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 Neon Soft X-Ray Optimization of AECS-PF2 Plasma Focus Device

Numerical experiments have been investigated on modified AECS-PF2 with neon filling gas using the latest version of Lee model. The model was applied to characterize the 2.8 kJ plasma focus AECS-PF2, finding a neon soft X-ray yield (Y_sxr) of 0.04 J in its typical operation. By numerical experiments the optimum combination of pressure of 0.57 Torr, anode length of 9 cm and anode radius of 1.57 cm was found. The optimum Y_sxr found also to be 0.87 J. Thus we expect to increase the neon Y_sxr of AECS-PF2 22-fold from its present typical operation; without changing the capacitor bank, merely by changing the electrode configuration. The Lee model code was also used to run numerical experiments on AECS-PF2 with neon gas for optimizing soft X-ray yield with reducing L₀, varying z₀ and ‘a’. From these numerical experiments we expect to increase the neon Y_sxr of AECS-PF2 with reducing L₀, from the present 0.04 J at L₀ = 280 nH to maximum value of near 21 J at an achievable L₀ = 15 nH at the pressure 2.8 Torr.     

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.     

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.     

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.     

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.     

Numerical Experiments on Soft X-ray Emission Optimization of Nitrogen Plasma in 3 kJ Plasma Focus SY-1 Using Modified Lee Model

The X-ray emission properties of nitrogen plasmas are numerically investigated using corona plasma equilibrium model. The X-ray emission intensities of nitrogen Ly _α , Ly _β and He _α , He _β lines are calculated. The optimum plasma temperature for nitrogen X-ray output is concluded to be around 160 eV. The Lee model is modified to include nitrogen in addition to other gasses (H₂, D₂, He, Ne, Ar, Xe). It is then applied to characterize the 2.8 kJ plasma focus PF-SY1, finding a nitrogen soft X-ray yield (Ysxr) of 8.7 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 = 0.09 Torr, anode length = 7.2 cm and anode radius = 2.58 cm. The optimum Ysxr was 64 mJ. Thus we expect to increase the nitrogen Ysxr of PF-SY1 sevenfold from its present typical operation; without changing the capacitor bank, merely by changing the electrode configuration and operating pressure.     

Soft X-Ray Emission Optimization Study with Nitrogen Gas in a 1.2 kJ Plasma Focus

Measurement of soft x-ray emission from a low-energy plasma focus operated with nitrogen within the pressure range of 0.1–1.0 mbar is presented. The x-rays are detected by using an assembly of Quantrad Si PIN-diodes with differential filtering and with a multipinhole camera. In the 1.0–1.3 keV and 1.0–1.5 keV windows, the x-ray yield in 4 geometry is 1.03 J and 14.0 J, respectively, at a filling pressure of 0.25 mbar and the corresponding efficiencies are 0.04% and 1.22%. The total x-ray emission in 4 geometry is estimated at 21.8 J, which corresponds to the system efficiency of about 1.9%. The soft x-ray emission is found dominantly as a result of electron beam activity on the anode tip, which is confirmed by the images recorded by a pinhole camera.     

Comprehensive Study on Soft X-Ray Emission from Admixtures of Nitrogen and Neon Gases in the APF Plasma Focus Device

The present work is an investigation on the effect of working gas composition as well as applied voltage and operating pressure on the behavior of SXR emitted from the APF device. Three volumetric ratios(90:10), (75:25), and (50:50) of nitrogen:neon (N₂:Ne) admixture were used with operating conditions at applied voltages of 11, 12, and 13 kV and operating pressures of 1.5, 2, 2.5, 3, 3.5, 4, 4.5, and 5 torr. Using (N₂:Ne) gas mixture ratios of (90:10) and (75:25) and at applied voltage of 11 kV, the optimum pressure for maximum intensity of SXR was 3.5 torr. However, for the percentage of (50:50), it shifts to higher pressure of 4 torr. At higher applied voltages of 12 and 13 kV, the optimum pressures shift to higher values, 4 torr for both volumetric ratios (90:10) and (75:25), and 4.5 torr for the ratio of (50:50). It was found that the intensity of SXR increases with the increase of neon (Ne) percentage in the admixture of (N₂:Ne) and applied voltage. The highest intensity was for the volumetric ratio of (50:50) operating at the voltage of 13 kV. Our results illustrated that mixing neon (Ne) with nitrogen (N₂) as the working gas in the PF is a power source of SXR emission.     

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.     

Study of the Soft and Hard X-Ray Emitted by APF Plasma Focus Device in Different Pressures

In this paper, an investigation on the X-rays emitted in different pressures by APF plasma focus devices using filtered PIN-diodes and fast plastic scintillation detector is reported. The highest X-ray emission was observed in the pressure of 1.6 torr and the behavior of X-ray intensities registered by different filters versus applied pressure were seemed to be similar. The X-ray angular distribution was bimodal, peaked approximately at ±18°. The intensity of X-rays decreased abruptly along the central axis of the device where the cylindrical plasma pinch was formed.     

Numerical Experiments on IR-MPF-100 Plasma Focus Operated in Neon and Deuterium Gases

In this paper, using the current fitting method, the Lee model parameters are computed for the IR-MPF-100 plasma focus (maximum energy ～115 kJ) operated in the neon and deuterium gases and the results are presented in the different operational conditions. The values of f_c, f_cr and f_mr were obtained 0.43, 0.55 and 0.05 respectively for the neon gas in all values of pressure and voltage. f_m varies as a function of pressure and voltage. f_m varies from 0.03 to 0.04 for 23.3 kJ of energy and it is almost constant equal to 0.024 for 10.2 kJ of energy. In the case of deuterium gas, f_c and f_cr are found 0.3 and 0.4 respectively. In this case, \({\text{f}}_{\text{m}}\) varies between 0.028 and 0.1 and f_mr varies between 0.05 and 0.20. It is noted that in the case of deuterium gas, f_m and f_mr decrease with the pressure increasing approximately and in the case of neon gas f_m increases with pressure increasing. So we calculate neutron yield and soft X-ray yield using the Lee model code for the different operational conditions.     

Numerical Experiments on Radiative Cooling and Collapse in Plasma Focus Operated in Krypton

The Plasma Focus has wide-ranging applications due to its intense radiation of SXR, XR, electron and ion beams and fusion neutrons when operated in deuterium. The 5-phase Lee Model code has been developed for the focus operated in various gases including D, D–T, He, Ne, N, O, Ar, Kr and Xe. Radiation-coupled motion is included in the modelling. In this paper we look at the effect of radiation cooling and radiation collapse in krypton. The Pease–Braginskii current is that current flowing in a hydrogen pinch which is just large enough for the Bremsstrahlung to balance Joule heating. This radiation-cooled threshold current for a hydrogen pinch is 1.6 MA. It is known that in gases undergoing line radiation strongly the radiation-cooled threshold current is considerably lowered. We show that the equations of the Lee Model code may be used to compute this lowering. The code also shows the effect of radiation cooling leading to radiative collapse. Numerical experiments based on experimentally fitted model parameters are run to demonstrate a regime in which radiation collapse is observed in Kr at a pinch current of 50–100 kA.     

Characterization of the Soft X-Ray Emission from the APF Plasma Focus Device Operated in Neon

Experimental results related to soft X-ray (SXR) properties of Neon plasma on the APF plasma focus device is presented. The experiments were carried on over wide range of neon pressure and at voltages 11, 12 and 13 kV six filtered photo PIN diodes and pin-hole camera. For the charging voltages of 11–13 kV with 2.17–3.04 kJ stored energy, the optimum operating pressure in neon is found to be in the range of 3.5–5 torr. The behavior of SXR intensities was registered by different filters and found out that Al-Mylar 6 μm and Cu 10 μm has the highest and lowest amount of X-ray transmission, respectively.     

Comparison of Measured Soft X-Ray Yield Versus Pressure for NX1 and NX2 Plasma Focus Devices Against Computed Values Using Lee Model Code

The soft X-ray yield versus pressure curves of NX1 and NX2 plasma focus machines have been measured and published for different pressures and electrode configurations. In this work, the numerical experiments are carried out, using Lee model code. The Lee model code is configured for each of these devices NX1 and NX2 by fitting computed total discharge current waveform against a measured total discharge current waveform. The computed soft X-ray yield versus pressure curves are compared with the laboratory measured soft X-ray yield versus pressure data. The comparison shows agreement between computation and measurement of several important features of the yield versus pressure curves.     

Properties of Ion Beams Generated by Nitrogen Plasma Focus

Numerical experiments have been systematically carried out using the modified Lee model code on various plasma focus devices operated with nitrogen gas. The ion beam properties (ion beam energy, ion beam flux, ion beam fluence, beam ion number, ion beam current, power flow density, and damage factor) of the plasma focus have been studied versus gas pressure for each plasma focus device. The results show that, for these studied plasma focus devices, the mean ion energies decrease with increasing gas pressure, while the beam ion number increases with higher pressure. The fluence, flux, ion current, power flow density and damage factor have maximum values at the optimum pressure. It is shown that, the maximum power flow densities range from 10¹² to 10¹⁴ W m^?2 and the damage factor values reach almost 10⁹–10¹¹ W m^?2 s^0.5. The obtained results provide much needed benchmark reference values and scaling trends for ion beams of a plasma focus operated in nitrogen gas. These results could be used as an indicator for ion properties emitted from nitrogen plasma focus for various applications including material processing.     

Numerical Experiments on PF1000 Neutron Yield

Numerical experiments are carried out, using the Lee model code to compute the neutron yield Y_n of PF1000 as a function of pressure. Computed results are compared with available published results of neutron yield. Relevant plasma focus properties such as peak discharge current I_peak, pinch current I_pinch, pinch ion density n_i and energy input into the pinch EINP are also discussed as functions of pressures so as to provide correlation of Y_n with relevant plasma focus properties over the operational range of pressures.     

Study the Influence of the Bank Energy on the Dynamical Pinch in Plasma Focus

The plasma focus discharge can generate, accelerate and pinch the plasma up to high density and temperature in a pulsed mode manner. Applications aspects of discharge require high efficiency of the fusion products. This situation acquires optimized operational parameters for the proper discharge. In this article, we have studied the plasma parameters and neutron performance dependency on bank energy. First, analytical expressions are derived from the equation of motion for the plasma particles in the radial phase. Then, the related fusion neutrons, both thermal and non-thermal, together with the discharge anisotropy in the low pressure regimes for the ‘Dena’ plasma focus device as function of bank energy are presented. The analytic models are compared with experimental data.     

Study of Dense Nitrogen Plasma Irradiation of Aluminum Targets by APF Plasma Focus Device

The nitridation of Al surfaces is obtained by irradiating nitrogen ions from APF device. The Vickers Micro-Hardness values are improved approximately three times for the nitrided samples comparing to the non-nitrided ones. The X-ray diffraction analysis is carried out in order to explore the phase changes in the near surface structure of the metals. The Nuclear Reaction Analysis shows the depth of the nitride composed on the metal surfaces clearly and quantitatively. The results of Scanning Electron Microscopy indicate changes in surface morphology which are the emergence of a smooth and uniform film scattered on the surface of the nitrided specimens.     

Influence of Nitrogen on Hydrogenated Amorphous Carbon Thin Films Deposited by Plasma Focus Device

To carry out our research, a plasma focus device is used to deposit thin films of nitrogen doped hydrogenated amorphous carbon (a-C:H:N) onto the stainless steel-AISI-304 substrates at room temperature. Thin films are deposited with the same numbers of focus shots, at the same distance from the anode tip and with different partial pressures of nitrogen in the mixtures of acetylene/nitrogen as working gas. The nitrogen contents of deposited films are studied using nuclear reaction analysis (NRA) techniques. The results prove that nitrogen contents of the samples do not increase significantly by increasing partial pressure of nitrogen of the working gas for both sets of the samples. Moreover, NRA results exhibit the limitation of nitrogen incorporated into the samples, when this experimental setup is used. G-peak position and peak intensity ratio of the D-band to G-band (I_D/I_G) are used to investigate the diamond characters. Also, they show that sp² clustering is highly dependent on the nitrogen atomic contents and angular position of the samples. Scanning electron microscopy (SEM) shows the granular surface morphology of the films. Furthermore, it shows that angular position of the samples with respect to the anode axis plays an important role in the grain size of the surface of the samples. The thickness of the films decreases significantly by increasing angular position of the samples, while it decreases slightly by increasing partial pressure of nitrogen of the working gas. The Vickers surface hardness of the thin films exhibits significant dependency on the sp² clustering.