) and Cary B. Forest (a1)


We present a series of experiments on novel, line-tied plasma geometries as a study of the generation of chaos and turbulence in line-tied systems. Plasma production and the injection scale for magnetic energy is provided by spatially discrete plasma guns that inject both plasma and current. The guns represent a technique for controlling the injection scale of magnetic energy. A two-dimensional (2-D) array of magnetic probes provides spatially resolved time histories of the magnetic fluctuations at a single cross-section of the experimental cylinder, allowing simultaneous spatial measurements of chaotic and turbulent behaviour. The first experiment shows chaotic fluctuations and self-organization in a hollow-current line-tied screw pinch. These dynamics is modulated primarily by the applied magnetic field and weakly by the plasma current and safety factor. The second experiment analyses the interactions of multiple line-tied flux ropes. The flux ropes all exhibit chaotic behaviour, and under certain conditions develop an inverse cascade to larger scales and a turbulent inertial range with magnetic energy ( $E$ ) related to perpendicular wave number ( $k_{\bot }$ ) as $E\propto k_{\bot }^{-2.5\pm 0.5}$ .


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Alexakis, A. 2011 Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field. Phys. Rev. E 84 (5), 19.
Bandt, C. & Pompe, B. 2002 Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88 (17), 174102.
Bergerson, W. F., Forest, C. B., Fiksel, G., Hannum, D. A., Kendrick, R., Sarff, J. S. & Stambler, S. 2006 Onset and saturation of the kink instability in a current-carrying line-tied plasma. Phys. Rev. Lett. 96 (1), 015004.
Brookhart, M. I., Stemo, A., Zuberbier, A., Zweibel, E. & Forest, C. B. 2015 Instability, turbulence, and 3D magnetic reconnection in a line-tied, zero net current screw pinch. Phys. Rev. Lett. 114 (14), 145001.
Cooper, C. M., Wallace, J., Brookhart, M., Clark, M., Collins, C., Ding, W. X., Flanagan, K., Khalzov, I., Li, Y., Milhone, J. et al. 2014 The Madison plasma dynamo experiment: a facility for studying laboratory plasma astrophysics. Phys. Plasmas 21, 013505.
Delzanno, G. L., Evstatiev, E. G. & Finn, J. M. 2007 The role of resistivity on line-tied kink modes in cylindrical geometry. Phys. Plasmas 14 (7), 070702.
Fiksel, G., Almagri, A. F., Craig, D., Iida, M., Prager, S. C. & Sarff, J. S. 1996 High current plasma electron emitter. Plasma Sources Sci. Technol. 5 (1), 7883.
Forest, C. B., Flanagan, K., Brookhart, M., Clark, M., Cooper, C. M., Désangles, V., Egedal, J., Endrizzi, D., Khalzov, I. V., Li, H. et al. 2015 The wisconsin plasma astrophysics laboratory. J. Plasma Phys. 81 (5), 121.
Furno, I., Intrator, T. P., Hemsing, E. W., Hsu, S. C., Abbate, S., Ricci, P. & Lapenta, G. 2005 Coalescence of two magnetic flux ropes via collisional magnetic reconnection. Phys. Plasmas 12 (5), 055702.
Furno, I., Intrator, T. P., Lapenta, G., Dorf, L., Abbate, S. & Ryutov, D. D. 2007 Effects of boundary conditions and flow on the kink instability in a cylindrical plasma column. Phys. Plasmas 14 (2), 022103.
Gekelman, W., Maggs, J. E. & Pfister, H. 1992 Experiments on the interaction of current channels in a laboratory plasma: relaxation to the force-free state. Plasma Sci. IEEE 20 (6), 614621.
Gekelman, W., Van Compernolle, B., Dehaas, T. & Vincena, S. 2014 Chaos in magnetic flux ropes. Plasma Phys. Control. Fusion 56 (6), 064002.
Hood, A. W. 1993 The stability of line-tied coronal loops and an extended Suydam criterion. Adv. Space Res. 13 (9), 105108.
Hsu, S. C. & Bellan, P. M. 2003 Experimental identification of the kink instability as a poloidal flux amplification mechanism for coaxial gun spheromak formation. Phys. Rev. Lett. 90 (21), 14.
Intrator, T. P., Sun, X., Lapenta, G., Dorf, L. & Furno, I. 2009 Experimental onset threshold and magnetic pressure pile-up for 3D reconnection. Nat. Phys. 5 (7), 521526.
Khalzov, I. V., Ebrahimi, F., Schnack, D. D. & Mirnov, V. V. 2012 Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics. Phys. Plasmas 19 (1), 012111.
Lawrence, E. & Gekelman, W. 2009 Identification of a quasiseparatrix layer in a reconnecting laboratory magnetoplasma. Phys. Rev. Lett. 103 (10), 25.
Maggs, J. E. & Morales, G. J. 2013 Permutation entropy analysis of temperature fluctuations from a basic electron heat transport experiment. Plasma Phys. Control. Fusion 55 (8), 085015.
Paz-Soldan, C., Bergerson, W. F., Brookhart, M. I., Hannum, D. A., Kendrick, R., Fiksel, G. & Forest, C. B. 2010 The rotating wall machine: a device to study ideal and resistive magnetohydrodynamic stability under variable boundary conditions. Rev. Sci. Instrum. 81 (12), 123503.
Paz-Soldan, C., Brookhart, M. I., Clinch, A. J., Hannum, D. A. & Forest, C. B. 2011 Two-dimensional axisymmetric and three-dimensional helical equilibrium in the line-tied screw pinch. Phys. Plasmas 18 (5), 052114.
Rappazzo, A. F., Velli, M. & Einaudi, G. 2013 Field lines twisting in a noisy corona: implications for energy storage and release, and initiation of solar eruptions. Astrophys. J. 771 (2), 76.
Rosso, O., Larrondo, H., Martin, M., Plastino, a. & Fuentes, M. 2007 Distinguishing noise from chaos. Phys. Rev. Lett. 99 (15), 154102.
Russell, C. T., Priest, E. R. & Lee, L. C.(Eds) 1990 Physics of Magnetic Flux Ropes. American Geophysical Union.
Ryutov, D. D., Furno, I., Intrator, T. P., Abbate, S. & Madziwa-Nussinov, T. 2006 Phenomenological theory of the kink instability in a slender plasma column. Phys. Plasmas 13 (3), 032105.
Sun, X., Intrator, T. P., Dorf, L., Sears, J., Furno, I. & Lapenta, G. 2010 Flux rope dynamics: Experimental study of bouncing and merging. Phys. Rev. Lett. 105 (25), 36.
Suydam, B. R. 1958 Stability of a linear pinch. J. Nuclear Energy 7 (3–4), 275276.
Taylor, J. B. 1986 Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 58 (3), 741763.
Van Compernolle, B. & Gekelman, W. 2012 Morphology and dynamics of three interacting kink-unstable flux ropes in a laboratory magnetoplasma. Phys. Plasmas 19 (10), 102102.
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Driving magnetic turbulence using flux ropes in a moderate guide field linear system

  • Matthew I. Brookhart (a1), Aaron Stemo (a1) (a2), Roger Waleffe (a1) and Cary B. Forest (a1)


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