Insufficient cleaning of quasi-bound UCN

Chapter IV: Systematic effects

4.7 Insufficient cleaning of quasi-bound UCN

Section 2.8 described how quasi-bound UCN were removed from the trap before the holding process begins. Monte Carlo simulations have shown that this process is not perfect [43]. The probability that a quasi-bound UCN was lost out of the trap increased as the length of the holding process increased. Therefore, a correction to the extracted lifetime due to insufficiently cleaned quasi-bound UCN that escaped from the trap could have only increased the extracted lifetime.

In a typical production run, the cleaners were lowered to 38 cm above the bottom of the trap during the filling and cleaning processes. Additionally, the primary detector was lowered to the same height as the cleaners during the filling process, but was raised to 43 cm above the bottom of the trap during the cleaning process.

In order to study the systematic effect of insufficient cleaning of quasi-bound UCN, 30 runs were performed in 2017 and an additional 30 runs were performed in 2018 while the cleaners were held at their raised height of 43 cm above the bottom of the trap during the filling and cleaning processes. These runs were referred to as

“no-cleaning” runs. The no-cleaning running configuration significantly increased the number of UCN with 𝐸/𝑚_𝑛𝑔 > 38 cm that were in the trap after the cleaning process.

A method similar to the global method of extracting a lifetime presented in Section 3.9 was used to separately analyze the data from each year’s no-cleaning runs.

Due to the small number of no-cleaning runs, the values for 𝑓 were held fixed at the value from the rest of each year’s data instead of calculating it based on the no-cleaning runs. In 2017, there were 10 free parameters used to fit the data:

a lifetime 𝜅no clean, 2017, and nine normalization parameters (three each for three normalization subsets). In 2018, there were seven free parameters used to fit the data: a lifetime𝜅no clean, 2018, and six normalization parameters (three each for two normalization subsets). In both years, the relatively low number of free parameters allowed for finding the maximum likelihood estimate of the free parameters by directly minimizing a version of Equation 3.14 that had been updated to use𝜅_{no clean} instead of 𝜏. These fits resulted in values of 𝜅no clean, 2017 = 848.8± 2.8 s and 𝜅no clean, 2018 =862.3±3.7 s. Figure 4.7 shows the results of these fits. The values for 𝜅_{no clean} differed significantly between 2017 and 2018 due to the instillation of the buffer volume pre-cleaner. In the 2018 no-cleaning runs, the two cleaners inside of the trap remained raised during the filling and cleaning processes, but the buffer volume pre-cleaner remained at its standard lowered height.

Figure 4.7: The results of fitting the no-cleaning data. Top: the 2017 no-cleaning data. Bottom: the 2018 no-cleaning data. In 2017, the residuals of the fit had 𝜒²/𝜈 = 42.1/20 (p-value = 0.003). The scale of the uncertainty of the normal- ization estimate was held constant at the value calculated from the entirety of the 2017 production data, and therefore may not haven been a good representation of the uncertainty of the normalization estimate for these 30 runs. This could have contributed to the high value for for 𝜒²/𝜈. In 2018, the residuals of the fit had 𝜒²/𝜈 =26.8/23 (p-value=0.26).

The values for the 𝜅_{no clean}s differed from the neutron lifetime 𝜏 because some of the insufficiently cleaned quasi-bound UCN that were counted in the unloading process of short runs escaped from the trap during the holding process of long runs. The difference in the extracted lifetime between production runs and no- cleaning runs was roughly half as large in 2018 than in 2017 because the cleaning from the pre-cleaner in the buffer volume significantly reduced the number of UCN with 𝐸/𝑚_𝑛𝑔 > 38 cm that ever make it to the trap. The effect on the extracted lifetime from insufficiently cleaned quasi-bound UCN that escaped from trap can be analytically calculated by considering a short-long pair of runs with short holding length𝑡_𝑆,long holding length𝑡_𝐿,andΔ𝑡 ≡𝑡_𝐿−𝑡_𝑆. If:

1. exactly𝑁trappable UCN were loaded into the trap,

2. exactly𝑁_ICinsufficiently cleaned quasi-bound UCN were loaded into the trap, 3. none of the insufficiently cleaned quasi-bound UCN escaped from the trap

before the unloading process of the short run, and

4. all of the insufficiently cleaned quasi-bound UCN escaped from the trap before the unloading process of the long run,

then the extracted lifetime from that short-long pair would have been

𝜅= Δ𝑡

ln^{(𝑁+𝑁IC)𝑒−}

𝑡𝑆/𝜏

𝑁 𝑒^{−𝑡𝐿/𝜏}

= Δ𝑡

lnh 1+ ^𝑁IC

𝑁

𝑒^Δ𝑡/𝜏

i. (4.7)

Equation 4.7 was rearranged as 𝑟 =exph

𝜅⁻¹−𝜏⁻¹

Δ𝑡 i

−1, (4.8)

where𝑟 ≡ ^𝑁IC

𝑁

.

It was assumed that the number of insufficiently cleaned quasi-bound UCN that es- caped from the trap between the short and long unloading processes was proportional to the Peak 1 yields for runs with a holding length of 20 s. Therefore,

𝑟_clean=

𝑌¹

clean

𝑌¹

no clean

𝑟_{no clean}, (4.9)

where𝑌¹was the Peak 1 yield.

Equations 4.7 through 4.9 were combined to derive

𝜅_clean = Δ𝑡

ln 1+ h^𝑌_clean¹ i h^𝑌_{no clean}¹ i

exph

𝜅⁻¹

no clean−𝜏⁻¹

Δ𝑡 i

−1 𝑒^Δ𝑡/𝜏

. (4.10) The difference between 𝜅_clean and 𝜏 was the estimate of the shift in the extracted lifetime due the insufficiently cleaned quasi-bound UCN that escaped from the trap.

Choice of Δ𝑡 affected the calculated value for 𝑟 ,but the effect of choice of Δ𝑡 on 𝜅_cleanwas insignificant.

Table 4.1 shows the Peak 1 yields separated by year and by run type. The Peak 1 yields for no-cleaning runs were roughly 100×the Peak 1 yields of production runs.

The only difference between production runs and no-cleaning runs was the height of the cleaners. Quasi-bound UCN that would have avoided the cleaners in production runs would still have avoided the cleaners in no-cleaning runs. UCN with non-stable trajectories and𝐸/𝑚_𝑛𝑔 > 38 cm that would have been removed from the trap by the cleaners during a production run were able to remain in the trap until the unloading process of short no-cleaning runs. These UCN with non-stable trajectories were not a concern during production runs because they were rapidly removed by the cleaners, but the potential for the trajectories of insufficiently cleaned quasi-bound UCN to have evolved into non-stable trajectories and to have escaped from the trap was a concern.

Year

𝑌¹

clean

𝑌¹

no clean

𝑌¹

no clean

/ 𝑌¹

clean

2017 (5.8±1.6) ×10⁻⁵ (3.4±0.1) ×10⁻³ 57±11 2018 (−0.4±2.9) ×10⁻⁵ (15.2±0.6) ×10⁻³ 284±153^(∗)

Table 4.1: Peak 1 yields of both production and no-cleaning short runs, separated by year. ^(∗): The Peak 1 yield of production runs in 2018 was not significantly different than zero, so the value of (−0.4+2×2.9) ×10⁻⁵ was used when calculating the ratio of the Peak 1 yields from 2018. 𝑌¹ = 10⁻⁴ corresponds to having counted

∼1−4 UCN in Peak 1.

The average Peak 1 yield from production runs in 2018 was smaller than that of 2017.

These yields were a measure of the number of quasi-bound UCN in the trap, and the pre-cleaning in the buffer volume significantly reduced the number of potential quasi-bound UCN that ever made it to the trap. In contrast, the average Peak 1 yield from no-cleaning runs was greater in 2018 than in 2017. As explained in the above paragraph, these yields were mostly a measure of the number of UCN with non- stable trajectories and 𝐸/𝑚_𝑛𝑔 > 38 cm in the trap. One factor that contributed to

this increase was the aluminum block discussed in Section 4.2. As shown in Figure 4.1, the aluminum block caused high-energy UCN to be lost from the trap, but did not significantly affect low-energy UCN. The no-cleaning runs from 2017 were done (unknowingly) while the aluminum block was in the trap, which decreased the Peak 1 yields from the no-cleaning runs from 2017. Upgrades to the primary detector also caused the Peak 1 yields from the no-cleaning runs from 2018 to be greater than in 2017. The layer of ¹⁰B on the primary detector was twice as thick in 2018 as compared to 2017, which roughly doubles the efficiency per interaction of capturing low-velocity UCN. However, there was significant uncertainty of the thickness of¹⁰B on the primary detector from 2017, so this factor could have been even greater than two. In each version of the primary detector, the efficiency of capturing low-velocity UCN is thought to be≤20%.UCN that are not captured are reflected and counted later in the unloading process, likely after the end of Peak 1.

Additionally, the primary detector in 2017 was accidentally dropped 45 cm onto the Halbach array, which damaged the detector and decreased the efficiency of UCN capture on the lower part of the primary detector. Imperfections and impurities in the¹⁰B could have caused even more differences in the efficiency of UCN capture, but no data exist to support this hypothesis.

Given all of these differences (and potential differences) between the primary detectors of 2017 and 2018, a factor of 5 difference in the calculated value of

𝑌¹

no clean

/ 𝑌¹

clean

was not unreasonably large. What mattered for estimating the uncertainty of the extracted lifetime due to insufficient cleaning of quasi-bound UCN was not the number of UCN that were counted at Peak 1, but the actual number of UCN that had quasi-bound trajectories. The addition of the pre-cleaner in the buffer volume significantly decreased shifts in the lifetime due to not cleaning the population of UCN in the trap. If all else was held equal between the two years, then this should have resulted in a smaller value of

𝑌¹

no clean

/ 𝑌¹

clean

in 2018 than in 2017, but the opposite was observed. Several reasons have been presented to explain this discrepancy. The measurement of this ratio in 2018 was made using upgraded versions of multiple pieces of hardware, and theoretically the ratio should have been greater in 2017 than in 2018, so the measured ratio for 2018 was used to estimate the uncertainty of the extracted lifetime due to insufficient cleaning of quasi-bound UCN in both 2017 and 2018.

Using 𝑌¹

no clean

/ 𝑌¹

clean

=284±153 resulted in extracted lifetimes of𝜅clean, 2017= 877.50±0.34 s and 𝜅clean, 2018 = 877.57± 0.46 s. These extracted lifetimes cor- responded to decreases in the extracted lifetime of𝜏₂₀₁₇−𝜅_clean,2017 =0.12±0.03 s and 𝜏₂₀₁₈ −𝜅_clean,2018 = 0.06± 0.03 s. A lifetime extracted from just the 2017 production data had a statistical uncertainty of 0.34 s. A lifetime extracted from just the 2018 production data had a statistical uncertainty of 0.46 s. An average of the decreases in extracted lifetimes that was weighted by the statistical variances of the lifetimes extracted from the production data resulted in a combined decrease of 𝜏−𝜅_clean=0.10±0.03 s.

The analysis presented in this section estimated that insufficiently cleaned quasi- bound UCN that escaped from the trap caused the extracted lifetime to be 0.10±0.03 s less than it otherwise would be. If this 0.10±0.03 s decrease was correct, then the extracted lifetime should have been increased by 0.10±0.03 s to correct for it. This correction was estimated using multiple assumptions that were difficult to verify. There was too much uncertainty to justify applying a 0.10 s correction to the extracted lifetime, so 0.10 s was reported as a systematic uncertainty instead of a systematic correction. As explained at the beginning of this section, any correction to the extracted lifetime due to insufficiently cleaned quasi-bound UCN that escaped from the trap must have been strictly non-negative. Therefore, the systematic uncertainty of the extracted lifetime due to insufficient cleaning of quasi-bound UCN was reported as+0.10 s.