# Monitor and operate the microwaves / know how to find correct frequency

# Using LabView for mmWaves

- (David?)

# Finding the mmWave Frequency to Enhance Polarization

In order to start looking for the optimum millimeter/microwave frequency, the variables below are important to know. Note that here the frequencies are given in GHz for finding mmwave frequency, as the frequency for 5 T fields will always be around 140 GHz, and in MHz for nuclei to aid in finding NMR signals.

- Electron Gyromagnetic Ratio: <math>\frac{\gamma_e}{2\pi}=28.024~951~6~\mathrm{GHz/T}</math>
- Proton Gyromagnetic Ratio: <math>\frac{\gamma_p}{2\pi}=0.042~577~478~92~\mathrm{GHz/T}=42.577~478~92~\mathrm{MHz/T}</math>
- Deuteron Gyromagnetic Ratio: <math>\frac{\gamma_D}{2\pi}=0.006~535~902~311~\mathrm{GHz/T}=6.535~902~311~\mathrm{MHz/T}</math>

In order to find both the ideal mm-wave and NMR frequencies, some combination of the above numbers are multiplied by the magnetic field strength <math>B</math> in T. This gives the particle's Larmor frequency, <math>\nu_i = \frac{\gamma_i}{2\pi}B</math>, that is used in the descriptions below.

## Proton Enhancement

The image below shows the energy level splitting of the proton, along with the expected NMR spectra along the top. These energy splittings are a useful guide for determining a good initial estimate of the polarization enhancement frequency for the mm-waves.

- Find & measure TE using the Larmor Frequency
- <math> \nu_p = \frac{\gamma_p}{2\pi}B</math>
- Use the central value of the measured TE to extract the magnetic field for the calculations below

- <math> \nu_p = \frac{\gamma_p}{2\pi}B</math>
- To calculate the best positive enhancement frequency for mm-waves:
- <math>f_{\uparrow}=\nu_e-\nu_p</math>

- To calculate the best negative enhancement frequency for mm-waves:
- <math>f_{\downarrow}=\nu_e+\nu_p</math>

Note that the above should be considered starting points. The actual frequency will shift slightly due to the number and position of free radicals in the material (this causes <math>\nu_e</math> to shift slightly). It's good practice to:

- Start at the frequencies calculated above
- Carefully go up in frequency and note if the maximum polarization increases or decreases
- Typically the above calculations tend to be slightly lower than the actual polarization numbers, though this may not always be the case

- If a point of maximum polarization is not found:
- Go back to the starting frequency
- Carefully go down in frequency to see if the maximum polarization improves

- Keep track of where maximum polarization occurred and use that as your frequency

## Deuteron Enhancement

Due to a combination of the additional spin-0 state and energy-level shifts due to quadrupole effects in nuclei such as ND_{3}, find ideal frequencies is much more complicated than it is for the proton. However, the same basic procedure can be followed using energy level diagrams as a guide.