resonance frequency shift effects due to cavity...
TRANSCRIPT
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RESONANCE FREQUENCY SHIFT EFFECTS DUE TO CAVITY LENGTH AND WINDOW
VARIATION
By Gabriela Arriaga
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Who I am.
• Name: Gabriela Arriaga. • Institution: Northern Illinois University. • Major: Physics, junior year. • Fun Fact: I like to crochet toys for
children (when there is time)!
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Who I am (continued)
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• Have participated in two previous research programs. • Research Rookies.
• 2 rounds. • Summer Research Opportunities
Program (SROP). • In total, 5 semesters of research
experiences (6 including this experience!).
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Who I am (continued).
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• Homeschooled for most of my education before college.
• Am #4 of 8 children (yes, it is chaotic)! • Am the first child in my family to
attend college, and for Physics (Oh, my!)
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Agenda
• Project Description • Goal • Why we care • Methods
• Results and discussion • Thanks • Questions
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Project Goals
• Design Radio Frequency (RF) cavities for muon cooling channel (for future muon colliders).
• Reduce beam size. • Find a mathematical formula to model and
predict cavity shift phenomenon.
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Why do we care
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Muon Colliders are smaller than others
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• It is great to be small. • Can fit anywhere!
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Change in energy is small
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That is the hope.
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What does a muon cooling channel look like?
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Beginning of the channel
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The channel! (what we are working on)
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Methods
Primarily
• Simulations (lots of Simulations!) using Superfish.
• Mathematica.
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What is Superfish?
Superfish is a computer software program created by Los Alamos Laboratory that solves Maxwell's equations for RF, electrostatic, or magnetic cavity problems. Useful due to “ease” of use and speed.
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What is Mathematica?
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Software program from Wolfram to manage data and mathematical problems. • Plot neat graphs from data, which can be
2D or 3D. • Model trends. • Ect.
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Conditions
• Bowed cavity windows • The window radius (a) ranged from
2cm – 16 cm [increments of 4 cm] • The bow height of the windows (h) ranged
from 0.0 cm – 1.0 cm [increments of 0.2 cm]
• Cavity length • Ranged from 5, 10, and 20 cm.
• Cavity radius • 17.65 cm
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Simple sketch of the idea
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My Efforts
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• Running simulations for the bowed window • Plot the data and trends in Mathematica. • Calculate other properties for the cavities.
Sounds easier than it is!
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Bowed cavity windows Results
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First observation( frequency vs. h)
• Frequency decreases as h increases.
• Looks parabolic.
• Same trend for larger cavity lengths.
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Second observation (frequency vs a)
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Figure 4: Listplot of frequency change vs bow height. The red dots or for a window radius of 2 cm, green is for 4 cm, blue is for 8 cm, and 0rqnge is for 12 cm
• Parabolic looking as well.
• Critical point or minimum at a= 8 cm.
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Possible model
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Proposed model: 𝑓 = 𝑓 1 + 𝛼ℎ2 Where 𝑓 is the change in frequency, α is a constant that is a function of the cavity length and window radius, and h is the height of the bow. Does it work?
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Working out and testing proposed equation
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• Solved for 𝛼 with 3x3 matrix, using critical point a=8 cm for symmetry. • Resulting equation: 𝑓 = 𝑓(1 + (3.4226 ∗ 106)ℎ2).
• Standard deviation: ≈ 0.382.128𝐻𝑧. • Still needs more testing to be sure.
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Now for the electric field!
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Parmela Tableplot
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Figure 1: Table plot output from Parmela SF program. Data used in Parmela was from a simulated cavity with window bow height of 0.2 and window radius of 4 cm. The red line indicates the change in the electric field between the two cavity windows.
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Parmela Tableplot 2
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Table plot output from Parmela of a cavity of length 5 cm, window radius 4 cm, and bow heigth of 1 cm.
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Tableplot 3
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Table plot output from Parmela of a cavity of length 5 cm, window radius 16 cm, and bow heigth of 0.2 cm.
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Tableplot 4
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Table plot output from Parmela of a cavity of length 5 cm, window radius 16 cm, and bow heigth of 1 cm.
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Summary
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• Mathematical Model 𝑓 = 𝑓 1 + 3.4226 ∗ 106 ℎ2 represents the change in RF with a standard deviation of ≈ 0.2𝑀𝐻𝑧.
• Need to run more simulations to see if there is a more accurate model.
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Summary
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• Electric field decreases between the two windows, indicating acceleration.
• Larger bow heights have a greater effect on electric field change.
• Larger window radii reduce this effect. • More analysis needed to develop a
model.
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Extra Thought and possible next step
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• Look into multi cell condition. • What will happen if the
windows bow at different heights?
• If bowing is different as beam passes through the structure, how will electric field and beam be effected?
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Thanks
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• Supervisor Katsuya Yonehara, and the rest of the group
• Mentors at Northern Illinois University • DOE • SIST committee