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

The 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.

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