Diffusion rate

email from Jin

I am writing to propose another possible quick target lab measurement to extract the diffusion rate.

As introduction, for two chamber dynamic model, polarization VS time in both chambers are imposition of two exponential curves, fast and slow ones.

· The slow time constant (~4 hour) is sensitive to spin exchange rate and pumping chamber spin destruction rate, which we have good data from production data. However, it is not directly related to the polarization difference between two chambers.

· The fast time constant (~<1hour) is sensitive to the diffusion rate and polarization difference between two chambers. However, our online data usually do not contain good constrain to this, due to the reasons such as unknown initial polarization for spin up curves.

Therefore, I am proposing a fast time constant measurement at target lab, which do not require an good calibration of absolute polarization at target chamber. This measurement require a working cell in the oven and working target chamber NMR setup (NMR signal on pumping chamber is a plus).

The procedure (~24 hour total) are

1. Heat a Transversity cell or a similar cell to 230C @ oven. Turn on laser wait for equilibrium.

2. complete destruction of cell polarization

a. reduce NMR RF power to ~1% (Yi Qiang have the magic number) of normal used one.

b. Perform field sweep couple time to ensure complete destruction of NMR signal

3. spin up curve

a. perform a NMR field sweep every 30min

b. measure spin up curve for 3 spin up time (~15 hour total?)

4. Optional: perform EPR polarimetry on pumping chamber. This will help determine spin exchange rate, which is a correction term to diffusion rate when calculated from fast time constant. A cross calibration between EPR AFP and field NMR sweep is necessary.

5. An AFP loss test

a. Set identical NMR field sweep as spin up curve

b. Perform 5 NMR field sweep, 30 second apart.

After lots of email exchange with Georgios Laskaris at Duke, I found they have performed a spin up measurement from 0 polarization. And I was able to extract the diffusion rate from their data with a 20% stat. precision which is consist with my model calculation to same level.

email from George

Please check the Results and Discussion part and the Appendix B where we proved the time dependent equations for the polarization for the two volume cell taking into account the diffusion rates Gt and Gp. Actually, we measured also the diffusion rate from pumping to target chamber and it was ~50 min much shorter than the pumping time or the relaxation time.

http://hallaweb.jlab.org/equipment/targets/polhe3/lab/doc/epja101183-offprints.pdf

measurement

test coil

230C oven, 230C pumping, 87.8, 48.3C, 37.8C target cell

4 ohm coil, 1-2w output, 0.5V source, 10cm close to target cell

Due to oven control PID setting is aggressive at P=??? , so the oven temperature is not very stable, fluctuate about 0.5C

1. NMR_He_20110709_132050, 10x120m, spin up

• before NMR_He_20110711_175209
• applying NMR_He_20110711_175520 (one way field sweep)
• after NMR_He_20110711_175635,NMR_He_20110711_175754,NMR_He_20110711_180036,NMR_He_20110711_181703 (12 times every 10 mins, with laser on)

test RF power

use different RF Power (Vrms) to do NMR, calculate H1 from resonance width, derive what the magic field H1 which destroys pol of Boris completely at 0.07Vrms

temperature: oven 210, pumping 212.7, target 81.7,38.2,45.1

• 3.2 NMR_He_20110713_182419
• 2.0 NMR_He_20110713_182547
• 1.0 NMR_He_20110713_182641
• 0.5 NMR_He_20110713_182748
• 0.2 NMR_He_20110713_182829
• 0.1 NMR_He_20110713_182925
• 3.2 NMR_He_20110713_183006
• 3.2 NMR_He_20110713_183041

test diffusion

1. oven 225, PC 234.8, TC 31.4 47.0 34.6

NMR_He_20111209_181404            before destroy, PC 27 TC 22
NMR_He_20111209_181636            destroy at 3.2V
NMR_He_20111209_181748            after destroy, PC 27 TC 14
NMR_He_20111209_182105            5x2m
NMR_He_20111209_183244            destroy 1.5V
NMR_He_20111209_183503            after destroy, PC 27 TC 12
NMR_He_20111209_183833            destroy 0.5V
NMR_He_20111209_184027            after destroy, (with 0.5), PC 17.5 TC 7
NMR_He_20111209_184626            20x10m

2. oven 230, PC 239.3, TC 31.8 48.0 35.3

NMR_He_20111212_170702  before destroy, PC 19 TC 15
NMR_He_20111212_171058  destroy at 1V
NMR_He_20111212_171230  after destroy, PC 7 TC 8
NMR_He_20111212_171819  before destroy,PC 7.5 TC 9
NMR_He_20111212_172029  destroy at 3.2V
NMR_He_20111212_172227  after destroy, PC 3 TC 5
NMR_He_20111212_172522  destroy at 3.2V
NMR_He_20111212_172659  after destroy, PC 2, TC 2.7
NMR_He_20111212_172853  destroy at 3.2V
NMR_He_20111212_173018  after destroy, PC 0.8, TC 1.8

NMR_He_20111212_180750  before destroy PC 3.3 TC 2.4
NMR_He_20111212_180858  destroy at 3.2V  
NMR_He_20111212_181012  after destroy, PC 1.8 TC 1.3

3. oven 230, PC 238.4, TC 32 49.8 36.1

NMR_He_20111215_174131  before destroy 24 18
NMR_He_20111215_174300  destroy at 3.2V
NMR_He_20111215_174359  after destroy, PC 23 TC 11
NMR_He_20111215_174555  destroy at 3.2V
NMR_He_20111215_174704  after destroy, PC 20 TC 7
NMR_He_20111215_175126  30x10m