Abstract

Arc plasmas are common and important phenomena, which have been widely used in scientific research and industrial fields. It is a non-intrusive way to understand the dynamic characteristics of arc plasma by measuring magnetic field distribution and applying inverse method. Aiming to investigate the motion characteristics of arc plasma, a high-speed magneto-optical imaging system was developed, which mainly consists of a laser-driven light source, achromatic collimator, beam expander, polarized beam splitter, analyzer and high-speed camera. The calibration experiment of the system, which was conducted using a Faraday indicator with a Verdet constant of −96 rad/(T·m)@632.8 nm and Helmholtz coils, shows its magnetic sensitivity reaches 1 mT, spatial resolution is about 500μm, temporal resolution is 100μs as for a circular measuring area of 42 mm in diameter. The arcing experimental results also demonstrate that the developed system can obtain the 2D magnetic field distribution in real time with relatively high spatial and temporal resolution and reasonable magnetic sensitivity. It also provides an effective method to study the motion characteristics of arc plasma inside of an enclosed chamber.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  29. P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
    [Crossref] [PubMed]
  30. Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
    [Crossref]

2018 (2)

C. Liu, J. Chen, J. Liu, and X. Han, “High frame-rate computational ghost imaging system using an optical fiber phased array and a low-pixel APD array,” Opt. Express 26(8), 10048–10064 (2018).
[Crossref] [PubMed]

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

2017 (2)

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

2016 (1)

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

2015 (1)

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

2014 (2)

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

2013 (3)

Z. W. Sun, J. J. Zhu, Z. S. Li, M. Aldén, F. Leipold, M. Salewski, and Y. Kusano, “Optical diagnostics of a gliding arc,” Opt. Express 21(5), 6028–6044 (2013).
[Crossref] [PubMed]

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

2012 (6)

P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
[Crossref] [PubMed]

G. Y. Tian, A. Al-Qubaa, and J. Wilson, “Design of an electromagnetic imaging system for weapon detection based on GMR sensor arrays,” Sens. Actuators A Phys. 174, 75–84 (2012).
[Crossref]

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

L. Ghezzi, D. Piva, and L. Di Rienzo, “Current density reconstruction in vacuum arcs by inverting magnetic field data,” IEEE Trans. Magn. 48(8), 2324–2333 (2012).
[Crossref]

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

2011 (1)

A. Gutsol, A. Rabinovich, and A. Fridman, “Combustion-assisted plasma in fuel conversion,” J. Phys. D Appl. Phys. 44(27), 274001 (2011).
[Crossref]

2010 (2)

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

H. Murakami and M. Tonouchi, “High-sensitive scanning laser magneto-optical imaging system,” Rev. Sci. Instrum. 81(1), 013701 (2010).
[Crossref] [PubMed]

2008 (3)

K. H. Hauer, R. Potthast, and M. Wannert, “Algorithms for magnetic tomography - on the role of a priori knowledge and constraints,” Inverse Probl. 24(4), 045008 (2008).
[Crossref]

R. Merwa and H. Scharfetter, “Magnetic induction tomography: comparison of the image quality using different types of receivers,” Physiol. Meas. 29(6), S417–S429 (2008).
[Crossref] [PubMed]

J. Svensson and A. Werner, “Current tomography for axisymmetric plasmas,” Plasma Phys. Contr. Fusion 50(8), 085002 (2008).
[Crossref]

2006 (1)

M. Keidar and I. D. Boyd, “Ablation study in the capillary discharge of an electrothermal gun,” J. Appl. Phys. 99(5), 053301 (2006).
[Crossref]

2005 (1)

J. P. Toumazet, C. Brdys, A. Laurent, and J. Ponthenier, “Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations,” Meas. Sci. Technol. 16(7), 1525–1533 (2005).
[Crossref]

1999 (1)

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

1997 (1)

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Al-Amayreh, M. I.

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Alden, M.

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

Aldén, M.

Al-Qubaa, A.

G. Y. Tian, A. Al-Qubaa, and J. Wilson, “Design of an electromagnetic imaging system for weapon detection based on GMR sensor arrays,” Sens. Actuators A Phys. 174, 75–84 (2012).
[Crossref]

Andre, V.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Bai, L.

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

Banerjee, S. S.

P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
[Crossref] [PubMed]

Barness, D.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Barrault, M.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Baziljevich, M.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Bencze, A.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Berta, M.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Bianchetti, R.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Biegel, W.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Boyd, I. D.

M. Keidar and I. D. Boyd, “Ablation study in the capillary discharge of an electrothermal gun,” J. Appl. Phys. 99(5), 053301 (2006).
[Crossref]

Brdys, C.

J. P. Toumazet, C. Brdys, A. Laurent, and J. Ponthenier, “Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations,” Meas. Sci. Technol. 16(7), 1525–1533 (2005).
[Crossref]

Bultel, Y.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Cauffet, G.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Chadebec, O.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Chen, J.

Chen, K.

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

Cheng, Y.

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

Chevrier, P.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Chowdhury, D.

P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
[Crossref] [PubMed]

Cross, K. J.

J. W. McBride and K. J. Cross, “Studies of high current arcs using an optical fiber array based imaging system,” in Proceedings of the 1st International Conference on Electric Power Equipment - Switching Technology (IEEE, 2011), pp. 475–479.
[Crossref]

Dedulle, J.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Deng, Y.

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

Di Rienzo, L.

L. Ghezzi, D. Piva, and L. Di Rienzo, “Current density reconstruction in vacuum arcs by inverting magnetic field data,” IEEE Trans. Magn. 48(8), 2324–2333 (2012).
[Crossref]

Dong, J. L.

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

Ehn, A.

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

Eisenmenger, J.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Feng, Z.

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

Fiévet, C.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Fleurier, C.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Fourneron, Y.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Franke, St.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Fridman, A.

A. Gutsol, A. Rabinovich, and A. Fridman, “Combustion-assisted plasma in fuel conversion,” J. Phys. D Appl. Phys. 44(27), 274001 (2011).
[Crossref]

Gao, J.

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

Gati, R.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Geng, J.

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

Geng, Y. S.

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

Ghezzi, L.

L. Ghezzi, D. Piva, and L. Di Rienzo, “Current density reconstruction in vacuum arcs by inverting magnetic field data,” IEEE Trans. Magn. 48(8), 2324–2333 (2012).
[Crossref]

Gutsol, A.

A. Gutsol, A. Rabinovich, and A. Fridman, “Combustion-assisted plasma in fuel conversion,” J. Phys. D Appl. Phys. 44(27), 274001 (2011).
[Crossref]

Hácek, P.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Han, X.

Hauer, K. H.

K. H. Hauer, R. Potthast, and M. Wannert, “Algorithms for magnetic tomography - on the role of a priori knowledge and constraints,” Inverse Probl. 24(4), 045008 (2008).
[Crossref]

Hofmann, H.

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Huang, W.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Jamone, L.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Jia, S. L.

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

Jogschies, L.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Keidar, M.

M. Keidar and I. D. Boyd, “Ablation study in the capillary discharge of an electrothermal gun,” J. Appl. Phys. 99(5), 053301 (2006).
[Crossref]

Klaas, D.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Kong, L.

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

Kristanto, H.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Kruppe, R.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Kuhn, M.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Kuo-Peng, P.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Kuroki, T.

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

Kurrat, M.

C. Wolf, M. Kurrat, M. Lindmayer, and E. Wilkening, “Optical investigations of high-current vacuum arc behavior on spiral-shaped and cup-shaped RMF-contacts,” in Proceedings of the 55th IEEE Holm Conference on Electrical Contacts (IEEE, 2009), pp. 270–272.
[Crossref]

Kusano, Y.

Laurent, A.

J. P. Toumazet, C. Brdys, A. Laurent, and J. Ponthenier, “Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations,” Meas. Sci. Technol. 16(7), 1525–1533 (2005).
[Crossref]

Le Ny, M.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Leiderer, P.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Leipold, F.

Li, R.

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

Li, X. W.

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

Li, Z.

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

Li, Z. S.

Lindmayer, M.

C. Wolf, M. Kurrat, M. Lindmayer, and E. Wilkening, “Optical investigations of high-current vacuum arc behavior on spiral-shaped and cup-shaped RMF-contacts,” in Proceedings of the 55th IEEE Holm Conference on Electrical Contacts (IEEE, 2009), pp. 270–272.
[Crossref]

Liu, C.

Liu, J.

Mandal, P.

P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
[Crossref] [PubMed]

McBride, J. W.

J. W. McBride and K. J. Cross, “Studies of high current arcs using an optical fiber array based imaging system,” in Proceedings of the 1st International Conference on Electric Power Equipment - Switching Technology (IEEE, 2011), pp. 475–479.
[Crossref]

Merwa, R.

R. Merwa and H. Scharfetter, “Magnetic induction tomography: comparison of the image quality using different types of receivers,” Physiol. Meas. 29(6), S417–S429 (2008).
[Crossref] [PubMed]

Methling, R.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Mlynár, J.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Murakami, H.

H. Murakami and M. Tonouchi, “High-sensitive scanning laser magneto-optical imaging system,” Rev. Sci. Instrum. 81(1), 013701 (2010).
[Crossref] [PubMed]

Murphy, A.

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

Nilsson, O.

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Odstrcil, M.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Odstrcil, T.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Okubo, M.

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

Perel, E.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Petit, P.

C. Fiévet, M. Barrault, P. Petit, P. Chevrier, C. Fleurier, and V. Andre, “Optical diagnostics and numerical modelling of arc re-strikes in low-voltage circuit breakers,” J. Phys. D Appl. Phys. 30(21), 2991–2999 (1997).
[Crossref]

Piva, D.

L. Ghezzi, D. Piva, and L. Di Rienzo, “Current density reconstruction in vacuum arcs by inverting magnetic field data,” IEEE Trans. Magn. 48(8), 2324–2333 (2012).
[Crossref]

Ponthenier, J.

J. P. Toumazet, C. Brdys, A. Laurent, and J. Ponthenier, “Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations,” Meas. Sci. Technol. 16(7), 1525–1533 (2005).
[Crossref]

Potthast, R.

K. H. Hauer, R. Potthast, and M. Wannert, “Algorithms for magnetic tomography - on the role of a priori knowledge and constraints,” Inverse Probl. 24(4), 045008 (2008).
[Crossref]

Rabinovich, A.

A. Gutsol, A. Rabinovich, and A. Fridman, “Combustion-assisted plasma in fuel conversion,” J. Phys. D Appl. Phys. 44(27), 274001 (2011).
[Crossref]

Rissing, L.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Rittinger, J.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Rosini, S.

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

Saeki, N.

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

Salewski, M.

Scharfetter, H.

R. Merwa and H. Scharfetter, “Magnetic induction tomography: comparison of the image quality using different types of receivers,” Physiol. Meas. 29(6), S417–S429 (2008).
[Crossref] [PubMed]

Schey, B.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Schmitz, A.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Schwinne, M.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Shaulov, A.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Shi, Z. Q.

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

Sinvani, M.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Somlor, S.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Stritzker, B.

M. Kuhn, B. Schey, W. Biegel, B. Stritzker, J. Eisenmenger, and P. Leiderer, “Large area magneto-optical investigations of YBCO thin films,” Rev. Sci. Instrum. 70(3), 1761–1766 (1999).
[Crossref]

Sugano, S.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Sun, Z. W.

Svensson, J.

J. Svensson and A. Werner, “Current tomography for axisymmetric plasmas,” Plasma Phys. Contr. Fusion 50(8), 085002 (2008).
[Crossref]

Szabolics, T.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Tahara, M.

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

Tamegai, T.

P. Mandal, D. Chowdhury, S. S. Banerjee, and T. Tamegai, “High sensitivity differential magneto-optical imaging with a compact Faraday-modulator,” Rev. Sci. Instrum. 83(12), 123906 (2012).
[Crossref] [PubMed]

Taptimthong, P.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Tian, G. Y.

G. Y. Tian, A. Al-Qubaa, and J. Wilson, “Design of an electromagnetic imaging system for weapon detection based on GMR sensor arrays,” Sens. Actuators A Phys. 174, 75–84 (2012).
[Crossref]

Tomo, T. P.

T. P. Tomo, S. Somlor, A. Schmitz, L. Jamone, W. Huang, H. Kristanto, and S. Sugano, “Design and characterization of a three-axis hall effect-based soft skin sensor,” Sensors (Basel) 16(4), 491 (2016).
[Crossref] [PubMed]

Tonouchi, M.

H. Murakami and M. Tonouchi, “High-sensitive scanning laser magneto-optical imaging system,” Rev. Sci. Instrum. 81(1), 013701 (2010).
[Crossref] [PubMed]

Toumazet, J. P.

J. P. Toumazet, C. Brdys, A. Laurent, and J. Ponthenier, “Combined use of an inverse method and a voltage measurement: estimation of the arc column volume and its variations,” Meas. Sci. Technol. 16(7), 1525–1533 (2005).
[Crossref]

Uhrlandt, D.

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

Verdoolaege, G.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Wang, J. H.

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

Wang, W.

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

Wannert, M.

K. H. Hauer, R. Potthast, and M. Wannert, “Algorithms for magnetic tomography - on the role of a priori knowledge and constraints,” Inverse Probl. 24(4), 045008 (2008).
[Crossref]

Wei, F.

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

Weindl, C.

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Weinzettl, V.

M. Odstrčil, J. Mlynář, V. Weinzettl, P. Háček, T. Odstrčil, G. Verdoolaege, M. Berta, T. Szabolics, and A. Bencze, “Plasma tomographic reconstruction from tangentially viewing camera with background subtraction,” Rev. Sci. Instrum. 85(1), 013509 (2014).
[Crossref] [PubMed]

Werner, A.

J. Svensson and A. Werner, “Current tomography for axisymmetric plasmas,” Plasma Phys. Contr. Fusion 50(8), 085002 (2008).
[Crossref]

Wienecke, A.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Wilkening, E.

C. Wolf, M. Kurrat, M. Lindmayer, and E. Wilkening, “Optical investigations of high-current vacuum arc behavior on spiral-shaped and cup-shaped RMF-contacts,” in Proceedings of the 55th IEEE Holm Conference on Electrical Contacts (IEEE, 2009), pp. 270–272.
[Crossref]

Wilson, J.

G. Y. Tian, A. Al-Qubaa, and J. Wilson, “Design of an electromagnetic imaging system for weapon detection based on GMR sensor arrays,” Sens. Actuators A Phys. 174, 75–84 (2012).
[Crossref]

Wolf, C.

C. Wolf, M. Kurrat, M. Lindmayer, and E. Wilkening, “Optical investigations of high-current vacuum arc behavior on spiral-shaped and cup-shaped RMF-contacts,” in Proceedings of the 55th IEEE Holm Conference on Electrical Contacts (IEEE, 2009), pp. 270–272.
[Crossref]

Wurz, M. C.

L. Jogschies, D. Klaas, R. Kruppe, J. Rittinger, P. Taptimthong, A. Wienecke, L. Rissing, and M. C. Wurz, “Recent developments of magnetoresistive sensors for industrial applications,” Sensors (Basel) 15(11), 28665–28689 (2015).
[Crossref] [PubMed]

Xia, G.

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

Yeshurun, Y.

M. Baziljevich, D. Barness, M. Sinvani, E. Perel, A. Shaulov, and Y. Yeshurun, “Magneto-optical system for high speed real time imaging,” Rev. Sci. Instrum. 83(8), 083707 (2012).
[Crossref] [PubMed]

Zhang, G. G.

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

Zhu, J.

J. Gao, J. Zhu, A. Ehn, M. Alden, and Z. Li, “In-situ non-intrusive diagnostics of toluene removal by a gliding arc discharge using planar laser-induced fluorescence,” Plasma Chem. Plasma Process. 37(2), 433–450 (2017).
[Crossref]

Zhu, J. J.

Appl. Phys. Lett. (1)

Z. Feng, N. Saeki, T. Kuroki, M. Tahara, and M. Okubo, “Surface modification by nonthermal plasma induced by using magnetic-field-assisted gliding arc discharge,” Appl. Phys. Lett. 101(4), 041602 (2012).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

Y. Cheng, Y. Deng, L. Bai, and K. Chen, “Enhanced laser-based magneto-optic imaging system for nondestructive evaluation applications,” IEEE Trans. Instrum. Meas. 62(5), 1192–1198 (2013).
[Crossref]

IEEE Trans. Magn. (3)

L. Ghezzi, D. Piva, and L. Di Rienzo, “Current density reconstruction in vacuum arcs by inverting magnetic field data,” IEEE Trans. Magn. 48(8), 2324–2333 (2012).
[Crossref]

J. L. Dong, G. G. Zhang, Y. S. Geng, and J. H. Wang, “Influence of magnetic measurement modeling on the solution of magnetostatic inverse problems applied to current distribution reconstruction in switching air arcs,” IEEE Trans. Magn. 54(3), 8000704 (2018).
[Crossref]

M. Le Ny, O. Chadebec, G. Cauffet, J. Dedulle, Y. Bultel, S. Rosini, Y. Fourneron, and P. Kuo-Peng, “Current distribution identification in fuel cell stacks from external magnetic field measurements,” IEEE Trans. Magn. 49(5), 1925–1928 (2013).
[Crossref]

IEEE Trans. Plasma Sci. (2)

R. Li, X. W. Li, S. L. Jia, A. Murphy, and Z. Q. Shi, “Study of different models of the wall ablation process in capillary discharge,” IEEE Trans. Plasma Sci. 38(4), 1033–1041 (2010).
[Crossref]

H. Hofmann, C. Weindl, M. I. Al-Amayreh, and O. Nilsson, “Arc movement inside an AC/DC circuit breaker working with a novel method of arc guiding: part I—experiments, examination, and analysis,” IEEE Trans. Plasma Sci. 40(8), 2028–2034 (2012).
[Crossref]

Inverse Probl. (1)

K. H. Hauer, R. Potthast, and M. Wannert, “Algorithms for magnetic tomography - on the role of a priori knowledge and constraints,” Inverse Probl. 24(4), 045008 (2008).
[Crossref]

J. Appl. Phys. (1)

M. Keidar and I. D. Boyd, “Ablation study in the capillary discharge of an electrothermal gun,” J. Appl. Phys. 99(5), 053301 (2006).
[Crossref]

J. Phys. D Appl. Phys. (4)

W. Wang, L. Kong, J. Geng, F. Wei, and G. Xia, “Wall ablation of heated compound-materials into non-equilibrium discharge plasmas,” J. Phys. D Appl. Phys. 50(7), 074005 (2017).
[Crossref]

St. Franke, R. Methling, D. Uhrlandt, R. Bianchetti, R. Gati, and M. Schwinne, “Temperature determination in copper-dominated free-burning arcs,” J. Phys. D Appl. Phys. 47(1), 015202 (2014).
[Crossref]

A. Gutsol, A. Rabinovich, and A. Fridman, “Combustion-assisted plasma in fuel conversion,” J. Phys. D Appl. Phys. 44(27), 274001 (2011).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Principle of Faraday effect.
Fig. 2
Fig. 2 Structure of MOI system.
Fig. 3
Fig. 3 Integrated MOI system.
Fig. 4
Fig. 4 Helmholtz coil calibration.
Fig. 5
Fig. 5 (a) The gray value distribution when B is set to 0mT; (b) The gray value distribution when B is set to 10mT.
Fig. 6
Fig. 6 (a) The ratio of the gray value when B is equal to 10mT; (b) The relation between the ratio of gray value and magnetic flux density.
Fig. 7
Fig. 7 The data flow of the image processing system.
Fig. 8
Fig. 8 (a) Raw image; (b) Gray value image; (c) Magnetic field image.
Fig. 9
Fig. 9 Experimental arc discharge circuit.
Fig. 10
Fig. 10 The waveforms of arc current and voltage.
Fig. 11
Fig. 11 Arc plasma motion images over time.
Fig. 12
Fig. 12 The arc magnetic field distribution over time.

Equations (12)

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θ F =VBL,
I= I 0 e εL sin( θ F +θ),
E in = E 0 [ 1 0 ],
J 1 =[ cos 2 α+ σ 1 sin 2 α (1 σ 1 )sinαcosα (1 σ 1 )sinαcosα sin 2 α+ σ 1 cos 2 α ],
J 2 = J 4 =[ 1 0 0 1 ].
J 3 =[ cos θ F sin θ F sin θ F cos θ F ][ 1 0 0 1 ][ cos θ F sin θ F sin θ F cos θ F ],
J 5 =[ cos 2 β+ σ 2 sin 2 β (1 σ 2 )sinβcosβ (1 σ 2 )sinβcosβ sin 2 β+ σ 2 cos 2 β ],
E out = J 5 ( J 4 J 3 ( J 2 J 1 E in )).
Q out = E out [ E out ] * .
G out = Q out /ω,
G out =f( θ F ).
B=16.1812R16.3527,

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