Practical Optimization of AECS PF-2 Plasma Focus Device for Argon Soft X-ray Operation

For operation of the plasma focus in argon, a focus pinch compression temperature range of 1.4–5 keV (16.3 × 10⁶–58.14 × 10⁶ K) is found to be suitable for good yield of argon soft X-rays (SXR) Ysxr. This is based on reported temperature measurements of argon plasmas working at regime for X-ray output. Using this temperature window, numerical experiments have been investigated on AECS PF-2 plasma focus device with argon filling gas. The model was applied to characterize the 2.8 kJ plasma focus AECS PF-2. The optimum Ysxr was found to be 0.0035 J. Thus, we expect to increase the argon Ysxr of AECS PF-2, 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 on AECS PF-2 with argon gas for optimizing soft X-ray yield with reducing L₀, varying z₀ and ‘a’. From these numerical experiments we expect to increase the argon Ysxr of AECS PF-2 with reducing L₀, from the present computed 0.0035 J at L₀ = 270 nH to maximum value of near 0.082 J, with the corresponding efficiency is about 0.03%, at an achievable L₀ = 10 nH.     

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.     

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.     

Some Generalised Characteristics of the Electro-dynamics of the Plasma Focus in Its Axial Phase: Illustrated by an Application to Independantly Determine the Drive Current Fraction and the Mass Swept-Up Fraction

We describe the axial phase of the Mather plasma focus by two coupled equations of motion and circuit. We non-dimensionalised these equations resulting in two coupled equations which are characterised by only three scaling parameters α, β and δ which are ratios of electrical to transit times, inductances and impedances respectively. The normalised current waveform, trajectory and speed profile are unique for each combination of α, β, δ which are the ratios of characteristic times (electrical discharge vs. axial transit), inductances (tube inductance vs. static inductance) and impedances (stray resistance vs. electrical surge impedance). This leads to important information and insight into various aspects of the axial phase. In the present work we show that in a time-matched plasma focus shot we deduce the value of axial phase current fraction f_c simply by measuring the calibrated voltage waveform and the uncalibrated current waveform. The scaling parameters β and δ are fixed; and by form-fitting the measured current waveform to the normalised current waveform using the value of α of the shot is determined uniquely; from which the peak current and the ratio of peak to average speed [the speed form factor (SFF)] are obtained. The average transit speed is measured by time-of-flight using the voltage upturn as indicator of end of axial phase. Then the SFF yields the peak speed. The measured voltage (back EMF), peak current and peak axial speed (all at the end of axial phase) allows the unambiguous measurement of f_c. The value of the mass swept-up fraction f_m is deduced from α which is the ratio of the characteristic discharge and the characteristic transit times, both deduced during the non-dimensionalisation of the equations. Analysis of a time-matched shot in the INTI PF at 15 kV, 3 Torr D₂ gave f_c = 0.68 and f_m = 0.05.     

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.     

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.