University of Maryland College Park MD USA The Nonlinear Structure of Multipactor Rami A Kishek Research sponsored by National Science Foundation Earlier work by US DOE and U Maryland Division of Research ID: 812050
Download The PPT/PDF document "1 Institute for Research in Electronics ..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
1
Institute for Research in Electronics & Applied PhysicsUniversity of Maryland, College Park, MD, USA
The Nonlinear Structure of Multipactor
Rami A. Kishek
Research sponsored by
National Science FoundationEarlier work by US DOE, and U. Maryland, Division of Research
IREAP
Outline
:
A novel and comprehensive theory
Incorporation of yield maps
Validation with PIC simulation
Slide2Where can we find Multipactor?2Vacuum Windows
Superconducting Cavities
Bunched Electron Sources
Accelerators
Space Systems
High-Power Microwaves
High-Gradient Dielectric Structures
Vacuum Devices and Microwave Sources
Communication Systems:
waveguides, antennas,
couplers
Electron Cloud
Slide3Multipactor is a Difficult Problem – Inherently Nonlinear3
Any Surface
Primary electron
impact
energy
W
i
Secondary electrons
emission
energy
W
o
~
work function
Secondary
Electron Emission
Discontinuity
of velocity vector
at
surface is
primary
source of nonlinearity
Conventional Multipactor theory tiptoes around the nonlinear nature of the problem
A
priori
assumption of multipactor mode
Difficult to solve for higher periodicities
Over-emphasis
on stochasticity
Large, arbitrary margins!
Slide4How to tractably handle the complexity of multipactor?Do we need to catalogue all the possible modes and derive existence and stability limits for each?Higher-order modesPeriod-nHybrid (varying periods)Ping-pongNon-resonantDC electric/magnetic fields4
w
t
x
Experimental / Simulation studies are often device-specific.Without a comprehensive theory, successes in eliminating multipactor from one device are difficult to generalize to others.A new approach is needed
Slide55
Example: Dielectric surface with normal dc and rf fields
Normalize
:
t
w
t
h
E
DC
/E
o
For any given phase, find
next single-surface impact:
x
(
t
1
,
q
)
= 0
Integrate (assuming monoenergetic emission):
The details of the trajectory are irrelevant.
The only thing that matters is the
rf
phase at impact!
E
DC
E
o
sin(
w
t+
q
)
z
(m
w/
e)(v/E
o
)
R.A. Kishek,
Physics
of Plasmas
20
, 056702 (2013).
Slide6Solve for transit time to determine arrival phase
6
Multi-valued
Bifurcation responsible for cutoff of 2-surface multipactor
Accelerating rf
Retarding
rf
Map
zo
= 0.2,
h
= 0.3
Slide7Calculate map once - contains all the information
7
M
1mod 2p
Fixed phase, locally unstable
(|slope| > 1)
Slide8… apply map successively to advance particles
8
But
globally stable with period-4 cycleM
1mod 2p
Slide9Apply map repeatedly to itself to find attractor, then scan control parameter and repeat9
Successive bifurcations
z
o = 0.2
Slide10Extending Bifurcation Diagram Shows Chaos10zo = 0.2
How meaningful is this number-juggling?Is strong resonance better than chaotic multipactor?What parameters should I operate at?
Slide11Yield Map
11
z
izo = 0.2, h = 0.3
CopperWmax
, Wo = 271.0, 6.0dmax = 2.1Impact velocitySEE Yield
SEE Yield (
d) = # secondaries / primary
Theory uses modified Vaughan formulaC. Vicente, et al., Proc. 2006 Power Modulator Symposium, (IEEE, ISSN 1930-885X, p. 22-27, 2006).
Simulation uses POSINST library
M.A. Furman and M.T.F. Pivi,
PRSTAB
5
, 124404 (2002
).
Slide12Average yield curve12Copperzo
= 0.2
Color-code: d >> 1 d
~ 1 d <<1
Slide13Materials and Super-Periodicity 13
Alumina (94% purity)Wmax, W
o = 1000.0, 4.83d
max = 5.75zo = 0.2Same attractor, different yields
Slide14Verification by Simulation14WARP PIC code, stripline geometryCopper (POSINST model)f = 500 MHzEo = 91.7 kV/m Keep upper electrode far away, absorbing but no SEEOnly lower electrode emits secondaries
Slide15Arrival Phases in Simulation15
h
=
0.24
h
= 0.29
h = 0.3h = 0.33
Slide16Comparison of Growth Rates (1st attempt)zo = 0.2, h = 0.316
WARPTheory
z
oLeakageR.A. Kishek, "Coexistence of Mixed Mode Multipactor," Physics of Plasmas 19, 124501 (2012). h = 0.3
f(
z
o
)
Slide17Incorporating Random Emission Velocity – In ProgressFor each value of hScan zo over the range 0 to 1.0Calculate the net growth rate dave(h,
zo)Integrate growth rates over zo to get average yieldwhere
Note: details of the SEE model in the theory need be finessed
17
Slide18Theoretical Growth Rate Integrated Over Velocities18WARPTheory
Extended Range
Encouraging!
Slide1919
ConclusionsTowards a New, Predictive, Theoretical approachVerified by simulation
Straightforward to generalizeCapable of quickly sweeping vast regions of parameter spaceCan identify multipacting region, without
a priori assumptions, encompassing all possible modes for given geometrySpread of initial velocities smoothens bifurcations, different multipacting modes can coexistMaps embed considerable information on multipactor.
Slide20AcknowledgmentsDiscussionsTom AntonsenGregory NusinovichEd OttPerry MaloufBenito Gimeno-MartinezWARP SupportJean-Luc VayDave GroteAssistanceMoiz Siddiqi Poster tonight 5:30-7:30 PM
Woodrow Wilson A20
Slide21BACKUP21
Slide22Impact energy comparison22
zo = 0.2, h = 0.3
Impact Energy Map from TheoryImpact Energy Distribution from Simulation
Slide23Iterate map to determine higher periodicities
23
Higher-period maps have multiple fixed points, some of which are locally stable
M4
Slide24Apply map to itself to advance one iteration
24M1M1024
1,024 iterations:
4 stable fixed points
Slide25Zoom in on Window25
Slide26Scanning the other parameter, zo , h = 0.326