Post on 24-Jun-2020
Magnetic Mapping for the 6He ExperimentREU Final Presentation
Jessie Thwaites1
Mentor: Alejandro Garcıa2
1College of Saint Benedict/Saint John’s University
2CENPA, University of Washington
15 August 2018
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Outline
1 Motivation
2 BackgroundWeak InteractionHelicity and ChiralityFierz Interference
3 My ContributionGadgetMultipole Expansion
4 Discussion
5 Further Investigation
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Motivation
Search for Beyond theStandard Model (BSM)physics through precisionexperiment
predicted by other theories:supersymmetry, GrandUnified Theories
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Background - Weak Interaction
Weak interaction - fundamentalforce
responsible for β decay
6He→ 6Li + e− + νe
mediated by W− boson
new physics: interactions
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Background - Parity Violation
Parity is the inversion of spatial coordinates
(ct, x , y , z)→ (ct,−x ,−y ,−z)
P~r = −~rP~L = (−~r)× (−~p) = ~r × ~p
Parity shows symmetry under theinversion of spatial coordinates
with parity: expected both right-and left-handed particles
Chien Sheng-Wu 1957 -left-handed particles only
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Helicity and Chirality
Helicity:
H =~p · ~s|~p||~s|
= ±1
Helicity not Lorentz invariant→ solution: define Chirality
eL =
√1+ p
E2 eH=−1 +
√1− p
E2 eH=+1
eR =
√1− p
E2 eH=−1 +
√1+ p
E2 eH=+1
eReL =√
1− ( pE )2 = m
E
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Interaction Hamiltonian
Interaction Hamiltonian for 6He beta decay:
Hint = ψf γµγ5ψi (2CAe
−Lγµγ5νLe ) +
ψf σµνψi [(CT − C ′T )e−Lσµνν
Re + (CT + C ′T )e−Rσµνν
Le ]
Search for tensor currents (σµν)
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Chirality-flipping - Fierz Interference
terms that include RH & LHare chirality flipping
show small distortions tospectrum
dW = dW0(1 + a pe ·pνEeEν
+ b ΓmeEe
)
b ≈ (CT +C ′T )
CA
m/K0 1 2 3 4 5 6 7
) [a
.u.]
-2(b
=10
E/d
Γd
0
2
4
6
8
10
610×
m/K0 1 2 3 4 5 6 7
(b=
0)-1
E/d
Γ)/
d-2
(b=
10E
/dΓd
2−
0
2
4
6
83−10×
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Measuring the β spectrum - CRES technique
need precision measurements of the entire spectrum
6 GHz bandwidth, tune magnet
Cyclotron Radiation Emission Spectroscopy (Project 8)
m/K0 1 2 3 4 5 6 7
E/d
Nd
0
2
4
6
8
10
610× = 1 TB
= 2 TB
= 4 TB
= 6 TB
ωc =qBc2
Ee
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My ContributionMagnetic Modeling
1. adapt NMR probe2. multipole expansion
3. position mapping
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The Gadget
Place the probe in the magnet at a particular location (r , θ, z)
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Nuclear Magnetic Resonance (NMR) Principles
start with a sample in a magnetic field, B0
perturb with a small oscillating field, B1
at resonance, induces an energy transitionby flipping magnetization
produces a strong signal at this frequency- characteristic of magnetic field seen bynucleus
use this magnitude measurement & fit tomultipole expansion
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Multipole Expansion
Laplace’s Equation:∇2φm = 0
Solutions: Taylor Expansion with spherical harmonics:
φm =∞∑l=0
l∑m=−l
(aml rl + bml r
−(l+1))Yml
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Theodolite Mapping
accurate positionmeasurements for probe
position accuracy impactsaccuracy of Linear LeastSquares fit in code
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Position mapping: z=-20 cm
Mean (x,y) values for set r
colors show r-value
Additional measurements:z=0 and z=+20 cm (notyet finished)
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Future Investigation
Finish position mapping of magnet
Automate gadget & Teslameter data collection process
Improvements on multipole model
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Acknowledgements
NSF and INT REU Program
Dr. Alejandro Garcia and his group
Deep, Gray, Cheryl and Linda
References[1] A. Abragam. Principles of Nuclear Magnetism. Clarendon Press, 1961.
[2] D. M. Asner, R. F. Bradley, L. de Viveiros, P. J. Doe, J. L. Fernandes, M. Fertl, E. C. Finn, J. A. Formaggio,D. Furse, A. M. Jones, J. N. Kofron, B. H. LaRoque, M. Leber, E. L. McBride, M. L. Miller, P. Mohanmurthy,B. Monreal, N. S. Oblath, R. G. H. Robertson, L. J. Rosenberg, G. Rybka, D. Rysewyk, M. G. Sternberg, J. R.Tedeschi, T. Thuemmler, B. A. VanDevender, and N. L. Woods (Project 8 Collaboration). Single-ElectronDetection and Spectroscopy via Relativistic Cyclotron Radiation. Phys. Rev. Lett., 114(16), Apr. 2015.
[3] C. Boettcher. Theory of Electric Polarization. Elsevier Publishing Co., 1952.
[4] M. Fertl, B. Graner, A. Garcia, M. Guigue, D. Hertzog, P. Kammel, A. Leredde, P. Mueller, N. S. Oblath,R. G. H. Robertson, G. Rybka, G. Savard, D. Stancil, H. E. Swanson, B. A. VanDevender, and A. Young.Detection of cyclotron radiation applied to searches for chirality-flipping interactions. Not yet published, 2018.
[5] R. Hong, M. G. Sternberg, and A. Garcia. Helicity and nuclear beta decay correlations. Am. J. Phys., 85(45),2017.
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