Editing Marx generator

{{short description|High-voltage pulse generator}}
{{distinguish|Tesla coil}}
[[File:Marxgeneratorfz.JPG|thumb|A small demonstration Marx generator ''(tower on the right)''. It is a ten stage generator. The main discharge is on the left. The nine smaller sparks that can be seen in the image are the spark gaps that connect the charged capacitors in series.]]

A '''Marx generator''' is an [[electrical circuit]] first described by [[Erwin Otto Marx]] in 1924.<ref>{{cite journal |last1=Marx |first1=Erwin |author-link=Erwin Otto Marx |title=Versuche über die Prüfung von Isolatoren mit Spanningsstößen |language=de |trans-title=Experiments on the Testing of Insulators using High Voltage Pulses |journal=Elektrotechnische Zeitschrift |issn=0424-0200 <!-- also 0948-7387 --> |oclc=5797229 |date=1924 |volume=25 |pages=652–654}}. This reference is suspect: the year 1924 and volume 25 do not match; the year 1924 corresponds to volume 45; volume 25 would be too early for Marx. Volker Weiss says 1925 and volume 45 which would also be wrong. Electrical World https://books.google.com/books?id=o3FEAQAAIAAJ&hl=en suggests Marx' Flashover testing article was June 11, 1925.</ref> Its purpose is to generate a high-[[voltage]] pulse from a low-voltage DC supply. Marx generators are used in high-energy physics experiments, as well as to simulate the effects of lightning on [[Electric power transmission|power-line gear]] and aviation equipment. A bank of 36 Marx generators is used by [[Sandia National Laboratories]] to generate [[X-rays]] in their [[Z Pulsed Power Facility|Z Machine]].

==Principle of operation==
[[File:Marx Generator.svg|thumb|259x259px|Marx generator diagrams; Although the left capacitor has the greatest charge rate, the generator is typically allowed to charge for a long period of time, and all capacitors eventually reach the same charge voltage.]]The circuit generates a high-voltage pulse by charging a number of [[capacitor]]s in parallel, then suddenly connecting them in series. See the circuit diagram on the right. At first, ''n'' capacitors (''C'') are charged in parallel to a voltage ''V<sub>C</sub>'' by a DC power supply through the resistors (''R''<sub>C</sub>). The [[spark gap]]s used as switches have the voltage ''V<sub>C</sub>'' across them, but the gaps have a breakdown voltage greater than ''V<sub>C</sub>'', so they all behave as open circuits while the capacitors charge. The last gap isolates the output of the generator from the load; without that gap, the load would prevent the capacitors from charging. To create the output pulse, the first spark gap is caused to break down (triggered); the breakdown effectively shorts the gap, placing the first two capacitors in series, applying a voltage of about 2''V<sub>C</sub>'' across the second spark gap.<ref>Typical explanation; see, for example, http://www.kronjaeger.com/hv/hv/src/marx/index.html; the issue is more complicated.<!-- body cap --> Another site uses charging inductors instead of resistors: http://hibp.ecse.rpi.edu/~leij/febetron/marx.html.</ref> Consequently, the second gap breaks down to add the third capacitor to the "stack", and the process continues to sequentially break down all of the gaps. This process of the spark gaps connecting the capacitors in series to create the high voltage is called ''erection''. The last gap connects the output of the series "stack" of capacitors to the load. Ideally, the output voltage will be ''nV<sub>C</sub>'', the number of capacitors times the charging voltage, but in practice the value is less. Note that none of the charging resistors ''R''<sub>c</sub> are subjected to more than the charging voltage even when the capacitors have been erected. The charge available is limited to the charge on the capacitors, so the output is a brief pulse as the capacitors discharge through the load. At some point, the spark gaps stop conducting, and the low-voltage supply begins charging the capacitors again.

The principle of multiplying voltage by charging capacitors in parallel and discharging them in series is also used in the [[voltage multiplier]] circuit, used to produce high voltages for [[laser printer]]s and [[cathode-ray tube]] [[television set]]s, which has similarities to this circuit. One difference is that the voltage multiplier is powered with alternating current and produces a steady DC output voltage, whereas the Marx generator produces a pulse.

{{multiple image
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| image1   = High-Voltage Impulse Test System.jpg
| caption1 = Marx generator used for testing high-voltage power-transmission components at TU Dresden, Germany
| width1   = 157
| image2   = Marx generator Leipzig trade fair 1954.png
| caption2 = Marx generator at a utility trade fair, Leipzig, East Germany, 1954
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| image3   = Zap!.jpg
| caption3 = 600 kV  10-stage Marx generator in operation
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| image4   = 800 kV Marx Generator.jpg
| caption4 = 800 kV Marx generator in laboratory at the National Institute of Technology, Durgapur India.
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==Optimization==
[[Image:coaxial Marx generator.png|thumb|upright=1.25|To deliver 5 ns rise time pulses, the Marx generator is often built into a [[coaxial]] [[wave guide]]. The [[spark gap]]s are placed as close as possible together for maximum UV light exchange for minimum jitter. DC HV comes from underneath, pulsed HV leaves at the top into the coaxial line. The double line of spheres in the middle are the spark gaps, all other spheres are to avoid [[corona discharge]]. Blue=[[water capacitor]]. Grey=solid metal. Black= thin wire. The outer conductor also functions as a vessel, so that the gas and the pressure can be optimized.]]

Proper performance depends upon [[capacitor]] selection and the timing of the discharge. Switching times can be improved by doping of the [[electrode]]s with [[radioactive]] [[isotopes]] [[caesium]] 137 or [[nickel]] 63, and by orienting the spark gaps so that [[ultraviolet]] light from a firing spark gap switch illuminates the remaining open spark gaps.<ref>E. Kuffel, W. S. Zaengl, J. Kuffel ''High voltage engineering: fundamentals'', Newnes, 2000 {{ISBN|0-7506-3634-3}}, pages 63, 70</ref> Insulation of the high voltages produced is often accomplished by immersing the Marx generator in [[transformer oil]] or a high pressure [[dielectric gas]] such as [[SF6|sulfur hexafluoride]] (SF<sub>6</sub>).

Note that the less resistance there is between the capacitor and the charging power supply, the faster it will charge. Thus, in this design, those closer to the power supply will charge quicker than those farther away. If the generator is allowed to charge long enough, all capacitors will attain the same voltage.

In the ideal case, the closing of the switch closest to the charging power supply applies a voltage 2''V'' to the second switch. This switch will then close, applying a voltage 3''V'' to the third switch. This switch will then close, resulting in a cascade down the generator that produces ''nV'' at the generator output (again, only in the ideal case).

The first switch may be allowed to spontaneously break down (sometimes called a ''self break'') during charging if the absolute timing of the output pulse is unimportant. However, it is usually intentionally triggered once all the capacitors in the Marx bank have reached full charge, either by reducing the gap distance, by pulsing an additional trigger electrode (such as a [[Trigatron]]), by ionising the air in the gap using a pulsed [[laser]], or by reducing the air pressure within the gap.

The charging resistors, Rc, need to be properly sized for both charging and discharging. They are sometimes replaced with [[inductor]]s for improved efficiency and faster charging. In many generators the resistors are made from plastic or glass tubing filled with dilute [[copper sulfate]] solution. These [[liquid resistor]]s overcome many of the problems experienced by more-conventional solid resistive materials, which have a tendency to lower their resistance over time under high voltage conditions.

== Short pulses ==
The Marx generator is also used to generate short high-power pulses for [[Pockels cell]]s, driving a [[TEA laser]], ignition of the conventional explosive of a nuclear weapon, and radar pulses.
[[File:Marxi generaator AHHAAs.jpg|thumb|Marx generator. Air is a poor conductor of electricity, but with sufficient voltage (30 kV/cm), air transforms into a conductor, resulting in a spark discharge.]]
Shortness is relative, as the switching time of even high-speed versions is not less than 1 ns, and thus many low-power electronic devices are faster. In the design of high-speed circuits, electrodynamics is important, and the Marx generator supports this insofar as it uses short thick leads between its components, but the design is nevertheless essentially an electrostatic one. When the first gap breaks down, pure electrostatic theory predicts that the voltage across all stages rises. However, stages are coupled capacitively to ground and serially to each other, and thus each stage encounters a voltage rise that is increasingly weaker the further the stage is from the switching one; the adjacent stage to the switching one therefore encounters the largest voltage rise, and thus switches in turn. As more stages switch, the voltage rise to the remainder increases, which speeds up their operation. Thus a voltage rise fed into the first stage becomes amplified and steepened at the same time.

In electrodynamic terms, when the first stage breaks down it creates a spherical electromagnetic wave whose electric field vector is opposed to the static high voltage. This moving electromagnetic field has the wrong orientation to trigger the next stage, and may even reach the load; such noise in front of the edge is undesirable in many switching applications. If the generator is inside a tube of (say) 1 m diameter, it requires around 10 wave reflections for the field to settle to static conditions, which restricts pulse leading edge width to 30 ns or more. Smaller devices are of course faster.

The speed of a switch is determined by the speed of the charge carriers, which gets higher with higher voltage, and by the current available to charge the inevitable parasitic capacitance. In solid-state avalanche devices, a high voltage automatically leads to high current. Because the high voltage is applied only for a short time, solid-state switches will not heat up excessively. As compensation for the higher voltages encountered, the later stages have to carry lower charge too. Stage cooling and capacitor recharging also go well together.

==Stage variants==
[[Avalanche diode]]s can replace a spark gap for stage voltages less than 500 volts. The charge carriers easily leave the electrodes, so no extra ionisation is needed and jitter is low. The diodes also have a longer lifetime than spark gaps.{{citation needed|date=November 2008}}

A speedy switching device is an NPN [[avalanche transistor]] fitted with a coil between base and emitter. The transistor is initially switched off and about 300 volts exists across its collector-base junction. This voltage is high enough that a charge carrier in this region can create more carriers by impact ionisation, but the probability is too low to form a proper avalanche; instead a somewhat noisy leakage current flows. When the preceding stage switches, the emitter-base junction is pushed into forward bias and the collector-base junction enters full avalanche mode, so charge carriers injected into the collector-base region multiply in a chain reaction. Once the Marx generator has completely fired, voltages everywhere drop, each switch avalanche stops, its matched coil puts its base-emitter junction into reverse bias, and the low static field allows remaining charge carriers to drain out of its collector-base junction.

== Applications ==
One application is so-called [[boxcar function|boxcar]] switching of a [[Pockels cell]]. Four Marx generators are used, each of the two electrodes of the Pockels cell being connected to a positive pulse generator and a negative pulse generator. Two generators of opposite polarity, one on each electrode, are first fired to charge the Pockels cell into one polarity. This will also partly charge the other two generators but not trigger them, because they have been only partly charged beforehand. Leakage through the Marx resistors needs to be compensated by a small bias current through the generator. At the trailing edge of the boxcar, the two other generators are fired to "reverse" the cell.

Marx generators are used to provide high-voltage pulses for the testing of insulation of electrical apparatus such as large power [[transformer]]s, or insulators used for supporting power transmission lines. Voltages applied may exceed two million volts for high-voltage apparatus.

In the food industry, Marx generators are used for [[Food preservation#Pulsed electric field electroporation|pulsed electric field]] processing to induce cutting improvement or drying acceleration for potato and other fruits and vegetables.<ref>{{Cite journal|last1=Fauster|first1=T.|last2=Schlossnikl|first2=D.|last3=Rath|first3=F.|last4=Ostermeier|first4=R.|last5=Teufel|first5=F.|last6=Toepfl|first6=S.|last7=Jaeger|first7=H.|date=October 2018|title=Impact of pulsed electric field (PEF) pretreatment on process performance of industrial French fries production|url=https://linkinghub.elsevier.com/retrieve/pii/S0260877418301845|journal=Journal of Food Engineering|language=en|volume=235|pages=16–22|doi=10.1016/j.jfoodeng.2018.04.023|s2cid=103082055 |url-access=subscription}}</ref>

== See also ==
* [[ATLAS-I]]
* [[Cockcroft–Walton generator]] – a similar circuit with the same "ladder" structure; CW generator produce rectified DC from an AC input
* [[Vector inversion generator]] – a transmission-line device using a similar charge in parallel discharge in series approach
* [[Explosively pumped flux compression generator]] – a solution to the [[duality (electrical circuits)|dual problem]] of creating high current pulses
* [[Ignition coil]]
* [[Induction coil]]
* [[Istra High Voltage Research Center]]
* [[Tesla coil]]

==References==
{{reflist}}

==Further reading==
* Bauer, G. (June 1, 1968) "A low-impedance high-voltage nanosecond pulser", ''Journal of Scientific Instruments'', London, UK. vol. 1, pp.&nbsp;688–689.
* Graham et al. (1997) "Compact 400 kV Marx Generator With Common Switch Housing", ''Pulsed Power Conference, 11th Annual Digest of Technical Papers'', vol. 2, pp.&nbsp;1519–1523.
* Ness, R. et al. (1991) "Compact, Megavolt, Rep-Rated Marx Generators", ''IEEE Transactions on Electron Devices'', vol. 38, No. 4, pp.&nbsp;803–809.
* Obara, M. (June 3–5, 1980) "Strip-Line Multichannel-Surface-Spark-Gap-Type Marx Generator for Fast Discharge Lasers", ''IEEE Conference Record of the 1980 Fourteenth Pulse Power Modulator Symposium'', pp.&nbsp;201–208.
* Shkaruba et al. (May–June 1985) "Arkad'ev-Mark Generator with Capacitive Coupling", ''Instrum Exp Tech'' vol. 28, No. 3, part 2, pp.&nbsp;625–628, XP002080293.
* Sumerville, I. C. (June 11–24, 1989) "A Simple Compact 1 MV, 4 kJ Marx", ''Proceedings of the Pulsed Power Conference, Monterey, California'' conf. 7, pp.&nbsp;744–746, XP000138799.
* Turnbull, S. M. (1998) "Development of a High Voltage, High PRF PFN Marx Generator", ''Conference Record of the 1998 23rd International Power Modulation Symposium'', pp.&nbsp;213–16.

==External links==
* "''[http://hibp.ecse.rpi.edu/~leij/febetron/marx.html Marx Generator]''". ecse.rpi.edu. (''ed''. explains the Febetron 2020 pulser experimented within the [[Rensselaer Polytechnic Institute|RPI]] Plasma Dynamics Laboratory)
* Jochen Kronjaeger, "''"[http://www.kronjaeger.com/hv/hv/src/marx/index.html Marx generator]''". Jochen's High Voltage Page, 2003.
* Jim Lux, "[http://home.earthlink.net/~jimlux/hv/marx.htm Marx Generators] {{Webarchive|url=https://web.archive.org/web/20141129032942/http://home.earthlink.net/~jimlux/hv/marx.htm |date=2014-11-29 }}", High Voltage Experimenter's Handbook, 3 May 1998.
* "''[http://www.electricstuff.co.uk/marxgen.htm The 'Quick & Dirty' Marx generator]''". Mike's Electric Stuff, May 2003.

[[Category:Electrical circuits]]
[[Category:Electric power conversion]]
[[Category:Pulsed power]]
[[Category:Electronic test equipment]]
[[Category:Laboratory equipment]]