Hard x-ray source for flash radiography based on a 2 . 5 kJ plasma focus

A compact tabletop plasma focus suitable for hard x-ray imaging applications is presented. The hard x-ray emission was characterized by means of an effective energy analysis, based on images obtained with a single shot. The effective energy of the radiation was estimated to be around 83keV from radiographic images of metallic pieces. Numerical calculations, based on validated codes, are presented to give a quantitative interpretation of the experimental results. Experimental demonstration of the suitability of this device for introspective imaging of metallic pieces is also given.


I. INTRODUCTION
Plasma focus ͑PF͒ is one of the most cost-effective small fusion devices, which operates by producing intense electrical discharges between a pair of coaxial cylindrical electrodes located in a low pressure chamber ͑0.5-20 mbars͒.The device acts as a plasma accelerator gun in which the Lorentz force drives a plasma sheath along the electrodes, making it to collapse at the symmetry axis forming a hot dense plasma focus.Intense pulses of electromagnetic radiation as well as electron and ion beams are emitted as a result of the focalization process.Fusion reactions can be obtained if deuterium or deuterium-tritium mixtures are used, with the consequent emission of fast neutrons.
Apart from fusion and fundamental research, efforts were undertaken to investigate various technological applications based on either, the emitted particles, or the radiated electromagnetic field.Within the latter, applications such as soft x-ray imaging of biological specimens [1][2][3][4] or small samples 5 and soft x-ray lithography or micromachining [6][7][8][9][10][11] were reported.Other important results were obtained using a PF as an x-ray backlighter for photon energies of about 1 keV; 12,13 tailoring the output efficiency in the 1.2-1.3keV window, 14 or enhancing the Cu K␣ ͑Ref.15͒ line emission from the focus region.Specifically on x-ray imaging, Hussain et al. 16 studied a 1.8 kJ, 20 kV PF concluding that the device was suitable for good contrast radiography.More recently, a substantial enhancement of a PF performance as x-ray source was accomplished by preionizing the breakdown region with depleted uranium. 17In all of the above mentioned advances, achieved using relatively small PF facilities with operating voltages and stored energies up to 36 kV and 4.6 kJ, respectively, mainly the low region of the x-ray spectrum ͑h Ͻ 30 keV͒ was exploited.
On the other hand, hard x rays generated by a compact 4.7 kJ, 30 kV PF operated in deuterium were used to obtain radiographic images of metallic objects either static [18][19][20] or in fast rotation 21 and its neutron emission was used for side on water detection. 19,20n order to fully take advantage of the mentioned potentials, a PF device should be designed properly, providing flexibility, easy operation and maintenance, and portability.In this article, a compact design 2.5 kJ, 30 kV PF specially designed to perform as a hard x-ray radiation source suitable for flash radiography of metallic pieces is presented.The device is experimentally and theoretically characterized, and the suitability of applications is evaluated.

II. DEVICE AND METHODOLOGY
The PF capacitor bank is formed by eight capacitors ͑0.7 F each͒ connected in parallel surrounding both the spark gap and discharge chamber to provide a minimum inductance connection.The bank is charged up to 30 kV ͑2.5 kJ of stored energy͒, delivering a peak current of 350 kA to the discharge chamber in a quarter of period of ϳ1.3 s.The electrodes are coaxial and formed by a hollow high-conductivity oxygen-free copper anode ͑central elec-trode͒ and by a barred bronze cathode.The insulator is made of Pyrex glass.The electrode-insulator set is coaxially placed inside a cylindrical 1.5 l stainless-steel chamber and 3 mm thick walls.A sketch of the chamber design is shown in Fig. 1, and a comprehensive list of electrical and geometrical parameters is given in Table I.
The electrode-insulator base, made on polyamide 6, was designed to stand the high voltage spikes induced during the focalization.The thickness of the insulator wall was chosen to be 4 mm.Pyrex insulators having 2 mm thick walls were tested, but they did not last much more than a hundred of shots.Such thin insulators usually broke after a number of intense focalizations on which, presumably, the effects of dielectric fatigue were being accumulated on the glass.The insulator free length ensures that the breakdown condition always occurs on the right branch of Paschen curve for all of the operating pressures.This design criterion contributes to enhance the PF performance because the essential breakdown mechanisms are kept unchanged throughout whole pressure range of interest.Figure 2 presents the Paschen curve measured on the actual device, for the actual electrodeinsulator set showing the pressure operating region.
For ease of maintenance and operation, the device has only one triggerable high voltage switch, based on a presurized spark gap, which was constructed by modifying a Maxwell unit Model No. 40264, rated up to 100 kV, 100 kA.The modification consists in the addition of two extention rings to increase both the spark-gap chamber volume, and the interelectrode superficial distance.These pieces, made on polyacetal, increased the spark-gap total height by 45 mm.They hold the central spark-gap plate ͑trigger electrode, made on brass͒ and go in the middle of the assembly ͑see Fig. 3͒.The two main electrodes, made also on brass, were correspondingly lengthened to keep the interelectrode gap length unchanged.Except for the main electrodes and the eight assembling screws ͑which also needed to be lengthened͒ the rest of the Maxwell original parts were used in the modified unit.Figure 4 shows a picture of the assembled switch.
The x-ray output was monitored using a photomultiplier tube optically coupled to a NE102A plastic scintillator.The assembly was placed 6.7 m away from the chamber, inside a Faraday cage to reduce noise pickup.The recorded signals show that the x-ray pulse duration is 50 ns full width at half maximum ͑FWHM͒, which are suitable for x-ray imaging of pieces in fast motion.Commercial AGFA Curix Ortho Regular cassette-film system was used together with standard developer and fixer recommended for that film.No special procedures other than those indicated by the manufacturer were required to process the films.

A. Spatial location
At least two potential sources of hard x rays can be identified in PF discharges: the anode, against which accelerated electrons collide; and the focus itself, where unbounded electrons strongly interact with the ionic field of the  dense plasma.While the characteristics of the former are similar to those of high voltage x-ray tubes, the x-ray spectrum emitted from the focus is softer. 22he anode bombardment, in turn, could take place in more than one location.In order to determine the spatial locations of the hard x-ray sources, successive radiographies were taken placing a radiographic film along the electrodes axis at different distances from the chamber top, up to 15 cm.Three of such film-chamber distances ͑X i ͒ are illustrated on Fig. 5.It was concluded that the radiation beam is collimated since the area of the radiographic films exposed to the radiation was found to depend on its distance to the discharge chamber, as can be seen on Fig. 5 ͑shaded regions͒.
The complete set of the analyzed radiographs clearly shows a dark circle image corresponding to the hard x-ray illuminated zone.X rays with energies below 30 keV are strongly attenuated ͑ϳ10 9 times͒ by the chamber front wall.Measuring the diameter of the irradiated area for several film-chamber distances, the distance from the source to the chamber top ͑Y͒ and the half aperture angle of the hard x-ray beam ͑␣͒ were, respectively, calculated as ͑23.8± 3.5͒ cm and ͑0.24± 0.03͒ rad.The inferred spatial location is in agreement, within the experimental uncertainties, with a point source located at the bottom of the anode tube.

B. Effective energy
Since the spectrum of the emitted radiation is quite broad, it contains wavelengths far beyond the capability of the available spectrometers.Besides the pulse duration is so short that it prevents the use of single-event spectroscopy.Therefore, the spectrum was characterized by an efective average energy, defined as the energy that an equivalent monochromatic beam should have to experiment the same intensity attenuation.Assuming a continuous energy spectrum, the relative intensity attenuation due to a sample of thickness d is where I 0 and I͑d͒ are the incident and transmitted intensities, respectively, S͑E͒ is the spectral density, E is the energy of the photons, and ͑E͒ is the linear attenuation coefficient for the filter material.As follows from its definition, the effective energy E * is such that The magnitude ͑E * ͒ performs as an effective attenuation coefficient.
Measuring the attenuation ratio I͑d͒ / I 0 for known sample thicknesses d of the same material, it is possible to estimate ͑E * ͒ for that material using Eq.͑2͒.Once ͑E * ͒ is known, E * can be estimated from the tabulated ͑E͒ relationship.
Several sets of metallic plates were imaged to study their relative absorption I͑d͒ / I 0 .The following metals and thicknesses were used as filters ͑±0.02 mm͒: cadmium ͑1.10, 2.20, and 3.30 mm͒, copper ͑1.12, 2.24, 3.36, 4.48, and 5.60 mm͒, and nickel ͑1.60, 2.70, 4.30, and 5.40 mm͒.The film, together with the complete set of plates, was placed at ͑20.4± 0.02͒ cm from the chamber, and was irradiated with one shot.Figure 6 presents a digitized radiographic image of the filter set.The radiograph was obtained with a deuterium filling pressure of 3 mbars and a charging voltage of 30 kV.After digitizing the image, the relative intensity profile for each plate was obtained, corresponding to the attenuation dependence with the thickness and filter material.Thus, by comparing the corresponding gray tones of the digitized images, an estimation of the effective attenuation coefficient for each metal can be obtained.The effective attenuation coefficients obtained for cadmium, copper, and nickel are shown on Table II, along with their corresponding effective energies taken from Ref. 23.Even though the employed materials have absorption coefficients that differ significantly between each other, the obtained values for energy show good agreement with one another.All of them correspond to effective energies of ͑83± 10͒ keV.
To check if the film was not saturated, and if the gray level assignment by the digitizing process is proportional to the intensity reaching the film, it was verified that an exponential decay of the radiation intensity with the sample depth was obtained for each set of samples.
To verify that the measured effective energy is compatible with what can be expected for the voltage drop in the pinch V p such voltage was estimated as where I is the total current circulating through the pinch and L p represents the pinch inductance, which in turn can be estimated as

͑4͒
where h͑t͒ and r͑t͒ are the pinch length and radius, respectively, and r e represents the radius of the external electrode.
The temporal dependence of L p ͑t͒ and I͑t͒ were evaluated resorting to the well known Lee model. 24igure 7͑a͒ shows the calculated temporal evolution of V p considering a filling pressure of 3 mbars and a charging voltage of 30 kV.According to this model a voltage peak of approximately 110 kV can be expected during the focus, shortly before the maximum compression occurs.For this reason, a measured effective energy of 83 keV is considered to be compatible with what can be expected from a validated numerical code.Figure 7͑b͒ shows the calculated pressure dependence of the maximum pinch voltage.For this particular device, it can be seen that the expected pinch voltage peak decreases with the filling pressure in the explored operation range.

IV. RADIOGRAPHIC APPLICATIONS
The hard x-ray radiation output was used to obtain introspective images of metallic objects.Figure 8 shows a digitized radiograph of an aluminum climbing karabiner.The object was placed on the electrodes axis, outside the chamber, about 13 cm away from its front wall.The image has an overall spatial resolution of 1 / 50 mm ͑i.e., 50 pixels of the scanned image per millimeter measured on the object͒, limited by the digitizing process of the radiographic film.Submillimetric details of the internal mechanism can be easily distinguished, demonstrating the suitability of this PF device as a radiation source for introspective imaging of metallic objects.Although the geometric characteristics of the source itself are still to be determined, the degree of detail shown in Fig. 8 implies that the source size is well below the millimetric scale, since otherwise the images would not show sharp borders with such good contrast.This remains true even if three or four shots are superimposed on the same film; therefore, for radiographic purposes at least, the location of the hard x-ray source can be considered as presenting practically no variation from shot to shot.

V. CONCLUSIONS
A compact low energy plasma focus suitable for radiographic applications was presented and characterized as a hard x-ray radiation source.Radiographs of small metallic FIG. 6. Radiograph of the set of metallic filters employed to determine the effective energy of the hard x-ray radiation.Slabs of different thicknesses of each material were exposed, and their corresponding attenuations were compared.The lead filters were used as reference of total attenuation.samples can be achieved in single shots, reaching an image spatial resolution of 20 m per pixel of the scanned image.
The spatial location of the radiation source was found to be placed on the anode base, and its position does not vary appreciably from shot to shot.The use of a hollow anode helps to collimate the output beam, which, in our case, has a 14°half aperture.An effective energy of the hard x-ray emissions of 83 keV was experimentally determined.This value is compatible with what can be expected from the pinch induced voltage evaluated using a validated numerical model.

FIG. 1 .
FIG. 1. Scketch of the chamber design ͑longitudinal cross section͒.The chamber walls, electrodes, and insulator can be seen along with the NW-25 vacuum connector.

FIG. 5 .
FIG. 5. Experimental setup to determine the spatial location of the hard x-ray source.

TABLE I .
Electrical and geometrical parameters of the device.

TABLE II .
Linear attenuation coefficients and effective energies measured for different metals.͑a͒ Calculated temporal evolution of the pinch voltage at 3 mbars of deuterium as filling gas and 30 kV of charging voltage.͑b͒ Pressure dependence of the calculated maximum pinch voltage.
J. Appl.Phys.102,033304 ͑2007͒[This article is copyrighted as indicated in the article.Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: