1

Microwave-driven breakdown:

from dielectric surface multipactor

to ionization discharge†

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 the US AFOSR MURI grant FA9550-18-1-0062, and an MSU Foundation Strategic

Partnership Grant

Goals

• Understand basic physics of microwave-

driven breakdown

– Breakdown threshold dependence on

pressure, gas composition, geometric

features

– Low Pressure Dielectric Multipactor

– Transition to Ionization Discharge

– Compare Experiments and Theory

2

Experimental Setup (2.85 GHz)

HPM Load

Directional

Coupler

Directional

Coupler

Front Viewing Port

Rear Viewing Port

HPM from

Source

Test Section

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 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 Waveforms

tmicroseconds

Transmitted power

Self-luminosity

Absorbed power

2... 5 MW

up to 80% absorbed

“first indicator”

t – flashover delay time

UM RelMag: old window

7

Single-Surface RF Multipactor

zE

)sin(0 tEE rfy

-

-

+

+

+

+

+

-

-

-

Dielectric Window

y

z

Multipactor discharge is a secondary

electron avalanche frequently

observed in microwave systems.

EM wave

: leads to electron energy gain.

00,v2 zztransit eEmt

), ,( 000 tEf transitrfiy t E

(electron life time)

0

2

z,0v

2 z

transiteE

mz (maximum distance)

: attracts electrons

Dominates at low pressure

8

Secondary Electron Model

6.3 ,125.1

6.3 ,)( )

21(),(

35.0

12

0max ww

wwekE

kw

si

0

2

0max

0

)2/1( EkE

EEw

sw

i

6.31 ,25.0

1 ,56.0

w

wk

Energy and angular dependence of secondary emission coefficient

Vaughan et al, IEEE-TED (1989); IEEE-TED (1993)

- iE

i, i,

(Electron Impact Energy)

11 1

(Electron Impact Angle)

9

PIC Multipactor Susceptibility

• include transverse variation of ERF

• absorb at transverse wall

• neglect transverse space charge

high field susceptibility becomes vertical in

waveguide – no upper field cutoff

TE10 rectangular waveguideuniform plane wave

Discharge on(Positive growth rate)

Discharge off : low δ due to

• Too high impact energy

• Too small impact energy

10

At transient

rfEStrong

rfEWeak

rfEWeak

At the steady state

Time

At the beginning

Vacuum GHz, 2.85

MV/m 5E0

y

Time

X (

cm)

X (

cm)

Z (um) Z (um)

Z (um)

X (

cm)

TE10 Multipactor Migration

11

Explanation of Migration

Center

Periphery

At transient At steady state

Discharge on(Positive growth rate)

Susceptibility Curve

12

Multipactor Power

~ 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.

3 MV/m, 1 GHz

13

Collisional EffectsVacuum

Torr 0.01p

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.

ie NN

atm 1p

ie NN ~

1ctransitt

14

PIC: Electron Mean Energy

mTorr 01 and Vacuum p atm 1p

• 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.

Transition

15

1 Torr: surface and volume discharges

coexistcGHz ~) 7.5(cGHz ~) 85.2(

Transition Pressure (10~50 Torr Ar)

• 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 (c >> )

volumetric discharge

Low pressure regime:surface multipactor dominated

tpp

Eeff 1~pvngi

1~

1~

1~

t

Lau, Verboncoeur, and Kim, APL, 89, 261501 (2006)

17

Plasma Filamentary Arrays

Y. Hidaka, et al., Phys. Rev. Lett., 100, 035003 (2008).

Slow Image Limit: 0.0000 1.0000,

Fast Image Limit: 0.0000 1.0000, # contours: 8

500550600650700750800850

200

250

300

350

400

0

1

2

3

4

5

6

x 104

2 mm

k

H

Beam

671 to 677 ns

846 to 852 ns

1.212 to 1.218 µs

• 1.5 MW, 140 GHz Gyrotron

• 3 shots with slow (B&W) and fast

(color) cameras

• Filaments spaced slightly less than

l/4, propagate towards source

• Hypothesis: constructive interference

of reflected/diffracted waves,

propagation speed limited by diffusion

of seed electrons

Pressure Dependence

distinct filaments appear at high pressure

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EM Wave Model

* H.C. Kim and J. P. Verboncoeur, Comp. Phys. Comm. 177 (2007) 118-121

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

Z is spatial profile of E┴

ckk

2

3

2

1vacuum (1 and 3):

plasma (2):

frequency transfer momentum:

frequency plasma :

))((

)(1

,

,

2/1

,

2

,2

2

im

ip

i im

ip

zj

z

ck

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Fluid Model

Particle Continuity and Electron Energy Equations

22

||

||

2

5

2

3

)~

(2

3

,

EnEm

enP

TJTnDq

nnKnnKnnKPqTnt

n

nDDE

EnnDJnnKJt

n

ee

me

e

abs

eeeeee

gasemomgaseexcexcgaseionionabseee

e

e

ei

ei

eeeeegaseione

e

S. K. Nam and J. P. Verboncoeur, Phys. Rev. Lett., 103, 055004 (2009)

Filaments: 1D Model

21

<λ/4• Filaments propagate

slowly toward source

• Explained via 1D fluid-EM model

• Ionization by 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

100

10-5

10-10

10-15

10-20

No

rma

lize

d in

ten

sity (

a.u

.)

z (mm)

E(z)

ne(z)

n*(z)

22

Filament Spacing

0 5 10 15 20 25 30 35 40

0.09

0.12

0.15

0.18

0.21

0.24

Ga

p b

etw

ee

n t

wo

pe

aks (

z/l

)

Eo(MV)

f = 110 GHz, p = 760 Torr

Increasing field strength decreases filament spacing as breakdown

threshold is exceeded closer to the previous filament.

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Conclusions

• Modeling breakdown phenomena across a wide parameter regime– Multipactor dominates at low p– Susceptibility depends on transverse waveform– Time dependent behavior understood– Multipactor and ionization discharge compete at intermediate

pressure (10-50 Torr)– Ionization discharge dominates at atmospheric pressure

• Wave-fluid model reproduces filamentary experiment well– Filament distance slightly less than l/4– Propagation speed ~ ambipolar or free diffusion times

Future Work: Multipactor MURI

• MSU, TT, UM, UNM, UW

• Space device multipactor

• Develop 3 open platforms (model and

experiment):

– Planar

– Coaxial

– Stripline

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