A PF is a kind of pinch discharge in which a high pulsed voltage is applied to a low-pressure gas between coaxial cylindrical electrodes, generating a short-duration high-density plasma region in the axis. 

Figure 1 shows a schematic diagram of the equivalent electrical circuit and the discharge evolution in a Mather-type PF. The electrodes are in the vertical position; the anode in the centre is partially covered from its base by a coaxial insulator. The discharge starts over the insulator surface, then the plasma sheath comes off and it is accelerated axially by the magnetic field auto-generated by the current. After the current sheath runs over the upper end of the central electrode, the plasma is compressed to a small region (the focus or pinch).  

Figure 1. The circuit and the plasma dynamics is shown. The capacitor C is discharged over the electrode through a spark gap (SG). The plasma dynamics is sketched in a side section of the electrodes; I: discharge starts over the insulator; II and III: the current sheath is accelerated along the coaxial electrodes; and IV: pinch.

In most of PF devices, these three stages last a few microseconds, and less than 500 ns in a new generation of fast PFs. The maximum pinch compression should be close to the peak current in order to achieve the best efficiency. Depending on the energy of the pulse power generator, the current in the pinch varies from tens of kA to about MA. The pinch generates beams of ions and electrons, and ultra-short x-ray pulses. The duration of these pulses is of the order of tens to hundreds of nanoseconds.  

Using deuterium gas, PF devices produce fusion D–D reactions, generating fast-neutron pulses (∼2.5 MeV) and protons (leaving behind ³He and ³H). 

Interestingly, in different PF devices some plasma parameters remain relatively constant in a wide range of energy, from 50 J to 1 MJ (with an electron density ∼10²⁵ m⁻³) and a temperature range from 300 eV to 1 keV. Also the velocity of the current sheath is practically the same in every optimized PF (for discharges in deuterium, it is of the order of 1 × 10⁵ m s⁻¹ in the axial phase and of the order of 2.5 × 10⁵ m s⁻¹ during the pinch compression). Those features are best described by two parameters: the so-called ‘drive parameter’, Io/ap^1/2 [1], and the ‘energy density’, 28E/a³ [2, 3] (E is the energy stored in the capacitor bank, I_o the peak current, a the anode radius and p the gas filling pressure for the maximum neutron yield). These parameters remain practically constant in a wide range of PF devices. For Mather-type and hybrid-type PF devices operated in the neutron emission optimized regime, the drive parameter is 77 ± 7 kA cm⁻¹ mbar^−1/2 [3]. 

The previous analysis is the starting point to consider the possibility of constructing PF devices operating at lower input energies. 

Small devices are not only interesting for pure plasma research but also especially suitable for field applications. More remarkable is that they could constitute a safe radiation on–off source. Operating in a deuterium atmosphere, the PF could be especially suited for pulsed neutron applications with considerable less risks compared to conventional isotopic radioactive sources. A passive radioactive source of neutrons with similar energy (∼2.5 MeV; for instance ²⁵²Cf or Am/Be) emits continuously, with contamination hazard in handling and storing. Of course, PF sources do not have such activation problems.

To explore the construction of compact and fast devices with an input energy lower than 1kJ was our goal.  This was an area of research not well explored, largely considered as impossible to achieve. Feasibility objections had been made arguing that those devices would not have enough energy and time to create, transport and compress the plasma. We have experimentally shown that those objections were not valid [2–6]. PF devices of 400, 50 and 0.1 J have been designed, constructed and operated in our laboratory, namely, the PF-400J (176–539 J, 880 nF, 20–35 kV, ∼300 ns of time to reach the peak current), the PF-50J (32–100 J, 160 nF, 20–35 kV, ∼150 ns of time to reach peak current) and the Nanofocus (60–250mJ, 5nF, 5nH, 5–10kV, 16ns time to reach peak current) [6]. Evidence of pinch has been obtained in all of these devices.

These small PF devices, operating with deuterium gas, produce neutrons, an importtant evidence of the ocurrence of thermonuclear reactions. Neutron yield have been obtained for PF-400J, operating at ∼400 J, and for PF-50J, operating at 50 and 70J. In the PF-400J, the maximum measured neutron yield was (1.06 ± 0.13) × 10⁶ neutrons per shot at 9 mbar [5]; in the PF-50J, (3.6 ± 1.5) × 10⁴ neutrons per shot at 9 mbar, operating at 70 J, and (1.3 ± 0.5) × 10⁴ neutrons per shot at 6 mbar, operating at 50 J [6].

From the above results, the following scale rules for PF devices operating under 1 kJ have been obtained: Y ∼7.73 × 10⁻⁵ I₀ ^4.82 (with I₀ being the pinch current in kA), Y ∼ 3.15E^2.13 (with E being the energy in the capacitor bank, in J). 

After our work in small PF devices, operating under 1kJ of input energy, an increased interest in the research and development of this kind of apparati has arisen in other laboratories [7].

Figure 2. The Nanofocus, ultraminiature plasma focus device, operating at 0.1 J.

[1] Lee S and Serban A 1996 IEEE Trans. Plasma Sci. 24 1101
[2] Silva P, Soto L, Kies W and Moreno J 2004 Plasma Sources: Sci. Technol. 13 329
[3] Soto L 2005 Plasma Physics and Controlled Fusion 47 A361.
[4] Moreno J, Silva P and Soto L 2003 Plasma Sources Sci. Technol. 12 39
[5] Silva P, Moreno J, Soto L, Birstein L, Mayer R and Kies W 2003 Appl. Phys. Lett. 83 3269
[6] Soto L, Silva P, Moreno J, Zambra M, Kies W, Mayer R E, Clausse A, Altamirano L, Pavez C and Huerta L 2008 Demonstration of neutron production in a table-top pinch plasma focus device operating at only tens of joules. J. Phys. D: App. Phys. 41, (2008) 205215.
[6] Soto L, Pavez C, Moreno J, Barbaglia M and Clausse A 2008 An ultra miniature pinch focus discharge operating with energy of 0.1 Joule and submillimetric anode: nanofocus, submitted.
[7] Mohammadi M A, Verma R, Sobhanian S, Wong C S, Lee S, Springham S V, Tan T L, Lee P and Rawat R S 2007 Plasma Sources Sci. Tech. 16 785.