X-ray emission from an ultra miniature pinch plasma focus discharge operating at 0.1 Joule: Nanofocus
Cristian Pavez+, José Moreno, Patricio Silva, and Leopoldo Soto*
Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
+Universidad de Concepción, Chile
Abstract. Experiments in hydrogen, argon and neon have been developed in an ultra miniature device for pinch discharges
(nanofocus NF: 5nF, 5-10kV, 5-10kA, 60-250 mJ, 16 ns time to peak current). Sub-millimetric anode radii covered by
coaxial insulators were used in the experiments. Evidence of pinch was observed in electrical signals in discharges
operating at ~100 mJ. A single-frame image converter camera (4 ns exposure) was used to obtain plasma images in the
visible range. The dynamic observed from the photographs is consistent with a dynamic observed in conventional plasma
focus discharges. Evidence of X-rays emission from this ultraminiature pinch plasma focus device that operates at only
100mJ per shot is shown in discharges in H2, Ar and Ne.
Keywords: Z-pinch, plasma focus, soft X-ray sources,
Until a few year ago there has been some scepticism in the researchers of the plasma physics community toward
the possibility to construct and operate plasma focus (PF) devices below 1 kJ. In particular, the main objection is
there would not be sufficient energy available to generate, accelerate and compress the plasma. Recently, it has been
experimentally demonstrated that is possible produce a plasma focus operating at energies of 50 J with peak currents
of 40 kA [1-3, 5, 6]. Contrary to the popular believe that devices powered by such low energies would not function
properly, X rays and neutrons produced in pinch plasma foci were measured in 400 J and 50 J PF devices. The
average neutron yields were 106 for 400 J and 104 for 50 J [4, 6].
On the one hand, one of the main motivation for the low energy limit accounts for the possibility to design
pulsed radiation sources (nanoflashes) operating with discharge trains at high frequency. On the other hand, these
small devices are very useful to study the physics of high energy plasma densities.
A characteristic feature of the PF devices is that the plasma parameters remain relatively constant for facilities in
a wide range of energy, from 1kJ to 1MJ, electron density in the range 5×1024 – 1026 m-3, electron temperature in the
range 200eV – 2keV, ion temperature in the range 300eV – 1.5 keV. Other interesting feature is that the velocity of
the current sheath is of the order, in particular of 1×105 m/s in the axial phase and of the order of 2.5×105 m/s in the
pinch compression in every optimized plasma foci that operate in deuterium.
A comparison between plasma foci of different energies is interesting. Although only fraction of the initial
energy stored E in the capacitor bank is transferred to the plasma, the parameter E/Vp (with Vp the plasma volume) is
usually used to characterize the plasma energy density in order to compare different devices. According with scaling
laws  and optical diagnostics  the final plasma volume Vp (previous to appearance of probable instabilities) is
of the order of ~a3/28, and the plasma energy density at the pinch moment is proportional to E/Vp ~ 28E/a3. In
references [5, 8] the parameter 28E/a3 is listed for various PF devices and his value is of the order of (1-10)x1010
Other relevant parameter in plasma foci is the called drive parameter (Io/ap1/2) , where Io is the peak current, a
the anode radius, and p the gas filling pressure for the maximum neutron yield. This drive parameter (Io/ap1/2) is
related with the velocity of the axial and radial phase of the plasma motion (of the order of (0.8-1)x105 and (2-
2.5)x105 m/s respectively for a wide range of plasma focus sizes). In fact the axial and radial velocity are
proportional to (Io/ap1/2) [7, 11]. For devices over the range 50J-1MJ operating in deuterium the drive parameter
Io/ap1/2 = 77±7 kA/cm· mbar1/2 [7, 8]. Thus the plasma energy density and drive parameters can be used as design
Considering that the plasma energy density parameter E/Vp =28E/a3 and the drive parameter (Io/ap1/2) are
practically constant in all of plasma focus devices that operate in the range from 50J to 1MJ we can question, how
low can we go in loading energy keeping the same energy density and still obtaining the pinch plasma and neutron
and X-ray emission?.
Using the experimental fact that the plasma energy density parameter and the drive parameter are practically
constant in all of plasma focus devices that operate in the range from 50J to 1MJ, an ultraminiature device
“nanofocus”: 4.9nF, 4.8nH, ~5-10kV, ~5-10kA, 60-250 mJ, 16 ns time to peak current, was constructed. The design
and electrical characterization of the device has been described in the reference . The total dimensions of the
device are 20cm x 20cm x 5cm. The current temporal derivative was measured using a Rogowski coil, the charging
voltage was controlled using a resistive divider. Images from the plasma were obtained with a visible ICCD camera
gated at 4ns exposure time. An estimation of the X-ray emission was obtained using 4 filters of different thickness.
The correlation of the X-ray emission with the discharge was obtained using a BPX 65 diode without mica and
covered with 10μm of aluminium. Experiments have been performed in hydrogen, argon, and neon. Also
preliminary discharges in deuterium have been performed.
Plasma dynamics and pinch evidence. In a first stage of experiment s the plasma dynamics was studied using a
visible ICCD camera gated at 4ns exposure time [8-10]. Discharges in Hydrogen at 1-20 mbar, with an initial
charge of 6.5 kV (i.e., 0.1 J) were performed using a Cu anode radius of a=0.8 mm covered with and alumina tube
used as insulator [8-10]. Pinch evidence in the current derivative signals was observed in discharges at 3mbar in H2.
A clear evidence that a radial compression (pinch) actually occurred was the dip observed in the current -derivative
signal (it is the frequency change of the dI/dt oscillation and it has used as time 0 in the graph), concurring with a
drop in the electrical current and a small peak in the voltage signal. In turn, the mentioned features were not
observed in the electrical signals of the discharge at high pressure, 20 mbar for instance [8-10]. A current peak of
4.5 kA was obtained. The dynamic observed from the photographs was consistent with: a) the plasma is initiated
over the insulator, b) the plasma covers the anode, c) there is a radial compression of the plasma over the anode, d)
finally the plasma separates from the anode in the axial direction. The time from stages (a) to (d) is about 40 ns.
Figure 1 shows the results obtained in H2 at 3mbar. Similar results have been observed in preliminary discharges
performed in deuterium at 2-4mbar of pressure.
Evidence of X-ray emission. In a second stage of experiments the possibility of X-ray emission from this
ultraminiature device is being studied. In principle, X-rays are generated in pinch devices by Bremmstrahlung from
the thermal electrons; by line emission from high Z ions (if present because they form the filling gas or either as
impurities) and by high energy electron beams (tens and hundreds of keV) colliding with the anode. For discharges
in H2 and for the same conditions of the experiments of the figure 1 a BPX 65 diode without mica and covered with
10μm of aluminium was implemented and placed at 27mm radially from the anode axis. No signals in the BPX
diode were observed, probably due to the low intensity of the radiation. Then a diagnostics including the integration
of several discharges was performed. Radiographs of a array of aluminum filters of 30, 45 and 60 μm on HP5 Ilford
film were obtained operating the discharge at 0.4 Hz. Figure 2 shows radiographs after 1200 shots.
In order to estimate an average energy of the X-ray emitted by this ultra miniature pinch focus discharges a
monoenergetic radiation was assumed. When a monoenergetic radiation interacts with an element, the classical
exponential radiation decay relation through the matter is, I(x)/I0 = exp (-K· x), where I(x)/I0 is the normalized
radiation intensity after travelling a distance x inside the material characterized by a linear attenuation coefficient K.
From this relation it is possible to obtain an effective linear attenuation coefficient k, when different grey shades of
the digitalised images are linked to the I(x)/I0 ratio This method [12, 13] allows to obtain a correlation between K
and the X-ray energy. Thus, analyzing the radiographs of figure 2, a linear attenuation coefficient K =751±49
cm-1 and an effective mean energy of 4.3±0.3 keV were obtained.
Discharges in argon and neon. Discharges in argon and neon were performed for pressures in the range 2-
20mbar. Signals in the BPX 65 PIN (without mica and covered with a 10μm filter of Al) were obtained in the range
4-13mbar for argon, and in the range 5-15 mbar for neon. Figure 3 shows the signal in the PIN BPX 65 in
correlation with the discharge.
920 940 960 980 1000 1020 1040 1060
Photodiode(V) I(kA) dI/dt(kA/ns) V(kV)
Shot#304 Ar, 4 mbar
920 940 960 980 1000 1020 1040 1060
Photodiode(V) I(kA) dI/dt(kA/ns) V(kV)
Shot#319 Ne, 7.5 mbar
Figure 1. Electrical signals obtained in an ultra-miniature plasma focus operating in hydrogen at 3 mbar, with
an initial charge of 6.5 kV (i.e., 0.1 J). A current peak of 4.5 kA was obtained. Clear evidence that a radial
compression (pinch) actually occurred is the dip observed in the current-derivative signal (it is the frequency
change of the dI/dt oscillation and it has used as time zero in the graph), coinciding with a drop in the electrical
current and a small peak in the voltage signal. Also a sequence of photograph in the visible region of the
evolving plasma is shown. The plasma dynamic is similar to which observed in conventional plasma focus
Figure 2. Radiographs of a array of aluminum filters of 30, 45 and 60 μm on HP5 Ilford film obtained
after 1200 shots. Assuming a monoenergetic X-ray emission, an effective mean energy of 4.3±0.3 keV is
estimated from the radiographs.
DISCUSSIONS AND CONCLUSIONS
A plasma focus operating with energy of the order of ~0.1J has been designed and constructed. Results using a
Cu anode of 0.8mm radius shown pinch evidence [8-10]. Evidence of X-ray emission from this ultraminiature pinch
focus discharge have been obtained. Assuming a monoenergetic X-ray emission, an effective mean energy of 4.3±0.3
keV is estimated from the radiographs. In plasma focus discharges in hydrogen, the main source of X-ray radiation
is the interaction of the electron beam from the focus region with the anode. When electron beams are directed on to
anode with an energy greater than K shell energy , the dominant line radiation are Ká and Kb. In the case of the lines
are between 8 and 9 keV approximately. This value is greater than to the results obtained in our experiments,
therefore we can conclude that the energy of the electron beams are less than the K shell energy. Regarding the
roughly method used and the assumption of a monoenergetic emission in the data analysis, it is possible consider
that the ultraminiature pinch focus discharge (nanofocus) operating only at 0.1J per shot, emits X-rays of some KeV
of energy probably from the Bremmstrahlung radiation generated by electron beam colliding with the anode. In
addition in discharges in Ar and in Ne short pulses of X-rays have been detected with a PIN diode. The emission
occurs close to the peak current and the pulse duration (FWMH) is of the order of 5ns or less. This radiation is
probably due to Bremmstrahlung from the thermal electrons in the plasma.
Future works are required in order to obtain a better characterization of the X-ray emission. Also future works
include the characterization of the size source in repetitive regime and in single shot using pinhole camera. In the
case of single shot a MCP combined with a pinhole camera will used. In parallel in order to increase the value of
drive parameter and plasma energy parameter an anode with a radius of only a=0.21mm are being used .
In summary evidence of X-rays emission from an ultraminiature pinch focus discharge operating in H2, Ar, and
Ne at only 0.1J per shot have been shown. This is the smallest PF device in the world in which X-rays have been
Research supported by FONDECYT grant 1030062.
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