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Ada)Staticinceptionstage
Theinceptionstageismainlyanalyzedwithrespecttotherequiredstaticinceptionelec-
tricfieldstrength;i.e.,otherconditionssuchastheavailabilityofthestartingelectron/
timelag,residualchargesandmemoryeffects,dielectricsurfacecondition,orspace
chargearenotconsidered[PAN20,BART08,FLOR16,FLORM18].Themainnovelty
introducedinthisaspectisrelatedtotheinfluenceofthevoidlayerresistivityonthe
inceptionconditions.Usually,thevoid(gaseous)resistivityistakenintothecalculations
oftheresistivepotentialdistribution;however,itshouldbenoticedthattheveryhigh
resistivityofagaseouscavityisusuallybypassedbytheadjacentsoliddielectriclayer
(itsresistanceisgraphicallyillustratedinFigure3.9a).ThestaticvoltagedropUc0on
thecavityresultsfromtherelationshipbetweenresistanceRArepresentingthevolume
resistanceadjacenttothevoid(assumingRa2,R′
a2<<Rc)andresultantresistanceR0
beingacombinationofcomponentsRa1,R′a1,Ra3,R′a3,Rb,andR′b.
U
c
0
=
U
DC
R
0
R
+
A
R
A
Adb)Chargingstage
(3.15)
Immediatelyafterthedischargeevent,thevoltage-recoveryprocessbegins,leadingto
thechargingofthevoidcapacitancewithatimeconstantresultingfromtheresidual
levelaccordingtoresistancedivision.ThenextPDwilloccurwhentheinceptionvoltage
levelwillbereached.Inthisprocess,bothvolumedielectricresistivityandvoidwall
surfaceresistivityareinvolved.Thevoltagewaveformacrossthevoidrepresentedby
capacitanceCcisdescribedasfollows:
U
c
=
U
c
0
−
(
U
c
0
−
U
ext
)
⎛
⎜
⎜
⎜
⎝
e
−
τ
DC
t
⎞
⎟
⎟
⎟
⎠
where:
τDC–voltagerecoverytimeconstant,
Uext–PDextinctionvoltage.
(3.16)
WhilecrossingthethresholdlevelofthePDIV(Uinc),theconsecutivedischargeis
triggered.ThetheoreticaltimetpelapsingbetweenconsecutivePDpulsesisequaltothe
following[DENS79]:
t
p
=−τ
DC
⋅
ln
⎛
⎜
⎝
U
U
c
c
0
0
−
−
U
U
inc
ext
⎞
⎟
⎠
whereUinc–PDinceptionvoltage.
(3.17)
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