Content Background I II Main research of my dissertation Papers - - PDF document
2010/8/16 Seminar Presentation: Research on mechanism of HPM dielectric window breakdown and its application Dr. C. Chang Department of Engineering Physics, Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2010/8/16 1
Seminar Presentation:
Department of Engineering Physics, Department of Engineering Physics, Tsinghua University, Beijing 100084, China changc02@mails.tsinghua.edu.cn
2010/8/16 2
Breakdown at vacuum/dielectric interface of HPM window has been major limitation of power radiation [1]. Methods of improving breakdown threshold become key issues of HPM system [1]. y y [ ]
vacuum SF6 bag HPM Source [1] R. Barker, E. Schamiloglu, High power microwave source and technology, 2001.
Breakdown is triggered by multipactor and finally realized by plasma avalanche in ambient desorbed or evaporated gas layer above dielectric. Seed electron production Seed electron production
The principle courses of HPM window breakdown under vacuum:
Gas desorption or material vaporization Gas desorption or material vaporization Multipactor, charge accumulation, power deposition Multipactor, charge accumulation, power deposition Space charge shielding Space charge shielding Saturation in ambient gas Saturation in ambient gas Plasma avalanche in bi t Plasma avalanche in bi t Saturation strengthening Saturation strengthening g g g g Interaction of plasma and dielectric surface Interaction of plasma and dielectric surface HPM transmission cutoff HPM transmission cutoff ambient gas ambient gas
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(A)
(B)
5 P i di t i l f (C)
Propose model considering collision and ionization of multipactor electrons with ambient desorption or evaporation gases.
The former models [1,2] assuming vacuum contrast to experiments showing desorption or evaporation gas forming local high p.[3,4]
( ) exp( )
DC DC z t z t t
eE eE u t t u m m ν ν ν ⎛ ⎞ = − + − + ⎜ ⎟ ⎝ ⎠ ( ) ( ) ( )
2 2 2 2
exp ( ) sin( ) cos( ) sin( ) cos( ) ( ) ( )
rf t rf y t t
eE t eE u t t t m m ν ω φ ν φ ω ω φ ν ω φ ω ν ω ν − = + − + + + + +
Tangent and normal velocity: g p p g g g p
( ) ( )
t t
m m ω ν ω ν + +
( ) ( )
( )
2 2 2 2 2
2
1 exp 1 2cos( )exp 2 4 ( )
t t t
e E mu t t t m ν ω ν ω ν = − + − − +
Collision energy: Transit time: ( )
1 exp( )
DC DC t z t
eE eE u m m ν τ τ ν − − + − =
⎛ ⎞ ⎜ ⎟ ⎝ ⎠ 1, R. Kishek, et al. Phys. Rev. Lett. , 1998; 2,Valfells, et al. Phys. Plasmas, 2000. 3,A. Neuber, et al, J. Appl. Phys., 1999 ; 4,A. Neuber, et al. IEEE Trans. Plasma Sci. 2000. Firstly fit νm and νi
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( ) ( )
2
4 1 exp 1
i i i
a b a ε ε ε ε σ ε ε ε ε ε ⎛ ⎞ ⎛ ⎞ − = − − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ − + ⎝ ⎠ ⎝ ⎠
fitting ionization and collision cross-section of N2 from eV to keV
( )
1
i
aε ε + ⎝ ⎠ ⎝ ⎠
Assuming Maxwellian distribution, numerically integrating νm and νi
( )
1.2 2 1.2 2.5
1.5* /(1+0.008* ) +70* /(1+1.05* )
m
σ ε ε ε ε ε =
( )
5 / 2
8 1 exp( ) v d p m kT kT ε σ ε ε ε π
∞
−
⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ ∫
Vaccuum [1] Kishek 98
1, R. Kishek, et al. Phys. Rev. Lett. , 1998;
Obtain variation of εe and saturation boundaries with p. Extend the vacuum solutions[1]to that under different p. Calculation: the power deposited by multipactor leads to surface material melting, evaporating, to further improve local pressure
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BWO, 1GW, X-band, 20ns, single and repetitive 50Hz
Distinguished ΔP for different material
ΔP : PMMA>PE>PTFE> QTZ EB: PMMA<PE<PTFE< QTZ
Deduced ΔP ~1-10Torr in 20ns EB: PMMA PE PTFE QTZ Close relation between EB with ΔP Guide material selection and conditioning: Guide material selection and conditioning: Weak SEY, low gas absorption, high melting point; multiple conditioning
Space charge influences multipactor, improves the deposited power. The former model [1, 2] only considered multipactor electrons. Plasma significantly affects field. Propose space charge model of multipactor electrons and plasma
( ) ( ) ( )
( )
2 2 0.5 2
exp exp (1 ) 1
esB es
n e d d x T ψ ψ β αψ β γψ ε
−
= + − + −
Analytical φ under vacuum： Extend former solution[1] to positive space potential showing β=1 curve
[1] valfells 00 Co-decided potential
Solving Poisson Equations:
2 ln exp( ) 2
p es w es t
T e x e T v ω φ φ ⎛ ⎞ − = + ⎜ ⎟ ⎝ ⎠ 1, A. Valfells, et al., IEEE Trans. Plasma Sci. 2000;2, A. Neuber, et al, J. Appl. Phys., 1999
( )
ln 1
es e
T m e M β φ β γ α ⎛ ⎞ Δ ≈ − + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
Analytical positive φ by plasma and multipactor electrons：
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No shielding No shielding
[1]
plasma and multipactor electrons shielding multipactor electrons
1,H. Kim, et al. Phys. Plasmas, 2006 2, L. Schiesko, et al., J. Nucl. Mater., 2007.
Plasma leads to further shielding Ex, improving P↑。 Analytical curves agree with PIC simulation [1] Positive space potential was experimentally found [2]
Strong interaction between HPM dielectric breakdown and plasma discharge in local gas, no corresponding analytical model.
( (1 ) )
e i w t l e
dn n dt ν δ δ ν = − − ( )
e e rf e m
d n u m en E n m u dt ν = −
/ 2)
e e e ie cL
d n T en u E P P dt = − < ⋅ > − −
) 2
ie QW i e l e e l
P eV T n v T n v = + +
cL e i c
P nν ε =
Secondary electron compensation Space charge field and diffusion loss
( ) ( ) (
)
2 2 2
( ) 2 2 2 1 3 3
rf t e c e i QW e i W t e l t
d T T eV T T T dt ν ε ν δ δ ν ω ν ⎛ ⎞ ⎛ ⎞ = − + − + + − − ⎜ ⎟ ⎜ ⎟ + ⎝ ⎠ ⎝ ⎠
2
e E 3m
( )
( ) ( )
2
1 3 ln ln 1 ln ln 2 2 2
e QW w t w t w t e
T M V e m δ δ γ γ γ δ δ γ δ δ π ⎛ ⎞ ⎛ ⎞ = + − + + − + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠
Potential drop
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τ by PIC simulation[1]
1.Y. Lau, et al., Appl. Phys. Lett., 2006 2.D. Hemmert, et al, SPIE, 2000
Considered interaction of plasma and dielectric surface, τ↓ Experiment [2] found, τ diel< τspace
(A)
(B)
5 P i di t i l f (C)
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Plasma avalanche In ambient gas Multipactor
Periodic dielectric surfaces to alter the trajectories of electrons to decrease εe<εp1 and τ<< T/2 and τ<< T/2 Suppress multipactor in developmental stage Isolate local high pressure and plasma avalanche
2 2 2
2 2 / 2 sin arctan( )
rf
eE T m π τ ϕ ω π + ⎛ ⎞ = = − ⎜ ⎟ ⎝ ⎠
y
S ( ) 2.86-9.38GHz，Erf~30kV/cm Sm(T/2)~0.56-6.1mm
Width d decided by Erf, ω, p, Edc. d<<λ, not to influence HPM transmission Erf ↑, Sy ↑; Edc↑, Sy ↓, Sx ↓; p↑, Sy ↓, Sx ↓, Edc and p significant influence
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X(mm) X(mm) Y(mm) Y(mm)
f=2.86GHz, Erf=30kV/cm, d=1mm, h=1mm
X(mm)
τ1< T/2 , Frf strong restoring force. SE: τ<<T/2, εe <<εp1, within the duration T/2-τ1
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Experiment platform： Klystron，S-band(2.86GHz)，μs width
Four port circulator
Incident
vacuum SF6
Transmitted Reflected Intense reflection+transmission cutoff
PTFE, H=1mm H/mm P/mm Capacity/MW EB /kV/cm 0.5 1 >16 >28 1 2 >16 >28 1 3 5-6 16 Fl t f 4 14
increase EB
P=2mm Flat surface 4 14
When Pin >16MW, the alumina windows limit power further increasing.
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For rectangular dielectric: multipactor can occur on top and bottom surfaces; sensitive to p and Edc
Analysis of the field convergence and enhancement on periodic triangular surface: Positive effect on multipactor suppression ( )
1
= sin( ) cos( )
n es r r y r
r E E e E e E n e n e d
θ θ θ
β θ θ
−
⎛ ⎞ + = − + ⎜ ⎟ ⎝ ⎠
A) flying to-and-from between the slopes and ionizing the ambient gases
x y
B) impacting, multipactoring along the slopes until Frf reversing
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( ) ( ) ( )
2 2 2 2
( )exp ( ) ( ) sin cos sin( ) cos( ) ( ) ( )
t n t t t t
eE t eE u t t t m m E E
θ θ
α ν α ν φ ω φ ν ω φ ω ω φ ω ν ω ν − = − − + − + + + ⎛ ⎞
Multipactor along the slopes：
( )
( )
2 2 2 2
( ) sin cos + 1-exp sin( ) ( ) ( )t
t DC z t t t t
m eE u eE m E
θ
ω ν ω φ φ ν τ ωτ φ ν α ν ν ν ω ν ⎛ ⎞ ⎛ ⎞ + − + − + + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ +
Transit time:
exp( )
DC DC t z t t
eE eE t u m m ν ν ν ⎛ ⎞ − + − + ⎜ ⎟ ⎝ ⎠
( ) ( ) ( )
2 2 2 2
( )exp ( ) ( ) sin cos sin( ) cos( ) ( ) ( )
r t r t t t t t
eE t eE u t t t m m α ν α ν φ ω φ ν ω φ ω ω φ ω ν ω ν − ≈ − − + − + + +
( )
2 2
( )t sin cos cos( ) + =0 ( )
t DC t t
E Eθ ν ω ν φ φ ωτ φ ω α ν + − − − +
( ) ( )
* 0 sin(
)
x y y t x y
d u iu ieE t S u iu dt d m
ν
β ω φ ν + + ⎛ ⎞ + + + = ⎜ ⎟ ⎝ ⎠
Flying to-and-from between the slopes：
Main factors influencing suppression effect:
Impact energy εe along slope Transit time τ along slope Flight time τ1 between slopes
Suppression mechanism: εe<εp1, δ<1, τ <<T/2. τ ↓ and τ1↓, impact number↑, decay faster. ξ ↑, τ and τ1↓ ( Eθ↑, distance↓); Erf ↑, τ and τ1↓ (Eθ↑, uy↑); Consider β (Erf↑), τ and τ1 ↓; f ↓, τ/(T/2) and τ1 /(T/2) ↓; εe, τ and τ1 depended
Increase ξ, enhance Erf, decrease f, strengthen suppression.
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For the same f=2.86GHz, ξ =45o, Erf=30kV/cm
For the same f, ξ, and Erf , larger P with weaker suppression and lower EB Faster suppression at bottom: Erf convergence, smaller τ; shorter d, smaller τ1; Weaker suppression upward: Erf ↓, d↑, τ ↑, τ1 ↑
H=1mm, P=2mm H=3mm, P=6mm
f=9.4GHz, H=1mm 45o P=2mm 30kV/cm 63o P=1mm 50kV/cm 45o, P=2mm, 30kV/cm 63o, P=1mm, 50kV/cm For higher f=9.4GHz , ξ=45o and P=2mm at 30kV/cm , no suppression ξ=63o at 50kV/cm effective suppression
Increasing f weakens the suppression effect!
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Angle ξ /o H /mm P /mm Capacity /MW EB /kV/cm 1 2 16 28
Experiment platform：Klystron, S-band，μs width
45 1 2 >16 >28 2 4 >16 >28 3 6 11 23 4 8 6 17 26.6 1 4 ~10 22 Flat surface 4 14 ξ =45o, P=2mm
EB dependent on ξ and P consistent with theory, good repeatability By SF6 at 2atm and downstream vacuum, Capacity >36MW and EB>42kV/cm
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BWO, X-band 9.6GHz, 20ns, GW power
vacuum
TE11 dominant mode horn
Incident Transmitted Reflected Flat dielectric(1.1GW) Triangular 60o (1.65GW)
For flat, tail erosion, intense reflected peak, pressure rise For periodic surface, slow erosion
Flat Flat
ξ 60o
ξ=60o H=0.7mm P=0.8mm Capacity 1.6GW
ξ=60o
For flat, Pon↑, pulse width ↓, Pref ↑ ↑ for Pon >1GW, >10 times For periodic, no obvious width ↓, Pref linearly ↑, <<Pref of flat
ξ=60o
Flat surface 1GW
Physical method of improving EB, suitable for different materials
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Metallic sawtooth surfaces on beam-chamber wall, Erf perpendicular to the slopes, reduce photoelectron emission [1] and SEY [2-3]. Reduction of SEY depends on dimensionless parameter ξ [3], rather than both ξ and d a larger and a smaller grooves the same restraint
than both ξ and d, a larger and a smaller grooves, the same restraint . For dielectric window with parallel Erf , restraint depends on both ξ and d related to f and Erf.
Erf
Dielectric window Metallic wall of waveguide When B⊥(Erf×Edc) and Ω~ω, resonantly accelerating under Erf×B, impact εe>εp2, δ<1 M i t l T t i f Mechanism of multipactor suppression:
More importanly τ～T, twice reverses of Erf×B, the same impact and emission phase, SE immediately pull away
du m eu B eE dt = − ×
2 2
( ) ( ) cos( )
y rf y
d u t E u t t dt B ω ω θ Ω + Ω = − +
Analytical θ=0o Simulative θ=-180o
Ω~ω Analytical and simulative agreement of εe
2 2 2 2 2 2 2 2
( sin cos )cos( ) sin cos ( ) sin( ) ( ) ( ) cos( ) ( sin cos )sin( ) sin cos ( ) cos( ) ( ) ( ) sin( )
rf y rf x
E t E u t t B B t E t E u t t B B t θ ω θ θ θ θ θ ω ω ω ω θ θ ω θ θ θ θ θ ω ω ω θ Ω ⎡ ⎤ − Ω + Ω + Ω = − Ω + ⎢ ⎥ −Ω +Ω + + ⎣ ⎦ Ω ⎡ ⎤ Ω + Ω + Ω = − Ω + ⎢ ⎥ −Ω +Ω −Ω + ⎣ ⎦
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Ω~ω, highest resonant εe, lowest δ, best suppression
Ω/ω=0 7 Ω/ω 0.7
Chang, et al., Appl. Phys. Lett. 96, 111502, 2010.
Klystron system, S-band，500ns
Incident Transmitted
B Magnet
B(T) Capacity(MW) EB(kV/cm) 0 07 0 08 8 9 20 21
Reflected Incident Transmitted
Erf
B
0.07-0.08 8-9 20-21 0.09-0.1 >36 >42 0.12-0.15 17-18 29-30 Flat surface 4-4.5 14-15 Periodical triangular surface of ξ=45o and p=2mm under B ~0.09-0.1T capacity>36MW.
Reflected
(Ω~ω)
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SES device, rectangular waveguide cavity, compress 2μs to 14ns Q~8000, Self-breakdown switch, gas of SF6 and N2 of 2-4atm,
power gain ~ 30-40
research in progress
Output compression
SES device Switch
Reflected
0.5μs/div Magnet
Waveform for dielectric
Incident Transmitted
no B at 52MW, 50kV/cm
Reflected Incident Transmitted
Waveform for B~0.07-0.08T at 144MW,
Reflected
, 80kV/cm
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Alter trajectories, impact energy εe and transit time τ to suppress multipactor
Periodic rectangular grooved surface Periodic triangular surface Periodic slopes diminish the tangent accelerating force and generate a l i Perpendicularly impact the side wall, Frf plays restoring f il i External B⊥ (Erf ×Edc) with Ω~ω resonantly accelerate under Erf×B, τ~T, undergo two reverses f E ×B d i εe<εp1, δ<1, τ<<T/2 strong normal restoring force force until reversing after T/2
flights εe>εp2, δ<1, τ~T
(A)
(B)
5 P i di t i l f (C)
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Optimize aperture field and radiation patterns of multi-mode horn by CST software. Achieve uniformed aperture field and equal E/H plane far-field. Agreement of theoretical and experimental radiation patterns:
Incident Radiated With periodic surface
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As 1st author, published 9 SCI papers+2 conference papers
4.C. Chang, et al., Phys. Plasmas 17, 053301, 2010.
10 C Ch l b bli h d i Ph Pl (APS DPP I i d lk)
As 1st inventor, apply for two Chinese national patents with
No.200910121391.1, No.2010101062929
Invited talk in 52nd APS-DPP Annual Meeting in Chicago in Nov. 8-12 2010
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