microwave-driven breakdown: from dielectric surface...
TRANSCRIPT
Microwave-driven breakdown: from dielectric surface multipactor
to ionization discharge†
1
J. P. Verboncoeur1, J. Booske2, R. Gilgenbach3, Y. Y. Lau3, A. Neuber4, J. Scharer2, R. Temkin5
1Michigan State University/University of California-Berkeley, 2University of Wisconsin, 3University of Michigan, 4Texas Tech University,
5Massachussets Institute of Technology
† Research supported by an AFOSR grant on the Basic Physics of Distributed Plasma Discharges
Goals• Understand basic physics of microwave-driven breakdown– Breakdown threshold dependence on pressure, gas composition, geometric featuresfeatures
– Low Pressure Dielectric Multipactor
– Transition to Ionization Discharge
– Compare Experiments and Theory
2
Experimental Setup (2.85 GHz)Experimental Setup (2.85 GHz)
HPM Load
Directional Coupler
Directional Coupler
Rear Viewing Port
HPM from
Test Section
Front Viewing Port
HPM from Source
Test Section Features
•WR284-WR650 Standards
•Not optimized for transmission(Simple geometry to study effects)
•High-loss silicone rubber sheets
•Side and 45° Viewing Ports
•Atmospheric Control
Gasket
Test Sample
Nylon bolts
RF Window FlashoverRF Window Flashover
> MW transmitted power (High Power Microwaves, HPM)� Field amplitudes in excess of several 10 kV/cm
Flashover can be initiated
with or without the presence of a triple point
Observed WaveformsObserved Waveforms
Transmitted power
Self-luminosity
2... 5 MW
“first indicator”
tmicroseconds
Self-luminosity
Absorbed powerup to 80% absorbed
“first indicator”
ττττ – flashover delay time
UM RelMag: old window
Single-Surface RF Multipactor
)sin(0 tEE rfy ω=
-
+
+
+-
- �Multipactor discharge is a secondary
electron avalanche frequently
observed in microwave systems.
�Multipactor discharge is a secondary
electron avalanche frequently
observed in microwave systems.
EM wave
: leads to electron energy gain.
7
zE
-+
+-
Dielectric Window
y
z
00,v2 zztransit eEm=τ
), ,( 000 tEf transitrfiy ωφωτω ==E
(electron life time)
0
2z,0v
2 z
transiteE
mz = (maximum distance)
: attracts electrons
Dominates at low pressure
Secondary Electron Model
>
≤+=
−
6.3 ,125.1
6.3 ,)( )
21(),(
35.0
12
0max ww
wwekE
kw
si π
θδθδ δ0
20max
0
)2/1( EkE
EEw
sw
i
−+−=
πθ
≤≤<
=6.31 ,25.0
1 ,56.0
w
wk
� Energy and angular dependence of secondary emission coefficient
8Vaughan et al, IEEE-TED (1989); IEEE-TED (1993)
θ- iE
i, i,
(Electron Impact Energy)
1>δ1<δ 1<δθ (Electron Impact Angle)
PIC Multipactor Susceptibility
• include transverse variation of ERF• absorb at transverse wall• neglect transverse space charge
TE10 rectangular waveguideuniform plane wave
Discharge on(Positive growth rate)
9
high field susceptibility becomes vertical in waveguide – no upper field cutoff
Discharge off : low δ due to• Too high impact energy• Too small impact energy
At transient
Time
At the beginningX (cm
)
X (cm
)
TE10 Multipactor Migration
10
rfEStrong
rfEWeak
rfEWeak
At the steady state Vacuum GHz, 2.85
MV/m 5E 0y =
Time
Z (um) Z (um)
Z (um)
X (cm
)
Explanation of Migration
Center
Discharge on
� Susceptibility Curve
11
Periphery
At transient At steady state
Discharge on(Positive growth rate)
Multipactor Power
12
~ 5%
• ~2 % of the input EM power is absorbed• The phase difference between the discharge power and input EM power means that the electrons are not totally in equilibrium with the local rf electric field.
• ~2 % of the input EM power is absorbed• The phase difference between the discharge power and input EM power means that the electrons are not totally in equilibrium with the local rf electric field.
3 MV/m, 1 GHz
Collisional EffectsVacuum atm 1=p
ie NN ~
1>ctransitντ
13
Torr 0.01=p
Argon GHz, 1at MV/m 30 =rfE
• As the pressure increases, electron-impact ionization collisions dominate secondary electron emission as the electron source.
• At high pressures, the number of ions becomes comparable to that of electrons.
• As the pressure increases, electron-impact ionization collisions dominate secondary electron emission as the electron source.
• At high pressures, the number of ions becomes comparable to that of electrons.
ie NN >>
PIC: Electron Mean Energy
14
mTorr 01 and Vacuum =p atm 1=p
• Electrons in the multipactor discharge gain their energy by being accelerated by the rf electric field during the transit time.
• Electrons in the multipactor discharge gain their energy by being accelerated by the rf electric field during the transit time.
Argon GHz, 2.85at MV/m 82.20 =rfE
• At high pressures, electrons suffer many collisions and lose a significant amount of energy gained from the rf electric field.
• At high pressures, electrons suffer many collisions and lose a significant amount of energy gained from the rf electric field.
TransitionTransition Pressure (10~50 Torr Ar)
15
1 Torr: surface and volume discharges coexist
cGHz νω ~) 7.5(cGHz νω ~) 85.2(
• Below 10 Torr, the secondary yield is nearly unity so multipactor is dominant.
• As the pressure increases and hence the volume discharge suppresses the secondary electron emission, it decreases to nearly zero.
• Below 10 Torr, the secondary yield is nearly unity so multipactor is dominant.
• As the pressure increases and hence the volume discharge suppresses the secondary electron emission, it decreases to nearly zero.
Breakdown Scaling Law
16
High pressure regime:collision dominated (νc >> ω)
volumetric discharge
Low pressure regime:surface multipactor dominated
τpp
Eeff 1~pvngi
1~
1~
1~
σντ
Lau, Verboncoeur, and Kim, APL, 89, 261501 (2006)
PIC: Electron Energy Distribution
17
• Below 50 Torr, the EEPF is bi-Maxwellian like• At high pressures, the EEPF becomes cutoff, with the depletion of high-energy electrons
• Below 50 Torr, the EEPF is bi-Maxwellian like• At high pressures, the EEPF becomes cutoff, with the depletion of high-energy electrons
Spatially averaged
ων >c
Argon GHz, 2.85at MV/m 82.20 =rfE
Kinetic Global Model
1
10
100
τ (ns)
PIC/MC GM (Maxwellian) GM (EEDF with x = 6.5)
xcecf
εεε 22/11 )( −=
Assume general distribution function:
Solve continuity, energy, and power absorption equations for each species
Get x for distribution function from
18
0.1 1 10 100 10000.1
1
Pressure (Torr)
decm
e K
ion
xc
ion
ePICion ∫
−⋅⋅=ε
ε εεεσε22/1
1)(2
From PIC:
Argon GasEo = 2.82 MV/mf = 2.85 GHz
Get x for distribution function from PIC: Good over 4 orders in pressure!
Works for all gases tried – shape depends only on cross sections
(Ar)
Kinetic Global Model* II
• Coupled continuity equations for all species, e.g. for oxygen:
−+−+ ++−−=OOOeOerecgaseattgaseion
e
dn
nnKnnKnnKnnKnnKdt
dn
22det2det
1919
−++−−
−
+−+
+
−−−=
−−=
OOOOmutOegaseattO
OOmutOerecgaseion
O
nnKnnKnnKnnKdt
dn
nnKnnKnnKdt
dn
22
22
2
det2det
∫=ε
εεεσεdf
m
eK
e
)()(2
where
* Nam and Verboncoeur, APL 23, 231502 (2008)
Oxygen Reactions
)4,3,2,1,(
)(
22
22
22
nnOeOe 6)-3
rOeOe 2)
OeOe 1)
==+→++→++→+
υ eOeOe 14)
DODOeOe 13)
DOPOeOe 12)
++→+
++→+++→+
+22
2
2
)1()1(
)1()3(
2020
)3()3(
),(
)(
)(
2
3122
2
122
122
POPOeOe 11)
AcOeOe 10)
OOOe 9)
bOeOe 8)
aOeOe 7)
uu
g
g
++→+ΣΣ+→+
+→+
Σ+→+
∆+→+
+−
−
+
eOOOO 19)
OOOO 18)
eOeOe 17)
OOOe 16)
PpOOeOe 15)
++→+
+→+++→+
+→+
++→+
−
+−
−
+
22
22
2
3*2 )3(
Enhanced Global Model III
• Electron energy equation:
)~
(2
3gasemom
exc
gaseexcexcgaseionionabseffe nnKnnKnnKPkTndt
d ++−=
∑εε
2121
( )∫
+= εε
ωνν
νdf
E
m
neP
m
m
m
e
abs
2
22
02
2
• Improved RF power absorption model:
Enhanced Global Model IV
� The general EEDF equation in the isotropic velocity space *:
� Maxwellian: x=1, Druyvestyn: x=2� Determine x by the ionization and dissociative
xcecf
εεε 22/11 )( −=
2222
� Determine x by the ionization and dissociative attachment from PIC model:
* J. T. Gudmundsson, Plasma Sources Sci. Technol., 10, 76 (2001).
∫∫
−
−
⋅⋅⋅⋅
=
attion
2/11
2/11 )(
2- )(
2
-
ε
ε
ε
ε
εεεσεεεεσεdec
m
edec
m
e
KK
x
eff
x
eff Tc
att
e
Tc
ion
e
PICattPICion
Enhanced Global Model in Ar
Argon GasEo = 2.82 MV/mf = 2.85 GHz
10
100
(ns)
PIC/MC GM (Maxwellian) GM (EEDF with x = 6.5)
2323
0.1 1 10 100 10000.1
1
10
τ (ns)
Pressure (Torr)
Breakdown Time in Air
AirEo = 4.23 MV/m
f = 2.85 GHz f = 5.70 GHz
PIC/MCC GM (EEDF with x = 0.99)
PIC/MCC GM (EEDF with x = 0.99)
2424
100 10000.1
1
10
τ (ns)
Pressure (Torr)
100 10000.1
1
10
τ (ns)
Pressure (Torr)
Energy loss rate and Teff
Eo = 4.23 MV/mf = 2.85 GHz
1E13
Energy loss rate (eV/s)
Ionization Dissociation
Effective Electron Tem
perature (eV) Oxygen
Argon
oxygen
2525
0.01 0.1 1 10 100 10001E9
1E10
1E11
1E12
Energy loss rate (eV/s)
Pressure (Torr)
100 10001
10
Effective Electron Tem
perature (eV)
Pressure (Torr)
Applied E vs f for Kratio=1 in air
E/p (V/cm/Torr)
760 Torr 500 Torr 200 Torr 100 Torrion
attratio
K
KK =
Kratio < 1Breakdown Region
2626
1E-3 0.01 0.1 110
100
E/p (V/cm/Torr)
f/p (GHz/Torr)
Breakdown Region
Kratio > 1Decay Region
Effect of Frequency
Oxygen and NitrogenEo = 4.23 MV/mp = 500 Torr
1000
PIC-MCC for argon GM for argon PIC-MCC for xenon GM for xenon
PIC-MCC for oxygen GM for oxygen PIC-MCC for nitrogen GM for nitrogen
Argon E0 = 2.82 MV/m, p=500 TorrXenonEo = 2.82 MV/m, p = 700 Torr
Constant x is inadequate at high frequency for Ramsauer gases
27
10 100
10
100
τ (ns)
Frequency (GHz)
GM for xenon
10 1001
10
τ (ns)
Frequency (GHz)
GM for nitrogen
Sang Ki Nam and J. P. Verboncoeur, Appl. Phys. Lett., 93, 151504 (2008).
Argon: frequency dependence of xThe image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again.
2828
Comparison to Experiment
103
104
/p (V/(cm
Torr))
Oxygen (GM, E = 5.64 MV/m) Oxygen (Experiment)
29
101
102
10-9 10-8 10-7 10-6 10-5
Eeff/p (V/(cm
Torr))
pτ (Torr sec)
* P. Felsenthal and J. M. Proud, Phys. Rev., 139, A 1796 (1965).
UV Illumination of WindowsUV Illumination of WindowsReduction in flashover
delay time and standard
deviation
•4 MW, 2.5 µs incident pulse
•Illumination intensity of approximately 4 mW/cm2
over 240-400 nm rangeover 240-400 nm range
•Equivalent illumination of “sunny” day at 3000 ft. above sea level
•Breakdown delay times exhibit less fluctuations with UV illumination
•Sample-to-sample variance also somewhat reduced
Plasma Filamentary Arrays
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2 mm
k
H
Beam
671 to 677 ns
• 1.5 MW, 140 GHz Gyrotron
• 3 shots with slow (B&W) and fast (color) cameras
• Filaments spaced slightly less than λ/4, propagate towards source
• Hypothesis: constructive interference of reflected/diffracted waves,
31Y. Hidaka, et al., Phys. Rev. Lett., 100, 035003 (2008).
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846 to 852 ns
1.212 to 1.218 µs
of reflected/diffracted waves, propagation speed limited by diffusion of seed electrons
Pressure Dependence
distinct filaments appear at high pressure
EM Wave Model
z1 z2Medium 2Medium 1 Medium 3
Plasma filament
-∞ +∞
Filament propagation
Wave propagation
E┴
)Re(
)(
0
0
2,
2,
2
2
2
2
tj
nymxz
z
ZeEE
kkkk
Zkz
Z
ω−⊥ =
+−=
=+∂∂
Z is spatial profile of E┴
33* H.C. Kim and J. P. Verboncoeur, Comp. Phys. Comm. 177 (2007) 118-121
Z is spatial profile of E┴
ckk
ω== 23
21
vacuum (1 and 3):
plasma (2):
frequency transfer momentum:
frequency plasma :
))((
)(1
,
,
2/1
,
2,2
2
im
ip
i im
ip
zj
z
ck
νω
νωωωω
+−= ∑
Fluid Model
Particle Continuity and Electron Energy Equations
||
||
)~
(3
,
++−+⋅−∇=∂
∇+−
=
−∇−=+⋅∇−=∂
∂
nnKnnKnnKPqTn
n
nDDE
EnnDJnnKJt
n
e
e
ei
ei
eeeeegaseione
e
εε
µµ
µ
34
22
2
5
2
3
)~
(2
3
⊥⊥ ==
+∇−=
++−+⋅−∇=
∂∂
EnEm
enP
TJTnDq
nnKnnKnnKPqTnt
ee
me
e
abs
eeeeee
gasemomgaseexcexcgaseionionabseee
µν
εε
S. K. Nam and J. P. Verboncoeur, Phys. Rev. Lett., 103, 055004 (2009)
Filaments: 1D Model
<λ/4• Filaments propagate slowly toward source• Explained via 1D fluid-EM model• Ionization by electrons heated by
100
10-5
10-10
Normalized intensity (a.u.)
E(z)ne(z)n*(z)
35
electrons heated by EM absorption• Standing waves via reflection• Filament spacing depends on E, ω, gas
Kim et al., Comput. Phys. Comm. 177 (2007)Nam et al., Phys. Rev. Lett. 103 (2009)
0 1 2 3 4
10-15
10-20
Normalized intensity (a.u.)
z (mm)
Filament Spacing
0.12
0.15
0.18
0.21
0.24
Gap between two peaks (∆z/
λ) f = 110 GHz, p = 760 Torr
36
0 5 10 15 20 25 30 35 40
0.09
0.12
Gap between two peaks (
Eo(MV)
Increasing field strength decreases filament spacing as breakdownthreshold is exceeded closer to the previous filament.
Conclusions• Modeling breakdown phenomena across a wide parameter regime– Multipactor dominates at low p– Multipactor and ionization discharge compete at intermediate pressure (10-50 Torr)
– Ionization discharge dominates at atmospheric pressure• Enhanced kinetic global model agrees with PIC model over 4 orders in pressure, 3 orders in f– EEDF shape nearly independent of p, E
37
– EEDF shape nearly independent of p, E– EEDF shows some dependence on f for Ramsauer gases
• UV reduces statistical delay time• Wave-fluid model reproduces filamentary experiment well– Filament distance slightly less than λ/4– Propagation speed ~ ambipolar or free diffusion times