Filamentary structures in dense plasma focus: Current filaments or vortex filaments?

Transcription

1 Filamentary structures in dense plasma focus: Current filaments or vortex filaments? Leopoldo Soto, Cristian Pavez, Fermin Castillo, Felipe Veloso, José Moreno, and S. K. H. Auluck Citation: Physics of Plasmas 21, (2014); doi: / View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in Filamentary structure of plasma produced by compression of puffing deuterium by deuterium or neon plasma sheath on plasma-focus discharge Phys. Plasmas 21, (2014); / Spatially resolved high-resolution x-ray spectroscopy of high-current plasma-focus dischargesa) Rev. Sci. Instrum. 81, 10E312 (2010); / Tomographic interferometry of a filtered high-current vacuum arc plasma J. Appl. Phys. 101, (2007); / Miniature hybrid plasma focus extreme ultraviolet source driven by 10 ka fast current pulse Rev. Sci. Instrum. 77, (2006); / Anode length optimization in a modified plasma focus device for optimal x-ray yields J. Appl. Phys. 99, (2006); /

2 PHYSICS OF PLASMAS 21, (2014) Filamentary structures in dense plasma focus: Current filaments or vortex filaments? Leopoldo Soto, 1,2,3,a) Cristian Pavez, 1,2,3 Fermin Castillo, 4 Felipe Veloso, 5 Jose Moreno, 1,2,3 and S. K. H. Auluck 6 1 Comision Chilena de Energıa Nuclear, CCHEN, Casilla 188-D, Santiago, Chile 2 Center for Research and Applications in Plasma Physics and Pulsed Power, P 4 3 Departamento de Ciencias Fısicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Republica 220, Santiago, Chile 4 Universidad Nacional Autonoma de Mexico, Cuernavaca, Mexico 5 Instituto de Fısica, Pontificia Universidad Catolica de Chile, Santiago, Chile 6 Bhabha Atomic Research Center, Mumbai , India (Received 21 February 2014; accepted 17 June 2014; published online 1 July 2014) Recent observations of an azimuthally distributed array of sub-millimeter size sources of fusion protons and correlation between extreme ultraviolet (XUV) images of filaments with neutron yield in PF-1000 plasma focus have re-kindled interest in their significance. These filaments have been described variously in literature as current filaments and vortex filaments, with very little experimental evidence in support of either nomenclature. This paper provides, for the first time, experimental observations of filaments on a table-top plasma focus device using three techniques: framing photography of visible self-luminosity from the plasma, schlieren photography, and interferometry. Quantitative evaluation of density profile of filaments from interferometry reveals that their radius closely agrees with the collision-less ion skin depth. This is a signature of relaxed state of a Hall fluid, which has significant mass flow with equipartition between kinetic and magnetic energy, supporting the vortex filament description. This interpretation is consistent with empirical evidence of an efficient energy concentration mechanism inferred from nuclear reaction yields. VC 2014 AIP Publishing LLC. [ INTRODUCTION Filamentary plasma structures forming a network of currents and transporting energy and momentum over large distances are ubiquitous in the cosmos 1 and are an active area of current research. 2 Similar filamentary structures were discovered and extensively studied by Bostick and coworkers 3 in the laboratory plasma device for fusion research known as dense plasma focus 4 (DPF), which continued to inspire research into the structure of the plasma universe. 2 Their investigations 5 also indicated existence of super-dense plasma domains which generate and trap fast ions causing enhanced rates of nuclear reactions, such as 16 O(d,n) 17 F with oxygen admixture and also trap the tritons from the proton-emitting branch of the D-D fusion reaction to produce unaccountably-high yields of 14-MeV neutrons 3 from a pure deuterium plasma. However, there were no definitive conclusions regarding relationship, if any, between the filamentary structure and formation such super-dense plasma domains. Failure to observe these filamentary structures by interferometry in large DPF devices, such as POSEIDON 6 and PF was, till recently, taken as an indication that they played a relatively minor role in the significantly-higherthan-thermal fusion reactivity 8 of the DPF. Recent observations 9 of an azimuthally distributed array of sub-millimeter size sources of fusion protons and of filaments in XUV pictures 10 in PF-1000 DPF have re-kindled interest in the a) lsoto@cchen.cl possibility of filamentary structures existing and playing a prominent role in this large DPF device: The high neutron yield shots in PF are found to have more abundant filaments as compared with low neutron shots. A question that is still not resolved pertains to the nature of these filaments. Some authors have referred to these as vortex filaments 3,11 and others 12,13 refer to them as current filaments. There does not appear to be any conclusive experimental evidence in support of either description in accessible literature. The only supporting data for the vortex description is the measurement of radial magnetic field component in the run-down phase of plasma focus reported by Bostick and coworkers. 14 The current filament description is supported by observation of azimuthally distributed erosion marks on the plasma focus anode. 9 Observations of sub-millimeter-sized intense sources of highly energetic deuterons, 6,9,15 fusion protons, 9 unaccountably high yield of DT neutrons from a pure deuterium pinch, 3 and high breeding ratios of short-lived radioactive isotopes 5 in DPF with gaseous admixtures have been attributed to some kind of energy-concentrating mechanism, without any additional experimental evidence linking it with filaments. Most published information about filaments in plasma focus pertains to their self-luminosity (either in visible region 3,16,17 or in soft X-ray or XUV region 10,12,13 ), which could be due to any combination of high temperature, high density, or high impurity concentration. To the authors best knowledge, the only mention of observation of filaments in DPF using other-than-luminosity diagnostics is in a paper by X/2014/21(7)/072702/6/$ , VC 2014 AIP Publishing LLC

3 Soto et al. Phys. Plasmas 21, (2014) Nardi 11 using schlieren, by Gribkov et al. 18 again with schlieren, and in the paper by Lu using interferometry. 19 The limited information provided in the paper by Lu 19 coupled with the categorical mention of absence of filaments in PF-1000 device using a much more sophisticated 16- frame interferometry experiment, 7 a similar statement about absence of filaments in interferometry data on POSEIDON 5 and comparatively abundant evidence from luminosity diagnostics leads to the impression that the filaments are localized high temperature regions within the plasma having similar density as the plasma surrounding them. This description would be in conformity with models of current filamentation, 1,20,21 where current density distribution gets modulated in space and the resulting localized heating would raise plasma temperature so that these regions become more luminous than the surrounding plasma. Local concentrations of current may cause local plasma compression establishing a local Bennett equilibrium. But local increase in density over the surrounding plasma would be limited if the temperature is high. Higher current in the filament may then correlate well with higher temperature with or without the necessity of assuming a local increase in density. This may explain the relatively meager, but not completely absent, data on filaments using refractivity based diagnostics. However, this logic of current filamentation interpretation crucially relies on the near absence of data on density modulation accompanying filamentation in plasma focus. It is therefore of interest to see whether filaments can be observed by luminosity, schlieren, and interferometry in the same device. The significance of such study can be appreciated by the fact that in case density modulation with respect to azimuthal coordinate is observed and its scale length is as small as is observed in luminosity, a very different interpretation becomes plausible. Gravitational instability (also known as interchange or Rayleigh-Taylor instability) in a magnetized plasma can give rise to short scale-length perturbations in density, with wave vector parallel to the ambient magnetic field. 22 For the plasma focus case, the ambient magnetic field is in the azimuthal direction leading to azimuthal modulation of density. Thermal conduction parallel to the ambient magnetic field would be expected to suppress formation of temperature gradient in the azimuthal direction. In a supersonic flow like plasma focus, the pressure gradient is aligned with the flow direction. Therefore, the azimuthal density perturbation would be expected to generate non-parallel gradients of density and pressure. 23 Non-parallel gradients of density and temperature can also arise from a thermoelectric instability, 24 which can amplify a temperature perturbation propagating in the azimuthal direction, producing an azimuthal modulation of temperature but not density. The baroclinic source term resulting from any (or both) of these instabilities can create a component of magnetic field 25 orthogonal to the ambient magnetic field, 23,24 changing its topology and can simultaneously create vorticity 26 anti-parallel to the generated magnetic field component. In this scenario, the luminosity increase over the ambient plasma would be both because of increase in density and because of viscous heating from sheared fluid flow, not resistive heating. The filament would be truly a vortex filament as proposed by Bostick, Nardi, and Prior 3 and would have a great significance because it would represent a large, unsuspected reservoir of ion kinetic energy within the plasma current sheath. It would also be in conformity with models of relaxation of a Hall-magnetofluid, 27,28 which tend to have equipartition of magnetic and kinetic energy. 27,29 Azimuthally distributed erosion marks on the anode, 9 cited above as possible evidence for the current filament viewpoint, could equally arise from high local ion kinetic energy density related with such equipartition, which would also be consistent with observations of an energy-concentrating mechanism referred above. An experimental enquiry designed to distinguish between the vortex filament and current filament pictures and, in particular, looking for signatures of Hall-magnetofluid relaxation, should therefore be of considerable significance. On this background, we present first ever experimental evidence for filaments on the same plasma focus device PF-400 J 30 using three techniques: framing photography of visible luminosity from the plasma using an Intensified Charge Coupled Device (ICCD) camera and schlieren and interferometry using a pulsed Nd-YAG laser. EXPERIMENTS AND DIAGNOSTICS Taking advantage of the self-scaling properties of empirically-optimized plasma foci, which approximately maintain the same values of ion density, magnetic field, plasma sheath velocity, Alfven speed, and the quantity of energy per particle 31,32 regardless of their energy or size, experiments were carried out on a table-top plasma focus device, PF-400 J 30 (880nF, 38nH, 30 kv, peak current 130 ka achieved in 300 ns from 400 J stored energy). Electrode configuration consisted of a 12 mm diameter central anode, partially covered by alumina at its base. The anode had an effective length (above the insulator) of 7 mm and a central hole of 3 mm radius. The cathode consisted of a coaxial outer electrode of 26 mm diameter made of eight copper rods uniformly spaced on the cathode base. The experiments were performed using deuterium as working gas. The standard diagnostics, voltage V(t), measured with a fast resistive divider located close to the plasma focus and current derivative di(t)/dt, measured with a Rogowskii coil calibrated in situ, were supplemented with the following optical diagnostics: Images from the visible plasma self-luminosity: An ICCD camera, gated at 4 ns exposure time, and synchronized with the discharge, was used to obtain side-view images of the visible light emitted from the plasma. For imaging the plasma over the micro-channel plate in the ICCD camera, a regular bi-convex lens with a focal length of 12.5 cm and 5 cm diameter was used. In order to increase the depth of field, a mask with an open circle of 1 cm diameter was attached to the lens, so an optical stop number F ¼ 1/12.5 was obtained. A magnification m ¼ 0.2 was used. The resolution of the camera for magnification

4 Soto et al. Phys. Plasmas 21, (2014) FIG. 1. Electrical signals for a shot in deuterium at 9 mbar, charging voltage ¼ 28 kv. The typical dip in the signal of the current derivative associated with the formation of a pinched plasma column on the axis was observed. m ¼ 1is23lm, thus for m ¼ 0.2, a resolution of 95 lm (0.1 mm) is achieved. Optical refractive diagnostics: In order to study the structure of the plasma density, schlieren and interferometry diagnostics were established using a pulsed Nd-YAG laser (532 nm, 8 ns Full Width at Half Maximum (FWHM)) synchronized with the discharge. The image acquisition was done using a digital camera with a CMOS size of 14.8 mm 22.2 mm (5.2 lm pixel size). To produce the interferograms, a Mach-Zender interferometer was implemented. In both cases, a regular bi-convex lens with a focal length of 25 cm and 5 cm of diameter was used to produce the image of the plasma on the CMOS. A magnification m ¼ 0.52 was used, thus one pixel corresponds to 10 lm. For schlieren, a pinhole of 500 lm was positioned at the focal point of the lens. A resolution for the electron density gradient of the order m 4 is obtained with the schlieren system. Electrical signals for a discharge, with ka peak current, in deuterium at 9 mbar pressure are shown in Figure 1. The typical dip in the signal of the current derivative associated with the formation of a pinched plasma column on the axis was observed. The global radial plasma dynamics of the PF-400 J was previously studied. 32,33 In particular, a pinch plasma column with a radius of ( ) mm with a density on the axis of ( ) m 3 was produced; similar to density obtained in large devices, such as PF ,32 In this article, we report on the observations and characterization of the filamentary structures. Side-view plasma images from visible light from the plasma obtained for discharges operating at 9 mbar are shown in Figure 2. The time for each picture is referred with respect to the minimum of the dip in the di/dt signal in Figure 1. Sub-millimeter-scale bright filamentary structures are observed during the radial plasma motion before the plasma pinch. Schlieren images of the plasma before the pinch phase are shown in Figure 3. Sub-millimeter-scale modulation of the optical refractive index of the plasma is observed. Figure 4 shows interferograms for a time before the pinch. Filamentary structures can be clearly seen in the interferograms in Figures 4(a) and 4(b). Radial electron density profiles of filaments are calculated using Abel inversion under the assumption of symmetry and shown in Figures 5(a) and 5(b). The visible ICCD camera images show the presence of filamentary structure occurring in pairs confirming that the phenomenon observed by Bostick, Nardi, and Nardi 3 and Bostick et al. 14 is indeed present 21 in the device. Since spatial resolving element of the schlieren experiment is a spatial filter, the dark regions correspond to absolute value of plasma density gradient. As in the focal point of the lens a small aperture (pinhole) is placed, rays of the collimated laser light, deflected by the plasma density gradient, are stopped. Therefore, the regions with plasma density gradient appear black in the image. The picture represents density modulation of the plasma sheath forming a grid-like pattern. Specifically, it shows azimuthal density modulation. From the interferograms in Figure 4, a sharp variation of density on the sub-millimeter scale (filaments with diameter of the order of 0.3 to 0.4 mm) in many localized features is observed. DISCUSSION AND CONCLUSIONS Abel inversion (Fig. 5(a)), of a particular feature in shot #13 (Fig. 4(a)) indicates a peak density of m 3. The collision-less ion skin depth c/x pi for deuterium at this density is mm, which matches with the radius of the feature. In shot #33, the peak density of a similar feature (Fig. 4(b)) is m 3 and the corresponding value of c/x pi is 0.13 mm, which also matches with the radius of the feature (Fig. 5(b)). This, together with the extraordinary stability of filamentary structure reported by Bostick, Nardi, and Prior 3 is strong evidence that these features represent a FIG. 2. Side view plasma images from visible light from the plasma obtained for discharges operating at 28 kv charging voltage and 9 mbar. The time for each picture is referred to the minimum value of the dip in the di/dt signal. Sub millimeter scale bright filamentary structures are observed.

5 Soto et al. FIG. 3. Schlieren images of the radial motion of the plasma for discharges operating at 28 kv charging voltage and 9 mbar in D2. Sub-millimeter scale variation in the optical refractive index of the plasma is observed. Turner Relaxed State (TRS):28,29 a state of minimum magnetic and kinetic energy subject to conservation of magnetic helicity and hybrid helicity, which are invariants of dissipationless Hall MHD. FIG. 4. Interferograms for two different discharges operating at the same conditions (28 kv charging voltage and 9 mbar in D2). The interferograms show a sharp variation of density on the sub-millimeter scale in many localized features (filaments). The vertical arrows indicated the imploding plasma layer. The oblique arrow marks the filament selected for Abel inversion in Figure 5. Phys. Plasmas 21, (2014) FIG. 5. Abel inversion of a particular feature in shot #13 (a) indicates a peak density of m 3. The collisionless ion skin depth c/xpi for deuterium at this density is mm (indicating by the arrow), which matches with the radius of the feature. In shot #33 (b), the peak density of a similar feature is m 3 and the corresponding value of c/xpi is 0.13 mm, which also matches with the radius of the feature. One of the features of the TRS is the presence of rotation even in a rotationally symmetric cylindrical plasma. This is corroborated by the observation of the azimuthal density modulation in schlieren pictures, which, as discussed earlier, implies presence of the baroclinic source term comprising non-parallel gradients of density and pressure (or temperature), which is known to generate both spontaneous magnetic field25 and vorticity.26 The observed azimuthal modulation of visible luminosity can be either due to modulation of density or temperature or both. Although presence of density modulation is directly confirmed by our schlieren observations, the presence of azimuthal temperature modulation cannot be ruled out by the reported data. This supports the possibility of a gravitational (or interchange) instability with wave vector parallel to ambient magnetic field22 being responsible for generation of filaments,23 but does not rule out the possibility of a simultaneous occurrence of thermoelectric instability.24 It can be shown29 that there is equipartition between kinetic and magnetic energy in the case of a TRS and the ion energy can reach very high values Ei(keV) 600 I2(MA), where I is the current associated with the TRS. The conclusion that the filaments represent TRS is then also supported by the observations of emission of fast deuterium ions from multiple micro-sources of sub-millimeter dimensions.1,6,15 This conclusion also establishes a direct logical link between the filamentary structures and the localized intense sources

6 Soto et al. Phys. Plasmas 21, (2014) of high energy ions inferred 3,5 from high yields of secondary nuclear reactions. In this view, the interchange instability leads to azimuthal density modulation, which, along with temperature gradient perpendicular to the current sheath, leads to a baroclinic source term for vorticity and magnetic field components along the current sheath localized at the multiple sites of the azimuthal mode. Conditions favorable for approach to a minimum energy relaxed state are created at these locations. Simultaneous creation of vorticity and magnetic field locally conserves the canonical angular momentum leading to ion kinetic energy proportional to the square of vector potential, i.e., to square of current in the filament. Hall-MHD relaxation theories 27,28 deal mainly with re-configuration of the magnetic field resulting in spontaneous generation of an axial magnetic field component and associated rotational motion. The fact that the resulting magnetic and rotational flow field configurations together give rise to a net centrally-directed force density is used to infer that a finite pressure gradient can in principle be confined in a structure in equilibrium. The question of evolution of that equilibrium through compression and heating via a localized pinch effect is external to the structure of relaxation theories. The experimental evidence presented above unambiguously confirms density modulation and is silent on temperature modulations; its interpretation in terms of TRS therefore is also neutral towards suggestions that the filaments are localized z-pinches. The interpretation of filaments as TRS may explain the non-observation of filaments by interferometry on PF and POSEIDON. 6 Since the density of the PF-1000 and POSEIDON is similar to PF-400 J, the interpretation of filaments as TRS would suggests that filaments would have a sub-millimeter dimension. However, the plasma radius is of the order of 1 cm for PF-1000 and POSEIDON: 100 times larger than the filament radius interpreted as TRS. In contrast, in the present study, the plasma pinch radius is of the order of 1 mm, only 10 times larger than the filament size. An interferometer set to resolve the gross structure of the main plasma would miss the 100 times smaller phase change due to the filaments. An alternative diagnostics, 34 which could avoid the problems due to the differing ratio between plasma size and filament size between large and small plasma foci would be to compare the Doppler-shifted refractive index profiles of the plasma for laser beams traversing the plasma in opposite directions at the same time. This kind of interferogram would be insensitive to the gross plasma and would show only those regions having significant plasma rotational flux. If the filaments are indeed vortex filaments as suggested by our data, they should show up in such experiments. In summary, we have presented the first experimental study of filamentary structure in the same plasma focus device using three complementary diagnostic techniques, namely, visible gated framing, schlieren, and interferometry using nanosecond time resolution and sub-millimeter space resolution. Abel-inverted density profiles of filaments, also reported for the first time, show a close agreement between collisionless ion skin depth and filament radius. Along with the well-known stability of filaments, this agreement provides strong evidence in favor of a Turner Relaxed State model 29 for the filamentary structure. This interpretation suggests a natural explanation of non-observation of filaments by interferometry on large plasma focus installations while at the same time supporting their suggested role in generating observed records of azimuthally distributed submillimeter-scale sources of fusion protons. The perceived analogy 2 between filaments in dense plasma focus and those in the cosmos suggests that our observations could have a significance much beyond the limited confines of laboratory plasma fusion. Our interpretation of the reasons for considering filaments as reservoirs of highly energetic confined ions, coupled with the recent observations of filaments in PF- 1000, 10 strongly supports the suggestion that the dense plasma focus could emerge as a possible producer of shortlived radioisotopes 5 for medical diagnostics in the future. ACKNOWLEDGMENTS This work was supported by the Grant No. ACT-1115, PIA-CONICYT. 1 H. Alfven, IEEE Trans. Plasma Sci. 18, 5 (1990). 2 A. L. Peratt, IEEE Tran. Plasma Sci. 35, 741 (2007). 3 W. H. Bostick, V. Nardi, and W. Prior, Ann. NY Acad. Sci. 251, 2 (1975). 4 J. W. Mather, Dense plasma focus, Methods Exp. Phys. 9B, 187 (1971). 5 J. S. Brzosko, V. Nardi, J. R. Brzosko, and D. Goldstein, Phys. Lett. A 192, (1994). 6 U. J ager and H. Herold, Nucl. 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