In blongworth/HybridGIS: Data, Functions, and Analysis for the NOSAMS Hybrid Gas Ion Source

First tests of the USAMS SNICS-134 Hybrid gas ion source. Where not specified, flows are given in $\frac{\mu L}{m}$ and pressure in kPa, and ion currents are in uA of 12C.

library(tidyverse)
library(amstools)
library(here)
library(HybridGIS)

theme_set(theme_bw())
options(digits = 3)

Flow rates

Calculated flow

To model laminar flow in a capillary, Poiseuille's equation is used.

$$ Q = \frac{\Delta P \pi R^4}{8 \mu \Delta x} $$

Where $\Delta P$ is change in pressure (Pa ($\frac{kg}{m \cdot s^2}$)), $R$ is radius of pipe (m), $\mu$ is dynamic viscosity ( $P \cdot s$ ($\frac{kg}{s \cdot m}$)), and $\Delta x$ is the length of the pipe (m). Q is in $\frac{m^3}{s}$

The following functions calculate flow using this equation and convert base units to more convenient flow in $\frac{\mu L}{m}$ and pressure in kPa.

# Poiseuille's; convert delta pressure in Pa to flow in m^3/s
prestoflow <- function(dp, r, u, l) {
  # r = radius of capillary
  # l = length of capillary
  # u = viscosity kg/m
  flow <- dp * pi * r^4 / 8 / u / l
  flow
}

# convert gauge kPa to uL/min
flowcalc <- function(pres, ...) {
  dppa <- pres * 1E3 #convert kPa to Pa
  flowcms <- prestoflow(dppa, ...)
  flowuls <- flowcms * 1E6 * 1E3
  flowulm <- flowuls * 60
  flowulm
}

Initial tests used a 0.050mm x 8.2m deactivated silica capillary. For this capillary, parameters for Poiseuille's equation are as follows:

r <- 2.5E-5
u <- 1.49E-5
x <- 8.2
factor <- flowcalc(1, r, u, x)

$\Delta P$ is regulator pressure

R is r r*1E6 $\mu m$

$\mu$ is r u*1E6 $\mu Pa\cdot s$

x is r xm

Given these,

Q($\frac{\mu L}{m}$) = r factor x P (kPa)

flow <- function(f) {
  flowcalc(f, r, u, x)
}
ggplot(data = data.frame(pressure = 0, flow = 0),
       mapping = aes(x = pressure, y = flow)) +
  stat_function(fun = flow) +
  xlim(0,400) +
  ggtitle("Theoretical flow for given pressure",
          subtitle = "8.2m x 50um capillary")

Measured flow

Kalina and I measured flow at the end of the capillary using two methods; direct measurement with a bubble flow meter and as a helium leak rate with the leak detector.

Bubble meter

Kalina made measurements with both helium and CO2. The measurements below are with helium and converted to CO2 by the ratio of their viscosities.

bflow <- read.csv(here("data/bubbleflow.csv")) %>%
  mutate(heflow = volume/time,
         flow = heflow * 1.49E-5/1.90E-5, # co2/He viscosity
         pressure = pressure - 14.7, # subract 1 Atm for delta P
         pressure = pressure * 6.8948, # convert psi to kPa
         calcflow = flowcalc(pressure, r, u, x)) # calculate flow with Poiseuille's 

ggplot(bflow, aes(pressure, flow)) + 
  stat_function(fun = flow, color = "blue") +
  geom_point() +
  geom_line() +
  xlim(0,400) + ylim(0,80) +
  ggtitle("Flow vs pressure",
          subtitle = "measured by gauge and bubble flow meter")

ggplot(bflow, aes(calcflow, flow)) + 
  geom_point() +
  geom_line() +
  ggtitle("Measured (bubble meter) vs predicted flow")

Leak detector

2017-10-17?

Measured leak rate using Helium leak detector. Ran capillary to KF adapter flange. Pressures in kPa, leak rates in $\frac{Pa\cdot m^3}{s}$. Leak detector switched to gross leak mode between 150 kPa and 200 kPa.

ldflow <- read.csv(here("data/HeLeakCapillaryFlow.csv"), skip = 3)

ldflow <- ldflow %>% 
  mutate(sccm = Leakrate / 0.0016, # convert to sccm
         co2sccm = sccm * 1.49E-5/1.90E-5, # co2/He viscosity
         flow = co2sccm * 1E3, # convert to ul/m
         calcflow = flowcalc(Regulator, r, u, x)) # calculate flow with poiseulle's 

ggplot(ldflow, aes(Regulator, flow)) + 
  stat_function(fun = flow, color = "blue") +
  geom_point() +
  geom_line() +
  ggtitle("Flow (measured by leak detector) vs pressure")

ggplot(ldflow, aes(calcflow, flow)) + 
  geom_point() +
  geom_line() +
  ggtitle("Measured (by leak detector) vs predicted flow")

Efficiency functions

These functions convert volume of CO2 and coulombs of charge to atoms of C. The ratio of these is the measurement efficiency of a gas ion source system. These are used for later calculations of efficiency given flow rate and ion current.

# convert L CO2 to atoms C
lCO2toatC <- function (vol) {
  molC <- vol * 1/22.4 # 22.4 L of gas per mole at stp
  atC <- molC * 6.022E23
  atC
}

# convert current in A to atoms C/sec
CcurtoatC <- function(cur, cs) {
  at12C <- cur * 6.25E18 # electrons per coulomb
  at12C <- at12C / cs # divide by charge state
  at12C
}

# calculate efficiency from ml/m CO2 and uA C12
hgis_eff <- function(ulm, uA, cs = 3) {

  # if flow is zero or less, efficiency doesn't make sense
  ulm <- ifelse(ulm <= 0, NA, ulm)

  vol <- ulm * 1E-6 # conv to L
  cur <- uA * 1E-6 # conv to A
  atCin <- lCO2toatC(vol) / 60 # gives atoms/s
  atC12out <- CcurtoatC(cur, cs)
  atCout <- atC12out / .99 # 99% of C is 12C, we need total C
  atC12out / atCin
}

Test Wheels

Two days of testing to date. Same wheel both days. Wheel had 5 AA, 4 OX-I, and 10 gas targets.

USAMS032817

Currents

For the first target, we turned up the gas supply pressure while measuring source current at the high energy FC. These currents are roughly equivalent to le12C (~30% transmission @ 3+ charge state).

Load and massage the data...

cur <- read_tsv(here("data/2017-03-28Currents.tsv")) %>%
  mutate(flow = flowcalc(regp, r, u, x),
         eff = hgis_eff(flow, he12c, cs = 1)) %>% # cs 1 to estimate LE current
  filter(t > 5) 

ggplot(cur, aes(regp, he12c)) +
  geom_line() +
  geom_point() +
  ggtitle("Current vs Pressure",
          subtitle = "2017-03-28")

ggplot(cur, aes(flow, he12c)) +
  geom_line() +
  geom_point() +
  ggtitle("Current vs Flow",
          subtitle = "2017-03-28")

data <- get_hgis_data(here("data/USAMS032817R.txt")) %>%
           mutate(Num = ifelse(Pos == 11, "U", Num))
stdrat <- mean(data$cor1412he[data$Num == "S"])
data <- mutate(data, normFm = norm_gas(cor1412he, stdrat))
# data <- readResfile("/mnt/shared/USAMS/Results/2017 Results/USAMS032817R.txt") %>%
#   mungeResfile() 

Currents were very stable after an initial burn in of ~10m. Initial current started at ~12uA without gas on target and decayed (roughly) exponentially to a minimum around 1.2uA.

data %>% 
  filter(Pos %in% c(11,12)) %>%
  ggplot(aes(ts, he12C, color = Pos)) +
    geom_line() + geom_point() + ylim(c(0,8))

Efficiency

Using efficiency functions defined above. Efficiency drops with increasing flow as currents go up.

ggplot(cur, aes(flow, eff)) + geom_line() + geom_point()

Ratios

Ratios for live and dead CO2 were recorded in 180 blocks of 10s each. Solid AA and OX-I were run with 10 blocks of 180s. These results are summarized and roughly normalized to solid OX-I below.

Summary table

sum_hgis(data)

Plots

Boxplots of modern and dead samples. Ratios were essentially stable over time. Positions < 10 are solid samples run for comparison.

Modern samples.

data %>% 
  filter(X14.12he > .4,
         Pos %in% c(7, 11)) %>%
  mutate(type = ifelse(Pos == 7, "solid", "gas")) %>%
        ggplot(aes(type, X14.12he)) + 
        geom_boxplot() +
        labs(x = "Sample type", y = "Fraction modern")

Dead gas and alpha aesar.

data %>% filter(X14.12he < .02,
                X14.12he > 0.0005,
                Pos %in% c(3, 12)) %>%
  mutate(type = ifelse(Pos == 3, "solid", "gas")) %>%
           ggplot(aes(type, X14.12he)) + 
        geom_boxplot() +
        labs(x = "Sample type", y = "Fraction modern")

USAMS040317

The same target wheel was loaded again. Karl and I experimented with the source tune and target position to try and get more current. We were able to increase the currents by about 1/3 by moving the target closer to the immersion lens. Flow rates were lower for a given current. After tuning, I looked at flow vs. ratio and current. The gas used was the modern standard, but the flask may not have been fully flushed.

data <- get_hgis_data(here("data/USAMS040317R.txt")) %>% 
  filter(Pos == 13)

sum_hgis(data)

# data <- readResfile(here("data/USAMS040317R.txt")) %>%
#   filter(Pos == 13) %>%
#   mungeResfile() 

# Assign Run numbers
counter <- 0
Run <- c(1:190)
for (i in 1:nrow(data)) {
  if (data$Meas[i] == 1) {
    counter <- counter + 1
  }
  Run[i] <- counter
} 
data$Run <- Run

# Load pressure data
pres <- read.csv(here("data/USAMS040317Pressure.csv"))
pres$Run <- as.numeric(row.names(pres))

# Join to run data
data <- inner_join(data, pres) %>%
  mutate(Source = Source * 1E-7, # I think the source pressures were to the -7, but unsure...
         flow = flowcalc(Bottle, r, u, x),
         eff = hgis_eff(flow, he12C, cs = 1)) # cs 1 to estimate LE current

# summarize
d.s <- data %>% group_by(Run, Bottle, Source, flow) %>% summarize(le12C = mean(le12C),
                                              he12C = mean(he12C),
                                              counts = sum(CntTotGT),
                                              interr = 1/sqrt(counts),
                                              C1412he = mean(X14.12he),
                                              C1412he_sd = sd(X14.12he),
                                              ferr = interr * C1412he,
                                              cor1412he = mean(cor1412he),
                                              eff = mean(eff))
d.s

Gas flow vs source pressure

ggplot(d.s, aes(Bottle, Source)) + 
  geom_smooth() +
  geom_point() 
ggplot(d.s, aes(flow, Source)) + 
  geom_smooth() +
  geom_point() 

Currents

ggplot(d.s, aes(Bottle, he12C)) +
  geom_smooth() +
  geom_point() 
filter(d.s, flow > 0) %>%
  ggplot(aes(flow, le12C)) +
  geom_smooth() +
  geom_point() +
  labs(x = expression(CO[2]~flow~rate~~mu~L %.% min^{-1}),
       y = bquote('12C-  ' *mu~ 'A')) +
  scale_y_reverse() +
  ylim(0,-10) +
  xlim(0,15.5)

Ratio vs current

ggplot(d.s, aes(he12C, C1412he)) + 
  geom_linerange(aes(ymin = C1412he - ferr, ymax = C1412he + ferr)) +
  geom_smooth() +
  geom_point() 

Efficiency

ggplot(d.s, aes(Bottle, eff)) + 
  geom_smooth() +
  geom_point() 
ggplot(d.s, aes(Source, eff)) + 
  geom_smooth() +
  geom_point() 
ggplot(d.s, aes(flow, eff*100)) + 
  geom_smooth() +
  geom_point() +
  labs(x = expression(CO[2]~flow~rate~~mu~L %.% min^{-1}), y = "Measurement efficiency  %") +
  xlim(0,15.5)

blongworth/HybridGIS documentation built on Dec. 19, 2021, 10:41 a.m.