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Many experiments have been carried out on the (16.8 kJ, 17 kV) dense plasma focus PF-24 device operated with pure deuterium and deuterium-argon admixture. The main purpose of the work was to investigate the influence of the doping argon on the average total neutron yields experimentally and numerically. The 103 discharges (34 for D2, 69 for D2- $x$ %Ar, where $x = 3, 5, 10, 15, 22, 25, 30, 45, 60$ ) were performed in four experimental sessions under constant total initial optimum pressure of about 2.2 torr. The total current and its time derivative traces, as well as the total neutron yield values, were recorded, and the electro-kinetic plasma parameters were estimated for each shot. The Lee model has also been adapted for gas mixture plasma focus modeling, and then the enhanced code was used for simulation of each of the PF-24 discharge with D2 and D2- $x$ %Ar. The fitting parameters for each shot are found and discussed. The measured and computed values of the neutron yield and the electro-kinetic plasma parameters are in good agreement. The obtained results showed that there is no neutron yield enhancement with argon seeding. The scaling law of the neutron yield $Y_{n}$ against argon fraction has been deduced. Additionally, our results illustrate that the PF-24 plasma focus device has an optimized configuration for the DD fusion neutron emission.

This program was designed to introduce a plasma platform to examine the field programmable gate array (FPGA) of the link boards typically used at the CERN’s Large Hadron Collider (LHC). Pulsed plasma systems with accelerating gradient of 1 kV/ $\mu \text{m}$ generate high-intensity, high-energy radiation beams. Single-event upset (SEU) is caused by radiation deposition in the FPGA. In FPGA, the SEU probability for 1-MeV protons and 10-keV X-rays are 0.1 and $2 \times 10^{-9}$ particle $^{-1}$ . The number of SEU induced in the Si by 1-MeV proton irradiation at 0.8-V bias computed from simulation in COMSOL Multiphysics was $1.8 \times 10^{5}$ . Although more experimental research is needed to identify the underlying mechanisms, pulsed plasma is perceived as being a smart alternative to investigate the error structure in FPGA.

This paper shows the correlation of the characteristic Ne soft X-ray (SXR) signal pulse with computed dynamics of the plasma focus using doped neon in Ne (97.5%)/Kr (2.5%) admixtures. The Lee model code is coupled with a specifically designed correlation excel template. The results show that typically, the characteristic Ne SXR pulse signal starts after the start of the reflected shock (RS) and before the beginning of the pinch. Specifically, in the illustrated shot, the RS phase starts at $3.375~\mu \text{s}$ while the pinch phase starts at $3.384~\mu \text{s}$ . The characteristic Ne SXR signal pulse starts at $3.377~\mu \text{s}$ , which is 2 ns after the start of the RS and 7 ns before the pinch starts. There is a consistent trend of Ne SXR correlation with the computed dynamics in the Ne doped with Kr admixtures up to a doping level of 2.5%.

The plasma focus (PF) emerged as a potential prospect to produce radionuclide, but the experimental data are not significant in favor of practical medical radioactivity. Empirical scaling grants a set of magnetic lens to enhance the nuclear activity. The experimental radioactivity of low-energy devices is in the range of kilobecquerel and rises to megabecquerel by optimizing and operating at a few hertz. Magnetically driven ion beam improves the radioactivity to the prescribed value of gigabecquerel for nuclear imaging. Magnetic radioactivity competence scheme reflects the vision that small PF, as a smart alternative to cyclotron, generates medical grade radioactivity.

The measured current waveforms of PF1000 plasma focus operating in neon are first fitted to the computed currents using the Lee model for the pressures of 0.5 and 0.8 torr. The fitting fixes the model parameters. The code is then run to study and to optimize the soft X-ray yield from (~352 kJ) PF1000 device. The maximum characteristic soft X-ray (H-like and He-like lines) yield of 4.2 kJ is found to occur at the pressure of 0.85 torr, with the pinch duration of 207 ns and with an all-line yield of 4.8 kJ. Maximum compression (corresponding to smallest pinch radius) of 0.585 cm with the duration of 224 ns is obtained at 1 torr with the greatest all-line yield of 7.1 kJ but a lower characteristic soft X-ray yield of 3.2 kJ. Detailed computation results indicate that the maximum compression (minimum pinch radius) at 1 torr is attributed to two mechanisms: thermodynamics specific heat ratio effects and radiative losses.

The Lee model is extended to study and characterize the electron beams emitted from plasma-focus devices. It is then first applied to characterize the electron beams emitted from low and high-energy plasma focus operated with deuterium gas. The numerical experiments on NX2 device at 15 torr of deuterium give the following results: electron fluence = $5.7 \times 10^{{\mathbf {22}}}~\text{m}^{{\mathbf {-2}}}$ , electron flux = $16 \times 10^{{\mathbf {29}}}~\text{m}^{{\mathbf {-2}}}~\text{s}^{{\mathbf {-1}}}$ , the relativistic kinetic mean energy of the electron = 56 keV, electron number = $2 \times 10^{{\mathbf {16}}}$ , electron current = 91 kA, and damage factor = $2.7 \times 10^{{\mathbf {12}}}~\text {W}\cdot \text {m}^{{\mathbf {-2}}}\text {s}^{{\mathbf {0.5}}}$ . Then, the effect of pressure on the beam characteristics is studied. The energy of the beam at pinch exit changes from around 57 J (1.9% of the stored energy $E_{{\mathbf {0}}}$ ) to 176 J (6% $E_{{\mathbf {0}}}$ ) with maximum value of 180 J (6.1% $E_{{\mathbf {0}}}$ ) at 15 torr, and these results are compared with the measured values 3.2% $E_{{\mathbf {0}}}$ on NX2. Scaling trends are suggested for electron beam characteristics. The energy fluence and the power flow density (energy flux) have a variation $4.3- 265 \times 10^{{\mathbf {7}}}~\text {J}\cdot \text {m}^{{\mathbf {-2}}}$ and $2.2 - 19 \times 10^{{\mathbf {15}}}~\text {W}\cdot \text {m}^{{\mathbf {-2}}}$ , respectively. The electron beam current ranges from 12 to 700 kA being 9%–35% of $I_{{\mathbf {peak}}}$ . The energy beam $Y_{{\mathbf {EB}}}$ scales on average as $Y_{\mathrm {EB}} =6.55\times E_{0}^{1.45} $ at energies in the 1 to 500 kJ regions ( $Y_{{\mathbf {EB}}}$ in J and $E_{{\mathbf {0}}}$ in kJ), and $Y_{\mathrm {EB}} =1\times 10^{-6}I_{\mathrm {pinch}}^{3.53} $ and $Y_{\mathrm {EB}} =2\times 10^{-6}I_{\mathrm {peak}}^{3.14} $ ( $I_{{\mathbf {peak}}}$ and $I_{{\mathbf {pinch}}}$ in kA and $Y_{{\mathbf {EB}}}$ in J). These results provide much needed benchmark reference values and scaling trends for electron beams of a plasma focus operated in deuterium gas.

Measured current waveforms at different neon pressures from two different plasma focus (PF) devices, namely, NX2 and NX1 are used for analysis using the Lee code. The model parameters of mass ( $f_{m}$ and $f_{{\text {mr}}}$ ) and current ( $f_{\text {c}}$ and $f_{\mathrm {cr}}$ ) in axial and radial phase, respectively, are obtained by fitting the computed current waveform to the measured current waveform for each pressure over a range of pressures in neon. The results show that the value of $f_{m}$ and $f_{\mathrm {mr}}$ ranges from 0.07 to 0.12 and 0.09 to 0.20, respectively, over the pressure range 1.0–5.0 Torr for NX2, whereas for NX1 it ranges from 0.020 to 0.024 and 0.048 to 0.08, respectively, over the pressure range 7.5–12 Torr. In all cases, the values of $f_{c}$ and $f_{\mathrm {cr}}$ are fixed at 0.7. Comparison of computed and measured soft X-ray (SXR) yield using fit model parameters for both devices shows good agreement. An important finding is that despite the noticeable variation of mass factors over the whole pressure range, a representative set of model parameters is found for each machine which may be taken as fixed over the range of pressures producing a good yield. In particular, for a high-performance PF using conventional electrode structure the representative set is: $f_{m} = 0.075$ , $f_{c} \,\, = \,\, 0.7$ , $f_{\mathrm {mr}} =0.1$ , and $f_{\mathrm {cr}}= \,\, 0.7$ . This is valuable information for neon SXR design purposes.

Reduced Pease–Braginskii currents are estimated for a linear pinch in a range of gases, namely, D, He, Ne, Ar, Kr, and Xe. A characteristic depletion time is defined as the time it takes for the plasma focus (PF) pinch energy to be radiated away. This quantity is used as an indicator for expectation of radiative collapse. The depletion times in various gases are estimated in units of pinch duration. The values indicate that in D and He, the radiation powers are small, resulting in such long depletion times that no radiative collapse may be expected in the lifetime of the focus pinch. In Ne, low tens of percent are radiated and significant cooling and reduction in radius ratio may be anticipated. In Ar, Kr, and Xe, the depletion time is only a fraction of the estimated pinch duration, so radiative collapse may be expected. Numerical experiments are then carried out with a circuit-coupled code, which incorporates radiation-coupled dynamics with PF pinch elongation and plasma self-absorption. The latter eventually limits the radiated power and stops the radiative collapse. These results show the detailed dynamics and confirm the expectations arising from depletion times discussed above.

In plasma focus (PF), the thermodynamic parameters such as ion fraction $\alpha $ , effective ionic charge number $Z_{\rm eff}$ , and effective specific heat ratio $\gamma $ at different temperatures may be calculated by corona model (CM). In the Lee model code, the neon $Z_{\rm eff}$ and $\gamma $ are stored in subroutines using convenient tables and polynomials derived from the CM (we call this approach approximated CM). In this paper, the thermodynamic parameters of the CM are close fitted to the data, thus replacing the approximate CM data with a more accurate close-fitting CM (CFCM). The comparisons of the Lee model code using the approximated CM and CFCM subroutines are conducted, with the main emphasis on optimum neon soft X-ray (SXR) emission and their properties. The suitable focus pinch temperature window of 200–500 eV is applied to generate the optimum neon SXR yield ( $Y_{\rm sxr}$ ). The optimum neon $Y_{\rm sxr}$ is found to be 3.19 and 3.49 J at the optimum pressure $P_{0}=3.1$ torr with approximated CM and CFCM subroutines, respectively. A high optimum value of SXR yield is obtained using CFCM subroutines in the Lee model, which is nearer to the experimental value compared with the approximated CM subroutines. The use of CFCM in the Lee model contributes to better estimation for further numerical experiment studies and gives confidence that the model is sufficiently realistic in describing the PF dynamics and SXR emission.

Ion beams emitted from the low-inductance kJ NX2 plasma focus have been numerically characterized and trends of these beams in various gases have been reported. In this paper, the ion beams from high-inductance kJ plasma focus machines AECS PF2 and INTI operated with various gases are studied. The obtained results show that the beam ions mean energy depends on the gas type and increases with increasing ion mass of the gas. It also indicates a higher ion fluence for H 2 (4.4 × 10 20 ions m −2 ), and a very small fluence value for Xe (0.085 × 10 20 ions m −2 ). The ion number reduces from H 2 (24 × 10 14 ) to Xe (0.074 × 10 14 ). The ion current decreases from H 2 (20.5% of the discharge current) to 5.4% for Xe. The beam energy drops from H 2 (0.63% of stored energy E 0 ) to 0.4% for O 2 ; however, then increases from Ne to the radiatively-collapsed gases Ar, Kr, and Xe. Argon has the highest damage factor (77 × 10 10 Wm −2 s 0.5 ), while the lightest gases have the lowest (2–6 × 10 10 Wm −2 s 0.5 ). The magnetic field compressing the pinch is higher for the heavier gases. This paper confirms that the trends of ion beam production with various gases in high- inductance machines are the same as the trends in low-inductance machines.

It is known that the radius ratio of a plasma pinch depends on the specific heat ratio γ of the pinch plasma, where radius pinch ratio is defined as: radius of plasma pinch column/radius of anode. The lower the specific heat ratio the lower would be the pinch radius ratio with corresponding increased compression and pinch density. The deuterium plasma focus pinch is invariably fully ionized and has a specific heat ratio of practically the highest possible value of 5/3. If the deuterium plasma focus could have its specific heat ratio reduced below 5/3 we might expect its radius ratio to be correspondingly reduced, increasing the pinch density, thus improving the D-D fusion neutron yield. To demonstrate this effect we run the Lee model code in deuterium but hypothetically fix the specific heat ratio, reducing it at each run. The results show that indeed the radius ratio is reduced, increasing the compression, and the neutron yield is substantially increased. The effect is used to explain the observed neutron yield enhancement when a deuterium plasma focus doped with a small amount of krypton.

The six-phase Lee model code was developed to compute the anomalous resistance phase (RAN) following the pinch phase in a plasma focus (PF) discharge. One important method to check such modeling is to look at the soft X-ray (SXR) emission time profile and to correlate this to the PF dynamics. A two-channel filtered SXR spectrometer coupled with an Excel-based analytical template was recently developed to speed up the correlation process. Using this system, we have determined that the neon PF typically operates in a normal (N) mode in which it emits characteristic He-like H-like neon line SXR (in a photon energy window of 900-1550 eV) reproducibly and efficiently. The characteristic neon line SXR pulse straddles the pinch duration starting strongly 10 ns before the start of the pinch, then diminishes through the 10-ns pinch and tails off into the subsequent RAN1 phase. We present the correlated time profiles of shots operating in the efficient N mode as well as, for comparison, poor shots, which are distinctly different in SXR time profiles. The profiles indicate the difference in dynamics of normal and poor shots. Statistics are presented as well as comparison of the yields from the numerical experiments and measurements. In the series that were studied the proportion of N-mode operation ranges from 70% in one series to 80% in another series over pressure range 1-4 torr. At 2 torr, it was found that 90% recorded the normal N profile. The results reinforce the view that while the Lee Model code incorporates the correct physics in its sequence of phases, refinement is needed to extend the radiative phase to the period before the pinch.

We adapted the Lee Model code as a branch version RADPF5.15K to gases of special interest to us, namely, nitrogen and oxygen and applied numerical experiments specifically to our AECS PF-1 and AECS PF-2. We also generalized the numerical experiments to other machines and other gases to look at scaling laws and to explore recently uncovered insights and concepts. The required thermodynamic data of nitrogen, oxygen, neon, and argon gases (ion fraction, the effective ionic charge number, the effective specific heat ratio) were calculated, the X-ray emission properties of plasmas were studied, and suitable temperature range (window) for generating H- and He-like ions (therefore soft X-ray emissions) of different species of plasmas were found. The code is applied to characterize the AECS-PF-1 and AECS-PF-2, and for optimizing the nitrogen, oxygen, neon, and argon SXR yields. In numerical experiments we show that it is useful to reduce static inductance L0 to a range of 15-25 nH; but not any smaller. These yields at diverse wavelength ranges are large enough to be of interest for applications. Scaling laws for argon and nitrogen SXR were found. Model parameters are determined by fitting computed with measured current waveforms in neon for INTI PF and in argon for the AECS PF-2. Radiative cooling effects are studied indicating that radiative collapse may be observed for heavy noble gases (Ar, Kr, Xe) for pinch currents even below 100 kA. The creation of the consequential extreme conditions of density and pulsed power is of interest for research and applications.

Kansas State University (KSU) dense plasma focus (DPF) is a 2.5-kJ DPF machine newly commissioned at the Plasma Radiation Physics Laboratory at KSU. The machine was designed to be used as a multiradiation source for applications in nuclear science and engineering. Neutrons are emitted from deuterium-deuterium (D-D) fusion reactions during high-power electric discharges at 17 kV, 140 kA, and 5 mbar. The machine circuit parameters were calculated using the short-circuit test. The emitted neutrons were measured using several radiation detection techniques. The 2.45-MeV characteristic D-D neutron energy was confirmed using the time-of-flight technique using a BC-418 plastic scintillator. The maximum neutron yield was roughly measured to be 2.8 × 108 neutrons per shot using a set of BTI BD-PND bubble detectors. Moreover, the neutron yield variation with pressure was measured and compared with the computed neutron yield using Lee model. Finally, the measured current showed good agreement with Lee six-phase model.

The six-phase Lee model code is used to fit the computed current waveform to the measured current waveform of INTI plasma focus (PF; 2.2 kJ at 12 kV), a T2 PF device, operated as a source of neon soft X-ray (SXR) with optimum yield around 2 torr of neon. The characteristic He-like and H-like neon line SXR pulse is measured using a pair of SXR detectors with selected filters that, by subtraction, has a photon energy window of 900 to 1550 eV covering the region of the characteristic neon SXR lines. From the analysis of the fitted current and the measured SXR pulses, the characteristic neon SXR pulses are correlated to the pinch dynamics, and the subsequent slightly harder SXR pulses are correlated to the anomalous resistance phase. The characteristic neon SXR yield is measured; the pulse has a duration of 25 ns. The characteristic neon SXR typically starts 10 ns before the pinch phase and continues through the end of the 10-ns pinch phase, tailing into the anomalous resistance phase. Harder SXR pulses, probably Bremsstrahlung, are correlated to the anomalous resistance phase, with the main pulse occurring nearly 200 ns after the characteristic neon SXR pulse.

The United Nations University/International Centre for Theoretical Physics Plasma Focus Facility (UNU/ICTP PFF), a 3.3-kJ plasma focus, was designed for operation in deuterium with a speed factor S such that the axial run-down time matches the current rise time at an end axial speed of nearly 10 cm/mus. For operation in neon, we first consider that a focus pinch temperature between 200 and 500 eV may be suitable for a good yield of neon soft X-rays, which corresponds to an end axial speed of 6-7 cm/mus. On this basis, for operation in neon, the standard UNU/ICTP PFF needs to have its anode length z0 reduced by some 30%-40% to maintain the time matching. Numerical experiments using the Lee model code are carried out to determine the optimum configuration of the electrodes for the UNU/ICTP PFF capacitor system. The results show that an even more drastic shortening of anode length z0 is required, from the original 16 to 7 cm, at the same time, increasing the anode radius ldquoardquo from 0.95 to 1.2 cm, to obtain an optimum yield of Y sxr = 9.5 J. This represents a two- to threefold increase in the Y sxr from that computed for the standard UNU/ICTP PFF.

Dense plasma focus (DPF) can be a powerful source of X-rays at the wavelengths useful for microlithography and micromachining depending on its working gas (Ne or Ar correspondingly) and operating parameters of the device. Experimental investigations were carried out with /spl sim/0.4-nm wavelength radiation from a specially designed medium-power soft X-ray tube with a water-cooled silver anode and highly sensitive chemically amplified resist SU-8. They have shown us that it is possible to produce 10-/spl mu/m structures replicated in 100-/spl mu/m resist layer and 4-/spl mu/m structures produced in a 35-/spl mu/m resist layer for 30 min. To decrease the time, a DPF device must be implemented for the task. Using pure argon and mixtures of argon with deuterium or krypton, we have found regimes ("hot spots," plasma pinching, and plasma compression by a "heavy shell") with appreciable soft X-ray yield. Influence on the results of chamber-circuit matching, pinch dynamics, and electron runaway processes are also discussed.

The United Nations University/International Center for Theoretical Physics Plasma Focus Facility (UNU/ICTP PFF), a small plasma focus, has proven very useful as a training device for research initiation and as a test bed for applications. In this work, its performance in terms of a soft X-ray (SXR) source is examined. The total SXR yield when operated in neon is measured using low-cost detectors, including a calorimeter and a five-channel filtered PIN system. For a charging voltage of 14 kV with 2.9 kJ stored energy, the optimum operating pressure in neon is found to be in the range of 2.7-3.3 torr, resulting in a total SXR yield of 6J/shot into 4/spl pi/ steradians measured by the calorimeter in agreement with the PIN detectors. Spectral data shows that 64% of the total SXR yield is contributed by the Ly-/spl alpha/ and He-/spl alpha/ lines and 36% by the rest, mainly the radiative recombination. The low total SXR yield (0.2 % of stored energy) is consistent with numerical computations of focus dynamics, which reveals that 3% of stored energy is converted into plasma energy. This low conversion rate into plasma energy is due to the large inductance of 110 nH of this simple single-capacitor device. Thus, for development as a SXR source, reduction of inductance is necessary.

Basic operational characteristics of the plasma focus are considered from design perspectives to develop powerful radiation sources. Using these ideas we have developed two compact plasma focus (CPF) devices operating in neon with high performance and high repetition rate capacity for use as an intense soft X-ray (SXR) source for microelectronics lithography. The NX1 is a four-module system with a peak current of 320 kA when the capacitor bank (7.8 /spl mu/F/spl times/4) is charged to 14 kV. It produces 100 J of SXR per shot (4% wall plug efficiency) giving at 3 Hz, 300 W of average SXR power into 4/spl pi/. The NX2 is also a four-module system. Each module uses a rail gap switching 12 capacitors each with a capacity of 0.6 /spl mu/F. The NX2 operates with peak currents of 400 kA at 11.5 kV into water-cooled electrodes at repetition rates up to 16 Hz to produce 300 W SXR in burst durations of several minutes. SXR lithographs are taken from both machines to demonstrate that sufficient SXR flux is generated for an exposure with only 300 shots. In addition, flash electron lithographs are also obtained requiring only ten shots per exposure. Such high performance compact machines may be improved to yield over 1 kW of SXR, enabling sufficient exposure throughput to be of interest to the wafer industry. In deuterium the neutron yield could be over 10/sup 10/ neutrons per second over prolonged bursts of minutes.

In spite of intensive studies of the plasma focus, scaling laws, with the exception of those for neutron yield, are not well known. This paper points out that Mather-type plasma focus devices operated in the neutron-optimized regime have remarkably little variation in a drive parameter, (I/sub p//s)//spl rho/p/sub 0//sup 1/2/, the peak drive current per unit anode radius divided by the square root of the fill density; this quantity having the value of 89 kA/cm per torr deuterium equivalent of fill gas with a standard deviation of less than 10%. This parameter controls the speed of the plasma in both the axial and radial phases; and its constancy over a wide range of plasma focus devices really indicates that these devices all operate at the same axial and radial speeds, and hence by inference they all have the same temperatures in the axial and radial phases. Using a simple dynamical model the linear dimensions and time scales of the gross plasma focus pinch are shown to be related to the anode radius of the plasma focus device. The results of experiments performed with a 3-kJ device using different anodes are in good agreement with the theoretical predictions.

Shadowgraph studies suggest that a target disk placed downstream of the anode of a plasma focus may become an auxiliary anode producing a second focusing event when the current sheet climbs over it after the first focus event. A model is put forth in which each event is assumed to comprise three phases: an axial phase, a radial phase, and a radial extension or expanded column phase. This model produces the current dip, voltage spike, and high radial speeds characteristic of a plasma focus. With two separated disks acting as auxiliary anodes downstream of the usual anode, there are three focus events with nine phases in the computation. The results of the model indicate that each anode produces sequentially the current dip, voltage spike, and high radial speeds characteristic of the plasma focus. These computations suggest the possibility and design of a sequential or cascading plasma focus. >