High-voltage Pulsed Power Engineering, Fall 2018Electrical Breakdown in GasesFall, 2018Kyoung-Jae ChungDepartment of Nuclear EngineeringSeoul National University

Gas breakdown: Paschen’s curves for breakdown voltagesin various gases Friedrich Paschen discovered empirically in 1889.Left branchRight branchPaschen minimumF. Paschen, Wied. Ann. 37, 69 (1889)]2/40High-voltage Pulsed Power Engineering, Fall 2018

Generation of charged particles: electron impact ionization ProtonElectron Electric fieldAccelerationSlow electronFast electronElectric fieldAccelerationElectric fieldAccelerationIonization energy of hydrogen: 13.6 eV3/40High-voltage Pulsed Power Engineering, Fall 2018

Behavior of an electron before ionization collision Electrons moving in a gas under the action of an electric field are bound to makenumerous collisions with the gas molecules.4/40High-voltage Pulsed Power Engineering, Fall 2018

Electron impact ionization Electron impact ionization𝑒𝑒 𝐴𝐴 2𝑒𝑒 𝐴𝐴 Electrons with sufficient energy ( 10 eV) can remove an electron from anatom and produce one extra electron and an ion.5/40High-voltage Pulsed Power Engineering, Fall 2018

Townsend mechanism: electron avalanche𝑉𝑉𝐸𝐸 𝑑𝑑 Townsend ionization coefficient (𝛼𝛼) : electron multiplication: production of electrons per unit length along the electric field(ionization event per unit length)6/40𝑑𝑑𝑛𝑛𝑒𝑒 ‘’𝑒 𝑛𝑛𝑒𝑒𝑒 exp(𝛼𝛼π‘₯π‘₯)High-voltage Pulsed Power Engineering, Fall 2018𝑛𝑛𝑒𝑒𝑀𝑀 𝑒𝑒 𝛼𝛼π‘₯π‘₯𝑛𝑛𝑒𝑒𝑒

Townsend 1st ionization coefficient When an electron travels a distance equal to its free path πœ†πœ†π‘’π‘’ in the direction ofthe field 𝐸𝐸, it gains an energy of π‘’π‘’π‘’π‘’πœ†πœ†π‘’π‘’ . For the electron to ionize, its gain inenergy should be at least equal to the ionization potential 𝑉𝑉𝑖𝑖 of the gas:11πœ†πœ†π‘’π‘’ π‘’π‘’πœ†πœ†π‘’π‘’ 𝐸𝐸 π‘’π‘’π‘‰π‘‰π‘–π‘–π‘›π‘›πœŽπœŽ 𝑝𝑝 The Townsend 1st ionization coefficient is equalto the number of free paths ( 1/πœ†πœ†π‘’π‘’ ) times theprobability of a free path being more than theionizing length πœ†πœ†π‘–π‘–π‘–π‘– Ό exp exp œ†πœ†π‘’𝑒 𝐸𝐸𝜢𝜢 𝒑𝒑 π‘¨π‘¨πžπžπžπžπžπž 𝑩𝑩𝑬𝑬 𝒑𝒑 A and B must be experimentally determined fordifferent gases.7/40High-voltage Pulsed Power Engineering, Fall 2018

Townsend’s avalanche process is not self-sustainingIonization-free region (recombinationregion saturation region)Townsend firstionization regionTownsend secondionization region𝑖𝑖(𝑑𝑑) 𝑖𝑖0 𝑒𝑒 𝛼𝛼𝑑𝑑 Townsend’s avalanche process cannot be sustained without external sources forgenerating seed electrons.8/40High-voltage Pulsed Power Engineering, Fall 2018

Townsend’s criterion for breakdown Secondary electron emission by ion impact: when heavy positive ions strike thecathode wall, secondary electrons are released from the cathode material. The self-sustaining condition is given by𝑒𝑒 𝛼𝛼𝑑𝑑 𝑀𝑀 1 𝛾𝛾(𝑒𝑒 𝛼𝛼𝑑𝑑 1) Paschen’s law𝜢𝜢 𝒑𝒑 π‘¨π‘¨πžπžπžπžπžπž 1𝛼𝛼𝑑𝑑 ln 1 𝛾𝛾𝑩𝑩𝑬𝑬 𝒑𝒑Townsend 2nd ionization coefficientπœΆπœΆπ’…π’… π₯π₯π₯π₯ 𝟏𝟏 ŸπŸπœΆπœΆπ’…𝒅 π‘¨π‘¨π‘¨π‘¨π‘¨π‘¨πžπžπžπžπžπž π‘¨π‘¨π’‘π’‘π’…π’…πžπžπžπžπžπž π₯π₯π₯π₯ 𝟏𝟏 πœΈπœΈπ‘¬π‘¬ ’…𝑽𝑽𝑩𝑩 π₯π₯π₯π₯ 𝑨𝑨𝒑𝒑𝒅𝒅 π₯π₯π₯π₯ 𝟏𝟏 𝟏𝟏 𝜸𝜸 𝒇𝒇(𝒑𝒑𝒑𝒑)High-voltage Pulsed Power Engineering, Fall 2018

Paschen curve Minimum breakdown /40e𝐡𝐡1 ln 1 π‘šπ‘še1 ln 1 𝛾𝛾𝐴𝐴 Main factors: Pressure Voltage Electrode distance Gas species Electrode material (SEE) Small pd : too small collisionLarge pd : too often collisionHigh-voltage Pulsed Power Engineering, Fall 2018

Summary of Townsend gas breakdown theoryABreakdown&Glow Plasma---NVoltageΞ±-process :Dependent on gas speciesElectron avalanche by electronmultiplication-N- - -N- -pN-N -dN-- Ξ³-process :Dependent mainly on cathodematerial and also gas speciesSupplying seed electron for Ξ±process-NΞ³ - Two processes (𝛼𝛼 and 𝛾𝛾) are required to sustain the discharge.UVx How about electronegative gases (e.g. SF6) which are widely used for gasinsulation?11/40High-voltage Pulsed Power Engineering, Fall 2018K

Typical characteristic curve for gas discharges: selfsustaining or ingBreakdownRadiation detection12/40Plasma generationHigh-voltage Pulsed Power Engineering, Fall 2018

Limitation of Townsend theoryThe Townsend quasi-homogeneous breakdown mechanism can be applied only forrelatively low pressures and short gaps (pd 200 Torr Β· cm).1. The spark breakdown at high pd and considerable overvoltage develops muchfaster than the time necessary for ions to cross the gap and provide thesecondary emission. 𝛾𝛾 process fails.2. The spark channel is observed to have a zig-zag shape at high pd regime.3. The discharge at high pd is independent of electrode material.13/40High-voltage Pulsed Power Engineering, Fall 2018

Pulsed breakdown Static characteristics : slowly-varying voltage Townsend mechanism Dynamic characteristics : fast rising pulse Overvoltage breakdown & discharge time lag t0 : the time until the static breakdownvoltage is exceeded ts : the statistical delay time until anelectron able to create an avalancheoccurs ta (tf) : the avalanche build-up time untilthe critical charge density is reached(formative time) tarc : the time required to establish alow-resistance arc across the gapBreakdown delay time statistical delay time formative time14/40High-voltage Pulsed Power Engineering, Fall 2018

Statistical delay time The statistical delay time results from the statistics of electron appearance in thegap. The sources of electrons that initiate the self-breakdown of a gap Natural radioactivity and cosmic radiation They produce 0.1 10 free electrons per cm3 per second in a gas atatmospheric pressure Field emission by tunneling Fowler-Nordheim eq.𝐸𝐸 2π‘Šπ‘Š 3/2𝐽𝐽 𝐢𝐢exp π·π·π‘Šπ‘ŠπΈπΈ Electron detachment from molecules Total number of electrons appearing in the gap𝑡𝑡̇ 𝒕𝒕 𝑡𝑡̇ 𝟎𝟎𝟎𝟎 𝑡𝑡̇ 𝑭𝑭 (𝒕𝒕) 𝑡𝑡̇ 𝜹𝜹 (𝒕𝒕)Natural occurrence15/40Field emissionElectron detachmentHigh-voltage Pulsed Power Engineering, Fall 2018

Formative time measurements The statistical delay time can be neglected if the gap is intensely irradiated withthe light of an auxiliary spark. Then the measured delay time will be equal to theformative time. In an early experiment with 30% overvoltage for air gap, Rogowski found that theformative time was 10-8 sec, order of the drift time of the electrons in the gap. Many experiments confirmed that the formative time depends on the overvoltageand the intensity of irradiation. Need for new theory Streamer mechanism16/40High-voltage Pulsed Power Engineering, Fall 2018

Streamer mechanism The streamer concept was proposed by Loeb and Meek for the positive streamerand, independently by Raether for the negative streamer. Basic idea is that at a certain stage in the development of a single avalanche,photoionization of the gas in the inter-electrode space becomes the mostimportant mechanism in determining the breakdown of the gap.17/40Meek & LoebRaetherCathode-directed streamerAnode-directed streamerHigh-voltage Pulsed Power Engineering, Fall 2018

Effect of space charge A distinctive feature of Townsend breakdown mechanism is that the spacecharge of a single electron avalanche does not distort the electric field in the gap.𝑒𝑒 𝛼𝛼𝑑𝑑 𝑁𝑁𝑐𝑐𝑐𝑐𝛾𝛾 𝑒𝑒 𝛼𝛼𝑑𝑑 1 1 When the number of electrons reaches 𝑁𝑁𝑐𝑐𝑐𝑐 , the avalanche acquires somecharacteristic features that may be favorable for a streamer discharge to occur.𝑒𝑒 𝛼𝛼𝑑𝑑 𝑁𝑁𝑐𝑐𝑐𝑐 Then, small-diameter, weakly conductingfilaments (streamers) propagate from theavalanche toward the anode and cathode.As a result, the gap is bridged by a narrowchannel. The energy deposited in this channelincreases its conductivity, which results inthe formation of a spark discharge.18/40High-voltage Pulsed Power Engineering, Fall 2018

Formative time for a streamer breakdown The time from the onset of the streamer stage to the formation of a highconductivity channel is often shorter than the time needed for an avalanche withthe charge-carrier number 𝑁𝑁𝑐𝑐𝑐𝑐 to develop (formative time for streamerbreakdown). Raether’s criterion for the avalanche-to-streamer transition: The avalanche-tostreamer transition takes place at the time 𝑑𝑑𝑐𝑐𝑐𝑐 when the resulting electric field𝐸𝐸 𝐸𝐸0 𝐸𝐸𝐸 vanishes at the point 𝑑𝑑 𝑋𝑋𝑐𝑐𝑐𝑐 𝑣𝑣𝑒𝑒 𝑑𝑑𝑐𝑐𝑐𝑐 on the avalanche axis. Formative time: The time for an initial electron avalanche to build up a spacecharge field comparable to the applied filed.𝑁𝑁𝑐𝑐𝑐𝑐 𝑒𝑒 𝛼𝛼𝑋𝑋𝑐𝑐𝑐𝑐 108𝑑𝑑𝑓𝑓 ‘π‘π‘ ln 𝑁𝑁𝑐𝑐𝑐𝑐 18 20𝑋𝑋𝑐𝑐𝑐𝑐1 ln ‘£π‘£π‘’𝑒High-voltage Pulsed Power Engineering, Fall 2018

Streamer mechanism: Raether’s criterion Raether observed that streamers developed when𝛼𝛼𝑋𝑋𝑐𝑐𝑐𝑐 20𝑬𝑬𝑺𝑺𝑺𝑺 𝒆𝒆𝒆𝒆 𝟏𝟏𝟏𝟏 π’Œπ’Œπ’Œπ’Œ π’„π’„π’„π’„πŸ’πŸ’π…π…πππŸŽπŸŽ ‡ 𝑡𝑡 πŸπŸπŸπŸπŸ•πŸ• 𝒂𝒂𝒂𝒂𝒂𝒂 𝜢𝜢 𝟏𝟏 𝟏𝟏𝟏𝟏 𝟐𝟐 𝒄𝒄𝒄𝒄 The avalanche-to-streamer transformation takes place when the internal field ofan avalanche becomes comparable with the external one.20/40High-voltage Pulsed Power Engineering, Fall 2018

Formation of space-charge electric fieldNcr 108(ne 1014 cm-3) Ions are rather immobile and form a dipolefield together with the electrons removedfrom the ions. This field will enhance the initially appliedelectric field E0 at the avalanche head. UV light emitted in recombination and deexcitation events creates electrons byphotoionization ahead of and behind theavalanche, initiating further avalanches.21/40High-voltage Pulsed Power Engineering, Fall 2018

Negative streamer (anode-directed streamer) If the gap and overvoltage are large, the avalanche-to-streamer transformationcan take place far from the anode, and the anode-directed or negative streamergrows toward both electrodes.22/40High-voltage Pulsed Power Engineering, Fall 2018

Positive streamer (cathode-directed streamer) If the gap is short, the transformation occurs only when the avalanche reachesthe anode. Such a streamer that grows from anode to cathode and called thecathode-directed or positive streamer.0.1 1 mm23/40High-voltage Pulsed Power Engineering, Fall 2018

Limits of occurrence for the Townsend and streamerbreakdown mechanisms The overvoltage coefficient plays a decisive part for a transition from theTownsend to the streamer mechanism. Depending on the conditions in the prebreakdown stage, the discharge maydevelop by the Townsend or streamer mechanism.StreamerTownsend24/40High-voltage Pulsed Power Engineering, Fall 2018

Typical current-voltage characteristics for electricaldischarge of gasesEDHCFGIBJA25/40High-voltage Pulsed Power Engineering, Fall 2018K

Electrical discharge regime Dark discharge A–BDuring the background ionization stage of the process the electric field applied along the axis of the dischargetube sweeps out the ions and electrons created by ionization from background radiation. Background radiation from cosmicrays, radioactive minerals, or other sources, produces a constant and measurable degree of ionization in air at atmosphericpressure. The ions and electrons migrate to the electrodes in the applied electric field producing a weak electric current.Increasing voltage sweeps out an increasing fraction of these ions and electrons. B–CIf the voltage between the electrodes is increased far enough, eventually all the available electrons and ions areswept away, and the current saturates. In the saturation region, the current remain constant while the voltage is increased.This current depends linearly on the radiation source strength, a regime useful in some radiation counters. C–DIf the voltage across the low pressure discharge tube is increased beyond point C, the current will riseexponentially. The electric field is now high enough so the electrons initially present in the gas can acquire enough energybefore reaching the anode to ionize a neutral atom. As the electric field becomes even stronger, the secondary electron mayalso ionize another neutral atom leading to an avalanche of electron and ion production. The region of exponentiallyincreasing current is called the Townsend discharge. D–ECorona discharges occur in Townsend dark discharges in regions of high electric field near sharp points, edges, orwires in gases prior to electrical breakdown. If the coronal currents are high enough, corona discharges can be technicallyβ€œglow discharges”, visible to the eye. For low currents, the entire corona is dark, as appropriate for the dark discharges.Related phenomena include the silent electrical discharge, an inaudible form of filamentary discharge, and the brushdischarge, a luminous discharge in a non-uniform electric field where many corona discharges are active at the same timeand form streamers through the gas.26/40High-voltage Pulsed Power Engineering, Fall 2018

Electrical discharge regime Breakdown EElectrical breakdown occurs in Townsend regime with the addition of secondary electrons emitted from thecathode due to ion or photon impact. At the breakdown, or sparking potential VB, the current might increase by a factor of104 to 108, and is usually limited only by the internal resistance of the power supply connected between the plates. If theinternal resistance of the power supply is very high, the discharge tube cannot draw enough current to break down the gas,and the tube will remain in the corona regime with small corona points or brush discharges being evident on the electrodes.If the internal resistance of the power supply is relatively low, then the gas will break down at the voltage VB, and move intothe normal glow discharge regime. The breakdown voltage for a particular gas and electrode material depends on theproduct of the pressure and the distance between the electrodes, pd, as expressed in Paschen’s law (1889). Glow discharge F–GAfter a discontinuous transition from E to F, the gas enters the normal glow region, in which the voltage is almostindependent of the current over several orders of magnitude in the discharge current. The electrode current density isindependent of the total current in this regime. This means that the plasma is in contact with only a small part of thecathode surface at low currents. As the current is increased from F to G, the fraction of the cathode occupied by the plasmaincreases, until plasma covers the entire cathode surface at point G. G–HIn the abnormal glow regime above point G, the voltage increases significantly with the increasing total currentin order to force the cathode current density above its natural value and provide the desired current. Starting at point G andmoving to the left, a form of hysteresis is observed in the voltage-current characteristic. The discharge maintains itself atconsiderably lower currents and current densities than at point F and only then makes a transition back to Townsend regime. Arc discharge H–KAt point H, the electrodes become sufficiently hot that the cathode emits electrons thermionically. If the DCpower supply has a sufficiently low internal resistance, the discharge will undergo a glow-to-arc transition, H-I. The arcregime, from I through K is one where the discharge voltage decreases as the current increases, until large currents areachieved at point J, and after that the voltage increases slowly as the current increases.27/40High-voltage Pulsed Power Engineering, Fall 2018

Structure of glow discharge28/40High-voltage Pulsed Power Engineering, Fall 2018

Structure of glow dischargeCathode- PlasmaAston Cathode glowNegative glowdark spaceCathode dark spaceFaraday dark spaceVAAnodeAnode glowPositive columnAnode dark space Cathode : cathode material, secondary electron emission coefficients Aston dark space : a thin region with a strong electric field, and a negative space charge. Electrons are too low density and/orenergy to excite the gas Cathode glow : reddish or orange color in air due to emission by excited atoms sputtered off the cathode surface, or incomingpositive ions. High ion number density Cathode (Crookes, Hittorf) dark space : moderate electric field, a positive space charge and a relatively high ion density Cathode region : Most of the voltage drop, known as cathode fall Vc, most of the power dissipation, electrons are accelerated inthis region, the axial length of the cathode region determined by Paschen minimum Negative glow : accelerated electrons produce ionization and intense excitation, hence brightest light intensity, relatively lowelectric field, longer than cathode glow, typical electron density of 1016 electrons/m3 Faraday dark space : low electron energy due to ionization and excitation, electron number density decreased byrecombination and radial diffusion Positive column : quasi-neutral plasma, small electric field of 1V/cm, electron number density of 1015-1016 electrons/m3,temperature of 1-2 eV, long uniform glow Anode glow : bright region at the boundary of the anode sheath Anode dark space : anode sheath, negative space charge, higher electric field than positive column29/40High-voltage Pulsed Power Engineering, Fall 2018

Arc discharge Electrons emitted from the cathode spot can be produced mainly by thermionicemission if the cathode is made of a high-melting-point metal (e.g., carbon,tungsten, or molybdenum). With cathodes of low melting point, electrons can besupplied by field emission from points of micro-roughness where the electric fieldis highly concentrated. An additional important source of electrons at the cathode is ionized metal vapor.30/40High-voltage Pulsed Power Engineering, Fall 2018

Arc as a circuit element The arc equivalent resistance varies with the current and 𝑑𝑑𝑑𝑑/𝑑𝑑𝑑𝑑 is negative.Therefore, a stabilizing impedance must be included in series with the arc inboth AC and DC circuits.31/40High-voltage Pulsed Power Engineering, Fall 2018

Arc erosion Erosion of the contacts by arcing is caused partly by evaporation of metal fromelectrode spots during the arc. The energy of the arc, rather than its charge, is the deciding factor for arcerosion. The current wave shape also has an effect on the rate of arc erosion. For otherwise similar conditions, the rate of contact erosion is lower for contactmetals with high melting points, greater latent heats of evaporation, and higherthermal conductivities.32/40High-voltage Pulsed Power Engineering, Fall 2018

Arc vs. glow Glow discharge-μ „κ·Ήκ°„ μ „μ•• : 수백 V-μ „λ₯˜ : 수 mA-μ–‘μ΄μ˜¨μ΄λ‚˜ κ΄‘μžμ— μ˜ν•œ μŒκ·Ήμ—μ„œμ˜ μ΄μ°¨μ „μž λ°©μΆœμ— μ˜ν•˜μ—¬ 방전이 μ§€μ†λ˜λ©°κΈ°μ²΄ 쀑에 μ „κ·Ήλ¬Όμ§ˆμ˜ μ¦λ°œμ„±λΆ„μ„ ν¬ν•¨μ‹œν‚€μ§€ μ•ŠλŠ”λ‹€. Arc discharge33/40-μ „κ·Ήκ°„ μ „μ•• : μˆ˜μ‹­ V-μ „λ₯˜ : 수 A 이상-음극의 2μ°¨ κΈ°κ΅¬λ‘œμ„œ μ—΄μ „μž 방좜 및 μžκ³„ 방좜이 μ€‘μš”ν•œ 역할을 ν•˜κ³  μ¦λ°œν•œμ „κ·Ή λ¬Όμ§ˆμ€ κΈ°μ²΄λΆ„μžμ™€ λ”λΆˆμ–΄ λ°©μ „μ˜ ν˜•μ„±κ³Ό μœ μ§€μ— κ΄€κ³„ν•œλ‹€.High-voltage Pulsed Power Engineering, Fall 2018

Corona discharges Corona discharges appear in gases when electrodes have strong twodimensional variations. Corona (crown in Latin) is a pattern of bright sparks near a pointed electrode. Insuch a region, the electric field is enhanced above the breakdown limit so thatelectron avalanches occur.34/40High-voltage Pulsed Power Engineering, Fall 2018

Positive corona35/40High-voltage Pulsed Power Engineering, Fall 2018

Positive corona Mechanism depending on the applied voltage levela. At the onset level: When a free electron is driven by the field toward theanode, it produces an electron avalanche. The cloud of positive ionsproduced at the avalanche head near the anode forms an eventualextension to the anode. Secondary generations of avalanches get directedto the anode and to these dense clouds of positive ions. This mode ofcorona consists of what are called onset streamers.b. At slightly higher voltages: A cloud of negative ions may form near theanode surface such that the onset-type streamers become very numerous.They are short in length, overlap in space and time, and the dischargetakes the form of a β€˜glow’ covering a significant part of the HV conductorsurface. The corresponding current through the HV circuit becomes aquasi-steady current.c. At still higher voltages: The clouds of negative ions at the anode can nolonger maintain their stability and become ruptured by violent prebreakdown streamers, corresponding to irregular, high-amplitude currentpulses. If we continue to raise the voltage, breakdown eventually occursacross the air gap.36/40High-voltage Pulsed Power Engineering, Fall 2018

Onset voltage of various positive corona modes37/40High-voltage Pulsed Power Engineering, Fall 2018

Negative corona38/40High-voltage Pulsed Power Engineering, Fall 2018

Negative corona Mechanism depending on the applied voltage levela. At the onset level: The corona at the cathode has a rapidly and steadilypulsating mode; this is known as Trichel pulse corona. Each current pulsecorresponds to one main electron avalanche occurring in the ionizationzone. Drifting away from the cathode, more and more of the avalancheelectrons get attached to gas molecules and form negative ions whichcontinue to drift very slowly away from the cathode. During the process ofavalanche growth, some photons radiate from the avalanche core in alldirections. The photoelectrons thus produced can start subsidiaryavalanches that are directed from the cathode.b. At slightly higher voltages: The Trichel pulses increase in a repetition rateup to a critical level at which the negative corona gets into the steadyβ€œnegative glow” mode.c. At still higher voltages: Pre-breakdown streamers appear, eventuallycausing a complete breakdown of the gap.39/40High-voltage Pulsed Power Engineering, Fall 2018

Positive corona vs. negative corona40/40High-voltage Pulsed Power Engineering, Fall 2018

arc: the time required to establish a low-resistance arc across the gap Breakdown delay time statistical delay time formative time. 15/40 High-voltage Pulsed Power Engineering, Fall 2018 Statistical delay time The statistical delay time results from the statistics of electron appearance in the