# Research

## Radio Frequency Probe Post #2: 2019 Update

(Written by Jonathan Sheppard) Intro This summer the team took the previous year team’s RF probe design and both updated and upgraded it, in an attempt to optimize its functions. As with last year’s design, we used the text Experimental Pulse NMR: A Nuts and Bolts Approach by Eiichi Fukushima and Stephen B. W. Roeder as a guide. The main sections used will be noted throughout this post. As noted in the previous post, below are some general guidelines on the inductor coil specifications (from the section “V.

## Summer Science 2019 Summary

(Written by Jonathan Sheppard and Aaron Conover) This summer, Jon Sheppard and Aaron Conover joined Merideth Frey’s physics research team through the Sarah Lawrence Summer Science Internship program. Last summer, the team focused on setting up the new TeachSpin equipment and optimizing the Halbach Mandhala design. They were successful in both endeavors. Thus, this summer, the attention has been on designing and creating a Radio Frequency transceiver and an easily manipulated gradient field (while also attempting to optimize all magnetic fields even further).

## Optimizing Positions of Magnets in Mandhala - 2019

This work was a follow-up to the work discussed in the previous post from 2018 on optimizing positions of magnets in the NMR MANDHALA based on a close reading of of Soltner and Blumler’s 2010 article “Dipolar Halbach Magnet Stacks Made from Identically Shaped Permanent Magnets for Magnetic Resonance”. There the dipole approximation is used for each cubic magnet in order to optimize magnet position to take into account inhomogeneities in the magnetic moments of the magnets used in the Mandhala (see ‘Variation of Magnet Properties’ section of article).

## Introducing the GitHub Repository

In order to more easily share the data analysis templates we produce to analyze our data, we have created a GitHub respository. Most of these are Jupyter notebooks, but if you don’t have Jupyter installed, no worries! Click on the `launch binder’ button that appears in the opened README file, and this will launch an external server with Jupyter so you can run and interact with the notebooks yourself. (Make sure to save/download a copy of the notebook if you want to save any changes you make!

## RF Probe Building

(Written by Jianlong (Ken) Zhu) RF Probe We designed our own RF probe with the aid of a manual, Experimental Pulse NMR: A Nuts and Bolts Approach (Eiichi Fukushima and Stephen B. W. Roeder). Below are some takeaways from the section “V.C.4. Probes” (p.p. 373-385): A good coil for RF probe has a large inductance, which is given by the equation: $L = \frac{n^2 a^2}{23a+25b}$ μH, where n is the number of loops, and a and b are the radius of the loop and the length of the coil measured in centimeters.

## T1 and T2 Plotting

(Written by Nicholas Torres) An important aspect of conducting NMR analysis is finding two time-constants: T1 and T2. The T1 constant represents the longitudinal relaxation time or how long it will take for a proton that has been energized by a radiofrequency (RF) pulse to go back to realign with the magnetic field, whereas the constant T2 or transversal relaxation time tells us roughly how long it will take for a proton that has been struck with a 90° RF pulse to dephase from its neighboring protons due to different local magnetic environments.

## Summer Science 2018 Summary

(Written by Jeremiah O’Mahony) This summer, Ken Zhu and Nick Torres joined Jerry O’Mahony to help improve Merideth Frey’s lab at the Sarah Lawrence Summer Science Physics Internship. The bulk of our focus over the summer was split between improving the Halbach Mandhala design from last summer and getting the TeachSpin system up and running. We succeeded in both–the current Mandhala is more powerful and versatile than the last, and as of the last week of the internship, the TeachSpin system is reliably detecting 1-D images of samples.

## Optimizing Positions of Magnets in Mandhala

As part of my close reading of Soltner and Blumler’s 2010 article “Dipolar Halbach Magnet Stacks Made from Identically Shaped Permanent Magnets for Magnetic Resonance”, I noted using the dipole approximation for each magnet in order to optimize magnet position to take into account inhomogeneities in the magnetic moments of the magnets used in the Mandhala (see ‘Variation of Magnet Properties’ section of article). The article creates a ‘cost function’ that measured the deviation of the magnetic field at the center of the Mandhala from what one would get if all the magnets were exactly identical with magnetic moments equal to the mean of the magnets being used.

## Optimizing NMR Mandhala Design

For the 2018 version of our NMR Mandhala (working towards higher homogeneity along the cylindrical axis), I did a close reading of Soltner and Blumler’s 2010 article “Dipolar Halbach Magnet Stacks Made from Identically Shaped Permanent Magnets for Magnetic Resonance”. Below are some particularly useful findings. Useful Information Regarding Comparing Finite Sized Magnets with Theory: Magnetic field of final magnet is in very good approximation the sum of the field of its pieces.

## Theoretical Simulations using FEMM

This post will go over the various FEMM 4.2 simulations we did to estimate magnetic field strengths and magnet placements for our NMR Mandhalas. Useful Links: FEMM Manual Mathematica Interface (FEMM 4.2) In order to do the simulations for the NMR Mandhala, it was very useful to first go over the following tutorials, since we were essentially simulating the effects of multiple N52 permanent magnets. One can then simple extend these tutorials to simulate multiple permanent magnets in the particular placement and orientation necessary for the NMR mandhala (see DOI 10.