Paper on Physics no 2531100

7/23/2019 Paper on Physics no 2531100

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Plasma physics: Paschen curve

PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P2531100 1

Related Topics

Glow discharge, electron avalanches, free path length,Townsend breakdown theory, Paschen curve.

Principle

The electric breakthrough voltage in air is measured in depen-dence on electrode distance and gas pressure. The results arecompared to the Paschen curve which is a result of Townsendelectric breakdown theory. The Townsend electric breakdowntheory assumes the product p · d of electrode distance d andgas pressure p to be the similarity parameter describing theelectric breakdown behavior of a gas.

Equipment

Plasma Physics Operating Unit 09108.99 1Plasma Physics Experimental Set 09108.10 1Digital multimeter with peak-hold function 07128.00 1

Vacuum pump, rotary sliding vane, one stage 02750.93 1Oil mist filter 02752.00 1 Vacuum hose, di = 8 mm, 1 m 39288.00 2Fine control valve for pressure bottles 33499.00 1Moving coil instrument 11100.00 1 Vacuum range, Pirani gauge 11112.93 1Hose connector, T-piece, di = 8-9 mm 47519.03 1Connecting cord, safety, 32 A, 100 cm, red 07337.01 1Connecting cord, safety, 32 A, 100 cm, blue 07337.04 1

Task

Measure the voltage between plane parallel electrodes atwhich electric breakthrough occurs in dependence on elec-trode distance d at different gas pressures p in the hPa range.Create plots of the breakthrough voltage over electrode dis-tance d and over product of electrode distance and pressurep · d.

Set-up and procedure

– Set the equipment up as seen in Fig. 1.– Pay regard to the operating instructions of the vacuum

pump and the Plasma Physics Operating Unit.– Use only safety connecting cables to connect the digitalmultimeter to the Plasma Physics Experimental Set, selectthe 1000 V DC range of the multimeter.

– Close the fine control valve and turn on the vacuum pump.– Adjust the pressure p in the chamber to the desired value

by gently opening the fine control valve.– Set the operating mode switch on the Plasma Physics

Operating Unit to "cont." and the voltage adjustor to max-imal voltage.

– Vary the electrode distance d with the micrometer screw tofind out the minimal distance where the glow dischargecan ignite with the given maximal voltage.

– Lower the voltage setting again and adjust d to a value

larger than the minimum possible distance for this pres-sure.– Activate the peak hold function of the digital multimeter

and slowly increase the voltage until electrical breakdownoccurs and a glow discharge appears. This will increasethe current between the electrodes and decrease the elec-trode voltage at given voltage adjustor setting.

– Turn the voltage adjustor down again until glow dischargedisappears.

– Note down the multimeter reading as breakthrough volt-age Ubr.

– Repeat measurement five times for each electrode dis-tance, average the voltage values.

– Table 2 shows a possible measurement protocol.– Increase electrode distance d while keeping pressure p

constant, note down next breakthrough voltages.

Fig. 1: Fundamental set-up



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P2531100 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen2

– At relatively high pressures (above 5 hPa) the voltageincrease has to be slower than 1 V/s near the breakthroughvoltage in order to obtain correct values since it may take

some time until sufficient initial ionization appears statisti-cally to start the breakthrough.– Measure the dependence of breakthrough voltage U on

electrode distance d at 2.5 hPa, 4 hPa and 6 hPa.– Calculate the product of pressure and electrode distance

p · d.– Plot the breakthrough voltage Ubr for several given pres-

sure values over d and over p · d and compare the results.

Theory

Electrical breakthrough or breakdown in a gas is the transitionfrom a non-self-sustaining to a self-sustaining electrical dis-charge.If the discharge is to be self-sustaining, a charge carrier has to

produce in average at least one more charge carrier during itslifetime. Otherwise, only outer sources of electrical carrierscan supply for the discharge current.Outer sources of charge carriers may be ambient radioactivityionizing some gas molecules in the discharge gap or ultravio-let light irradiating the electrodes releasing some electronsfrom them by external photo effect. Radioactivity produces inany case at least some ubiquitous background ionization. So,if the conditions in the discharge gap are such, that the chargecarriers multiply themselves, the self sustaining discharge willfollow. The former neutral gas transforms to a partly ionizedgas, a plasma.

Charge transport

Charge carriers in a gas are free electrons and ions. Themobility of electrons is by far higher than the mobility of ionsbecause of their much smaller mass. So the electrons are thespecies that extract far more energy from the electrical fieldthan the ions. Their temperature, and therefore their meankinetic energy, rises to such a great extent that they can effectionizations while the ions' kinetic energy is not elevated much. Any particle in a gas is characterized by a random diffusionvelocity proportional to its mobility. If a force acts on it, a driftcomponent of velocity proportional to the acting force as wellas to the mobility is superimposed over the diffusion move-ment. The charge transport occurs due to this drift movementof the charged particles in the field between the electrodes.Electrons may get absorbed by the anode when they impingeon it and positive ions may recombine at the cathode captur-

ing an electron from it. Many other processes involving elec-trons and ions take place on metal surfaces, but theseprocesses are the ones that effect charge transport betweenthe electrodes and close the electric circuit. The electron driftvelocities are three orders of magnitude higher than the iondrift velocities.In the present experiment, the electrical breakdown which isdetected as a glow discharge is examined. The gas pressureand the ionization rate are low. The current is low enough asnot to heat the electrodes to such an extent, that thermionicemission occurs, and the electric fields are low enough so thatno field emission from the electrodes takes place. The elec-trodes are flat and plane parallel and their edges are isolatedin order to prevent corona discharges.

Charge carrier multiplication

The main two charge carrier multiplying processes are ioniza-tion by electron impact and secondary electron emission fromelectrodes by positively charged ions. The first process, colli-

sion electron ionization by electron impact, occurs if the ener-gy of the impinging electron on a neutral gas particle some-where in the gas phase exceeds the ionization energy of that

gas molecule releasing another electron and leaving a positiveion behind. The second process, secondary electron emissionby positive ion impact, occurs when the total energy (sum ofthe kinetic and ionization energy) of the positive ions formedat the anode approaching the cathode is greater than twicethe work function of the metal of the anode, thus resulting inrecombination of the positive ion and a release of one free(Auger) electron from the metal. The process of energy trans-fer to a nearby bound electron is referred to as Auger effect.

Townsend theory

In Townsend theory of electrical breakdown, mainly these twoprocesses are considered to describe the breakdown.The breakdown is modeled for plane parallel electrodes with a

gap of width d between them.The probability of collisional ionization per unit path length ofthe electrons along the electric field is called Townsend firstionization coefficient a. If a is greater than unity, an electronavalanche can develop with number of electrons in theavalanche

Ne = e ax

where x is the distance from the cathode.

Ni = e ax – 1

positive ions are left behind by this avalanche. These numbersare maximal for an avalanche starting at the cathode using thewhole gap width, so for x = d.The probability gamma of a positive ion to release one sec-ondary electron from the cathode is called Townsend’s sec-ondary ionization coefficient.The number of secondary electrons released after an electronavalanche started at the cathode with electrode spacing d isthen

Ne,sec = g ( e a d – 1),and if

g ( e a d – 1) = 1, (1)

then the ions resulting from a single electron avalanche pro-duce a single electron by secondary emission at the cathode

and the situation is exactly self sustaining. (1) is thereforecalled the Townsend breakdown criterion.If an electronegative gas is present, free electrons are attract-ed and attached to the gas molecules, thus forming negativeions. This loss of electrons can be introduced into this modelthrough a lowered g.Townsend theory of electrical breakdown also assumes thatthe first ionization coefficient divided by pressure, a / p, is afunction of the reduced electric field strength, E / p, with

, (2)

where A and B are gas-specific constants to be derived from

the measurement. It should be kept in mind that in contrast tothe coefficient a, g is also strongly dependent on electrodematerial and surface condition and not only on the propertiesof the gas.

a

p A expaB

p

Eb



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PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen P2531100 3

The assumption (2) is reasonable because the mean free pathis inversely proportional to the particle density or the pressureand the energy gained by an electron in an electric field is pro-

portional to the mean free path. Furthermore, the impact reac-tion setting free more electrons has an energy thresholdexpressed through the coefficient B now, compared to aver-age electron energy scaled to E / p and not to kB T as in theMaxwell-Boltzmann formula. The factor A has then the mean-ing of a sort of a reaction cross-section.(1) can be written as

and for the breakdown voltage Ubr and a given distance dbetween the electrodes, the electric field strength E is givenby E = Ubr / d, and thus

,

which can be written for the breakdown voltage as

(3)

For large values of the product pd, Ubr grows nearly linearlywith ist. For small values of the product pd, such that the log-arithm in the denominator approaches zero, Ubr growssharply, and for intermediate values, Ubr shows a minimum

Umin.This function Ubr( pd ) is called Paschen curve and the minimalbreakdown voltage Umin is called Paschen minimum.It is

with e = 2.71828… the base of natural logarithm.

The result (3) can be interpreted in the way that at small elec-trode distances there is not enough space for large electronmultiplication in the electron avalanches – e a d stays limited

and so no breakdown occurs. At large distances, the expo-nential decrease of a with decreasing field strength plays themain role and in order to keep the field strength constant, thevoltage has to increase linearly with the electrode distance d.Literature values of A and B are shown in Table 1. As the ion-ization energy of He is high, one might expect a high B valuefor He. But electrons do not suffer much energy losses due torotational and vibrational excitations when scattered on neu-tral gas particles of He, so the overall average necessary ener-gy gain per electron needed for one ionization is rather small.

Table 1: Parameters A and B for calculation of Townsendcoefficient a

EvaluationFig. 2 shows the measurement results plotted as a function ofthe electrode distance. If the pressure is low, the branch of thePaschen curve for the electron distance larger than the dis-tance corresponding to the Paschen minimum does notappear. Only if the pressure is relatively high the breakthroughvoltage does rise with increasing electrode distance.

Umin e B

A lna 1

g1b , aE

p b

min

B, 1pd 2 min e 1

A ln a 1

g1b

Ubr

B p d

lnA p d

ln a 1

g 1b

.

d exp1B p d > Ubr 2 pA ln a 1

g 1b

e a d

1

g 1

Gas A / (Pa · m )–1 B / V (Pa · m )–1

Air 20 487

CO2 27 621

H2 7 173

N2 13 413

He 4 45

Ar 16 240

Fig. 2: Breakdown voltage in dependence on electrode distance for different values of the gas pressure



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P2531100 PHYWE series of publications • Laboratory Experiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen4

As seen in Fig. 3, the breakthrough voltages all lie on the samecurve if plotted over p · d. This confirms the validity of theTownsend’s theory for the examined range of conditions.

The calculated Paschen curve of Fig. 4 shows similar charac-teristics. However deviations are present. They may be due tohumidity so the values of Table 1 may not apply.

Fig. 4: The Paschen curve as calculated forA = 20 (Pa · m) –1,B = 487 (Pa · m) –1 and g = 0.0072.

Fig. 3: Breakdown voltage in dependence on product of elec-trode distance and gas pressure

Electrode Pressure p · d / Pa m Breakthrough Breakthrough Breakthrough Breakthrough Breakthrough Average

distance p / hPa voltage voltage voltage voltage voltage breakthrough

d / mm U / V U / V U / V U / V U / V voltage / V

0.20

0.22

0.25

0.28

0.32

0.36

0.40

0.45

0.50

0.56

0.63

0.71

0.80

0.89

1.00

1.10

1.25

1.40

1.60

1.80

2.00

2.20

2.50

2.80

3.20

3.60

4.00

4.50

5.00

Table 2: An example of a measuring protocol

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Paper on Physics no 2531100