Non intrusive plasma diagnostics for measuring sheath kinematics in plasma focus discharges

Texto completo

(1)Home. Search. Collections. Journals. About. Contact us. My IOPscience. Non-intrusive plasma diagnostics for measuring sheath kinematics in plasma focus discharges. This content has been downloaded from IOPscience. Please scroll down to see the full text. 2012 Meas. Sci. Technol. 23 087002 (http://iopscience.iop.org/0957-0233/23/8/087002) View the table of contents for this issue, or go to the journal homepage for more. Download details: IP Address: 146.155.94.33 This content was downloaded on 18/05/2016 at 18:41. Please note that terms and conditions apply..

(2) IOP PUBLISHING. MEASUREMENT SCIENCE AND TECHNOLOGY. Meas. Sci. Technol. 23 (2012) 087002 (7pp). doi:10.1088/0957-0233/23/8/087002. TECHNICAL DESIGN NOTE. Non-intrusive plasma diagnostics for measuring sheath kinematics in plasma focus discharges Felipe Veloso 1,2,3,5 , José Moreno 1,2,3 , Ariel Tarifeño-Saldivia 1,2,3 , Cristian Pavez 1,2,3 , Marcelo Zambra 1,2,3,4 and Leopoldo Soto 1,2,3 1 2 3 4. Comisión Chilena de Energı́a Nuclear, Casilla 188-D, Santiago, Chile Center for Research and Applications in Plasma Physics and Pulsed Power-P4, Santiago, Chile Facultad de Ciencias Exactas, Universidad Andrés Bello, Av. Republica 252, Santiago, Chile Universidad Diego Portales, Santiago, Chile. E-mail: veloso.felipe@gmail.com. Received 17 January 2012, in final form 8 May 2012 Published 28 June 2012 Online at stacks.iop.org/MST/23/087002 Abstract The description and use of a non-perturbative optical diagnostic technique for measuring sheath movement in plasma focus are presented. The method is based on a lens that collects the light emitted by the plasma sheath which is detected by fast photodiodes. Two different circuit connections for the photodiodes are presented using either several or a single scope channels to record the photodiode signals. The technique is applied to a 300 J plasma focus with a spatial resolution of ∼0.25 mm measuring its average propagation speeds (axial and radial) as well as its detachment time and an estimated thickness. The setup required in this technique is easy to implement and cost-effective, and it can be applied in any plasma focus, regardless of its stored energy or operational gas. Keywords: plasma focus, plasma diagnostics, plasma sheath, optical diagnostics. (Some figures may appear in colour only in the online journal). 1. Introduction. stated that the plasma foci are classified by their driver energy, and the physical properties of the pinched plasma are similar among them [4, 5]. On the other hand, it has been extensively reported that the device performance in terms of plasma compression and radiation emission is in close relation to a relatively uniform formation of the plasma sheath around the insulator and its movement prior to the pinching phase (i.e. along the axial and the radial phases) [3, 6–9]. For this reason, there are several experimental studies concerning the dynamics of the plasma sheath prior to the pinching phase in different gases. Different time-resolved diagnostic techniques have been used for studying the movement of the plasma sheath formation and propagation during both the axial and radial phases. For imaging the sheath movement, it is usual to. The plasma focus is a pulsed power device where the current flowing through the plasma produces its own confinement magnetic field, resulting in a dense z-pinch column [1–4]. These devices have been studied in both basic plasma physics and applied research related to x-ray, ions and neutron sources (the latter, from fusion reactions when operated in deuterium or deuterium–tritium gas). In these experiments, a plasma sheath is produced over an insulator surface after a pulsed discharge from a capacitor bank, moving later along the coaxial electrode assembly due to the Lorentz force acting on it. It has been 5. Present address: Departamento de Fisica, Pontificia Universidad Catolica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile.. 0957-0233/12/087002+07$33.00. 1. © 2012 IOP Publishing Ltd. Printed in the UK & the USA.

(3) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. Figure 1. Schematic diagram of the imaging system and photograph of the load, where the optical fibers image can be seen next to the copper anode. The lens and the optical fibers are located outside the vacuum chamber.. conditions. Also, a photomultiplier system has been used for determining the sheath axial velocity and thickness estimation locating optical fibers inside the discharge chamber [28]. This paper describes the application of a non-intrusive diagnostic method useful to measure sheath kinematics in plasma focus discharges, regardless of their physical dimensions or operating gas. The method is based on the detection of the visible light emission of the plasma using a simple and costconvenient circuit. The application of the technique and some considerations on its use for different cases are presented.. use ICCD (intensified charged coupled devices) [3, 9–12] or streak [12, 13] cameras which capture an image of a portion of the visible light coming from the plasma sheath or laser probing diagnostics (either schlieren or interferometry) [3, 14, 15], capturing the light refractivity due to the plasma of a synchronized pulsed laser. On the one hand, these cases usually use different shots under similar conditions in order to provide plasma dynamics, having the difficulty of shot-to-shot variation among discharges. Besides, the costs of the cameras and/or lasers are not always affordable for small labs. On the other hand, these imaging diagnostics have the advantage of being non-perturbative for the plasma sheath. In the case of studying the plasma dynamics on a single shot, the usual diagnostics are magnetic probes [16–20]. These probes detect the induced voltage on a coil located in the plasma pathway due to the time- and space-varying current carrying region. These probes are located at different axial/radial positions, having the disadvantage of producing perturbations on the plasma sheath. These perturbations must be considered when analyzing their results. Some efforts have been devoted to either correcting their signals using an appropriate model [19] or using very small probe sizes when compared to the plasma sheath dimensions [20]. These methods are particularly difficult to use on very small plasma focus devices (usually portable and sub-kJ of stored energy) where the physical dimensions of the load and the plasma sheath are in the millimeter range (or even lower) [10, 14, 21– 26]. Additionally, some optical diagnostic methods have been used for determining some sheath properties based on single shot measurements. A photodiode system has been used for determining sheath particle density profiles for a pure hydrogen plasma [27] under certain symmetry. 2. Experimental setup The experiments were performed in the PF-400J device [22], which is a fast and very low-energy plasma focus (quarter period ∼310–330 ns; stored energy ∼210–400 J). The load section consists of a central 6 mm radius electrode (live anode) surrounded by eight equally spaced rods which—together with the baseplate—constitute the grounded cathode. The anode dimensions are 28 mm in length and 6 mm in radius, whereas the cathode bar structures have internal radius of 13 mm. The anode is partially covered by a 21.6 mm alumina insulator leaving an effective anode length of 6.4 mm. This plasma focus cannot be classified as either a Mather-type [1] or a Filippovtype [2] device due to its anode dimensions (radius/effective length). This device is more accurately classified as a hybridtype plasma focus. Deuterium has been used as working gas. The electrical diagnostics of the discharge are the load voltage and the current derivative, measured with a resistive divider and a Rogowski coil, respectively. The vacuum chamber has two radial BK7 windows which allow the collection of the light emitted by the plasma (but for this diagnostic, only one 2.

(4) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. window is needed). The optical system consists of a convergent lens located outside the vacuum chamber in the radial direction of the plasma load (i.e. side-on), whose object plane lies in the middle of the anode. A screen is located in the image plane of the lens, where the optical fibers are positioned. In our experiments, the focal length is 175 mm, the lens to screen distance is 850 mm and the load to lens distance is 220 mm, having a depth of field of 0.7 mm. This configuration provides an optical magnification M∼3.9 and this can be easily adjusted by simply moving the lens and adjusting the image and object distances properly. In addition, a 25 mm diameter aperture has been located at 165 mm from the load in order to diminish the stray light emitted elsewhere inside the vacuum chamber. A schematic diagram is shown in figure 1. The optical fibers are standard polymer (polyethylene) fiber optic cables, with 1 mm core diameter. Given the optical magnification of the system, these fibers have a spatial resolution of ∼0.25 mm in the object plane (i.e. at the plasma load). This resolution should be lower than the thickness of the plasma sheath to be measured. If it is not the case, then the optical magnification should be adjusted properly. The fibers are coupled to negatively biased photodiodes (SFH250V) operating as light-driven current sources, having a temporal resolution of 10 ns (both rise and fall times, according to manufacturer specifications). If shorter temporal resolution is needed, faster photodiodes should be used. The photodiodes are not cross calibrated; hence, their signal amplitudes do not provide further information. The screen (image plane of the lens) has been made of wood, where several holes have been drilled for positioning the optical fibers in the desired configuration. This screen is mounted in a three-axis positioner for fine positioning adjustment. The corresponding position of the optical fibers in the object plane (i.e. at the load) is obtained from photographs of the load, using the anode dimensions as scale indicator. The uncertainties of each fiber position depend on the photograph resolution, which is usually lower than 0.1 mm. The fivefiber system uncertainties will not affect the average axial speed and estimated thickness measurements since they will be shifted as a whole. However, it can affect the average radial speed and detachment time estimations which are included in the calculations. An example of this kind of photograph is included in figure 1. The fibers are arranged in the image plane in such a way so as to measure the light emission from the plasma sheath during its movement close to the anode during the axial phase (as shown in figure 1). This positioning avoids misinterpretation from light emitted in the same line of sight, since no plasma lies on it before the passage of the sheath. However, in the radial phase, the fibers could not be arranged to view the anode top in the side-on direction, since the radial implosion of the plasma sheath has cylindrical symmetry, and it could lead to misinterpretations of the real position of the light emission. To overcome this situation, an optical fiber has been located for monitoring the anode corner, where the axial phase ends and the radial begins. This fiber will indicate the beginning time for the radial phase. If major detail is required for measuring the time-varying radial position of the sheath, the optical system and fiber arrangement should be put in the end-on direction. However, the plasma focus discharges have. Figure 2. Electrical signals in a 9 mbar D2, ∼310 J shot using one scope channel per optical fiber, as shown in the electrical diagram. Fiber position is indicated on each signal.. been stated as the plasma sheath implodes on axis up to a final radius of 0.1–0.2a (where a is the anode radius) at the time of the dip in the current derivative trace [4, 5, 28, 29]. Using this information and the measured time from the fiber located in the anode corner, a radial transit time can be obtained. Figure 1 shows a schematic of the experimental setup and an actual picture of the electrode load, where the image of the optical fibers can be seen next to the anode border.. 3. Diagnostic description and results Two different sets of experiments were performed for measuring the movement of the plasma sheath in the plasma focus. The first set was performed using the load parameters in 9 mbar D2, and charging voltage of 27 kV(∼310 J). These load parameters have been stated as the most reliable operation of our device, where larger neutron yields have been obtained (∼106 n/shot) [22]. In this case, the sheath movement is monitored using five optical fibers coupled to five independent photodiodes. Each photodiode is connected to a scope channel, as shown in figure 2. For the operational condition used in this set of experiments, the photodiode signals show single or double Gaussian-like curves, depending on the position that 3.

(5) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. Figure 4. Axial position versus time diagram for two particular shots. Extraction methods of the kinematic parameters of the sheath are shown.. properties such as characteristic times and speeds of the plasma front (i.e. the plasma that moves forward and ionizes the background gas) can be properly characterized by measuring the first peak evolution, without loss of generality. This first peak (due to either sheath widening or multi-filaments) will provide the time-varying position of the plasma front, and it will be the first to arrive on the symmetry axis when pinching phase begins. In contrast to magnetic probes, the detected signal from the sheath movement vanishes after its passage over the corresponding optical fiber position. At most, stray light coming from other zones of the load can be collected in the optical system, but it does not provide a significant signal. This advantage makes the diagnostic particularly useful for minimizing the scope channels to be used and combine signals together with only one or two signals (which is not possible when using magnetic probes). The minimization of the scope channels is extremely important for reducing the real costs of a diagnostic method. In order to test the proof of principle on the use of a single scope channel for detection, a second set of experiments was carried out. These experiments were performed in 15 mbar D2 and charging voltage of 21 kV (∼190 J). These load parameters are far from the optimal operational conditions, since compression occurs far from the current maximum, and neither neutrons nor x-rays are detected. However, these conditions have been chosen in order to detect a single plasma sheath, since no double Gaussian-like curves are observed in these conditions. Besides, this condition also provides a larger time separation of the curves detected by the optical fibers, since the sheath is much slower (even though this time separation can also be adjusted by using different optical fibres/cable lengths, taking advantage of the transit time of the signals). The detection of a slower sheath is needed in our experiments in an attempt to avoid overlapping of the signals, given the very short effective length in our device.. Figure 3. Electrical signals in a 15 mbar D2, ∼190 J shot using a single scope channel for four optical fibers, as shown in the electrical diagram.. monitors each optical fiber, as shown in figure 2. The single Gaussian-like curves are present in the optical fibers which monitor the plasma close to the insulator. The double Gaussianlike curves are more frequent in the fibers that monitor the second half of the axial phase. When measuring a single Gaussian-like curve, the photodiodes detect the movement of a compact sheath. In the case of double Gaussian-like curves, there are three possible explanations: the sheath has separated into two consecutive light-emitting zones, or there is a second breakdown toward the outer electrode instead of the insulator surface, or the sheath has become a complex multi-filamentary structure making the optical fiber detect more than one filament in the same line of sight. Using this diagnostic technique, it is not possible to discriminate which explanation is correct. However, several filamentary structures have been measured in larger devices using time-resolved visible images [3] and in the PF-400J itself using both visible and interferometric measurements of the radial phase [30]. These observations provide support to the last explanation, but widening of the sheath and/or a second breakdown could not be fully discarded. It is worthwhile to mention that similar doubled structures have been measured with magnetic probes in a 1.1 kJ plasma focus using nitrogen gas [19] which can be attributed to any of these explanations, and the analysis of its nature is beyond the scope of this paper. In any case, the kinematic 4.

(6) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. Table 1. Results and considerations on each case. Physical quantity. 9 mbar test case. 15 mbar test case. Considerations. Axial speed (m s−1). (4.18 ± 0.16) × 104. (2.44 ± 0.22) × 104. Average radial speed (m s−1). (6.95 ± 0.91) × 104. (3.14 ± 0.19) × 104. Sheath thickness (mm). (1.1 ± 0.4). (1.0 ± 0.3). Detachment time (ns). (103 ± 18). (107 ± 33). A better curve fitting will be obtained using as many fibers as possible. A second order polynomial fitting could also provide the acceleration of the plasma sheath. Special care should be taken on the last fiber position (at the anode corner) and appropriate choosing of the final pinch radius (given by observations or scaling laws) Signal-to-noise ratio of the signals and temporal resolution should be appropriate. It also depends on the axial speed measurement. It depends on the fitting (linear or polynomial) of the axial movement.. for studying characteristic features of the sheath movement. With these information and current derivative signal, the axial and radial transit times and averaged axial and radial speeds are easily obtained. It can also be seen from the fitting that the plasma sheath separates from the insulator at a certain time after the current starts flowing through the load. This is ascribed as the attachment time of the sheath and it is the summation of the time it takes the plasma to form from the ionization of the background gas and the time that the Lorentz force takes to be capable of lifting off the formed sheath. This time has also been observed using different diagnostic methods [8, 24] and it can be predicted using some theoretical models [32, 33]. Besides, the detachment time is usually defined as the summation of attachment time and the time it takes to separate the plasma by half its width (as shown in figure 4). On the other hand, from the fibers located during the first half of the axial movement (fibers 1 and 2 in our case), an initial thickness for the sheath can be estimated by multiplying its full-width at half-maximum (FWHM) and the measured axial speed. It should be noted that, in the 9 mbar case, the FWHM is close to the photodiode temporal resolution indicated by the manufacturer, which means that this thickness could be overestimated. If there are serious concerns regarding the more precise values of the sheath thickness, then the use of faster photodiodes is recommended. However, the measured value agrees closely with that estimated using electrical diagnostic analysis [8] and optical images of other very low-energy plasma focus devices [10, 14, 24]. Although this thickness could appear too small in comparison with traditional plasma focus devices, the temporal widths of the photodiode signals together with the observations of [10, 14, 24] indicate that sheath thickness in very low-energy plasma focus lies below the centimeter range. Further analysis on the sheath formation and the implications are beyond the scope of this paper. A summary of the information extracted from the diagnostic technique together with some considerations is given in table 1. The capability of determining sheath properties in single shot basis is a key factor when studying device performance properly. When extrapolating data from different shots, the possibility of data misinterpretation increases since every shot in plasma focus experiments behaves slightly different within certain parameters. In comparison with magnetic probes. However, this should not be the case in a Mather-type plasma focus, where the anode effective length (axial phase) is much larger than the anode radius (radial phase) and sheath width, providing the possibility of placing the optical fibers much more separated. In our experiments, the combination of the signals has been made using positive/negative combination pairs for detecting two consecutive optical fibers, as shown in figure 3. This configuration not only allows rapid recognition of consecutive detecting fibers, it also cancels out the signal coming from stray light emitted elsewhere. A combined photodiode signal can be seen in figure 3.. 4. Discussion The movement of the plasma sheath has been measured using an arrangement of optical fibers which monitor the light emission from the plasma in the axial phase of the plasma focus. From the measured signals, the time-varying position of the sheath can be obtained by measuring the peak time in the Gaussian-like signals. When double peaked signals are obtained, the first peak is considered for the analysis, since this first plasma will end each phase of the sheath movement (either axial or radial). Additionally, a characteristic radial transit time (tR in figures 2 and 3) can be obtained from the optical fiber located in the anode corner and the dip time in the current derivative trace. Hence, a time-averaged radial speed is obtained using the anode dimensions and the scaling laws known for Mather- and hybrid-type plasma foci for determining the final pinch radius. In our case, the pinch radius of 0.12a has been used [31]. The time of the dip in the dI/dt signal as a minimum radius indicator has been used after references [14, 29]. Regardless of the electrical configuration of the photodiodes (either independent or combined), a position–time plot can be constructed using the corresponding position of each optical fiber as shown in figure 4. The vertical error bars are assigned to the spatial resolution of the fibers in the load plane, whereas the horizontal ones are assigned to the possible error on the determination of the time of the peak in the Gaussian-like curve ( ± 10 ns). Our results show that the plasma sheath moves at a relative constant axial speed, fitting linearly with correlation coefficients (R) of 0.9977 (9 mbar case) and 0.992 15 (15 mbar case). Although polynomial fitting can be used instead, the linear approximation is useful 5.

(7) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. (which also provide single shot measurements), this method has attractive advantages such as the absence of perturbations in the plasma sheath and the spatial resolution. Although the perturbations can be minimized or calculated, they must be taken into account. Additionally, the spatial resolution is limited by the capability of constructing tiny loops on the probe. In our case, there are no perturbations on the sheath and the spatial resolution is only limited by the available optics and the diffraction limit. Besides, optical detection also allows the combination of the signals into a single scope channel. On the other hand, the detectors (photodiodes) are price convenient and can be afforded by small labs. This plasma diagnostic capability can also be applied using a matrix-like array of fibers in the image plane monitoring the axial phase, in order to determine sheath curvature and/or speed profiles as a function of radial position without a considerable increase in complexity or cost. The measurement of the plasma sheath kinematic in a single shot without perturbing the plasma is demonstrated obtaining precise values that can be used for providing further insight into the plasma properties in plasma focus discharges.. [11] Krompholz H, Neff W, Ruhl F, Schonbach K and Herziger G 1980 Formation of the plasma layer in a plasma focus device Phys. Lett. A 77 246 [12] Gribkov V A, Bienkowska B, Borowiecki M, Dubrovsky A V, Ivanova-Stanik I, Karpinski L, Miklaszewski R A, Paduch M, Scholz M and Tomaszewski K 2007 Plasma dynamics in PF-1000 device under full-scale energy storage: part I. Pinch dynamics, shock-wave diffraction, and inertial electrode J. Phys. D: Appl. Phys. 40 1977 [13] Tou T Y 1995 Multislit streak camera investigation of plasma focus in the steady-state rundown phase IEEE Trans. Plasma Sci. 23 870 [14] Tarifeño-Saldivia A, Pavez C, Moreno J and Soto L 2011 Dynamics and density measurements in a small plasma focus of tens-of-joules-emitting neutrons IEEE Trans. Plasma Sci. 39 756 [15] Zielinska E, Paduch M and Scholz M 2011 Sixteen-frame interferometer for a study of a pinch dynamics in PF-1000 device Contrib. Plasma Phys. 51 279 [16] Bruzzone H and Grondona D 1997 Magnetic probe measurements of the initial phase in a plasma focus device Plasma Phys. Control. Fusion 39 1315 [17] Aghamir F M and Behbahani R A 2011 Current sheath behavior and its velocity enhancement in a low energy Mather-type plasma focus device J. Appl. Phys. 109 043301 [18] Al-Hawat S 2004 Axial velocity measurements of current sheath in a plasma focus device using a magnetic probe IEEE Trans. Plasma Sci. 32 764 [19] Knoblauch P, Raspa V, Di Lorenzo F, Lazarte A, Clausse A and Moreno C 2010 Correcting magnetic probe perturbations on current density measurements of current carrying plasmas Rev. Sci. Instrum. 81 093504 [20] Bhuyan H, Mohanty S R, Neog N K, Bujarbarua S and Rout R K 2003 Magnetic probe measurements of current sheet dynamics in a coaxial plasma accelerator Meas. Sci. Technol. 14 1769 [21] Silva P, Soto L, Moreno J, Sylvester G, Zambra M, Altamirano L, Bruzzone H, Clausse A and Moreno C 2002 A plasma focus driven by a capacitor bank of tens of joules Rev. Sci. Instrum. 73 2583 [22] Silva P, Moreno J, Soto L, Birstein L, Mayer R E and Kies W 2003 Neutron emission from a fast plasma focus of 400 joules Appl. Phys. Lett. 83 3269 [23] Milanese M, Moroso R and Pouzo J 2003 D-D neutron yield in the 125 J dense plasma focus nanofocus Eur. Phys. J. D 27 77 [24] Hassan S M et al 2006 Pinching evidences in a miniature plasma focus with fast pseudospark switch Plasma Sources Sci. Technol. 15 614 [25] Rout R K, Mishra P, Rawool A M, Kulkarni L V and Gupta S C 2008 Battery powered tabletop pulsed neutron source based on a sealed miniature plasma focus device J. Phys. D: Appl. Phys. 41 205211 [26] Verma R, Roshan M V, Malik F, Lee P, Lee S, Springham S V, Tan T L, Krishnan M and Rawat R S 2008 Compact sub-kilojoule range fast miniature plasma focus as portable neutron source Plasma Sources Sci. Technol. 17 045020 [27] Bilbao L, Bruzzone H and Grondona D 1994 Errors and limits in the determination of plasma electron density by measuring the absolute values of the emitted continuum radiation intensity Meas. Sci. Technol. 5 165 [28] Serban A and Lee S 1995 A simple optical fiber axial speed detector Rev. Sci. Instrum. 66 4958 [29] Mejia F C, Milanese M, Moroso R and Pouzo J Some experimental research on anisotropic effects in the neutron emission of dense plasma-focus devices J. Phys. D: Appl. Phys. 30 1499 [30] Soto L, Pavez C, Castillo F, Veloso F, Moreno J and Auluck S K H 2011 Dense plasma filaments in a. Acknowledgments The authors would like to acknowledge Luis Altamirano for fruitful comments on the diagnostic method. The financial support from FONDECYT grant 1110940 and PBCTCONICYT Chile PSD-01 are also acknowledged.. References [1] Mather J W 1965 Formation of a high density deuterium plasma focus Phys. Fluids 8 366 [2] Filippov N V, Filippova T I and Vinogradov V P 1962 High temperature dense plasma in a non-cylindrical z-pinch Nucl. Fusion Suppl. 2 577 [3] Sadowski M J and Scholtz M 2008 The main issues of research on dense magnetized plasmas in PF discharges Plasma Sources Sci. Technol. 17 024001 [4] Soto L 2005 New trends and future perspectives on plasma focus research Plasma Phys. Control. Fusion 47 A361 [5] Soto L, Pavez C, Tarifeño A, Moreno J and Veloso F 2010 Studies on scalability and scaling laws for the plasma focus: similarities and differences in devices from 1 MJ to 0.1 J Plasma Sources Sci. Technol. 19 055017 [6] Zakaullah M, Waheed A, Ahmad S, Zeb S and Hussain S S 2003 Study of neutron emission in a low energy plasma focus with beta-source-assisted breakdown Plasma Sources Sci. Technol. 12 443 [7] Ahmad S, Hussain S S, Sadiq M, Shafiq M, Waheed A and Zakaullah M 2006 Enhanced and reproducible neutron emission from a plasma focus with pre-ionization induced by depleted uranium (U238) Plasma Phys. Control. Fusion 48 745 [8] Veloso F, Pavez C, Moreno J, Galaz V, Zambra M and Soto L 2012 Correlations among neutron yield and dynamical discharge characteristics obtained from electrical signals in a 400 J plasma focus J. Fusion Energy 31 30 [9] Kies W 1986 Power limits for dynamical pinch discharges? Plasma Phys. Control. Fusion 28 1645 [10] Moreno J, Silva P and Soto L 2003 Optical observations of the plasma motion in a fast plasma focus operating at 50 J Plasma Sources Sci. Technol. 12 39 6.

(8) Meas. Sci. Technol. 23 (2012) 087002. Technical Design Note. [32] Bruzzone H and Vieytes R 1993 The initial phase in plasma focus devices Plasma Phys. Control. Fusion 35 1745 [33] Bruzzone H, Acuña H and Clausse A 2007 The lift-off stage of plasma focus discharges Plasma Phys. Control. Fusion 49 105. subkilojoule plasma focus 14th Latin American Workshop on Plasma Physics (Mar del Plata, Argentina) J. Phys. Conf. Ser. in preparation [31] Lee S and Serban A 1996 Dimensions and lifetime of a plasma focus pinch IEEE Trans. Plasma Sci. 24 1101. 7.

(9)