Neutron Scaling Laws from Numerical Experiments

Experimental data of neutron yield Y _n against pinch current I _pinch is assembled to produce a more global scaling law than available. From the data a mid-range point is obtained to calibrate the neutron production mechanism of the Lee Model code. This code is then used for numerical experiments on a range of focus devices to derive neutron scaling laws. The results are the following: Y _n = 2 × 10¹¹ I _pinch ^4.7 and Y _n = 9 × 10⁹ I _peak ^3.9. It is felt that the scaling law with respect to I _pinch is rigorously obtained by these numerical experiments when compared with that obtained from measured data, which suffers from inadequacies in the measurements of I _pinch.     

Measurements and Simulations of Neutron Emission Versus Deuterium Filling Pressure in Plasma Focus Device PF-24

A series of experiments were carried out using the middle energy (dense) plasma focus device PF-24 with deuterium as a working gas under pressure in a range between 2 and 5 mbar for 17 kV of charging voltage. The relationship between these operating deuterium pressures in reference to the total neutron yield (Y_n) was estimated. The 5-phase Lee code was used to simulate the measured discharge current and neutron yield (Y_n) using a phenomenological beam-target neutron generating mechanism, which was incorporated in the model. Comparison of the Y_n versus pressure using fitted model parameters was made at each point of pressure. The good agreement between measured and computed Y_n values was achieved for discharges with lower neutron emission. The measured Y_n (below 2.6?×?10⁹ n/discharge—the median value) has been reproducible by the model for 73% of simulated discharges, while above the median value its prediction were incorrect. The kinetic plasma parameters which were measured and computed using the Lee code for different pressures are: the time to a current sheath collapse (t_c), the average axial current sheath velocity (v_z) and the so called velocity factor (RF). Good agreement was found in the whole range of deuterium pressures between the computed and measured results for these kinematic quantities. Presented findings in this work suggest that the character of neutron emission is more complex than it would seem from classical interpretation of neutron production based on a beam-target model.     

Dependence of Plasma Focus Argon Soft X-Ray Yield on Storage Energy, Total and Pinch Currents

Numerical experiments are carried out systematically to determine the argon soft X-Ray yield Y_sxr for optimized argon plasma focus with storage energy E₀ from 1 kJ to 1 MJ. The ratio c = b/a, of outer to inner radii; and the operating voltage V₀ are kept constant. E₀ is varied by changing the capacitance C₀. These numerical experiments were investigated on argon plasma focus at different operational gas pressures (0.41, 0.75, 1, 1.5, 2.5 and 3 Torr) for two different values of static inductance L₀ (270 and 10 nH). Scaling laws on argon soft X-Ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found. It was found that the argon X-ray yields scale well with \textY_\textsxr = 8 ×10 ^{- 11} \textI_\textpinch^4.12 {\text{Y}}_{\text{sxr}} = 8 \times 10^{ - 11} {\text{I}}_{\text{pinch}}^{4.12} for the high inductance (270 nH) and \textY_\textsxr = 7 ×10 ^{- 13} \textI_\textpinch^4.94 {\text{Y}}_{\text{sxr}} = 7 \times 10^{ - 13} {\text{I}}_{\text{pinch}}^{4.94} for the low inductance (10 nH), (where yields are in joules and current in kilo amperes). While the soft X-ray yield scaling laws in terms of storage energies were found to be as \textY_\textsxr = 0.05 ×\textE₀^0.94 {\text{Y}}_{\text{sxr}} = 0.05 \times {\text{E}}_{0}^{0.94} at energies in the 1–100 kJ region. The scaling ‘drops’ as E₀ is increased, and Y_sxr scales as \textY_\textsxr = 1.01 ×\textE₀^0.33 {\text{Y}}_{\text{sxr}} = 1.01 \times {\text{E}}_{0}^{0.33} at high energies towards 1 MJ for 10 nH at argon gas pressure of 1 Torr. The optimum efficiencies for SXR yield were found to be 0.00077% with a capacitor bank energy of 112.5 kJ for high inductance (270 nH) and 0.005% with a capacitor bank energy of 4.5 kJ for low inductance (10 nH). Therefore for larger devices, it may be necessary to operate at a higher voltage and use higher driver impedance to ensure increasing X-ray yield efficiency beyond the optimum values. As storage energy is changed the required electrode geometry for optimum yield is obtained and the resultant plasma pinch parameters are found. Required values of axial speed for argon soft X-ray emission were found to be in the range 11–14 cm/μs.     

Numerical Experiments on Oxygen Soft X-Ray Emissions from Low Energy Plasma Focus Using Lee Model

The X-ray emission properties of oxygen plasmas are numerically investigated using corona plasma equilibrium model. The Lee model is here modified to include oxygen in addition to other gases. It is then applied to characterize the Rico Plasma Focus (1 kJ), finding a oxygen soft X-ray yield (Ysxr) of 0.04 mJ in its typical operation. Keeping the bank parameters and operational voltage unchanged but systematically changing other parameters, numerical experiments were performed finding the optimum combination of pressure = 3 Torr, anode length = 1.5 cm and anode radius = 1.29 cm. The optimum Ysxr was 43 mJ. Thus we expect to increase the oxygen Ysxr of PF-1 kJ thousand-fold from its present typical operation; without changing the capacitor bank, merely by changing the electrode configuration and operating pressure. The modified version of the Lee model code is also used to run numerical experiments with oxygen gas, for optimizing the oxygen soft X-ray yield on the new plasma focus device PF-SY2 (2.8 kJ). The static inductance L₀ of the capacitor bank is progressively reduced to assess the effect on pinch current I_pinch. The experiments confirm the I_pinch, limitation effect in plasma focus, where there is an optimum L₀ below which although the peak total current, I_peak, continues to increase progressively with progressively reduced inductance L₀, the I_pinch and consequently the soft X-ray yield, Ysxr, of that plasma focus would not increase, but instead decreases. The obtained results indicate that reducing the present L₀ of the PF-SY2 device will increase the oxygen soft X-ray yield till the maximum value after that the Ysxr will decrease with I_pinch decreasing.     

Scaling Laws of Nitrogen Soft X-ray Yields from 1 to 200 kJ Plasma Focus

Numerical experiments are carried out systematically to determine the nitrogen soft X-ray yield for optimized nitrogen plasma focus with storage energy E₀ from 1 to 200 kJ. Scaling laws on nitrogen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found. It was found that the nitrogen X-ray yields scales on average with $ {\text{Y}}_{\text{sxr,N}} = 1.93 \times {\text{E}}_{0}^{1.21} {\text{J}} $ (E₀ in kJ) with the scaling showing gradual deterioration as E₀ rises over the range. A more robust scaling is $ {\text{Y}}_{\text{sxr}} = 8 \times 10^{ - 8} {\text{I}}_{\text{pinch}}^{3.38} $ . The optimum nitrogen soft X-ray yield emitted from plasma focus is found to be about 1 kJ for storage energy of 200 kJ. This indicates that nitrogen plasma focus is a good water-window soft X-ray source when properly designed.     

Numerical Experiments on Oxygen Plasma Focus: Scaling Laws of Soft X-Ray Yields

Numerical experiments have been investigated on UNU/ICTP PFF low energy plasma focus device with oxygen filling gas. In these numerical experiments, the temperature window of 119–260 eV has been used as a suitable temperature range for generating oxygen soft X-rays. The Lee model was applied to characterize the UNU/ICTP PFF plasma focus. The optimum soft X-ray yield (Y_sxr) was found to be 0.75 J, with the corresponding efficiency of about 0.03 % at pressure of 2.36 Torr and the end axial speed was v_a = 5 cm/μs. The practical optimum combination of p₀, z₀ and ‘a’ for oxygen Y_sxr was found to be 0.69 Torr, 4.8 cm and 2.366 cm respectively, with the outer radius b = 3.2 cm. This combination gives Y_sxr ~ 5 J, with the corresponding efficiency of about 0.16 %. Thus we expect to increase the oxygen Y_sxr of UNU/ICTP PFF, without changing the capacitor bank, merely by changing the electrode configuration and operating pressure. Scaling laws on oxygen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 1 kJ to 1 MJ. It was found that the oxygen soft X-ray yields scale well with $ {\text{Y}}_{\text{sxr}} = 2 \times 10^{ - 7} {\text{I}}_{\text{pinch}}^{3.45} $ and $ {\text{Y}}_{\text{sxr}} = 6 \times 10^{ - 7} {\text{I}}_{\text{peak}}^{ 2. 9 2} $ for the low inductance (L₀ = 30 nH) (where yields are in J and currents in kA). While the soft X-ray yield scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{\text{sxr,O}} = 5.354 \times {\text{E}}_{0}^{1.12} $ (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The oxygen soft X-ray yield emitted from plasma focus is found to be about 8.7 kJ for storage energy of 1 MJ. The optimum efficiency for soft X-ray yield (1.1 %) is with capacitor bank energy of 120 kJ. This indicates that oxygen plasma focus is a good soft X-ray source when properly designed.     

Pinch Current Limitation in Sahand Plasma Focus

In this paper a new version of ML model has been used to simulate discharge dynamics in a 90 kj Fillipove type plasma focus, Sahand. Comparing model predictions with experimentally measured data shows that, the ML model when properly is fitted, is able to realistically simulate the discharge dynamics and consequently can be used to investigate the effect of operational and structural parameters on Sahand PF operation. To determine the optimum parameters which maximize the pinch current I_pinch, the effect of gas pressure and static external inductance L₀, on discharge dynamics in Sahand were investigated. The obtained results show that, for fixed initial stored capacitor energy, there is an optimum gas pressure at which I_pinch has its maximum value. To further increase in I_pinch at the optimum pressure, the static inductance was reduced. The results indicated that there exists an optimum value of L₀, where I_pinch reaches a maximum value and reducing L₀ further will not increase I_pinch. The maximum I_pinch has been achieved at optimum low static inductance at the expense of reducing C.S velocity at the time of pinch. The results of this investigation can confirm the current pinch limitation indicated before for Mather type PFs, for a Fillipov type PF.     

Development and performance characterization of a compact plasma focus based portable fast neutron generator

The design details and performance characterization results of a newly developed plasma focus based compact and portable system (0.5 m × 0.5 m × 1.2 m, weighing ≈100 kg) that produces an average neutron yield of ~2 × 10⁸ neutrons/shot (of fast D-D neutrons with typical energy ~2.45 MeV) at ~1.8 kJ energy discharge are reported. From the detailed analysis of the experimental characterization and simulation results of this system, it has been conclusively revealed that specifically in plasma focus devices with larger static inductance: (i) pinch current is a reliable and more valid neutron yield scaling parameter than peak current, (ii) the ratio of pinch/peak current improves as static inductance of the system reduces, (iii) the benign role of the higher static/pinch inductance ratio enables the supply of inductively stored energy in densely pinched plasma with a larger time constant and it is well depicted by the extended dip observed in the discharge current trace, (iv) there is the need to redefine existing index values of the pinch (Ipinch ^4.7) and peak (Ipeak ^3.9) currents in neutron yield scaling equations to higher values.     

Pinch Current and Soft X-Ray Yield Limitations by Numerical Experiments on Nitrogen Plasma Focus

The modified version of the Lee model code RADPF5-15a is used to run numerical experiments with nitrogen gas, for optimizing the nitrogen soft X-ray yield on PF-SY1. The static inductance L ₀ of the capacitor bank is progressively reduced to assess the effect on pinch current I _pinch. The experiments confirm the I _pinch, limitation effect in plasma focus, where there is an optimum L ₀ below which although the peak total current, I _peak, continues to increase progressively with progressively reduced inductance L ₀, the I _pinch and consequently the soft X-ray yield, Ysxr, of that plasma focus would not increase, but instead decreases. For the PF-SY1 with capacitance of 25 μF, the optimum L ₀ = 5 nH, at which I _pinch = 254 kA, Ysxr = 5 J; reducing L ₀ further increases neither I _pinch nor nitrogen Ysxr. The obtained results indicate that reducing the present L ₀ of the PF-SY1 device will increase the nitrogen soft X-ray yield.     

Soft X-ray Emission Optimization Studies with Krypton and Xenon Gases in Plasma Focus Using Lee Model

The X-ray emission properties of krypton and xenon plasmas are numerically investigated using corona plasma equilibrium model. Numerical experiments have been investigated on various low energy plasma focus devices with Kr and Xe filling gases using Lee model. The Lee model was applied to characterize and to find the optimum combination of soft X-ray yields (Y_sxr) for krypton (~4 Å) and xenon (~3 Å) plasma focus. These combinations give Y_sxr = 0.018 J for krypton, and Y_sxr = 0.5 J for xenon. Scaling laws on Kr and Xe soft X-ray yields, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 2.8 to 900 kJ. Soft X-ray yields scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{{{\text{sxr}},{\text{Kr}}}} = 0.0003 \times {\text{E}}_{0}^{1.43} $ Y sxr , Kr = 0.0003 × E 0 1.43 and $ {\text{Y}}_{{{\text{sxr}},{\text{Xe}}}} = 0.0064 \times {\text{E}}_{0}^{1.41} $ Y sxr , Xe = 0.0064 × E 0 1.41 for Kr and Xe, respectively, (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The maximum soft X-ray yields are found to be about 0.5 and 27 J from krypton and xenon, respectively, for storage energy of 900 kJ. The optimum efficiencies for soft X-ray yields (0.0002 % for Kr) and (0.0047 % for Xe) are with capacitor bank energies of 67.5 and 225 kJ, respectively.     

Soft X-Ray Emission in the Water Window Region with Nitrogen Filling in a Low Energy Plasma Focus

For operation of the plasma focus in nitrogen, a focus pinch compression temperature range of 74–173 eV (0.86 × 10⁶–2 × 10⁶ K) is found to be suitable for good yield of nitrogen soft X-rays in the water window region. Using this temperature window, numerical experiments using five phase Lee model have been investigated on UNU/ICTP PFF and APF plasma focus devices with nitrogen filling gas. The Lee model was applied to characterize and optimize these two plasma focus devices. The optimum nitrogen soft X-ray yield was found to be Y_sxr = 2.73 J, with the corresponding efficiency of 0.13 % for UNU/ICTP PFF device, while for APF device it was Y_sxr = 4.84 J, with the corresponding efficiency of 0.19 % without changing the capacitor bank, merely by changing the electrode configuration and operating pressure. The Lee model code was also used to run numerical experiments for optimizing soft X-ray yield with reducing L₀, varying z₀ and ‘a’. From these numerical experiments we expect to increase the nitrogen soft X-ray yield of low energy plasma focus devices to maximum value of near 8 J, with the corresponding efficiency of 0.4 %, at an achievable L₀ = 10 nH.     

Experimental Study of the Variation of Neutron Emission Anisotropy in a Filippov-type Plasma Focus Facility

This paper presents the results of experimental studies of the variation of spatial anisotropy in neutron emission with working conditions in a 90 kJ Filippov-type plasma focus device. The working gases are D₂ and D₂ + 1%Kr. The results of our experiments have shown that the anisotropy factor decreases with increasing the initial pressure and/or discharge energy. Furthermore, it has been observed that by using D₂ + 1%Kr as working gas, the variation in anisotropy factor with initial pressure and/or discharge energy is relatively high, but by using D₂ it changes slowly. The highest neutron yield has been achieved by using D₂ + 1%Kr and a conic insert anode. Thus, we have studied the correlation between neutron yield and anisotropy factor for this case at fixed working conditions from shot to shot. At 16 kV discharge voltage and pressures around optimum, the behavior of anisotropy factor is generally increasing with neutron yield, whereas at low and high pressures, the anisotropy factor does not change significantly with yield.     

Current-Step Technique to Enhance Plasma Focus Compression and Neutron Yield

A current-step technique is applied to the plasma focus by modifying the Lee Model code, incorporating a current-step bank to add current to the focus pinch at the time of the current dip. For a 50?kV, 1?MJ, 6?μs rise-time bank, the current-step from a 200?kV, 0.4?MJ, 0.8?μs rise-time bank maintains the pinch current at 2.2 MA, enhances compression by 1.9 and increases the neutron yield from 2.5?×?10¹² to 1.03?×?10¹³. The increase is attributed mainly to the step nature of the current which favorably shifts the end-point of compression; rather than to the scaling in terms of energy or current.     

Correlations Among Neutron Yield and Dynamical Discharge Characteristics Obtained from Electrical Signals in a 400?J Plasma Focus

Dynamical discharge characteristics and their relation with the total neutron yield emitted from a 400 J plasma focus operating in deuterium gas are presented. The dynamical nature of the plasma focus is obtained merely from the analysis of the voltage and current electrical signals without considering any particular geometry for the plasma sheath. It is calculated that large neutron yields are obtained when plasma inductance, mechanical energy and plasma voltage at pinching time have larger values. In contrast, no correlations are found among neutron yields either with plasma propagation velocities or quantities at the beginning of the radial phase. There is also found that the current sheath geometry changes according to the gas pressure, having larger curvature for lower pressures. The calculations also provide estimations of sheath thicknesses at the detachment from the insulator in the range of 0.5–1 mm, being thicker for larger neutron yield.     

Radiation Emission Correlated with the Evolution of Current Sheath from a Deuterium Plasma Focus

The time resolved emission of neutrons and X-rays (both soft and hard) is correlated with the current sheath evolution during the radial phase of a 3.2 kJ Mather-type plasma focus device operated in deuterium at an optimised pressure of 4 mbar. A three-frame computer-controlled laser shadowgraphy system was incorporated in the experiment to investigate the time evolution of the radial phase of the plasma focus. The dynamics of the sheath was then correlated with the time resolved X-rays and neutron emission. The time-resolved neuron and hard X-ray emission was detected by a Scintillator-photomultiplier system while the time resolved soft X-rays were detected employing filtered PIN photo diodes. The observations were recorded with a temporal accuracy of a few ns. For the reference, the total neutron yield was also monitored by an Indium Foil activation detector. The correlation with the High Voltage Probe signal of the discharge, together with the X-ray and neutron emission regimes enabled to identify the important periods of the sheath evolution i.e. the radial compression (pre focus), minimum pinch radius (focus) and the post focus phenomena. During the initial stage of the radial phase, velocities of 10–23 cm/μs, while at the later stage of the radial phase (up till the compression), velocities up to 32–42 cm/μs were measured in our experiment. For the discharges with the lower neutron yield (lower than the average value ~1 × 10⁸ n/discharge), the current sheath appears to be disturbed and neutron and hard X-ray signal profiles do not carry much information whereas the soft X-ray emission is significant. For the discharges with high neutron yield (higher than the average value), the current sheath has a smooth structure until the maximum compression occurs. Hard X-ray emission is maximum for the discharges with high neutron yield, especially whenever there is development of m = 0 instability compressing the column to very high densities. The neutron are emitted long after the maximum compression supporting the beam target fusion. For the discharges with High neutron yield, the soft X-ray production is less as compared to the discharges with low neutron yield.     

Effects of Power Terms and Thermodynamics on the Contraction of Pinch Radius in Plasma Focus Devices Using the Lee Model

The influence of the power terms Joule heating and radiative losses on the pinch radius in plasma focus devices is studied. Numerical experiments were carried out using the Lee model on three plasma focus devices spanning a large range of storage energy (PF400, INTI PF, PF1000) with different filling gases (N, O, Ne, Ar, Kr, Xe). Six possible regimes each characterized by a combination of significant power terms affecting plasma focus dynamics are found and discussed. These six possible regimes are further moderated by thermodynamic effects related to the specific heat ratio SHR of the plasma. In PF1000, the thermodynamic compression effects are clearly apparent in the radius ratio versus pressure curve for nitrogen which with atomic number Z_n = 7 is less radiative than neon with Z_n = 10, the dominant line radiation being proportional to Z _n ⁴ . In neon radiative compression at optimum pressure is so dominant that it masks thermodynamic compression in the compression versus pressure graph. Results show that plasma radiation losses enhance the contraction of the plasma focus pinch radius within suitable pressure ranges characteristic of each machine for each gas discussed in this paper. The radiation enhancement of compression increases with the atomic number of the gas.     

Neon Soft X-Ray Yield Optimization from PF-SY1 Plasma Focus Device

Based on the consideration of that for operation of the plasma focus in neon, a focus pinch compression temperature of 200–500 eV (2.3 × 10⁶–5 × 10⁶ K) is suitable for good yield of neon soft X-rays (SXR), numerical experiments have been investigated on the plasma focus device PF-SY1 using the latest version Lee model code. The Lee model code is firstly applied to characterize the PF-SY1 Plasma Focus. Keeping the bank parameters and operational voltage unchanged but systematically changing other parameters, numerical experiments were performed finding the optimum Y _sxr was 0.026 J. Thus we expect to increase the neon Y _sxr of PF-SY1 from its present typical operation; without changing the capacitor bank and the electrode configuration merely by changing the operating pressure. The Lee model code was also used to run numerical experiments on PF-SY1 with neon gas for optimizing soft X-ray yield with reducing L ₀, varying z ₀ and ‘a’. From these numerical experiments we expect to increase the neon Y _sxr of PF-SY1 with reducing L ₀, from the present 0.026 J at L ₀ = 1600 nH to maximum value of near 26 J at an achievable L ₀ = 10 nH.     

Plasma Focus Radiative Model: Review of the Lee Model Code

The code couples the electrical circuit with plasma focus (PF) dynamics, thermodynamics and radiation. It is energy-, charge- and mass-consistent and accounts for the effects of transit times of small disturbances and plasma self-absorption. It has been used in design and interpretation of Mather-type PF experiments and as a complementary facility to provide diagnostic reference numbers in all gases. Information computed includes axial and radial dynamics, SXR emission characteristics and yield for various applications including microelectronics lithography and optimization of machines. Plasma focus neutron yield calculations, current and neutron yield limitations, deterioration of neutron scaling (neutron saturation), radiative collapse, speed-enhanced PF, current-stepped PF and extraction of diagnostic and anomalous resistance data from current signals have been studied using the code; which also produces reference numbers for fluence, flux and energy of deuteron beams and ion beams for all gases. There has been no pause in its continuous evolution in three decades so much so that the model code has no formal source reference except www.plasmafocus.net. This review presents, for the first time a comprehensive up-to-date version of the 5-phase model code. The equations of each phase are derived. Those of the first two phases are normalized to reveal important scaling parameters. The focus pinch phase is discussed with radiation-coupled dynamics necessitating the computation of radiation terms moderated by plasma self-absorption. Neutron and ion beam yields are computed. The 5-phase model code appears to be adequate for all Mather-type PF, lacking only in one aspect that for high inductance PF (termed Type 2) the measured current waveform contains an extended dip which cannot be fitted by the 5-phase code; necessitating an extended 6-phase code. This sixth phase (termed phase 4a) is dominated by anomalous resistance, providing a way to extract valuable data on anomalous resistivity from the current trace.     

Formation of Y2O3 nanoclusters in nano-structured ferritic alloys: Modeling of precipitation kinetics and yield strength

The solubility product of Y₂O₃ in ferrite and the diffusion coefficient of yttrium in ferrite have been obtained by fitting a model based on the classical nucleation-growth-coarsening theory of precipitation, as adapted to an anisothermal heat treatment, to experimental small angle neutron scattering results of Y₂O₃ precipitate size distributions in a mechanically alloyed and consolidated Fe-15 at.%Cr-0.13 at.%Y-0.18 at.%O ferritic alloy. This precipitation model is coupled to a dispersed barrier model of structural hardening to predict the yield strength of the alloys as a function of heat treatment. The resulting model and thermodynamic/kinetic properties are then applied to better understand how the precipitation kinetics impact the yield stress in various anisothermal heat treatments, as compared to an isothermal heat treatment. The modeling results clearly indicate that the anisothermal heat treatments can be tailored to establish a higher density and a smaller size distribution of Y₂O₃ precipitates, which also increase the yield stress.