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A dense plasma focus (DPF) is a machine that produces, by electromagnetic acceleration and compression, a short-lived plasma that is hot and dense enough to cause nuclear fusion and the emission of X-rays and neutrons. The electromagnetic compression of the plasma is called a pinch. It was invented in 1954 by N.V. Filippov[1] and also independently by J.W. Mather in the early 1960s. The plasma focus is similar to the high-intensity plasma gun device (HIPGD) (or just plasma gun), which ejects plasma in the form of a plasmoid, without pinching it. A comprehensive review of the dense plasma focus and its diverse applications has been made by Krishnan in 2012.[2]


When operated using deuterium, intense bursts of X-rays and charged particles are emitted, as are nuclear fusion byproducts including neutrons.[3] There is ongoing research that demonstrates potential applications as a soft X-ray source[4] for next-generation microelectronics lithography, surface micromachining, pulsed X-ray and neutron source for medical and security inspection applications and materials modification,[5] among others.

For nuclear weapons applications, dense plasma focus devices can be used as an external neutron source.[6] Other applications include simulation of nuclear explosions (for testing of the electronic equipment) and a short and intense neutron source useful for non-contact discovery or inspection of nuclear materials (uranium, plutonium).

An important characteristic of the dense plasma focus is that the energy density of the focused plasma is practically a constant over the whole range of machines,[7] from sub-kilojoule machines to megajoule machines, when these machines are tuned for optimal operation.[8] This means that a small table-top-sized plasma focus machine produces essentially the same plasma characteristics (temperature and density) as the largest plasma focus. Of course the larger machine will produce the larger volume of focused plasma with a corresponding longer lifetime and more radiation yield.

Even the smallest plasma focus has essentially the same dynamic characteristics as larger machines, producing the same plasma characteristics and the same radiation products. This is due to the scalability of plasma phenomena.

See also plasmoid, the self-contained magnetic plasma ball that may be produced by a dense plasma focus.

A charged bank of electrical capacitors is switched onto the anode. The gas within the reaction chamber breaks down and a rapidly rising electric current flows across the backwall electrical insulator, axisymmetrically, as depicted by the path (labeled 1) as shown in Fig. 1. The axisymmetric sheath of plasma current lifts off the insulator due to the interaction of the current with its own magnetic field (Lorentz force). The plasma sheath is accelerated axially, to position 2, and then to position 3, ending the axial phase of the device.

The whole process proceeds at many times the speed of sound in the ambient gas. As the current sheath continues to move axially, the portion in contact with the anode slides across the face of the anode, axisymmetrically. When the imploding front of the shock wave coalesces onto the axis, a reflected shock front emanates from the axis until it meets the driving current sheath which then forms the axisymmetric boundary of the pinched, or focused, hot plasma column.

The dense plasma column (akin to the Z-pinch) rapidly pinches and undergoes instabilities and breaks up. The intense electromagnetic radiation and particle bursts, collectively referred to as multi-radiation occur during the dense plasma and breakup phases. These critical phases last typically tens of nanoseconds for a small (kJ, 100 kA) focus machine to around a microsecond for a large (MJ, several MA) focus machine.

The whole process, including axial and radial phases, may last, for the Mather DPF machine, a few microseconds (for a small focus) to 10 microseconds for a larger focus machine. A Filippov focus machine has a very short axial phase compared to a Mather focus.
Design parameters

The fact that the plasma energy density is constant throughout the range of plasma focus devices, from big to small, is related to the value of a design parameter that needs to be kept at a certain value if the plasma focus is to operate efficiently.

The critical 'speed' design parameter for neutron-producing devices is \({\frac {I}{a{\sqrt {p}}}} \), where I is the current, a is the anode radius, and p is the gas density or pressure.[7]

For example for neutron-optimised operation in deuterium the value of this critical parameter, experimentally observed over a range of machines from kilojoules to hundreds of kilojoules, is: 9 kA/(mm·Torr0.5), or 780 kA/(m·Pa0.5), with a remarkably small deviation of 10% over such a large range of sizes of machines.

Thus if we have a peak current of 180 kA we require an anode radius of 10 mm with a deuterium fill pressure of 4 Torr (530 Pa). The length of the anode has then to be matched to the risetime of the capacitor current in order to allow an average axial transit speed of the current sheath of just over 50 mm/μs. Thus a capacitor risetime of 3 μs requires a matched anode length of 160 mm.

The above example of peak current of 180 kA rising in 3 µs, anode radius and length of respectively 10 and 160 mm are close to the design parameters of the UNU/ICTP PFF (United Nations University/International Centre for Theoretical Physics Plasma Fusion Facility).[9] This small table-top device was designed as a low-cost integrated experimental system for training and transfer to initiate/strengthen experimental plasma research in developing countries.[10]

It can be noted that the square of the drive parameter is a measure of the "plasma energy density".

On the other hand, another proposed, so called “energy density parameter” \({28E \over a^3} \), where E is the energy stored in the capacitor bank and a is the anode radius, for neutron-optimised operation in deuterium the value of this critical parameter, experimentally observed over a range of machines from tens of joules to hundreds of kilojoules, is in the order of 5 ⋅ 10 10 {\displaystyle {5\cdot 10^{10}}} {5 \cdot 10^{10}} J/m3.[8] For example for a capacitor bank of 3kJ, the anode radius is in the order of 12mm. This parameter has a range of 3.6x10^9 to 7.6x10^11 for the machines surveyed by Soto. The wide range of this parameter is because it is a "storage energy density" which translates into plasma energy density with different efficiency depending on the widely differing performance of different machines. Thus to result in the necessary plasma energy density (which is found to be a near constant for optimized neutron production) requires widely differing initial storage density.
Current research

A network of ten identical DPF machines operates in eight countries around the world. This network produces research papers on topics including machine optimization & diagnostics (soft x-rays, neutrons, electron and ion beams), applications (microlithography, micromachining, materials modification and fabrication, imaging & medical, astrophysical simulation) as well as modeling & computation. The network was organized by Sing Lee in 1986 and is coordinated by the Asian African Association for Plasma Training, AAAPT. A simulation package, the Lee Model,[11] has been developed for this network but is applicable to all plasma focus devices. The code typically produces excellent agreement between computed and measured results,[12] and is available for downloading as a Universal Plasma Focus Laboratory Facility. The Institute for Plasma Focus Studies IPFS[13] was founded on 25 February 2008 to promote correct and innovative use of the Lee Model code and to encourage the application of plasma focus numerical experiments. IPFS research has already extended numerically-derived neutron scaling laws to multi-megajoule experiments.[14] These await verification. Numerical experiments with the code have also resulted in the compilation of a global scaling law indicating that the well-known neutron saturation effect is better correlated to a scaling deterioration mechanism. This is due to the increasing dominance of the axial phase dynamic resistance as capacitor bank impedance decreases with increasing bank energy (capacitance). In principle, the resistive saturation could be overcome by operating the pulse power system at a higher voltage.

The International Centre for Dense Magnetised Plasmas (ICDMP) in Warsaw Poland, operates several plasma focus machines for an international research and training programme. Among these machines is one with energy capacity of 1 MJ making it one of the largest plasma focus devices in the world.

In Argentina there is an Inter-institutional Program for Plasma Focus Research since 1996, coordinated by a National Laboratory of Dense Magnetized Plasmas (www.pladema.net) in Tandil, Buenos Aires. The Program also cooperates with the Chilean Nuclear Energy Commission, and networks the Argentine National Energy Commission, the Scientific Council of Buenos Aires, the University of Center, the University of Mar del Plata, The University of Rosario, and the Institute of Plasma Physics of the University of Buenos Aires. The program operates six Plasma Focus Devices, developing applications, in particular ultra-short tomography and substance detection by neutron pulsed interrogation. PLADEMA also contributed during the last decade with several mathematical models of Plasma Focus. The thermodynamic model was able to develop for the first time design maps combining geometrical and operational parameters, showing that there is always an optimum gun length and charging pressure which maximize the neutron emission. Currently there is a complete finite-elements code validated against numerous experiments, which can be used confidently as a design tool for Plasma Focus.

In Chile, at the Chilean Nuclear Energy Commission the plasma focus experiments have been extended to sub-kilojoules devices and the scales rules have been stretched up to region less than one joule [15] [16] [17] .[18] Their studies have contributes to know that is possible to scale the plasma focus in a wide range of energies and sizes keeping the same value of ion density, magnetic field, plasma sheath velocity, Alfvén speed and the quantity of energy per particle. Therefore, fusion reactions are even possible to be obtained in ultraminiature devices (driven by generators of 0.1J for example), as they are in the bigger devices (driven by generators of 1MJ). However, the stability of the plasma pinch highly depends on the size and energy of the device.[8] A rich plasma phenomenology it has been observed in the table-top plasma focus devices developed at the Chilean Nuclear Energy Commission: filamentary structures,[19] toroidal singularities,[20] plasma bursts [21] and plasma jets generations.[22] In addition, possible applications are explored using these kind of small plasma devices: development of portable generator as non-radioactive sources of neutrons and x-rays for field applications,[16][17] pulsed radiation applied to biological studies, plasma focus as neutron source for nuclear fusion-fission hybrid reactors,[23] and the use of plasma focus devices as plasma accelerators for studies of materials under intense fusion-relevant pulses.[24] In addition, Chilean Nuclear Energy Commission currently operates the facility SPEED-2, the largest Plasma Focus facility of the southern hemisphere.

Since the beginning of 2009, a number of new plasma focus machines have been/are being commissioned including the INTI Plasma Focus in Malaysia, the NX3 in Singapore, the first plasma focus to be commissioned in a US university in recent times, the KSU Plasma Focus at Kansas State University which recorded its first fusion neutron emitting pinch on New Year's Eve 2009 and the IR-MPF-100 plasma focus (115kJ) in Iran.
Fusion power

Several groups proposed that fusion power based on the DPF could be economically viable, possibly even with low-neutron fuel cycles like p-B11. The feasibility of net power from p-B11 in the DPF requires that the bremsstrahlung losses be reduced by quantum mechanical effects induced by an applied powerful magnetic field. The high magnetic field also results in a high rate of emission of cyclotron radiation, but at the densities envisioned, where the plasma frequency is larger than the cyclotron frequency, most of this power will be reabsorbed before being lost from the plasma. Another advantage claimed is the capability of direct conversion of the energy of the fusion products into electricity, with an efficiency potentially above 70%.

Experiments and computer simulations to investigate the capability of DPF for fusion power are underway at Lawrenceville Plasma Physics (LPP) under the direction of Eric Lerner, who explained his "Focus Fusion" approach in a 2007 Google Tech Talk.[25] On November 14, 2008, Lerner received funding for continued research, to test the scientific feasibility of Focus Fusion.[26] On October 15, 2009, the DPF device "Focus Fusion-1" achieved its first pinch.[27] On January 28, 2011, LPP published initial results including experimental shots with considerably higher fusion yields than the historical DPF trend.[28] In March, 2012, the company announced that it had achieved temperatures of 1.8 billion degrees, beating the old record of 1.1 billion that had survived since 1978.[29][30] In 2016 the company announced that it had achieved a fusion yield of .25 joules.[31]
See also

List of plasma physics articles


1958: Петров Д.П., Филиппов Н.В., Филиппова Т.И., Храбров В.А. "Мощный импульсный газовый разряд в камерах с проводящими стенками". В сб. Физика плазмы и проблемы управляемых термоядерных реакций. Изд. АН СССР, 1958, т. 4, с. 170-181.
1958: Hannes Alfvén: Proceedings of the Second International Conference on Peaceful Uses of Atomic Energy (United Nations), 31, 3
1960: H Alfven, L Lindberg and P Mitlid, "Experiments with plasma rings" (1961) Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Volume 1, Issue 3, pp. 116–120
1960: Lindberg, L., E. Witalis and C. T. Jacobsen, "Experiments with plasma rings" (1960) Nature 185:452.
1961: Hannes Alfvén: Plasma Ring Experiment in "On the Origin of Cosmic Magnetic Fields" (1961) Astrophysical Journal, vol. 133, p. 1049
1961: Lindberg, L. & Jacobsen, C., "On the Amplification of the Poloidal Magnetic Flux in a Plasma" (1961) Astrophysical Journal, vol. 133, p. 1043
1962: Filippov. N.V., et al., "Dense, High-Temperature Plasma in a Noncylindrical 2-pinch Compression" (1962) 'Nuclear Fusion Supplement'. Pt. 2, 577
1969: Buckwald, Robert Allen, "Dense Plasma Focus Formation by Disk Symmetry" (1969) Thesis, Ohio State University.


Petrov DP, NV Filippov, TI Filippova, VA Khrabrov "Powerful pulsed gas discharge in the cells with conducting walls." In the Sun. Plasma physics and controlled thermonuclear reactions. Ed. Academy of Sciences of the USSR, 1958, т. 4, с. 170-181.
Krishnan, Mahadevan (December 2012). "The Dense Plasma Focus: A Versatile Dense Pinch for Diverse Applications". IEEE Transactions on Plasma Science. 40 (12): 3189–3221. Bibcode:2012ITPS...40.3189K. doi:10.1109/TPS.2012.2222676.
Springham, S V; S Lee; M S Rafique (October 2000). "Correlated deuteron energy spectra and neutron yield for a 3 kJ plasma focus". Plasma Physics and Controlled Fusion. 42 (10): 1023–1032. Bibcode:2000PPCF...42.1023S. doi:10.1088/0741-3335/42/10/302. Retrieved 2009-01-08.
Bogolyubov, E P; et al. (1970). "A Powerful Soft X-ray Source for X-ray Lithography Based on Plasma Focusing". Physica Scripta. 57 (4): 488–494. Bibcode:1998PhyS...57..488B. doi:10.1088/0031-8949/57/4/003. Retrieved 2009-01-08.
Rawat, R. S.; P. Arun; A. G. Vedeshwar; P. Lee (15 June 2004). "Effect of energetic ion irradiation on CdI
2 films". Journal of Applied Physics. 95 (12): 7725. Bibcode:2004JAP....95.7725R. arXiv:cond-mat/0408092 Freely accessible. doi:10.1063/1.1738538. Retrieved 2009-01-08. Check date values in: |date= (help)
U.S. Department of Defense, Militarily Critical Technologies List, Part II: Weapons of Mass Destruction Technologies (February 1998) Section 5. Nuclear Weapons Technology (PDF), Table 5.6-2, p. II-5-66. Retrieved on 8 January 2009.
Lee, Sing; Serban, A. (June 1996). "Dimensions and lifetime of the plasma focus pinch". IEEE Transactions on Plasma Science. 24 (3): 1101–1105. Bibcode:1996ITPS...24.1101L. ISSN 0093-3813. doi:10.1109/27.533118. Retrieved 2009-01-08.
Soto, Leopoldo; C. Pavez; A. Tarifeño; J. Moreno; F. Veloso (20 September 2010). "Studies on scalability and scaling laws for the plasma focus: similarities and differences in devices from 1MJ to 0.1J". Plasma Sources Science and Technology. 19 (055001-055017): 055017. Bibcode:2010PSST...19e5017S. doi:10.1088/0963-0252/19/5/055017. Retrieved 24 August 2015.
Lee, S and Zakaullah, M et al. and Srivastava, M P and Gholap, A V et al. and Eissa, M A and Moo, S P et al. (1988) Twelve Years of UNU/ICTP PFF- A Review. IC, 98 (231). Abdus Salam ICTP, Miramare, Trieste. Retrieved on 8 January 2009.
Lee, Sing; Wong, Chiow San (2006). "Initiating and Strengthening Plasma Research in Developing Countries". Physics Today. 59 (5): 31–36. Bibcode:2006PhT....59e..31L. ISSN 0031-9228. doi:10.1063/1.2216959. Retrieved 2009-01-08.
Lee, Sing (August 2014). "Plasma Focus Radiative Model: Review of the Lee Model Code". Journal of Fusion Energy. 33 (4): 319–335. ISSN 0164-0313. doi:10.1007/s10894-014-9683-8. Retrieved 2016-05-24.
"Universal Plasma Focus Laboratory Facility at INTI-UC". INTI University College (INTI-UC) Malaysia. 24 November 2008. Archived from the original on 28 October 2008. Retrieved 2009-01-08.
"Institute for Plasma Focus Studies". 19 November 2008. Retrieved 2009-01-08.
[1] (PDF) Archived March 25, 2012, at the Wayback Machine.
Soto, Leopoldo (20 April 2005). "New Trends and Future Perspectives on Plasma Focus Research". Plasma Physics and Controlled Fusion. 47 (5A): A361–A381. Bibcode:2005PPCF...47A.361S. doi:10.1088/0741-3335/47/5A/027. Retrieved 24 August 2015.
Soto, Leopoldo; P. Silva; J. Moreno; M. Zambra; W. Kies; R. E. Mayer; L. Altamirano; C. Pavez; L. Huerta (1 October 2008). "Demonstration of neutron production in a table top pinch plasma focus device operated at only tens of joules". Journal of Physics D: Applied Physics. 41 (202001-205503): 205215. Bibcode:2008JPhD...41t5215S. doi:10.1088/0022-3727/41/20/205215. Retrieved 25 August 2015.
Pavez, Cristian; Leopoldo Soto (6 May 2010). "Demonstration of x-ray Emission from an ultraminiature pinch plasma focus discharge operating at 0.1 J. Nanofocus". EEE Transactions on Plasma Sciences. 38 (5): 1132–1135. Bibcode:2010ITPS...38.1132P. doi:10.1109/TPS.2010.2045110. Retrieved 25 August 2015.
Silva, Patricio.; José Moreno; Leopoldo Soto; Lipo Birstein; Roberto E. Mayer; Walter Kies; L. Altamirano (15 October 2003). "Neutron Emission from a Fast Plasma Focus of 400 Joules". Applied Physics Letters. 83 (16): 3269. Bibcode:2003ApPhL..83.3269S. doi:10.1063/1.1621460. Retrieved 25 August 2015.
Soto, Leopoldo; C. Pavez; F. Castillo; F. Veloso; J. Moreno; S. K. H. Auluck (1 July 2014). "Filamentary structures in dense plasma focus: current filaments or vortex filaments". Physics of Plasmas. 21 (7): 072702. Bibcode:2014PhPl...21g2702S. doi:10.1063/1.4886135. Retrieved 25 August 2015.
Casanova, Federico; Ariel Tarifeño-Saldivia; Felipe Veloso; Cristian Pavez; Alejandro Clausse; Leopoldo Soto (6 September 2011). "Toroidal high-density singularities in a small Plasma Focus". Journal of Fusion Energy. 31 (3): 279–283. Bibcode:2012JFuE...31..279C. doi:10.1007/s10894-011-9469-1. Retrieved 26 August 2015.
Soto, Leopoldo; C. Pavez; J. Moreno; M. J. Inestrosa-Izurieta; F. Veloso; G. Gutiérrez; J. Vergara; A. Clausse; H. Bruzzone; F. Castillo; L. F. Delgado-Aparicio (5 December 2014). "Characterization of the axial plasma shock in a table top plasma focus after the pinch and its possible application to testing materials for fusion reactors". Physics of Plasma. 21 (12): 122703. Bibcode:2014PhPl...21l2703S. doi:10.1063/1.4903471. Retrieved 26 August 2015.
Paves, Cristian; J. Pedreros; A. Tarifeño Saldivia; L. Soto (24 April 2015). "Observations of plasma jets in a table top plasma focus discharge". Physics of Plasma. 22 (4): 040705. Bibcode:2015PhPl...22d0705P. doi:10.1063/1.4919260. Retrieved 26 August 2015.
Clausse, Alejandro; Leopoldo Soto; Carlos Friedli; Luis Altamirano (26 December 2014). "Feasibility study of a hybrid subcritical fission system driven by Plasma-Focus fusion neutrons". Annals of Nuclear Energy. 22: 10–14. doi:10.1016/j.anucene.2014.12.028.
Inestrosa-Izurieta, Maria José; E. Ramos-Moore; L. Soto (5 August 2015). "Morphological and structural effects on tungsten targets produced by fusion plasma pulses from a table top plasma focus". Nuclear Fusion. 55 (093011). Bibcode:2015NucFu..55i3011I. doi:10.1088/0029-5515/55/9/093011. Retrieved 26 August 2015.
Lerner, Eric (3 October 2007). "Focus Fusion: The Fastest Route to Cheap, Clean Energy" (video). Google TechTalks. Google. Retrieved 2009-01-08.
"LPP Receives Major Investments, Initiates Experimental Project". Lawrenceville Plasma Physics, Inc. November 22, 2008. Retrieved 2009-01-08.
"Focus-Fusion-1 Works! First shots and first pinch achieved October 15, 2009.". Lawrenceville Plasma Physics, Inc. October 15, 2009. Retrieved 2009-10-18.
"Theory and Experimental Program for p-B11 Fusion with the Dense Plasma Focus". Journal of Fusion Energy. January 28, 2011. Retrieved 2011-02-01.
Lerner, Eric J.; S. Krupakar Murali; Derek Shannon; Aaron M. Blake; Fred Van Roessel (23 March 2012). "Fusion reactions from >150 keV ions in a dense plasma focus plasmoid". Physics of Plasmas. 19 (3): 032704. Bibcode:2012PhPl...19c2704L. doi:10.1063/1.3694746. Retrieved 8 December 2013.
Halper, Mark (March 28, 2012). "Fusion breakthrough". Smart PLanet. Retrieved 1 April 2012.
"Next Big Future: Despite rocky start and funding for only about 25 shots - LPP Fusion yield is up 50% to a record for any dense plasma focus device". Next Big Future. Retrieved 2016-06-05.

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