Development of a portable pulsed fast ⩾106 neutron generator based on a flexible miniature plasma focus tube

A plasma focus device is a laboratory fusion device that is used to produce pulsed neutrons for a few tens of ns duration. A compact plasma focus tube (volume ≈ 130 cm3) has been developed, and this was connected to a newly developed capacitor bank using 24 coaxial cables, each 10 m long. The capacitor bank was of compact size and consisted of four energy storage capacitors (each 6 µF, 20 kV, size: 20 cm × 20 cm × 30 cm). The peak discharge current of the capacitor bank was estimated to be 176 kA with a rise time of around 3.6 µs at maximum 4.8 kJ operation energy. The average neutron yield was observed to be maximum (3.1 ± 1.0) × 106 neutrons/pulse with a pulse duration of 15–25 ns at an operating energy of 2.7 kJ (15 kV) and deuterium gas filling pressure of 4 mbar. Long coaxial cables allow only the plasma focus head (neutron source) to be moved as per need, making this a portable pulsed neutron source that is useful in many applications, including in extreme conditions, such as in borehole logging applications for oil and mineral mapping. This report describes the various components of this portable neutron generator together with its neutron emission characteristics.


Introduction
Portable fast neutron generators (PFNGs) have been proven to be a technically as well as commercially viable alternative to conventional neutron sources, such as Pu-Be, Am-Be and 252 Cf, in many applications covering vast areas, including security [1][2][3], industry [4], environmental and geological fields [5], medical fields, especially in biophysics [6,7], and in boron neutron capture therapy [8] among others. * Author to whom any correspondence should be addressed.
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Among the various PFNGs, compact light-ion acceleratorbased hermetically sealed tubes that use deuterium-deuterium (D-D) and deuterium-tritium (D-T) fusion reactions have found the most widespread use [8][9][10][11][12][13]. These accelerators generate neutrons of energies ∼2. 45 MeV and ∼14.1 MeV, respectively. This consists of a source able to generate positively charged ions, one or more devices to accelerate the ions, and a metal hydride target loaded with either deuterium or tritium or a mixture of the two. An alternative to this is the dense plasma focus (PF)device based [14] portable pulsed ∼2. 45 and ∼14.1 MeV neutron generator, which uses the same fusion reactions in D 2 and/or D-T mixture gases, respectively. Unlike in accelerator-based sealed neutron tubes, ions are selfaccelerated in the plasma focus device to high energies (a few keV to several hundred keV) due to its geometry and produce intense neutrons for a short duration (typically a few 10 s ns). The plasma focus device is simple in operation as well as economical as most of its components are either replaceable at a low cost or designed for long and repetitive operations.
Together with pulsed intense neutrons, the plasma focus device is a widely known pulsed source of ions, electrons and soft as well as hard x-rays. They have routinely been used for several applications, such as lithography [15], radiography [16], material processing and thin film depositions [17], irradiation on materials for the first wall of upcoming fusion reactors [18][19][20] and in biological and biomedicine research [21][22][23][24]. In view of this, plasma focus devices continue to be designed and developed with different geometries and with different radiation yields that, suitable for use in the above-mentioned applications.
Numerous portable pulsed neutron generators of neutron yield ∼10 6 neutrons/pulse or less based on the plasma focus device have been developed worldwide in different laboratories [25][26][27][28][29][30][31][32]. For example, Silva et al [25] reported a maximum neutron yield of (1.06 ± 0.13) × 10 6 neutrons/shot at 9 mbar filling pressure of D 2 gas in a very small and fast plasma focus device operated at ∼400 J. Similarly, Milanese et al [26] reported the design, construction and experimental study of a very small transportable dense plasma focus device with 125 J of energy as an intense, fast neutron source of yield ∼10 6 neutrons/pulse. In another report [27], a compact and portable pulsed neutron source was reported to generate an average neutron yield of (1 ± 0.27) × 10 4 neutrons/shot at 200 J of bank energy. Rout et al [28] designed and developed a compact and portable sealed-type PF device, which could generate 10 5 -10 6 neutrons/pulse at 200 J of bank energy for 150 discharges for a single filling. Neutron emission of more than 10 4 neutrons/shot from a table-top plasma focus device of size 25 cm × 25 cm × 50 cm at only tens of joules energy was reported by Soto et al [29]. Soto et al [33] reported on the neutron emission from the smallest plasma focus device in the world (size: ∼20 cm × 20 cm × 5 cm) operating only at 0.1-0.2 J. A total neutron yield of (100 ± 40) neutrons/pulse was reported to be produced using this device at an operating energy of 0.1 J (4.9 nF, 6.5 kV), which can further be increased if operated repetitively.
Portability in all the above-mentioned devices has been achieved mostly through the use of a compact capacitor bank operating at sub-joule to a few hundred joules with an appropriately matched plasma focus unit. A typical plasma focus unit consists of a pair of coaxial electrodes working as the anode and the cathode, and an insulator sleeve placed in between them at the bottom [14]. The cathode is either designed in a tubular shape or in the form of a squirrel cage consisting of multiple rods. The majority of the low-energy plasma focus devices have used a tubular-shaped cathode as it also works as the experimental plasma chamber, which helps in achieving the desired compactness in a portable neutron source. A compact and coaxial spark gap is generally used for fast transfer of the capacitor bank energy to the plasma focus unit. The overall dimension is minimized by connecting all three main components, i.e. the capacitor bank, the spark gap and the plasma focus unit, using parallel plate transmission lines in a compact and rigid geometry. Moreover, these devices are mostly operated with battery-powered supplies, making them suitable for use in those field applications where a low to moderate neutron yield is required. However, high electromagnetic noise generated during capacitor bank discharge has been an issue in applications that require a high signal-to-noise ratio (S/N) because of its proximity to the plasma focus unit. In addition, the capacitor bank and other associated high-voltage (HV) components of the portable plasma focus devices may not be compatible for use in extreme conditions, such as a neutron probe tool in borehole logging for deep geological surveys to find deep ore deposits and petroleum reservoirs [34,35], as high moisture among other factors severely effects its electrical operation in such conditions.
Taking into consideration the above-mentioned limitations, an electromagnetic-interference proof and HV safe pulsed neutron generator based on a flexible miniature plasma focus tube has been developed. A tubular-shaped miniature plasma focus tube of size 5 cm diameter × 16 cm length and weight around 1.2 kg has been connected to a compact capacitor bank of size around 40 cm × 40 cm × 30 cm using 10 m long commercially available RG213 coaxial cables. The long coaxial cables provide the desired flexibility to move the plasma focus tube to any specific location in 10 m radius, as well as to reduce the effects of EMIs, as the outer conductor of the cables also helps to partially screen the electromagnetic noise generated during the capacitor-bank discharge. Here, the plasma focus tube shall be at HV for only a short duration of a few microseconds, making this useful as a neutron probe tool in extreme conditions without any change in electrical characteristics and, in turn, neutron emission characteristics. Moreover, isolation of the plasma focus tube and the capacitor bank makes handling of the portable neutron generators safe from any electrical hazard, which was otherwise not possible with other available portable neutron generators, where the capacitor bank and the plasma focus unit were held together in a compact geometry. The present report includes a detailed description of the major components of the portable plasma focus device, i.e. the plasma focus tube design, the capacitor bank and the spark gap, followed by experimental observations of timeresolved and time-integrated neutron emission characteristics in the subsequent sections.

Experimental setup
A schematic and a photograph of the newly developed portable pulsed neutron generator are depicted in figures 1 and 2, respectively. The main components of the portable pulsed neutron generators are the capacitor bank, the triggerable spark gap switch and the plasma focus tube. All these components have been indigenously designed and developed. A compact DC HV power supply has been used to charge the capacitor bank to the desired voltage and to supply a fast negative trigger pulse to trigger and close the spark gap switch. All the electrical operations were performed remotely using a hand-held control unit.
The capacitor bank was assembled using four energy storage capacitors connected in parallel. The capacitors were custom-made for fast high-discharge current, thus were suitable for such applications. Each capacitor has a capacitance of around 6 µF and self-inductance of less than 30 nH. The size of each capacitor was around 20 cm × 20 cm × 30 cm (l × w × h). Each capacitor was tested for its operation at a maximum rated voltage of 20 kV before connecting them in parallel to form the capacitor bank. The HV terminals of all the capacitors were terminated on a common SS plate of size 26 cm × 26 cm × 1.2 cm (l × w × t). Over this plate, the triggerable spark gap switch was assembled in a compact coaxial geometry, as seen in figures 1 and 2. The spark gap switch was indigenously developed for operation at atmospheric air pressure. One end of the spark gap switch was screwed to the HV plate of the capacitor bank, and the other end was coupled to the plasma focus tube through the RG213 coaxial cables, as depicted in the schematic diagram of the setup (figure 1). The overall dimension of the spark gap switch was around 14 cm diameter × 6 cm height. The center pin trigger method was adopted to trigger and close the spark gap switch. To trigger the spark gap switch, an SS pin of 0.6 cm diameter was placed at the center of its top electrode and insulated from it using a 0.2 cm thick tube made of ultra-high molecular weight (UHMW) polyethene material. The spark gap electrodes were made out of SS304 material and its outer casing was made of UHMW. A dry compressed air flushing arrangement was made to clean the spark gap before and after operation. The overall size of the capacitor bank together with the spark gap was 40 cm × 40 cm × 36 cm (l × w × h) with a total weight of around 100 kg and it was placed over a movable trolley. The capacitor bank discharge current was delivered to the plasma focus tube using the RG 213 coaxial cables. Although the use of RG213 coaxial cables has various advantages, as described earlier, it must be noted that the lumped inductance and resistance of the RG213 coaxial cable are typically ∼250 nH m −1 and ∼6 mΩ m −1 , respectively [36]. Hence, heavy parallelization of the cables was used to obtain the overall inductance and resistance values in the range necessary for efficient plasma pinch formation. In total, twenty-four 10 m long RG213 coaxial cables were used to couple the capacitor bank and the plasma focus tube. Twenty-four cables were used to minimize the overall inductance of the setup, as well as to conveniently connect them in a compact geometry, similar to the existing 17 kJ plasma focus device of neutron yield ⩾10 9 neutrons/pulse [37]. Nevertheless, 48 RG213 coaxial cables (each 5 m long) were used in a 17 kJ plasma focus device. Further, the use of tubular geometry in the currently reported plasma focus device has made this more compact in size and lighter in weight compared to that of the squirrel-cage-geometry-based existing 17 kJ plasma focus device. The frequency of plasma focus operation in the newly developed device could be high (⩽5 min) compared to that of the existing 17 kJ plasma focus device (⩾15 min). As such, the newly developed plasma focus device has many advantages over the existing device in the form of enhanced transportability, enhanced flexibility, easy accessibility and improved repeatability.
All 24 RG213 coaxial cables from the capacitor bank were terminated coaxially over the plasma focus tube assembly at a pitch circle diameter of 10 cm, as shown in figure 1. The plasma focus tube consisted of an SS304 cathode in the form of a cylindrical tube and an SS304 anode in the form of a rod placed at its bottom center. The cathode also worked as the experimental chamber. The inner and outer diameters of the cathode were 3.4 cm and 5 cm, respectively. The overall length of the cathode was 16 cm with a total internal volume of around 130 cm 3 , excluding the anode. The diameter and the effective length of the anode were 1.2 cm and 10 cm, respectively. The anode at the tip was given a hollow shape to reduce its erosion due to melting and evaporation upon collision with the relativistic electrons produced post plasma focus disruption [38,39]. An alumina tube of 1.0 cm diameter was placed over the anode at the bottom as an insulator between the anode and the cathode. The insulator plays a crucial role in the plasma sheath formation during the initial gas breakdown phase. An insulator of appropriate dimension and with a smooth surface (free of surface defects, such as micro-cracks) results in a uniform plasma sheath in the initial breakdown phase, which subsequently results in strong plasma focus formation [40,41]. Out of the total length of 5 cm of alumina tube, the exposed length of around 1.5 cm was polished via a special technique using diamond paste to make it compatible for smooth and efficient plasma sheath formation [28]. The surface roughness of the insulator surface was reduced from a few micrometers to a few hundreds of nanometers after polishing. The insulator to the anode sealing was achieved through metal-insulator brazing at multiple locations [28]. A bellow-sealed Swagelok valve with quarter-inch end connectors was welded to the experimental plasma chamber for evacuation as well as filling of the deuterium gas. The overall size of the plasma focus head, including the plasma focus tube and associated assemblies, was around 16 cm diameter × 25 cm length with weight around 6.5 kg. All the important features of the plasma focus device are tabulated in table 1.
Multiple diagnostics were employed to measure electrical characteristics, such as the discharge current and its rise time, as well as neutron emission characteristics. The Rogowski coil was used to measure the derivative of the discharge current [42]. It was made in-house using the RG174 coaxial cable. The measured discharge current-derivative was integrated externally using a passive (RC) integrator to obtain the discharge current signal. An integrator with an appropriate time constant was chosen to avoid signal distortion and for high S/N. A factor of (0.2 ± 0.03) kA mV −1 was multiplied by the experimentally observed current to obtain the real current values. Measurements of time-resolved emission of neutrons were performed using a plastic scintillator detector (PSD) coupled to a photomultiplier tube. Two identical PSDs were used along the axial direction and in the radial direction to measure anisotropy in the time-resolved emission of neutrons. The PSD signals were also used to measure the energy of the neutrons in both directions using the time of flight technique. The D 2 gas filling pressure in the plasma focus tube was measured using an Edwards capsule dial gauge working in the range from 0.5 to 25 mbar. The time-resolved neutron signals through the PSDs and the dI/ dt signal were recorded using a digital storage phosphorous oscilloscope (1 GHz bandwidth and 5 GS s −1 ). To avoid pickup due to electromagnetic noise, all the signalrecording devices were kept inside a Faraday cage. The neutron yield was measured using a silver-foil-activation-based Geiger-Muller detector (SAD). The SAD detector was in situ calibrated using a radio-isotopic Pu-Be neutron source.

Results and discussion
Electrical parameters, such as static inductance, and the peak discharge current have been determined using a short-circuit method. For short-circuit current measurement, the plasma focus tube was filled with a high deuterium gas pressure (p) of 15 mbar and operated at a capacitor bank energy (E) of 2.7 kJ. An oscilloscope image of a typical short-circuit currentderivative waveform together with the current waveform and two PSD signals is shown in figure 3. The current-derivative waveform was observed to be of a simple underdamped L-C-R discharge, and its time-period was measured to be 14.3 µs. Using the short-circuit discharge current time-period (T 0 ), the inductance and the maximum peak discharge current were calculated using formulas described elsewhere [43]. The value of the inductance was calculated to be 215 nH. The maximum peak discharge current (I 0 ) deliverable to the plasma focus tube was calculated to be 132 kA at 2.7 kJ. During shortcircuit measurements, no radiation was produced, and hence no pulses were recorded in the PSDs.
The plasma focus tube was filled initially with low D 2 gas filling pressure (1-2 mbar) during the initial insulator conditioning shots [40,44]. After conditioning of the insulator surface during the initial few plasma focus discharges, a large dip was observed in the current-derivative waveform near the quarter time-period and, correspondingly, in the current waveform, as shown in figures 4(a) and (b). The dip is followed by a fast oscillatory structure, which could be due to reflections in the coaxial cables. The frequency of the oscillatory structure in the current-derivative waveform was observed to be (119 ± 17) ns, which was close to the calculated transit time (100 ns) for the 10 m long coaxial cable [36]. The slight variation in the frequencies could possibly be due to superposition of electromagnetic noise generated during fast pulsed electrical discharge of the capacitor bank [45]. An attempt was made to reduce the noise by using a triaxial cable to transport the Rogowski coil signal to the oscilloscope, but there was no visible effect on the oscillatory structures in the current-derivative signal. The noise is filtered out by externally integrating it using a passive integrator, as can be seen from the current signal. A clear dip in the current waveform can be seen in coincidence with the current-derivative waveform. Moreover, similar structures were also seen in the measured current-derivative and pinch voltage in the coaxialcable-based medium energy (17 kJ) plasma focus device, as mentioned earlier. The dip indicates the plasma focus formation. The shape of this dip is a signature of plasma focus characteristics and, in turn, neutron emission characteristics. Generally, a sharp and large dip indicates strong plasma focus and a high neutron yield, and vice versa. Two time-resolved pulses have been recorded in each PSD placed at 80 cm from the anode tip in the axial and the radial directions, as shown in figure 4(b). These pulses could be of hard x-rays and neutrons. The hard x-rays are bremsstrahlung radiations produced due to collisions of relativistic electrons with solid anode material post disruption of plasma focus because of rapid growth of instabilities (sausage, m = 0). The energies of the hard x-rays have been reported to be of a wide range, varying from a few keV to a few MeV [38,39]. The hard x-ray pulse was confirmed by placing one of the PSDs in a lead casing of 3 cm thickness in a few plasma focus shots. The x-ray pulse was observed to be either attenuated partially or fully cut-off, which could be possibly due to shot-to-shot variation in its energy spectrum. The hard x-ray pulse duration i.e. full width at half maximum (FWHM) was measured to be (16 ± 4) ns.
Opposite to electrons, deuterium ions move axially away from the anode and collide with the background deuterium gas atoms/molecules to produce neutrons via d(d, 3 He)n beamtarget fusion reactions [38,39,[46][47][48]. The neutrons produced here are monoenergetic. The neutron emission is confirmed by changing the PSD position in a few plasma focus shots. The peak-to-peak separation between the first and second pulse was found to change with the change in PSD position, which could be associated with the change in the flight time of the neutrons. The time-of-flight separation between the hard xrays and neutron pulse was used for the calculation of neutron energy, as described elsewhere [43]. The neutron energy along the axis was calculated to be (2.49 ± 0.23) MeV, whereas the same perpendicular to axis (radial) was calculated to be (2.03 ± 0.12) MeV. The neutron pulse duration (FWHM) was measured to be (20 ± 3) ns.
Optimum D 2 gas filling pressure at 2.7 kJ operation energy was determined by varying the D 2 gas filling pressure and simultaneously measuring the neutron yield at each filling pressure using the SAD detector placed in the radial direction at 30 cm distance from the plasma focus anode tip. The D 2 gas filling pressure was varied in the range of 1-6 mbar. At each filling pressure, six plasma focus shots were performed and the average neutron yield of all the plasma focus shots was calculated. The average neutron yield was observed to increase with the increase in filling pressure up to 4 mbar, and then it started decreasing with the further increase in filling pressure, as shown in figure 5.
A maximum average neutron yield of (3.1 ± 1.0) × 10 6 neutrons/pulse into 4π sr was observed in the radial direction at the optimum D 2 gas filling pressure of 4 mbar. A maximum neutron yield of (4.7 ± 0.3) × 10 6 neutrons/pulse was also observed at 4 mbar. This could well be the optimum pressure for the current geometrical and operational parameters of the plasma focus device. Considering the well-known anisotropic emission of neutrons in the plasma focus device, the neutron yield would further be greater by at least 30% in the axial direction than that observed in the radial direction [37,46]. The observed variation in neutron yield with filling pressure could possibly be due to the variation in the plasma/current sheath speed (v s ) in the axial acceleration phase, which varies as the inverse square root of the filling gas pressure (v s ∝ I 0 /ap 1/2 ; a: anode radius). Other possible reasons for neutron yield variation with D 2 gas filling pressure have been explained in detail elsewhere [43]. Nevertheless, more than 30% variation in neutron yield under the same operating conditions was observed, which could be due to poor shot-to-shot reproducibility of the plasma focus discharges. The possible reasons for this have been cited to be problems in the discharge initiation and the presence of contaminants in the discharge chamber among others [49,50].
Moreover, all the neutron-optimized Mather-type plasma focus, from small to large devices, has been reported to have practically the same values of the drive parameter (I 0 /ap 0 1/2 ; p 0 is the optimum filling gas pressure) and the energy density parameter (28E/a 3 ). The variation in the optimized neutron yield of different plasma focus devices could be due to the difference in the volume of the pinched plasma and its duration, which depend on the geometrical and operational parameters of the plasma focus device. Soto et al [51] listed the drive parameters for various neutron-optimized PF devices (operating at 0.1 J to 1064 kJ), and the values were found to be in the range from 68 to 95 kA cm −1 mbar −1/ 2 . Using this value, the optimized anode radius for the currently reported plasma focus device at optimum D 2 gas filling pressure of 4 mbar is calculated to be in the range from 0.69 to 0.97 cm. The anode radius (0.6 cm) chosen for the current plasma focus device is nearly the same as that of the value calculated above. The slight deviation in the chosen value of the anode radius from the optimized value could be due to differences in mass and current factors, which were not considered while comparing the drive parameter values of all the neutron-optimized devices, as reported by Lee et al [52,53]. The six-phase radiative LEE model code [53,54] was used to calculate the axial run-down time of the current sheath and the neutron yield over a wide range of deuterium gas filling pressures. The inputs used for the code were as follows: inductance (L 0 ) = 215 nH, capacitance (C 0 ) = 24 µF, cathode radius (b) = 1.7 cm, anode radius (a) = 0.6 cm, anode length (z 0 ) = 11.5 cm, resistance (r 0 ) = 3 mΩ, charging voltage (V 0 ) = 15 kV and three different deuterium filling pressures (p), i.e. 1, 4 and 6 mbar. The fitted model parameters were: f m = 0.03-0.035; f c = 0.3-0.35; f mr = 0.25; and f cr = 0.6. The anomalous resistance values used for fitting were 1.95-2 Ω with characteristic rise times and fall times of 90-150 ns and 40-80 ns, respectively. A typical simulated current waveform is plotted together with the measured current waveform at the above-mentioned filling pressures in figures 6(a)-(c). The simulated current waveform is found to be in good agreement with the measured current waveform in the axial phase as well as at the start of the radial compression phase, which are the main points of interest in the LEE model code. The model parameters at 4 mbar filling pressure have been used to determine the axial run-down time and the neutron yield for different D 2 gas filling pressures beyond 6 mbar and their variations are plotted in figure 7.
The computed neutron yield is also seen to vary with the D 2 gas filling pressure, similar to that which is experimentally observed. The maximum computed neutron yield is found to be 2.2 × 10 6 neutrons/shot at around 9 mbar of filling pressure, which is higher than the experimentally obtained optimum gas filling pressure. A possible reason for the vast difference between the experimentally obtained filling pressure and that obtained using the LEE model code could be the high current leakage and low snowplough efficiency due to the bad shape of the current sheath. Bruzzone et al [55] reported the measurements of the current leakage, i.e. the fraction of peak discharge current that actually flows through the current sheath structure as a function of the D 2 gas filling pressure, and found them to be filling-pressure dependent. They concluded that, among others, current leakage in the vicinity of the insulator and badly shaped current sheaths during the initial stages of the discharge can lead to irreproducible behavior and also can limit the useful operating pressure range of the device. Hence, to accurately determine the filling gas pressure range, the initial breakdown phase (gas breakdown, current sheath formation and detachment of the current sheath from the insulator surface) should be appropriately taken into account in the modeling of the plasma focus device [53,54]. Detailed investigations in very low energy plasma focus devices have shown that the current sheath remains attached for a period of time close to 20%-30% of the quarter period of the discharge, and the duration of the breakdown phase can be anywhere between 25% and 40% of the quarter period of the discharge [56]. This is due to the dependence of the breakdown phase duration on various parameters, such as the filling pressure, insulator material and its dimensions, and electrode dimensions [57]. The effect of the duration of the breakdown phase can be negligible on the duration of the axial acceleration phase and the radial compression phase in the medium and largesized plasma focus device when compared with its quarter discharge period, as may be the case with the reported plasma focus device. However, due to the compact size of the plasma focus tube (generally used with a low-energy capacitor bank) it might affect the current sheath characteristics (e.g. shape, thickness) and the current leakages, which subsequently affect the plasma focus device performance and the neutron yield.
Nevertheless, the majority of plasma focus devices, working from tens of joules to hundreds of kilojoules and with different geometrical and operational parameters, have experimentally obtained optimum filling pressure around 5 mbar, as seen with the reported device here [58]. Koh et al [59] reported a high-pressure operational regime of the plasma focus device. They used various combinations of filling gas pressures of deuterium, capacitor bank charging voltages, anode lengths and insulator sleeve lengths to optimize the neutron yield from the NX2 plasma focus device. They observed that at all the charging voltages for various combinations of anode  and insulator sleeve lengths, there was an optimum filling pressure, which produced a maximum neutron yield. They argued from the beam-target fusion point of view (which is considered to be the dominant mechanism of neutron production in plasma focus devices) that below the optimum pressure, the number density of the deuterons accelerated in the axial direction was lower and thus resulted in a lower neutron yield. At pressures above the optimum pressure, the speed of the deuterons decreased during the post-pinch phase as it has to pass through dense ambient conditions, which will result in less efficient beam-target interaction, leading to a low neutron yield. This has also been observed experimentally using a medium-energy plasma focus device, where a higher number density of deuterium ions with high energies was measured at the optimum filling pressure for a charging voltage, which in turn resulted in a higher neutron yield compared to other filling pressures [60].
Moreover, the neutron yield was also estimated using the existing scaling laws [61]: Y n ∼ 1.7 × 10 −10 I 0 3.3 (I 0 in ampere) for neutron emission. The experimentally observed maximum neutron yield was found to be less than that estimated (1.3 × 10 7 neutrons/shot) at 132 kA peak current. The possible reason for the large difference between the experimentally observed and estimated neutron yield could be attributed to the use of a tubular cathode. The operation with the tubular cathode increases loading of the current sheath as well as the current leakage, which in turn reduces the neutron yield [62]. The relatively lower values of the mass and current factors obtained using the LEE model code also support this argument. Also, in operation with tubular cathodes, addition of impurities (due to back-reflected particles from the cathode wall) during the axial flow, may result in a substantial drop in temperature due to increased radiation loss, which is also consistent with the reduction in neutron output.
The neutron yield is estimated to increase further with an increase in capacitor charging voltage to its maximum design operating voltage, i.e. 20 kV (4.8 kJ, 176 kA), as per the above-mentioned scaling law for neutron emission. The neutron yield estimated to be produced at 20 kV of charging voltage is 3.47 × 10 7 neutrons/shot. Currently, D 2 gas needs to be refilled after every plasma focus shot due to the silicon o-ring gasket that is used for vacuum sealing in the plasma focus tube. The plasma focus tube is being sealed using brazing of insulator-metal joints at various locations, similar to the miniature sealed plasma focus tubes published elsewhere [28,30,32]. With this, once filled with D 2 gas, the plasma focus tube can be operated to produce neutrons for multiple shots over a long duration without needing to purge and refill the D 2 gas. Furthermore, the lengths of all the 24 coaxial cables are being increased beyond 10 m to make it feasible to use a neutron probe deeper in applications, such as borehole logging.

Summary and conclusion
A portable-head plasma focus device that is suitable for field applications, specifically for borehole logging applications, has been developed and characterized. The long coaxial cables and low weight of the plasma focus head provide the desired flexibility to move this to anywhere around a 10 m radius while keeping all the other components (e.g. capacitor bank, power supplies) stationary. Moreover, the capacitor bank was designed for operation at a maximum of 4.8 kJ, and strong plasma focus formation was observed, even at a lower operation energy of 2.7 kJ or below. Hence, there is further scope to increase the length of the coaxial cables and operate the capacitor bank at its maximum energy to obtain the same peak discharge current and hence to observe the neutron yield of the same order with enhanced flexibility. A maximum neutron yield of (4.7 ± 0.3) × 10 6 neutrons/pulse into 4π sr in the radial direction with a pulse duration of (20 ± 3) ns was observed at a D 2 filling gas pressure of 4 mbar and 2.7 kJ operation energy. The average neutron yield in the radial direction was observed to be maximum (3.1 ± 1.0) × 10 6 neutrons/pulse into 4π sr at 4 mbar filling pressure. The neutron energy along and perpendicular to the plasma focus device axis was calculated to be (2.49 ± 0.23) MeV and (2.03 ± 0.12) MeV, respectively. Higher neutron energy along the axis than that in the radial direction has been attributed to highly energetic/highfluence deuterium ions along the axis than that perpendicular to this in accordance with the beam-target fusion mechanism of neutron emission. This would have also contributed to the increase in neutron emission along the axis.
The plasma focus tube is further being modified into an allmetal sealed tube via brazing and welding at different joints that will make it feasible for multiple-shot operations over a long duration with single filling of the D 2 gas. This can also be filled with D-T mixture gas for enhanced neutron emission over a long duration without any change in device parameters. Moreover, all the components of the plasma focus device have been indigenously developed, and these were replaceable at a very low cost. The use of customized coaxial cables with low lumped inductance and resistance can help in reducing its overall weight further and improving the portability. Thus, its simple operation makes this a low-cost, low-maintenance alternative to complex and accelerator-based sealed portable neutron tubes, currently being used for the type of applications mentioned earlier.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.