The physics of streamers and discharges
P.Fonte
My view, not a review. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte
Nostalgic anecdote Imaging HPC (1989) DELPHI’s HPC
Sparked disastrously owing to the alpha particles emitted by the lead converter.
Sparked also my lasting interest in breakdown phenomena in gaseous detectors, most of the way in partnership with V. Peskov. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Outlook • Known and suspected fundamental breakdown onset modes: slow, fast, rate-induced? • Experimental evidence • Physical origin (or speculations about…) •Suppression
• Streamer simulation • Detailed physics • Simulation strategies • Results
• The discharge • Phenomenology • SiSuppression The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte
Slow breakdown - experimental evidence [FON91a] [RAE64] PPAC CO2, 2 cm gap, 148 Torr Ar+8 Torr CH4 4 mm gap atm. press.
Extremely unstable situation. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Slow breakdown – physical origin (Townsend’s “generations” mechanism) time
Etc. d q0 Cathode Secondary electron bombarded emission from by cathode ions creates new photons generations of excited species avalanches metastable species A very elaborate theory exis ts (for instance [DAV73] chap . 2). α The stability condition is ηG <1 where Ge= d is the gas gain and η is the secondary electron yield per electron in the avalanche. But there is also an overlaying statistics. In detectors photon feedback generally dominates and the characteristic time is the electron’s drift time from cathode to anode. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Slow breakdown – “quenching” Gas “quenching”: adding complex molecules to the gas mixture Photoabsorption of the emitted photons in the UV (depends on details of the quencher gas) The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Slow breakdown – “quenching” Emission suppression: less dependent on details Photon yields in PPAC in the band:120-170nm
TEA molecular emission [FON91b]
There is some ev idence tha t the em iss ion or ig ina tes ma in ly from fragmen ts (likely carbon atomic emission lines) at λ>140nm. Photoemission strongly suppressed for quencher concentration 1-10%. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Slow breakdown – “quenching” Altogether: efficient photon feedback suppression
[FON91b] Secondary photons/electron
PPAC Stainl. steel mesh cathode 4 mm gap atm. press .
No matter the nature of the quencher, photon feedback is very effectively suppressed by a few percent concentration.
Slow breakdown is normally not a problem for stability, except in presence of very photosensitive surfaces (e.g. CsI photocathode) The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Fast breakdown - experimental evidence Cloud chamber observations (vapours, ~1cm gap) High gain – anode and cathode streamers C develops Cathode s hannel es A almost at A almost at A valanch node st node st Interpretation r r tablished e head treamer eamer eamer anode anode [KLI72]
[RAE64] The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Fast breakdown - experimental evidence Lower gain – only cathode streamer s s h F C C + a C tremaer c tarts the ead neart rom avala reaches a Cathode s lmost at a lmost at streamer hannel es hannel es athode st
a Is it relevant for b r n n n h tablished tablished treamer eamer thode ranches ode che ode e anode detectors?
[RAE64] The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Fast breakdown - experimental evidence Very fast process featuring a “precursor” pulse [RAE64] PPAC RPC [FON91]
[DUE94]
Gain
single-wire A signature of low-gain cathode streamer-only bkdbreakdown Precursor pulse at low gains
[HON96] The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Fast breakdown – physical origin (Meek and Raether’s “streamer”/”Kanalaufbau” mechanism) Photon-mediated local feedback in a stronggp space-charge field
] Higg()her field: anode (forward) streamer rr
Lower field: safe, but lowers avg. gain W.Riegle yy
Higher field: cathode streamer [courtes (but needs a secondary process) Streamers are triggered when the space-charge field becomes comparable to the applied field: Complex physical process, involving: a charge-dominated, electron transport in variable fields geometry-dependent process. electron multiplication in high fields space-charge distorted electric field emission of photons able to photoionize the gas at a certain distance (gas self-photoionization) Details later The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Raether limit – parallel fields
[RAE64] A charge-dominated RPC Streamer charge
process (pC) 2mm ggpap [CAR96] “streamer”
charge Precursor st aa saturation 96] F
Avalanche PPAC (4mm) Precursor charge d lli 199 [FON91a] [C
TFE +Ar +IB
The famous “Raether limit” AlAvalanc he ga in sa tura tion of ~108 electrons corresponds to the onset of streamers. No “limited proportionality ” in parallel fields (except in
SF6). The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Geometry Raether limit – micropattern detectors? dddependence + multistep
[PES01]
Reduction at high gain Like ly ow ing to: -avalanche statistics charge-limited -Corona discharge
For n0>~200 electrons the Raether limit applies, but depends on geometry. For n0<~200 electrons other factors start to dominate, such as: avalanche gain fluctuation Corona discharge from sharp edges The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Streamer suppression
By spatial variation of the By poisoning the gas with SF6 applied field: SQS mode (RPC only – not tried on PPC) (wire counters)
[KOR00]
[HON96]
+SF6
Freon+IsoB+SF6 The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Streamer enhancement … dielectric surfaces favour the streamer propagation SQS
[PES97] Direct spark The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Rate-induced breakdown? – experimental evidence
[IVA99] Qualitatively similar data measured by Low-rate: several authors streamers or Corona nn Can we interpret such plots solely in terms of statistics + Raether limit? vable gai ee (superimposition of avalanches exceeding Raether limit) imum achi
xx Rate-induced
Ma breakdown Is there a new breakdown mode? The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Breakdown statistics via superimposition and Raether limit Superimposition cell a For instance: A1A = 1 cm2 τ 2 Beam: R counts/(mm2 s) a = 1 mm A τ= 1 µs (ions)
P(spark in a cell)=p Time=1s λ= average # avalanches/cell There are N=A/a×(1s)/τ superimposition cells: N=108. We want to observe a relatively low absolute spark rate P(spark)=S~10-2 /s S1S=1-P(not spark) =1 -(1-p))N ⇒ p≈S/N: p=10-10. The number of avalanches n in each cell is Poisson-distributed with average λ=Raτ: λ=R ×1 ×10-6.
There will be a spark if nq>QR, q=is the average avalanche charge and QR the Raether limit. Then, the required gain reduction owing to superimposition is 1/ñ, with ñ the percentile 1-p of the Poisson distribution with average λ. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Rate-induced breakdown? – experimental evidence
[IVA99]
Never flat!
λ=1 λ=1
Mere statistics seem to qualitatively reproduce the data! BUT… The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Rate-induced breakdown? – spurious pulses
PPAC - high rate, low gain – single sparks
500 nA 500 nA
500 ms 500 ms
[IVA98] 5 μA
[IVA98] 1 μs
PPAC - medium rate - higher gain afterpulses after irradiation continuous sparking regime [IAC02]
+ memory effect (cannot reach same gain for hours) (Si cath od e)
200 nA 500 ms
20 μA [IVA98] 1 μs The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Rate-induced breakdown? – spurious pulses
beam
[IAC02]
GEM The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Rate-induced breakdown? – possible physical origin Peskov’s “cathode jets”
[IAC02]
Explosive field emission from dielectric insertions in the metal. Similar to the vacuum breakdown phenomenon. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Streamer calculation strategies: continuous approach Charge transport good reference: [DAV73] creation transport ∂ r 644474448 66844474448 nre ()( ,t) r rr 2 =+−SWnWnDn()αη −∇⋅+∇ () electrons { ee ee e e ∂t other 1424314243 1442443 rr⋅∇+∇ rr⋅ diffusion sources multiplication WnnWeeee 1424314243 attachment drift pile− up nrt(r , )= charge densityinspaceand time rr WE()=ve locit itfhyof charges Space-ch+lidfildharge + applied field r r Ert( , )= electricfield:applied+spacecharge 2 e ∇=−Vnnn()+ −−− α=first T ownsend coeffi ci ent ε iei 0 D=diffusion coefficient Boundary conditions ∂ r r nrt+ (,) r initialdensities:nrei, ± ( ,0) i =+SWnα ∂t ee behaviour of chargesat theelectrodes ∂nrt(,)r Ions, assuming Electrostatic B.C. i− =η r stationary ions Wnee ∂t Slight drawback: no avalanche statistics The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Streamer calculation strategies: continuous approach Other sources It is possible that just transport accounts for the forward (anode) streamer but for the cathode streamer (growing backwards) something else is needed. e.g photoemission proportional to the electron multiplication ∂ r nrtf ()( , ) r = δ Wn photon creation ∂t ee + gas self -photoionization source term (very debatable process) rrr−r '/λ Q ∂nrt(',)r distribute the photons Srt(,)r =Ω−f ( rrr r ') e dr r ' λ ∫ ∂ around and ionize the gas Volume t δ = photon yield per electron Ω=solid anglefraction fromemission toabsorption point Q =quantumefficiency Quite formidable! λ = phhtoton' smeanf ree path Don’ t know of any practical 3D calculation.
All this for each relevant emission wavelength… The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Some simplification from symmetry The minimum model: “1.5D” (discs) Much better: “2D” (rings=axial simetry)
Solution over a plane
Fixed
Solution over the central axis only
Started by Davies et al. in the 60’s
Unfortunately, still a bit artificial for many detectors. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Numerical strategies for continuous approach Method of “characteristics” Finite elements Solve the differential Integrate the equations along equations on the verti ces of “characteristic lines” that correspond a mesh. to the path of the charges
Equations become a set of “2D” uncoupled ordinary differential axial symmetry equatidlilliions and analytical solution exists for non-space charge regime.
For space-chilltiharge regime: small time steps and recalculate the field at Forward streamer each step nsity ee Electron d [GEO00]
Promising! The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Streamer (a&c) simulation in spark chamber
[DAV73]
1.5D, method of “characteristics” The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Cathode streamer simulation in PPAC Cathode Anode Proportional Avalanche-streamer Streamer stage avalanche stage transition stage
high-gain region Cathode Space charge upstream from the streamer ion cloud
[Fonte 1994][FON94]
Electric field distortion gas self photoionization ))
likely region for SF6 to cut the Kanal Space Space-chargecharge effect effect
- lower gas gain Current (µA 1.5D - cathode streamer method of “characteristics”
- anode streamer Time (ns) The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Cathode streamer simulation in PPAC Cathode Anode Proportional Avalanche-streamer Streamer stage avalanche stage transition stage
high-gain region Cathode Space charge upstream from the streamer ion cloud
[Fonte 1994][FON94]
Electric field distortion gas self photoionization ))
likely region for SF6 to Space charge effect cut the Kanal
- lower gas gain Current (µA 1.5D - cathode streamer method of “characteristics”
- anode streamer Time (ns) The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Another approach: particle-in-cell
A “mesoscopic” MonteCarlo where 1.5D approximation Space-charge only mini-avalanches are propagated 0.3mm timingg, RPC, 3kV no cathode streamer from cell-to-cell in a mesh. electrons, positive ions, negative ions, field Symmetries can be also applied. Incorporates naturally avalanche statistics.
[LIP04]
[Courtesy Werner Riegler] Also quite formidable: huge number of cells. 3D prohibitive The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte 2D particle-in-cell simulation Space-charge only Electric field in a single electron avalanche, 0.3mm timing RPC, 2.8kV no cathode streamer
[LIP04]
Strong widening of the electron cloud. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Discharge stages n w w rk he oo oo oo aa
Sp Slow breakdown: many stages Avalanc iffuse gl iffuse entary gl w formati DD oo mm Gl Fila [HAY67]
(very) Fast breakdown: spark grows directly from the anode & cathode streamers
Detectors not quite any of these (GEM maybe excepted) The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Discharge from cathode streamer Process may be stopped by external current limitation.
Resistive electrodes or very small electrode segments with individual resistors
cathode streamer discharge spark… cathode
[WON02]
anode The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte Summary My view, not a review. • What causes breakdown • Imperfections (sharp edges, etc) ⇒ Corona discharge. • In photosensitive detectors: photon feedback. • At low rate mainly the space-charge (“Raether”) limit ⇒ streamers • by its physical origin, it must depend on • specific geometry of the detector (lower for denser avalanches)
• avalanche statistics (lower for low n0) • number of amplification steps (spreading the charge around) • At high rate: maybe ion-bombardment induced electron jets from cathodes, maybe merely superimposition statistics+Raether limit
• Streamer ppyhysics and simulation • Subject is pursued since the 60’s. • Several methods and simplification strategies were devised. • There is a gggpood understanding of the process. • Some doubts persist about the cathode-streamer feedback mechanism • Full 3D solutions still missing.
• The discharge (final breakdown stages) • Well studied. (Interesting for electrical engineering.) • Likely, suppression only by external current limitation. The physics of streamers and discharges RD51 meeting, 13 Oct 2008, Paris P.Fonte References [CAR96] R. Cardarelli et al., Nucl. Instrum. and Meth. A 382 (1996) 470 [DUE94] I. Duerdoth et al., Nucl. Instrum. and Meth. A 348 (1994) 303 [FON91a ] P. Font e et . al ., N ucl . I nst rum. and M eth . A305 (1991) 91 [FON91b] P. Fonte et. al., Nucl. Instrum. and Meth. A310 (1991) 140 [FON96] P. Fonte, IEEE Nucl. Sci. 43 n.3 (1996) 21 [GEO00] G.E. Georghiou et al., J. Phys. D: Appl. Phys. 33 (2000) 27. [HAY67] S.C.Haydon, in J.A.Rees, “Electrical breakdown of gases”, Macmillan, 1973 [HON96] C. Hongfang et al., Nucl. Instrum. and Meth. A373 ( 1996) 430 [IAC02] C. Iacobaeus et al., IEEE Trans. Nucl. Sci. 49 (2002) 1622 [IVA98] Yu. Ivaniouchenkov et al., IEEE Trans. Nucl. Sci. 45 (1998) 258 [IVA99] Yu. Ivaniouchenkov et al., Nucl. Instrum. and Meth. A 422 (1999) 300 [KLI72] Kline and Siambis, Phys. Rev. A 5 (1972) 794 [LIP04] C. Lippmann, W.Riegler, Nucl. Instrum. and Meth. A 533 (2004) 11 [PES01] V. Peskov et al., IEEE Nucl. Sci. 48,2001,1070. [PES97] V. Peskov et al., Nucl. Instrum. and Meth. A 397 (1997) 243 [WON02] J. Yi Won et al., J. Phys. D: Appl. Phys. 35 (2002) 205