2006. 08. 29

H. C. Kim, Y. Chen, and J. P. VerboncoeurDept. of Nuclear Engineering, UC Berkeley

CCP 2006 (S05-I22: Invited Talk)

Modeling of RF Window BreakdownTransition of window breakdown

from vacuum multipactor discharge to rf plasma

Modeling of RF Window BreakdownTransition of window breakdown

from vacuum multipactor discharge to rf plasma

Topic 0.

0. Introduction and Models

I. Vacuum Multipactor Discharge

II. Transition to RF Plasma

Undesirable Discharge in HPMs

RF Window (Dielectric)

Incoming EM wave

RF generator

(e.g. Magnetrons, Linear beam tubes, Gyrotrons, Free-Electron Lasers, and so on)

Outgoing EM wave

Conductor(High-Power Microwave)

>

Either Vacuumor Background Gas

GHz s100'~1GHz

pulse ns 100~

MW 1powerPeak

z

y

x

z : direction of wave propagation

Discharge can degrade device performance or even damage devices, including catastrophic window failure.

Discharge can degrade device performance or even damage devices, including catastrophic window failure.

In Vacuum (Multipactor Discharge)

zE

)sin(0 tEE rfy

-

-

+

+

+

+

+

-

-

- Multipactor discharge* is an avalanche

caused by secondary electron emission.

Multipactor discharge* is an avalanche

caused by secondary electron emission.Vacuum

* Observed in various systems(e.g. RF windows, accelerator structures, microwave tubes and devices, and rf satellite payloads)

• Single-surface multipactor on a dielectric

: leads to electron energy gain.

: makes electrons return to the surface.

00,v2 zztransit eEm

) ,( 0 transitrfiy EfE

(= life time)

0

2z,0v

2 ztransit eE

mx

(TE or TEM mode)

(maximum distance)

Analytic Solution of Single Particle Motion

2

0

0,00

0

0,

2

020,

v)cos(

v2cos

2

1 , v

2

1

rf

y

z

zrfiyziz Ee

m

Ee

meE

mEmE

Solution of the equation of motion for the electron in Vacuum

• The z- and y-components of the impact electron energy

vx,0, vy,0: initial velocity of the electron emitted from the surface0: initial phase of the rf electric field at that time (t=t0)

-

0,0, v,v yz

))(sin(

)sin(

000

0

ttE

tEE

rf

rfy- iE

ftt

transit

rf

rf

transit

f

f

For the constant Ez = Ez0 during the flight,

0zz EE

00 t

(TE or TEM mode)

With Background Gas (RF Plasma)

-

--

-

-

++

+

+

+

+ Under the high-pressure

background gas, an rf plasma is

formed. The rf plasma is a candidate

for window breakdown on the

air side.

Under the high-pressure

background gas, an rf plasma is

formed. The rf plasma is a candidate

for window breakdown on the

air side.

Discharge Sustainment Electron generation mechanisms in the system

• Secondary Electron Emission (SEE) on a surface originated from electron impact to a material : Dominant in Vacuum or under the low-pressure gas

• Ionization in the volume originated from ionization collisions between electrons and the background gas : dominant under the high-pressure gas

- -+

-

--

-

probabilistic event

probabilistic event

• Another emission mechanisms: thermionic emission, photo emission, field emission, explosive emission, and so on.

+

Secondary Emission due to Electron Impact

- iE

i, i,

(Electron Impact Energy)

11 1

(Electron Impact Angle)[Ref] Vaughan et al, IEEE (1989); IEEE (1993)

Energy and angular dependence of secondary emission yield (the ratio of the incident flux to the emission flux)

1D3V Particle-In-Cell (PIC) Model

)sin(0 tEE rfy

-

-

+++++++++

-

-

-

Dielectric

y

x

L

Dielectric (δ=0)

-

-

-

-

0)0(:BC xEx

space in the ions and electrons ofnumber :,

000

)(,

ie

ieiieewallwallx

N

A

eNeNNNE

eV 2

1

1

eV 5.12

eV 400

2

0,0

0max

0max

yx

sw

s

th

T

k

k

E

E

• Condition ofleft dielectric

+

++

+

Simulation Tool : Modified XPDP1 from PTSG, UC Berkeley [Ref] J.P. Verboncoeur et al., J. Comput. Phys. 104, 321 (1993)

Topic I.

* Our model is based on electrostatic fields and the magnetic field is not taken into account.

0. Introduction and Models

I. Vacuum Multipactor Discharge

II. Transition to RF Plasma

Dynamics using Monte-Carlo Simulation*

* [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998)

Problem: No oscillation appears even though

zE

Discharge off : low due to• Too high impact energy• Too small impact energy

Discharge on(Positive growth rate)

Susceptibility Curve for Plane Wave

zE

1trans

Model of Monte-Carlo Simulation

• Emission of initial seed electrons from the surface

vz,0, vy,0: Maxwellian distribution: Uniform distribution

→ Calculate the impact energy and angle (from analytic solution of one particle motion)

→ Calculate the secondary electron yield (from model of SEC due to electron impact)

• Ejection of multiple secondary electrons (Nn+1) from the surface

vz,0, vy,0: (from the energy distribution of secondary electrons):

The phase of next injection is taken from the phase of impact for the parent electron.

• Update

0

11,0 2

ennz

NE

)particleparent : ,iteration:(secondary1 ini

transitinn

* [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998)

)(maxiterationitransit

it

rft ~:Problem iteration

00,v2 zztransit eEm

[Ref] H.C. Kim and J.P. Verboncoeur, Phys. Plasmas 12, 123504 (2005)

Dynamics using PIC Simulation

PIC simulation shows that the electron number and the Ez oscillate at twice the rf frequency, saturating after 1 ns. Ez oscillates in and out of the susceptibility region.

PIC simulation shows that the electron number and the Ez oscillate at twice the rf frequency, saturating after 1 ns. Ez oscillates in and out of the susceptibility region.

(solving field eqn. self-consistently)

Plane Wave band)-(L GHz 1at MV/m 30 rfE

PIC: Susceptibility Curve (Plane vs. TE10)

~ x 1.5

TE10 modePlane wave

In TE10 mode, the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant.

In TE10 mode, the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant.

)sin()sin(),( 0 xd

tEtxEx

yy

yE

xxd0

)sin(0 tEy

TE10 mode

• Effect of transverse field structure

)sin(),( : WavePlane cf. 0 tEtxE yy z : direction of wave propagation

dczdcy EE ,0, vs.

Summary for Topic I

In HPM systems, the time-dependent physics of the single-surface

multipactor has been investigated by using PIC simulation.

The normal surface field and number of electrons oscillate at twice the rf

frequency.

The effect of the transverse field structure on the discharge has

been investigated.

In TE10, the upper boundary of the susceptibility diagram is nearly

vertical so that only the lower boundary is relevant.

Topic II.

0. Introduction and Models

I. Vacuum Multipactor Discharge

II. Transition to RF Plasma

Collision with Argon Background Gas

• Electron-Neutral Collision • Ion-Neutral Collision

The argon gas is used in this study because of its simplicity in the chemistry (compared with air).

PIC: Number of Particles (I)

Vacuum

Argon band),-(S GHz 2.85at MV/m 82.20 rfE

The number of electrons still oscillates as in the vacuum case but increases slowly in time, as a result of electron-impact ionization.

The number of electrons still oscillates as in the vacuum case but increases slowly in time, as a result of electron-impact ionization.

ie NN mTorr 10p

# of ions ~ # of ionization events between electrons and argon gas

Vacuum multipactor discharge The secondary electron emission is the only mechanism for generating electrons.

Vacuum multipactor discharge The secondary electron emission is the only mechanism for generating electrons.

PIC: Number of Particles (II)

atm 1p

ie NN ~

Argon GHz, 2.85at MV/m 82.20 rfE

The numbers of electrons and ions are nearly the same and increase abruptly in time. Collisional ionization becomes the dominant mechanism to generate electrons.

The numbers of electrons and ions are nearly the same and increase abruptly in time. Collisional ionization becomes the dominant mechanism to generate electrons.

1ctransit

PIC: Electron Mean Energy

mTorr 01 and Vacuum p atm 1p

Electrons in the multipactor discharge gain their energy by being accelerated from the rf electric field during the transit time.

Electrons in the multipactor discharge gain their energy by being accelerated from the rf electric field during the transit time.

Argon GHz, 2.85at MV/m 82.20 rfE

At high pressures, electrons suffer lots of collisions and lose the significant amount of energy gained from the rf electric field.

At high pressures, electrons suffer lots of collisions and lose the significant amount of energy gained from the rf electric field.

PIC: Electron Energy Distribution

Below 50 Torr, the EEPF is bi-Maxwellian type. At high pressures, the EEPF becomes Druyvesteyn type since the electron temperature decreases with the collision frequency.

Below 50 Torr, the EEPF is bi-Maxwellian type. At high pressures, the EEPF becomes Druyvesteyn type since the electron temperature decreases with the collision frequency.

Spatially averaged

c

Argon GHz, 2.85at MV/m 82.20 rfE

PIC: Electron and Ion Densities

mTorr 20p

Torr 10p

* Time-averaged over a cycle

At low pressures, the multipactor discharge is formed near the dielectric window. At intermediate pressures, both multipactor discharge and rf plasma exist. At high pressures, only rf plasma is formed, away from the surface of the window.

At low pressures, the multipactor discharge is formed near the dielectric window. At intermediate pressures, both multipactor discharge and rf plasma exist. At high pressures, only rf plasma is formed, away from the surface of the window.

Torr 100p

1ctrans

PIC: Electric Field Profile

At low and intermediate pressures, the electric field is positive on the surface, indicating that the multipactor discharge can be sustained. At high pressures, the electric field is negative on the surface. The energy of electrons impacting the surface is low enough so that the secondary electron emission yield is less than 0.5.

At low and intermediate pressures, the electric field is positive on the surface, indicating that the multipactor discharge can be sustained. At high pressures, the electric field is negative on the surface. The energy of electrons impacting the surface is low enough so that the secondary electron emission yield is less than 0.5.

Argon GHz, 2.85at MV/m 82.20 rfE

PIC: Secondary Electron Emission

Secondary electron emission yield on the dielectric

* For particles accumulated over a cycle

Below 10 Torr, the secondary yield is near unity so that multipactor discharge can be sustained. As the pressure increases, collisions suppress the impact energy and hence the secondary electron yield decreases to less than unity.

Below 10 Torr, the secondary yield is near unity so that multipactor discharge can be sustained. As the pressure increases, collisions suppress the impact energy and hence the secondary electron yield decreases to less than unity.

Transition Pressure (10~50 Torr)

rfE :

cGHz ~) 7.5(cGHz ~) 85.2(

1ctransit

c

1transit

surface dischargeis collisionless.

c

EEPF of rf plasma is Druyvesteyn.

Experiment for the Breakdown on the Air Side

The HPM surface flashover experiments at Texas Tech Univ.

[Ref] G. Edmiston, J. Krile, A. Neuber, J. Dickens, and H. Krompholz, “High Power Microwave Surface Flashover of a Gas-Dielectric Interface at 90 to 760 Torr,” IEEE Trans. Plasma Sci. (to be published).

Absorbed P = Incident P – Transmitted P – Reflected P

Incident PTransmitted P

Reflected P

Flashover delay time

Experiment for the Breakdown on the Air Side

3 MW

3 MW, UV

4.5 MW

])(1[2 2

0

c

rfeff

EE

is universal for different Erf0 at the given pressure range.

is universal for different Erf0 at the given pressure range.

pτpEeff vs.

Simple theory: L. Gould and L. W. Roberts, J. Appl. Phys. 27, 1162 (1956).

f = 2.85 GHz

Air: 90 ~ 760 Torr

PIC: Discharge Formation Time (I)

Simulation results of argon gas for various E-fields and frequencies

• At very high pressures,

is universal for different Erf0 and .

is universal for different Erf0 and .

pτpEeff vs.

pτpEeff vs.

])(1[2 2

0

c

rfeff

EE

00

2rfcrfeff E

p

E

p

E

• At very low pressures

c

c ~

PIC: Discharge Formation Time (II)

Simulation results of argon gas for various E-fields and frequencies

• At low pressures,

is universal for different Erf0 and .

is universal for different Erf0 and .

pτ vs.

pτ vs.

[n

s]

cGHz ~) 85.2(cGHz ~) 43.1(

Summary for Topic II

In HPM systems, adding an argon background gas, we have

investigated the transition of window breakdown from single-surface

vacuum multipactor discharge to rf plasma.

• There is an intermediate pressure regime where both multipactor discharge

and rf plasma exist.

• In our parameter regime, the transition pressure ( less than unity) is

between 10 and 50 Torr in argon.

The discharge formation time () has been obtained as a function of the gas pressure.

• The normalization predicted by the simple theory holds only

at very high pressures.• At low pressures, the discharge formation time is independent of Erf0 and

.

pτpEeff vs.

Thank you for your attention.

Conference on Computational Physics 2006

* This work was supported in part by AFOSR Cathodes and Breakdown MURI04 grant FA9550-04-1-0369, AFOSR STTR Phase II contract FA9550-04-C-0069, and the Air Force Research Laboratory - Kirtland.

GHz 0.1 and MV/m 3.0:4 Case

GHz 10 and MV/m 3:3 Case

GHz 1 and MV/m 3.0:2 Case

GHz 1 and MV/m 3:1 Case

0

0

0

0

rfrf

rfrf

rfrf

rfrf

fE

fE

fE

fE

MC : E-Field Trace

The normal electric field and the number of electrons oscillate with time only for Case 1 in the MC model.

The normal electric field and the number of electrons oscillate with time only for Case 1 in the MC model.

MC versus PIC Results

Case 1

Like the PIC simulation result, the oscillation period in our MC simulation is half the rf period. However there is still a significant discrepancy in amplitude and phase between the MC and PIC results, which comes from the assumptions on which the MC simulation is based.

Like the PIC simulation result, the oscillation period in our MC simulation is half the rf period. However there is still a significant discrepancy in amplitude and phase between the MC and PIC results, which comes from the assumptions on which the MC simulation is based.

MC versus PIC Results

The parameter regime where the multipactor discharge develops is also the narrower in the MC simulation than in the PIC simulation.

The parameter regime where the multipactor discharge develops is also the narrower in the MC simulation than in the PIC simulation.

PIC : Power Trace Case 1

)MW/cm 2.1( 2S]mMV[

MW/cm 1033.12

0

220

12

0

rf

rfrf

E

EE

S

PIC : Power Trace

~ 5%

Case 1

In vacuum multipactor discharge, the rf phase randomization of electrons occurs only upon the collision with the surface. The phase delay of the discharge power with respect tothe input power comes from the finite transit time for electrons to interact with the surface. It means that the electrons are not totally in equilibrium with the local rf electric field. As the transit time is larger (or the electric field is smaller), the phase difference is larger.

In vacuum multipactor discharge, the rf phase randomization of electrons occurs only upon the collision with the surface. The phase delay of the discharge power with respect tothe input power comes from the finite transit time for electrons to interact with the surface. It means that the electrons are not totally in equilibrium with the local rf electric field. As the transit time is larger (or the electric field is smaller), the phase difference is larger.

~ 2% ~ 0.5%

Case 2

PIC : Scaling with Erf0/frf

• The shape of the closed curve of the trajectory depends on the amplitude of the rf electric field normalized to the rf frequency (Erf0/frf).

• The shape of the closed curve of the trajectory depends on the amplitude of the rf electric field normalized to the rf frequency (Erf0/frf).

Cases 1 and 4 Cases 2 and 3rf

transit

transit

rf

f

f

Decay

Grow

At transient

rfEStrong

rfEWeak

rfEWeak

At the steady state

Time

At the beginning

Vacuum GHz, 2.85

MV/m 5E0y

PIC: Spatial Distribution of Electrons in TE10

Time

X (

um)

X (

um)

Z (um) Z (um)

Z (um)

X (

um)

Susceptibility Curve

Center

Periphery

At transient At steady state

Explanation of Spatial Distribution in TE10

Discharge on(Positive growth rate)

zE

Experiment for the Breakdown on the Air Side

(Air)

The HPM surface flashover experiments at Texas Tech Univ.

[Ref] G. Edmiston, J. Krile, A. Neuber, J. Dickens, and H. Krompholz, “High Power Microwave Surface Flashover of a Gas-Dielectric Interface at 90 to 760 Torr,” IEEE Trans. Plasma Sci. (to be published).

• WR284 S-Band waveguide 7.21 cm X 3.40 cm (A = 24.5 cm2)

cm 52.10GHz 85.2 0 f

PIC: Discharge Formation Time

)(0

0)()( ttgetntn

42.18

10)(

)( , 8

0

0

g

ttn

ttnSay

• Discharge formation time

Assuming

g : effective volume ionization rate obtained by fitting the number trace

t0 : determined from the time that mean kinetic energy reaches steady state, assuming g also reaches steady state.

Torr 150 GHz, 2.85at mMV57.10 rfE

Comparison• Flashover time: Experiment at Texas Tech Univ. (Air)

3 MW

3 MW, UV

4.5 MW

• Discharge formation time: PIC (Argon)

Since the statistical delay time is not considered in the simulation and the background gas is different, there is an order of magnitude difference in time between experiment and simulation. But, the qualitative trends are similar.

Since the statistical delay time is not considered in the simulation and the background gas is different, there is an order of magnitude difference in time between experiment and simulation. But, the qualitative trends are similar. 0 , rfEpτ

PIC:2nd Order Method for Particle Collection

pn

p/n x 121 ,v

pn

p/n- x ,v 21

The velocity and position at time the particle crosses the boundary

tn

tn+1/2 tn+1

Velocity

Position

[Ref] H.C. Kim, Y. Feng, and J.P. Verboncoeur, “Algorithms for collection, injection, and loading in particle simulations ”, J. Comput. Phys. (to be published)

egn

en-g x ,v

PIC: 2nd Order Method for Particle Ejection

tn-1

tn-1/2 tn

Velocity

Position

ttg e 2''