2006. 08. 29 H. C. Kim, Y. Chen, and J. P. Verboncoeur Dept. of Nuclear Engineering, UC Berkeley CCP...
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Transcript of 2006. 08. 29 H. C. Kim, Y. Chen, and J. P. Verboncoeur Dept. of Nuclear Engineering, UC Berkeley CCP...
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
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.
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
~ 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)