Effects of reflections on TE-wave measurements of electron cloud density
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Transcript of Effects of reflections on TE-wave measurements of electron cloud density
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Effects of reflections on TE-wave
measurements of electron cloud density
Kenneth HammondMentors: John Sikora and Kiran Sonnad
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Overview• Need to measure electron cloud (EC)
density• TE-wave transmission method–Wave transmitted and received by BPM
buttons– EC acts as a dielectric–Modulations in EC affect wave speed
and thus the phase at the receiver
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Overview• Determines spatial average EC
density• Data interpretation– Fourier transform of transmitted wave
is analyzed
–Modulations in phase appear as frequency sidebands
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Overview• Challenges– Irregular beam pipe geometry• Cross-section makes theoretical modeling
difficult• Numerical simulation is necessary
– Amplitude modulation• Can occur in the presence of constant
magnetic fields– Reflections• Primarily due to changes in cross-sectional
geometry• Can greatly affect average phase advance
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Overview• Tasks–Use physical waveguide to confirm accuracy
of simulation– Simulate beam pipe with CESR geometry
–Measure changes in phase advance brought about by changes EC density and reflections
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The Physics of Waveguides• Resonance– In practice, reflection will occur • Waveguide exhibits properties of a resonant
cavity– Standing waves form at wavelengths
harmonic with waveguide length–
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The Physics of Waveguides
f 2 = an2 + b2
a = (c/2L)2
b = fc
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The Physics of Waveguides• Phase advance and ΔΦ– Dispersion relation:
– Phase velocity:
– Phase advance:
– “Phase shift”:
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Simulation• VORPAL software models waveguide
system numerically• Input boundary conditions– Conductor walls– Transmitting antenna
• Solve Maxwell’s Equations
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Simulation• Special features– Grid boundaries• Automatically ascribes perfect-conductor
boundary conditions to specified surfaces• Cubic cells may be “cut” diagonally
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Simulation• Special features– Particles• Distribution can be controlled• Simulation accounts for positions,
velocities, and forces
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Simulation• Special features– PML (perfectly matched layer)
boundaries• Absorb all incident waves• Allows simulation of a segment of an infinite
pipe with no reflections
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Simulation• Differences with physical
measurements– Time scale• Most simulations modeled the system for
70ns• Longer simulations exhibit roundoff error• Frequency sweeps are not practical
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Experiments• #1: Phase shifts without reflection
–Multiple trials at different electron densities
PML
PMLρ measure
voltage
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Results• #1: Phase shifts without reflection
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Experiments• #2: Phase shifts with reflection
– Add conducting protrusions– Transmit waves at resonant frequencies
to maximize reflection
PML
PMLρ measure
voltage
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Results• #2: Phase shifts with reflection
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Results• Physical evidence in support of
inconsistent phase shifts– Transmission through a plastic
dielectric
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Results
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So, what next?• Simulate phase shifts at more
frequencies• Streamline the method for
extracting phase shift• Study phase shifts for different
electron cloud distributions
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Acknowledgments
Special thanks toJohn Sikora
Kiran SonnadSeth Veitzer
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Effects of reflections on TE-wave
measurements of electron cloud density
Kenneth HammondMentors: John Sikora and Kiran Sonnad
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Simulation• Differences with physical
measurements– Transfer function• A 70ns signal is essentially a square pulse
carrier frequency
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Experiments• Calculating ΔΦ– Record voltage over time for two
simulations
–Normalize voltage functions– Subtract one set of data from the other
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Physical model
Pipe length: l = 1.219m
Flange walls: l = 1.329m Optimized length: 1.281m
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Physical model
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Physical model
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Physical model
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Physical model
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Physical model
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Physical model
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Physical model
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Physical model
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Physical model• Rectangular copper pipe
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The Physics of Waveguides• Waveguide: a hollow metal pipe
• Facilitates efficient RF energy transfer• Cutoff frequency: minimum
frequency required for transmission– Determined by cross-sectional geometry