Abstract
The mapping of the magnetic field and analysis of the plasma resistivity were used to study the change of magnetic field topology during the formation of a reversed field configuration. Using a theta pinch with straight coil, the formation of the torus was observed during the early time of the plasma radial implosion, in scale comparable to Alfvén’s time and shorter than the resistive diffusion. The non-intrusive excluded flux probe also indicated the formation of the torus even in the absence of mirror coils in the system. The plasma at the end region of the coil has distributed in the entire cross section of the tube, slightly peaked at the null field region. The anomalous plasma resistivity at the reconnection site was close to the prediction given by numerical calculation using numerical hybrid code with anomalous collision frequency either calculated using Chodura’s algorithm or evolution of microinstabilities, particularly the lower hybrid drift instability.
Similar content being viewed by others
References
L. Bilbao, D. Grondona, Measurement of plasma current distribution using magnetic probes. Meas. Sci. Technol. 5(3), 288 (1994). http://stacks.iop.org/0957-0233/5/i=3/a=013
J. Birn, J.T. Gosling, M. Hesse, T.G. Forbes, E.R. Priest, Simulations of three-dimensional reconnection in the solar corona. Astrophys. J. 541, 1078 (2000). https://doi.org/10.1063/1.1375150
H. Bruzzone, C. Moreno, H. Kelly, Measurements of current sheets in plasmas with a finite-sized magnetic probe. Meas. Sci. Technol. 2(12), 1195 (1991). http://stacks.iop.org/0957-0233/2/i=12/a=015
A.W. Carlson, . Phys. Fluids. 30(5), 1497 (1987)
T.A. Carter, H. Ji, F. Trintchouk, M. Yamada, R.M. Kulsrud, Phys. Rev. Lett. 88(1), 015001–1 (2002)
R. Chodura, A hybrid fluid-particle model of ion heating in high-Mach-number shock waves. Nuclear Fus. 15, 55 (1975). https://doi.org/10.1088/0029-5515/15/1/008. http://iopscience.iop.org/0029-5515/15/1/008
R.E. Chrien, S. Okada, . Phys. Fluids. 30(11), 3574 (1987)
R.J. Comisso, H.R. Griem, Experimental study of the postimplosion phase of a theta-pinch. Phys. Fluids. 20(1), 44 (1977). https://doi.org/10.1063/1.861694
R.J. Comisso, Plasma heating and dynamics in a theta-pinch. Phd thesis, University of Maryland, College Park, MD (1975)
R.C. Davidson, N.T. Gladd, Anomalous transport properties associated with the lower-hybrid-drift instability. Phys. Fluids. 18(10), 1327 (1975)
R.C. Davidson, N.T. Gladd, C.S. Wu, J.D. Huba, . Phys. Fluids. 20(2), 301 (1977)
L.A. Dorf, T.P. Intrator, T. Awe, R. Renneke, S.C. Hsu, G.A. Wurden, R. Siemon, V.E. Semenov, . J. Appl. Phys. 104, 073304 (2008)
M. Yamada, Y. Ren, H. Ji, J. Breslau, S. Gerhardt, Experimental study of two-fluid effects on magnetic reconnection in a laboratory plasma with variable collisionality. Phys. Plasmas. 13, 052119 (2006). https://doi.org/10.1063/1.2203950
T. Asai, T. Matsumoto, T. Roche, I. Allfrey, H. Gota, J. Sekiguchi, T. Edo, E. Garate, Ts. Takahashi, M. Biderhauer, T. Tajima, Compact toroid injection fueling in a large field-reversed configuration. Nuclear Fus. 57, 076018 (2017). https://doi.org/10.1088/1741-4326/aa6dcd
H. Gota, K. Fujimoto, Y. Ohkuma, T. Takahashi, Y. Nogi, Separatrix shapes and internal structures of a field-reversed configuration plasma. Phys. Plasmas. 10(12), 4763–4770 (2003). https://doi.org/10.1063/1.1624835
A.L. Hoffman, R.D. Milroy, L.C. Steinhauer, Appl. Phys. Lett. 41(1), 31 (1982)
A.L. Hoffman, H.Y. Guo, R.D. Milroy, Z.A. Pietrzyk, Resistivity scaling of rotating magnetic field current drive in FRCS. Nuclear Fus. 43(10), 1091 (2003). http://stacks.iop.org/0029-5515/43/i=10/a=010
A.L. Hoffman, H.Y. Guo, K.E. Miller, R.D. Milroy, Long pulse FRC sustainment with enhanced edge driven rotating magnetic field current drive. Nuclear Fus. 45(3), 176 (2005). http://stacks.iop.org/0029-5515/45/i=3/a =003
R. Horiuchi, T. Sato, . Phys. Plasmas. 6(12), 4565 (1999)
T. Ii, M. Inomoto, K. Gi, T. Umezawa, T. Ito, K. Kadowaki, Y. Kaminou, Y. Ono, Stability and confinement improvement of an oblate field-reversed configuration by using neutral beam injection. Nuclear Fus. 53(7), 073002 (2013). http://stacks.iop.org/0029-5515/53/i=7/a=073002
J.H. Irby, Observations and interpretations of magnetic-ficle-line reconnection and tearing in a theta pinch. Phd thesis, University of Maryland, College Park, MD (1979)
J.H. Irby, J.F. Drake, H.R. Griem, Observation and interpretation of magnetic-field-line reconnection and tearing in a theta pinch. Phys. Rev. Lett. 42, 228–231 (1979). https://doi.org/10.1103/PhysRevLett.42.228
M.E. Kayama, R.A. Clemente, R.Y. Honda, M.S. Dobrowolsky, Radial plasma dynamic in sequential pinches. IEEE Trans. Plasma Sci. 37(11), 2186 (2009)
M.E. Kayama, L.C. Nascimento, R.P. Mota, K.G. Kostov, M.A. Algatti, Analysis on the formation of a frc by flux measurements and mhd simulations. J. Phys. Conf. Series, 15th Latin American Workshop Plasma Phys. 591, 012019 (2015). https://doi.org/10.1088/1742-6596/591/1/012019
M.E. Kayama, Resistivity in the dynamic current sheath of a field reversed configuration. Phys. Plasmas. 19 (3), 032511 (2012). https://doi.org/10.1063/1.3698405
M. Keilhacker, Diffusion of trapped reversed magnetic fields in a theta pinch in the presence of a probe. Nucl. Fusion. 4, 287 (1964)
P.C. Liewer, R.C. Davidson, Sheath broadening by the lower-hybrid-drift instability in pos- implosion theta pinches. Nuclear Fus. 17(1), 1953 (1977). http://iopscience.iop.org/0029-5515/17/1/008
P.C. Liewer, N.A. Krall, Self-consistent approach to anomalous resistivity applied to theta pinch experiments. Phys. Fluids. 16(11), 1953 (1973)
M.W. Binderbauer, A high performance field-reversed configuration. Phys. Plasmas. 22, 056110 (2015). https://doi.org/10.1063/1.4920950
R.D. Milroy, J.T. Brackbill, Numerical studies of a field-reversed theta-pinch plasma. Phys. Fluids. 25(5), 775 (1982). https://doi.org/10.1063/1.863832
R.D. Milroy, J.T. Slough, . Phys. Fluids B. 30(11), 3587 (1987)
M. Ozaki, T. Sato, R. Horiuchi, C.S. Group, . Plasma Phys. 3(6), 2265 (1996)
W. Pei, R. Horiuchi, T. Sato, Long time scale evolution of collisionless driven reconnection in a two-dimensional open system. Phys. Plasmas. 8(7), 3251 (2001). https://doi.org/10.1063/1.1375150
D.J. Rej, W.T. Armstrong, Electron temperature measurements in the field-reversed configuration experiment FRX-C. Nuclear Fus. 24(2), 177 (1984). http://stacks.iop.org/0029-5515/24/i=2/a=004
E. Sevillano, F.L. Ribe, Reconnection studies in field-reversed configurations. Phys. Fluids. 28(10), 3142–3153 (1985). https://doi.org/10.1063/1.865356. http://scitation.aip.org/content/aip/journal/pof1/28/10/10.1063/1.865356
A.G. Sgro, C.W. Nielson, Hybrid model studies of ions dynamics and magnetic field diffusion during pinch implosions. Phys. Fluids. 19(1), 126 (1976)
J.T. Slough, A.L. Hoffman, R.D. Milroy, D.G. Harding, L.C. Steinhauer, Flux and particle life-time measurements in field-reversed configurations. Nuclear Fus. 24(12), 1537 (1984). http://stacks.iop.org/0029-5515/24/i=12/a=002
J. Slough, G. Votroubek, C. Pihl, Creation of a high-temperature plasma through merging and compression of supersonic field reversed configuration plasmoids. Nuclear Fus. 51(5), 053008 (2011). http://stacks.iop.org/0029-5515/51/i=5/a=053008
L.C. Steinhauer, Review of field-reversed configurations. Phys. Plasmas. 18(7), 070501 (2011). https://doi.org/10.1063/1.3613680. http://scitation.aip.org/content/aip/journal/pop/18/7/10.1063/1.3613680
N. Takeuchi, K. Yasuoka, S. Ishii, Surface modification of thin rods by theta-pinching mettalic plasmas. IEEE Trans. Plasma Sci. 34(4), 1112 (2006)
F. Trintchouk, M. Yamada, H. Ji, R.M. Kulsrud, T.A. Carter, . Phys. Plasmas. 10(1), 319 (2003). https://doi.org/10.1063/1.1528612
M. Tuszewski, Experimental study of the equilibrium of field-reversed configurations. Plasma Phys.Controlled Fus. 26(8), 991 (1984). http://stacks.iop.org/0741-3335/26/i=8/a=004
M. Tuszewski, A. Smirnov, M.C. Thompson, S. Korepanov, T. Akhmetov, A. Ivanov, R. Voskoboynikov, L. Schmitz, D. Barnes, M.W. Binderbauer, R. Brown, D.W. Bui, R. Clary, K.D. Conroy, B.H. Deng, S.A. Dettrick, J.D. Douglass, E. Garate, F.J. Glass, H. Gota, H.Y. Guo, D. Gupta, S. Gupta, J.S. Kinley, K. Knapp, A. Longman, M. Hollins, X.L. Li, Y. Luo, R. Mendoza, Y. Mok, A. Necas, S. Primavera, E. Ruskov, J.H. Schroeder, L. Sevier, A. Sibley, Y. Song, X. Sun, E. Trask, A.D.V. Drie, J.K. Walters, M.D. Wyman, Field reversed configuration confinement enhancement through edge biasing and neutral beam injection. Phys. Rev. Lett. 108, 255008 (2012). https://doi.org/10.1103/PhysRevLett.108.255008
M. Yamada, R. Kulsrud, H. Ji, Radial plasma dynamic in sequential pinches. Rev. Modern Phys. 82, 603 (2010)
Acknowledgements
We are grateful to P.H. Sakanaka for providing the numerical code; to R.Y. Honda, M.A. Algatti, and R.P. Mota for the discussions; and to J.B. Galhardo for the technical support.
Funding
This work had support from the Sao Paulo Research Foundation (FAPESP) and the National Council for Scientific and Technological Development (CNPq).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kayama, M.E., Michelin, T.J. & Nascimento, L.C. Topology of the Magnetic Field and Resistivity of a Compact Torus Generated in a Mirrorless Theta Pinch. Braz J Phys 49, 191–197 (2019). https://doi.org/10.1007/s13538-019-00644-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13538-019-00644-x