H. C. Kim, Y. Chen, and J. P. Verboncoeur

1
CCP 2006
(S05-I22 Invited Talk)

• Modeling of RF Window Breakdown
• Transition of window breakdown
• from vacuum multipactor discharge
• to rf plasma

2006. 08. 29
H. C. Kim, Y. Chen, and J. P. Verboncoeur Dept.
of Nuclear Engineering, UC Berkeley
2
Topic 0.

• 0. Introduction and Models
• I. Vacuum Multipactor Discharge
• II. Transition to RF Plasma

3
Undesirable Discharge in HPMs
(High-Power Microwave)
Conductor
RF Window (Dielectric)
RF generator (e.g. Magnetrons, Linear beam
tubes, Gyrotrons, Free-Electron Lasers, and so on)
Either Vacuum or Background Gas
Incoming EM wave
Outgoing EM wave
gt
z direction of wave propagation

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

4
In Vacuum (Multipactor Discharge)
(TE or TEM mode)

• Single-surface multipactor on a dielectric

• Multipactor discharge is an avalanche caused by
  secondary electron emission.

Vacuum

-
-
leads to electron energy gain.
-
( life time)
-
-
(maximum distance)
makes electrons return to the surface.
Observed in various systems (e.g. RF windows,
accelerator structures, microwave tubes and
devices, and rf satellite payloads)
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Analytic Solution of Single Particle Motion

• Solution of the equation of motion for the
  electron in Vacuum

(TE or TEM mode)
For the constant Ez Ez0 during the flight,
vx,0, vy,0 initial velocity of the electron
emitted from the surface ?0 initial phase of the
rf electric field at that time (tt0)
-
-

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

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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.

-


-
-

-


-

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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

probabilistic event
-
-

-

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

probabilistic event
-
-

-

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

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Secondary Emission due to Electron Impact

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

-
i,
i,
(Electron Impact Energy)
Ref Vaughan et al, IEEE (1989) IEEE (1993)
? (Electron Impact Angle)
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1D3V Particle-In-Cell (PIC) Model
x

• Condition of
• left dielectric

-
y

-

-
-
Dielectric
Dielectric (d0)
-
-
-
-


-
L

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

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Topic I.

• 0. Introduction and Models
• I. Vacuum Multipactor Discharge
• II. Transition to RF Plasma

Our model is based on electrostatic fields and
the magnetic field is not taken into account.
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Dynamics using Monte-Carlo Simulation

• Susceptibility Curve for Plane Wave

Discharge on (Positive growth rate)

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

Problem No oscillation appears even though
Ref Ang et al, IEEE Trans. Plasma Sci. 26,
290 (1998)
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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)

• Update

• Ejection of multiple secondary electrons (Nn1)
  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.
Ref Ang et al, IEEE Trans. Plasma Sci. 26,
290 (1998)
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Dynamics using PIC Simulation
(solving field eqn. self-consistently)

• 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.

Ref H.C. Kim and J.P. Verboncoeur, Phys.
Plasmas 12, 123504 (2005)
Plane Wave
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PIC Susceptibility Curve (Plane vs. TE10)

• Effect of transverse field structure

Plane wave
TE10 mode
x 1.5
TE10 mode
z direction of wave propagation

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

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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.

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Topic II.

• 0. Introduction and Models
• I. Vacuum Multipactor Discharge
• II. Transition to RF Plasma

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Collision with Argon Background Gas

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

• Electron-Neutral Collision

• Ion-Neutral Collision

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PIC Number of Particles (I)

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

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

of ions of ionization events between
electrons and argon gas
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PIC Number of Particles (II)

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

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PIC Electron Mean Energy

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

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

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PIC Electron Energy Distribution
Spatially averaged

• 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.

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PIC Electron and Ion Densities

• 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.

Time-averaged over a cycle
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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.

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PIC Secondary Electron Emission

• Secondary electron emission yield on the
  dielectric

Transition Pressure (1050 Torr)
EEPF of rf plasma is Druyvesteyn.
surface discharge is collisionless.

• 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.

For particles accumulated over a cycle
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Experiment for the Breakdown on the Air Side

• The HPM surface flashover experiments at Texas
  Tech Univ.

Incident P
Transmitted P
Reflected P
Absorbed P Incident P Transmitted P
Reflected P
Flashover delay time
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).
26
Experiment for the Breakdown on the Air Side
Air 90 760 Torr
3 MW, UV
3 MW
4.5 MW
f 2.85 GHz
Simple theory L. Gould and L. W. Roberts, J.
Appl. Phys. 27, 1162 (1956).

• is universal for
  different Erf0 at the given pressure range.

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PIC Discharge Formation Time (I)

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

• At very low pressures

• At very high pressures,

• is universal for
  different Erf0 and ?.

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PIC Discharge Formation Time (II)

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

? ns

• At low pressures,

• is universal for different Erf0
  and ?.

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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 ?.

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Conference on Computational Physics 2006
Thank you for your attention.
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.
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(No Transcript)
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MC E-Field Trace

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

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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.

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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.

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PIC Power Trace
Case 1
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PIC Power Trace
0.5
2
Case 2
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 to
• the 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.

5
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PIC Scaling with Erf0/frf
Grow
Decay
Cases 1 and 4
Cases 2 and 3

• 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).

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PIC Spatial Distribution of Electrons in TE10
X (um)
X (um)
At the beginning
At transient
Time
Z (um)
Z (um)
Weak
Time
Strong
X (um)
At the steady state
Weak
Z (um)
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Explanation of Spatial Distribution in TE10

• Susceptibility Curve

Center
Discharge on (Positive growth rate)
Periphery
At transient
At steady state
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Experiment for the Breakdown on the Air Side

• The HPM surface flashover experiments at Texas
  Tech Univ.

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

(Air)
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).
41
PIC Discharge Formation Time
Assuming

• Discharge formation time ?

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.
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Comparison

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

• Discharge formation time PIC (Argon)

3 MW, UV
3 MW
4.5 MW

• 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.

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PIC2nd Order Method for Particle Collection

• The velocity and position at time the particle
  crosses the boundary

Velocity
tn1/2
tn1
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)
tn
Position
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PIC 2nd Order Method for Particle Ejection
Velocity
tn-1/2
tn
tn-1
Position