# Townsend discharge

The

**Townsend discharge**is a gasionization process where an initially very small amount of freeelectron s, accelerated by a sufficiently strongelectric field , give rise to electrical conduction through a gas by avalanche multiplication: when the number of free charges drops or theelectric field weakens, the phenomena ceases. It is a process characterized by very low current densities: in commongas filled tube s, typical magnitude of currents flowing during this process range from about $10^\{-18\}$A to about $10^\{-5\}$A, while applied voltages are "almost constant". Subsequent transition to ionisation processes ofdark discharge ,glow discharge , and finally to arc discharge are driven by increasing current densities: in all these discharge regimes, the basic mechanism of conduction isavalanche breakdown . Townsend discharge is named afterJohn Sealy Townsend .**Quantitative description of the phenomenon**The basic setup of the experiments investigating

ionization discharges in gases consist of a planar parallel platecapacitor filled with agas and acontinuous current high voltage source connected between its terminals: the terminal at the lower voltage potential is namedcathode while the other is namedanode . Forcing the cathode to emit electrons (eg. by irradiating it with aX-ray source), Townsend found that the current $I$ flowing into the capacitor depends on theelectric field between the plates in such a way that gasions seems to multilply as they moved between them. He observed currents varying over ten or more orders of magnitude while the applied voltage was virtually constant: the experimental data obtained from his (and his school's) first experiments are described by the following formula:$frac\{I\}\{I\_0\}=e^\{alpha\_n\; d\},$

where

*$I,$ is the current flowing in the device,

*$I\_0,$ is thephotoelectric current generated at thecathode surface ,

*$e,$ is the

*$alpha\_n,$ is the "first Townsend ionisation coefficient", expressing the number ofion pairs generated per unit length (e.g.meter ) by a negative ion (anion ) moving fromcathode toanode ,

*$d,$ is thedistance between the plates of the device.The almost constant voltage between the plates is equal to thebreakdown voltage needed to create a self-sustaining avalanche: it "decreases" when the current reaches theglow discharge regime. Subsequent experiments revealed that the current $I$ rises faster than predicted by the above formula as the distance $d$ increases: two different effects were considered in order to explain the physics of the phenomenon and to be able to do a precise quantitative calculation.**Gas ionisation caused by motion of positive ions**Townsend put forward the natural hypothesis that "also positive ions produce ion pairs", introducing a coefficient $alpha\_p$ expressing the number of

ion pairs generated per unit length by a positive ion (cation ) moving fromcathode toanode . The following formula was found:$frac\{I\}\{I\_0\}=frac\{(alpha\_n-alpha\_p)e^\{(alpha\_n-alpha\_p)d\{alpha\_n-alpha\_p\; e^\{(alpha\_n-alpha\_p)d\; qquadLongrightarrowqquad\; frac\{I\}\{I\_0\}congfrac\{e^\{alpha\_n\; d\{1\; -\; \{alpha\_p/alpha\_n\}\; e^\{alpha\_n\; d$

since $etamath>,\; in\; very\; good\; agreement\; with\; experiments.$

**Cathode emission caused by impact of ions**Townsend and Holst and Oosterhuis also put forward an alternative hypothesis, considering augmented emission of electrons by

cathode caused by positiveions impact, introducing "Townsends second ionization coefficient" $epsilon\_i$, the average number of electrons released from asurface by an incident positive ion, and working out the following formula::$frac\{I\}\{I\_0\}=frac\{e^\{alpha\_n\; d\{1\; -\; \{epsilon\_i\}left(e^\{alpha\_n\; d\}-1\; ight)\}.$

These two formulas may be thought as describing limiting cases of the effective behavior of the process: note that they can be used to well describe the same experimental results. Other formulas describing, various intermediate behaviors, are found in the literature, particularly in reference 1 and citations therein.

**Applications***Avalanche multiplication during Townsend discharge is naturally used in gas phototubes, to amplify the

photoelectric charge generated by incident radiation (visible light or not) on thecathode : achievable current is typically 10~20 times greater respect to that generated by vacuum phototubes.

*The starting of Townsend discharge sets the upper limit to the blocking voltage aglow discharge gas filled tube can withstand : this limit is the Townsend dischargebreakdown voltage also called**ignition voltage**of the tube.*The presence of Townsend discharge and

glow discharge breakdownvoltage s shapes the $V\_A-I\_A$ characteristic of anygas diode orneon lamp in a way such that it has anegative differential resistance region of the S-type. This occurrence is typically used to generate electricaloscillation s andwaveform s, as in therelaxation oscillator whose schematic is shown in the picture on the right. The sawtooth shaped oscillation generated has frequency:$fcongfrac\{1\}\{R\_1C\_1lnfrac\{V\_1-V\_\{GLOW\{V\_1-V\_\{TWN\},$

:where :*$V\_\{GLOW\}$ is the

glow discharge breakdown voltage ,:*$V\_\{TWN\}$ is the Townsend dischargebreakdown voltage ,:*$C\_1$, $R\_1$ and $V\_1$ are respectively thecapacitance , the resistance and the supplyvoltage of the circuit.:Sincetemperature andtime stability of the characteristics ofgas diode s andneon lamp s is low, and also thestatistical dispersion of breakdown voltages is high, the above formula can only give a qualitative indication of what the real frequency of oscillation is.**See also***

Electric arc

*Avalanche breakdown

*Dark discharge

*Photoelectric effect **References***cite book

author = S. Flügge (edited by)

title = Handbuch der Physik/Encyclopedia of Physics band/volume XXI - Electron-emission • Gas discharges I

publisher = Springer-Verlag

year = 1956 First chapter of the article "Secondary effects" by P.F. Little.

*cite book

author = James W Gewartowski and Hugh Alexander Watson

title = Principles of Electron Tubes: Including Grid-controlled Tubes, Microwave Tubes and Gas Tubes

publisher = D. Van Nostrand Co, Inc.

year = 1965

*cite book

author = Herbert J. Reich

title = Theory and applications of electron tubes

publisher = McGraw-Hill Co, Inc.

year = 1939,1944 Chapter 11 "Electrical conduction in gases" and chapter 12 "Glow- and Arc-dischrage tubes and circuits".

*cite book

author = E.Kuffel, W.S. Zaengl, J.Kuffel

title = High Voltage Engineering Fundamentals, Second edition

publisher = Butterworth-Heinemann

isbn = 0-7506-3634-3

year = 2004

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