- Email: [email protected]
Visualization of the magnetic field and current path in Z-pinch and X-pinch plasmas
High Energy Density Physics 15 (2015) 1e3
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Visualization of the magnetic field and current path in Z-pinch and X-pinch plasmas A.A. Anderson*, V.V. Ivanov, D. Papp Department of Physics, University of Nevada, Reno, NV 89506, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 October 2014 Received in revised form 27 January 2015 Accepted 25 February 2015 Available online 6 March 2015
Laser diagnostics at the wavelength of 266 nm allow investigation of wire array Z-pinches and X-pinches at the 1 MA pulse power generator. Faraday rotation diagnostics at 266 nm is applied to study MG magnetic fields in Z-pinch plasma. Faraday diagnostics can qualitatively visualize magnetic fields in dense plasma and give additional information about the current flow even if the plasma density cannot be reconstructed with interferometry. A comparison of images from the three-channel polarimeter shows strong localized magnetic fields, revealing the path for the electric current inside the plasma. Faraday images present current switched to the trailing plasma. © 2015 Published by Elsevier B.V.
Keywords: Faraday rotation diagnostics Z-pinch X-pinch
1. Introduction Pulsed power generators can produce magnetized plasma with megagauss magnetic fields [1e3]. Faraday rotation diagnostics provide a powerful method to study magnetic fields in Z-pinch plasmas. Faraday rotation diagnostics at the optical wavelengths are applied to the wire-array precursor [4] and fiber Z-pinches at a current of 100 kA [5,6]. Ultraviolet (UV) laser diagnostics at the wavelength of 266 nm provide a flexible method to study dense Zpinch plasmas. The UV diagnostics show a strong advantage over diagnostics employed at the standard wavelength of 532 nm due to smaller absorption and less refraction at density gradients, allowing the probing laser to penetrate deeper into the dense plasma [7,8]. This also allows the Faraday rotation diagnostic to measure magnetic fields and study the current distribution in the trailing plasma of the stagnated Z pinch [9]. Current and magnetic field distributions could play a crucial role in implosion dynamics of the plasma, affecting the implosion and stagnation dynamics and the radiative properties of the Z-pinch. In addition, understanding current distribution can help to benchmark simulation models. The magnetic field and current can be reconstructed if the electron density and rotation angle are measured in the plasma. Interferometry is the most common method for measurement of
* Corresponding author. E-mail address: [email protected] (A.A. Anderson). http://dx.doi.org/10.1016/j.hedp.2015.02.005 1574-1818/© 2015 Published by Elsevier B.V.
the phase shift and electron density in plasma [10]. In a dense inhomogeneous plasma, interferometry can fail to measure the phase shift due to the strong absorption and complicated structure of fringes. This makes the quantitative reconstruction of magnetic fields not possible. In this paper we show that the Faraday rotation diagnostics can provide useful information about current distribution even if the plasma density cannot be reconstructed. A comparison of data from channels of the UV Faraday rotation diagnostic can show magnetic fields and display the path of current in dense plasma. Examples of the visualization of magnetic fields and current paths in Z-pinch and X-pinch plasmas are presented. The Faraday images qualitatively show the magnetic field and current flow in plasma. 2. Experimental setup Experiments were performed at the Nevada Terawatt Facility, which features Zebra, a 1-MA pulse power generator with a rise time of 90 ns from 10% to 90% of peak current. Parameters of plasma were measured with a regular laser and X-ray “core diagnostics” at the Zebra generator [1,5]. “Core diagnostics” include absolutely calibrated Photoconductive Detectors (PCDs), X-ray diodes (XRDs), and a bolometer to measure the temporal profile of the Z-pinch emission. Each detector has a different photon energy range. The XRD has a 2 mm Kapton filter to limit sensitivity to soft X-rays in <1 keV range. The PCD has an 8 mm Be filter to limit detection to xrays in the range > 1 keV, and the bolometer measures the total emission in the range of 10 eV to 5 keV.
2
A.A. Anderson et al. / High Energy Density Physics 15 (2015) 1e3
A three-channel UV polarimeter was used for the Faraday rotation diagnostic. Fig. 1 (a) shows the simplified optical set-up for the UV laser diagnostics system. A Glan prism polarizes the incident 266 nm laser beam prior to the Z pinch. A crystal wedge is set-up after the chamber which is rotated an angle a₀ in respect to the polarization angle for the Glan prism. This angle allows us to measure the direction of the Faraday rotation, allowing us to determine the direction of the magnetic field. To obtain electron density, part of the beam from the shadowgraphy channel is split off using an air-wedge shearing interferometer [11]. The polarimeter takes a shadowgram, interferogram, and Faraday image at one time moment. The images are relayed by lenses and captured using CCD cameras with narrowband interference filters and neutral density filters to attenuate the exposure. The difference in intensity between the Faraday image and shadowgram gives the Faraday rotation angles in the image. The magnitude and direction of the magnetic field in the cylindrically symmetrical plasma can be reconstructed using the Abel transform if the radial profiles of the rotation angle and electron plasma density are measured. Magnetic fields were studied in two types of wire-array loads. The first is an aluminum (alloy 5056) cylindrical wire array 8 mm in diameter and 2 cm tall which consists of eight wires, 15 mm in diameter. In addition, single-wire hybrid X-pinches [12] were used, which were formed by two W cones connected by an Al wire, 100 mm in diameter, in the middle hole. Standard X-pinches create a small, dense “hot spot” of plasma at the location of the crossed wires, or in the case of the hybrid X-pinch, the location of the connecting wire. The cones were made of tungsten as this does not contribute to the generation hotspots. These two loads were chosen to illustrate the Faraday rotation diagnostic's capability of working in a wide range of plasma parameters. 3. Experiments with Faraday rotation diagnostics Figs. 2 and 3 show images from the 3-channel polarimeter of the Faraday rotation diagnostic. Images (a), (b), and (c) in Fig. 2 display the shadowgram, Faraday image, and interferogram, respectively, of the stagnation stage in the Al 8-wire cylindrical wire-array Z pinch with a mass of 37 mg/cm. Images of the central part of the pinch are taken at the moment of the drop on the x-ray pulse between two peaks seen in the timing diagram (d). At this moment, Z pinch plasma expands and occupies a wide area. X-ray frames from the pinhole camera with a frame duration of 3 ns are presented in image (e). The fourth x-ray frame (d) in Fig 2(e) is taken at the same time as the laser images and shows a wide Z pinch with smaller intensity of x-ray radiation in the photon energy range > 1 keV. A white arrow in the shadowgram (b) points to the break in the stagnated Z pinch which may be formed by the explosion of the hot spot [13]. A possible current path cannot be derived from the shadowgram and interferogram in Fig. 2, as the interferometric lines are not readable. The 266 nm interferometry used in these
Fig. 1. A simplified optical schematic of the 3-channel Faraday rotation diagnostic. Three CCD cameras are used for interferometry (I), shadowgraphy (S), and Faraday channel (F).
Fig. 2. The shadowgram (a), Faraday image (b), and interferogram(c) of the central area of the wire-array Z pinch in the shot with Al 8-wire cylindrical load. (d) A timing diagram for this shot. Gray strips and the arrow show positions of x-ray and UV frames, respectively.
experiments is limited to plasma with Ne < (1e2) x 1020 cm-3, depending on Te and also the size of the plasma. The Faraday image (b) in Fig. 2 gives additional information about magnetic fields. By comparing the Faraday image and shadowgram, one can see regions of darkening and lightening in the plasma. These areas represent positive and negative Faraday rotations which are caused by the existence of a magnetic field, implying a current path along dashed lines given in (b). This image shows that current switches to another route after a break formed in the stagnated pinch. The break is, presumably, produced by the
Fig. 3. A shadowgram (a), Faraday image (b), and interferogram(c) of the hybrid X pinch. (d) A timing diagram. The arrow shows a position of UV frames. (e) A sketch of the hybrid X pinch with conical electrodes.
A.A. Anderson et al. / High Energy Density Physics 15 (2015) 1e3
collapse and explosion of the micropinch on the Z-pinch [13]. Micropinches are typical for implosions of cylindrical loads at the Zebra facility [8]. The expanded trailing plasma implodes later and produces additional kinetic energy which results in enhanced pinch radiation [9]. The magnetic fields are estimated to be in the (0.2e1) MG range. Fig. 3 shows images and timing for plasma in the hybrid X pinch at the beginning of the current pulse. A sketch of the hybrid pinch is shown in Fig. 3 (e). Shadowgram (a) presents only a bulge of the dense expanding plasma. Interferogram (c) shows a plasma flare with a smaller density in the vicinity of the hot spot of the X pinch. A strip with lightening and darkening in Faraday image (b) visualizes magnetic fields. An additional current path is highlighted with an arrow in the Faraday image. Comparison with interferogram (c) shows that current flows along the edge of the plasma flare. The switching of the current to the external trailing plasma of the hybrid X-pinch decreases the current in the “hot spot” and impacts its radiative ability. 4. Conclusions
densities. Quantitative measurements can also be performed at the shorter wavelength of laser probing, for example, at the fifth harmonic of the neodymium laser at 213 nm. Acknowledgments The authors thank A. M. Covington for support and B. R. Talbot, A. L. Astanovitskiy, V. Nalajala, and O. Dmitriev, for help with experiments. This work was supported by DOE/NNSA under the grant DE-SC0008824 and partly under the UNR grant DE-NA 0002075. References [1] [2] [3] [4] [5] [6] [7]
In conclusion, UV Faraday diagnostics can visualize magnetic fields and give additional information about the current distribution in the dense Z pinches even without detailed reconstruction of plasma parameters. Areas with lightening and darkening in the Faraday image show magnetic fields with opposite directions and present, qualitatively, the current flow. The quantitative reconstruction of magnetic fields can be performed at smaller plasma
3
[8] [9] [10] [11] [12] [13]
A.B. Sefkow, S.A. Slutz, J.M. Koning, et al., Phys. Plasmas 21 (072711) (2014). F.S. Felber, et al., J. Appl. Phys. 64 (1988) 3831. R. Presura, et al., IEEE Trans. Plasma Sci. 36 (2008) 17. V.V. Ivanov, G.S. Sarkisov, P.J. Laca, et al., IEEE Trans. Plasma Sci. 34 (2006) 2247. G.S. Sarkisov, A.S. Shikanov, B. Etlitcher, et al., JETP 81 (1995) 743. M. Tatarakis, R. Aliaga-Rossel, A.E. Dangor, M.G. Haines, Phys. Plasmas 5 (1998) 682. V.V. Ivanov, J.P. Chittenden, S.D. Altemara, et al., Phys. Rev. Lett. 107 (2011) 165002. V.V. Ivanov, J.P. Chittenden, R.C. Mancini, et al., Phys. Rev. E 86 (2012) 046403. V.V. Ivanov, A.A. Anderson, D. Papp, et al., Phys. Rev. E 88 (2013) 013108. I.H. Hutchinson, Principles of Plasma Diagnostics, Second ed., Cambridge University Press, Cambridge, UK, 2002. G.S. Sarkisov, Instrum. Exp. Tec. 39 (1996) 727. T.A. Shelkovenko, S.A. Pikuz, A.D. Cahill, et al., Phys. Plasmas 17 (2010) 112707. V.V. Ivanov, D. Papp, A.A. Anderson, et al., Phys. Plasmas 20 (2013) 112703.
Contents lists available at ScienceDirect
High Energy Density Physics journal homepage: www.elsevier.com/locate/hedp
Visualization of the magnetic field and current path in Z-pinch and X-pinch plasmas A.A. Anderson*, V.V. Ivanov, D. Papp Department of Physics, University of Nevada, Reno, NV 89506, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 October 2014 Received in revised form 27 January 2015 Accepted 25 February 2015 Available online 6 March 2015
Laser diagnostics at the wavelength of 266 nm allow investigation of wire array Z-pinches and X-pinches at the 1 MA pulse power generator. Faraday rotation diagnostics at 266 nm is applied to study MG magnetic fields in Z-pinch plasma. Faraday diagnostics can qualitatively visualize magnetic fields in dense plasma and give additional information about the current flow even if the plasma density cannot be reconstructed with interferometry. A comparison of images from the three-channel polarimeter shows strong localized magnetic fields, revealing the path for the electric current inside the plasma. Faraday images present current switched to the trailing plasma. © 2015 Published by Elsevier B.V.
Keywords: Faraday rotation diagnostics Z-pinch X-pinch
1. Introduction Pulsed power generators can produce magnetized plasma with megagauss magnetic fields [1e3]. Faraday rotation diagnostics provide a powerful method to study magnetic fields in Z-pinch plasmas. Faraday rotation diagnostics at the optical wavelengths are applied to the wire-array precursor [4] and fiber Z-pinches at a current of 100 kA [5,6]. Ultraviolet (UV) laser diagnostics at the wavelength of 266 nm provide a flexible method to study dense Zpinch plasmas. The UV diagnostics show a strong advantage over diagnostics employed at the standard wavelength of 532 nm due to smaller absorption and less refraction at density gradients, allowing the probing laser to penetrate deeper into the dense plasma [7,8]. This also allows the Faraday rotation diagnostic to measure magnetic fields and study the current distribution in the trailing plasma of the stagnated Z pinch [9]. Current and magnetic field distributions could play a crucial role in implosion dynamics of the plasma, affecting the implosion and stagnation dynamics and the radiative properties of the Z-pinch. In addition, understanding current distribution can help to benchmark simulation models. The magnetic field and current can be reconstructed if the electron density and rotation angle are measured in the plasma. Interferometry is the most common method for measurement of
* Corresponding author. E-mail address: [email protected] (A.A. Anderson). http://dx.doi.org/10.1016/j.hedp.2015.02.005 1574-1818/© 2015 Published by Elsevier B.V.
the phase shift and electron density in plasma [10]. In a dense inhomogeneous plasma, interferometry can fail to measure the phase shift due to the strong absorption and complicated structure of fringes. This makes the quantitative reconstruction of magnetic fields not possible. In this paper we show that the Faraday rotation diagnostics can provide useful information about current distribution even if the plasma density cannot be reconstructed. A comparison of data from channels of the UV Faraday rotation diagnostic can show magnetic fields and display the path of current in dense plasma. Examples of the visualization of magnetic fields and current paths in Z-pinch and X-pinch plasmas are presented. The Faraday images qualitatively show the magnetic field and current flow in plasma. 2. Experimental setup Experiments were performed at the Nevada Terawatt Facility, which features Zebra, a 1-MA pulse power generator with a rise time of 90 ns from 10% to 90% of peak current. Parameters of plasma were measured with a regular laser and X-ray “core diagnostics” at the Zebra generator [1,5]. “Core diagnostics” include absolutely calibrated Photoconductive Detectors (PCDs), X-ray diodes (XRDs), and a bolometer to measure the temporal profile of the Z-pinch emission. Each detector has a different photon energy range. The XRD has a 2 mm Kapton filter to limit sensitivity to soft X-rays in <1 keV range. The PCD has an 8 mm Be filter to limit detection to xrays in the range > 1 keV, and the bolometer measures the total emission in the range of 10 eV to 5 keV.
2
A.A. Anderson et al. / High Energy Density Physics 15 (2015) 1e3
A three-channel UV polarimeter was used for the Faraday rotation diagnostic. Fig. 1 (a) shows the simplified optical set-up for the UV laser diagnostics system. A Glan prism polarizes the incident 266 nm laser beam prior to the Z pinch. A crystal wedge is set-up after the chamber which is rotated an angle a₀ in respect to the polarization angle for the Glan prism. This angle allows us to measure the direction of the Faraday rotation, allowing us to determine the direction of the magnetic field. To obtain electron density, part of the beam from the shadowgraphy channel is split off using an air-wedge shearing interferometer [11]. The polarimeter takes a shadowgram, interferogram, and Faraday image at one time moment. The images are relayed by lenses and captured using CCD cameras with narrowband interference filters and neutral density filters to attenuate the exposure. The difference in intensity between the Faraday image and shadowgram gives the Faraday rotation angles in the image. The magnitude and direction of the magnetic field in the cylindrically symmetrical plasma can be reconstructed using the Abel transform if the radial profiles of the rotation angle and electron plasma density are measured. Magnetic fields were studied in two types of wire-array loads. The first is an aluminum (alloy 5056) cylindrical wire array 8 mm in diameter and 2 cm tall which consists of eight wires, 15 mm in diameter. In addition, single-wire hybrid X-pinches [12] were used, which were formed by two W cones connected by an Al wire, 100 mm in diameter, in the middle hole. Standard X-pinches create a small, dense “hot spot” of plasma at the location of the crossed wires, or in the case of the hybrid X-pinch, the location of the connecting wire. The cones were made of tungsten as this does not contribute to the generation hotspots. These two loads were chosen to illustrate the Faraday rotation diagnostic's capability of working in a wide range of plasma parameters. 3. Experiments with Faraday rotation diagnostics Figs. 2 and 3 show images from the 3-channel polarimeter of the Faraday rotation diagnostic. Images (a), (b), and (c) in Fig. 2 display the shadowgram, Faraday image, and interferogram, respectively, of the stagnation stage in the Al 8-wire cylindrical wire-array Z pinch with a mass of 37 mg/cm. Images of the central part of the pinch are taken at the moment of the drop on the x-ray pulse between two peaks seen in the timing diagram (d). At this moment, Z pinch plasma expands and occupies a wide area. X-ray frames from the pinhole camera with a frame duration of 3 ns are presented in image (e). The fourth x-ray frame (d) in Fig 2(e) is taken at the same time as the laser images and shows a wide Z pinch with smaller intensity of x-ray radiation in the photon energy range > 1 keV. A white arrow in the shadowgram (b) points to the break in the stagnated Z pinch which may be formed by the explosion of the hot spot [13]. A possible current path cannot be derived from the shadowgram and interferogram in Fig. 2, as the interferometric lines are not readable. The 266 nm interferometry used in these
Fig. 1. A simplified optical schematic of the 3-channel Faraday rotation diagnostic. Three CCD cameras are used for interferometry (I), shadowgraphy (S), and Faraday channel (F).
Fig. 2. The shadowgram (a), Faraday image (b), and interferogram(c) of the central area of the wire-array Z pinch in the shot with Al 8-wire cylindrical load. (d) A timing diagram for this shot. Gray strips and the arrow show positions of x-ray and UV frames, respectively.
experiments is limited to plasma with Ne < (1e2) x 1020 cm-3, depending on Te and also the size of the plasma. The Faraday image (b) in Fig. 2 gives additional information about magnetic fields. By comparing the Faraday image and shadowgram, one can see regions of darkening and lightening in the plasma. These areas represent positive and negative Faraday rotations which are caused by the existence of a magnetic field, implying a current path along dashed lines given in (b). This image shows that current switches to another route after a break formed in the stagnated pinch. The break is, presumably, produced by the
Fig. 3. A shadowgram (a), Faraday image (b), and interferogram(c) of the hybrid X pinch. (d) A timing diagram. The arrow shows a position of UV frames. (e) A sketch of the hybrid X pinch with conical electrodes.
A.A. Anderson et al. / High Energy Density Physics 15 (2015) 1e3
collapse and explosion of the micropinch on the Z-pinch [13]. Micropinches are typical for implosions of cylindrical loads at the Zebra facility [8]. The expanded trailing plasma implodes later and produces additional kinetic energy which results in enhanced pinch radiation [9]. The magnetic fields are estimated to be in the (0.2e1) MG range. Fig. 3 shows images and timing for plasma in the hybrid X pinch at the beginning of the current pulse. A sketch of the hybrid pinch is shown in Fig. 3 (e). Shadowgram (a) presents only a bulge of the dense expanding plasma. Interferogram (c) shows a plasma flare with a smaller density in the vicinity of the hot spot of the X pinch. A strip with lightening and darkening in Faraday image (b) visualizes magnetic fields. An additional current path is highlighted with an arrow in the Faraday image. Comparison with interferogram (c) shows that current flows along the edge of the plasma flare. The switching of the current to the external trailing plasma of the hybrid X-pinch decreases the current in the “hot spot” and impacts its radiative ability. 4. Conclusions
densities. Quantitative measurements can also be performed at the shorter wavelength of laser probing, for example, at the fifth harmonic of the neodymium laser at 213 nm. Acknowledgments The authors thank A. M. Covington for support and B. R. Talbot, A. L. Astanovitskiy, V. Nalajala, and O. Dmitriev, for help with experiments. This work was supported by DOE/NNSA under the grant DE-SC0008824 and partly under the UNR grant DE-NA 0002075. References [1] [2] [3] [4] [5] [6] [7]
In conclusion, UV Faraday diagnostics can visualize magnetic fields and give additional information about the current distribution in the dense Z pinches even without detailed reconstruction of plasma parameters. Areas with lightening and darkening in the Faraday image show magnetic fields with opposite directions and present, qualitatively, the current flow. The quantitative reconstruction of magnetic fields can be performed at smaller plasma
3
[8] [9] [10] [11] [12] [13]
A.B. Sefkow, S.A. Slutz, J.M. Koning, et al., Phys. Plasmas 21 (072711) (2014). F.S. Felber, et al., J. Appl. Phys. 64 (1988) 3831. R. Presura, et al., IEEE Trans. Plasma Sci. 36 (2008) 17. V.V. Ivanov, G.S. Sarkisov, P.J. Laca, et al., IEEE Trans. Plasma Sci. 34 (2006) 2247. G.S. Sarkisov, A.S. Shikanov, B. Etlitcher, et al., JETP 81 (1995) 743. M. Tatarakis, R. Aliaga-Rossel, A.E. Dangor, M.G. Haines, Phys. Plasmas 5 (1998) 682. V.V. Ivanov, J.P. Chittenden, S.D. Altemara, et al., Phys. Rev. Lett. 107 (2011) 165002. V.V. Ivanov, J.P. Chittenden, R.C. Mancini, et al., Phys. Rev. E 86 (2012) 046403. V.V. Ivanov, A.A. Anderson, D. Papp, et al., Phys. Rev. E 88 (2013) 013108. I.H. Hutchinson, Principles of Plasma Diagnostics, Second ed., Cambridge University Press, Cambridge, UK, 2002. G.S. Sarkisov, Instrum. Exp. Tec. 39 (1996) 727. T.A. Shelkovenko, S.A. Pikuz, A.D. Cahill, et al., Phys. Plasmas 17 (2010) 112707. V.V. Ivanov, D. Papp, A.A. Anderson, et al., Phys. Plasmas 20 (2013) 112703.