Strategy for O/P from thermodynamics

–Motivation• problem with uncertainty in MCNP kernel for determination

of O/P ratio• develop another method to estimate upperbound of O/P ratio

–Outline• describe the factors that goes into the estimation• rate equation• how we can measure it for the next beam cycle

dM/dt is determined by liquefier rate

Assumption:Stainless Steel line at 70 K. worst case scenario: para hydrogen reaches equilibrium in the SS line.

Steady State

• let k be ortho to para conversion rate in OPC• let k’ be the up-conversion rate in the line,

which is just ce*dM/dt, where ce is the equilibrium concentration at 70 K.

• rate equation is just • which gives an exponential • this gives us a steady state solution (dc/dt =0)

of

• well this is all fine and dandy, but where can we get these number???

• measuring k (OPC conversion rate) is not simple, let us suppose two cases.– conversion time is short• we observe saturation (no evidence of decay), use

filling time as time constant

– conversion time is long• in this case, we will see the exponential decay after

filling, which means we can measure the time constant, this will give us , but in the limit of small k’ and small para-concentration, second terms drops out

• In the following exercise, I will estimate our old data run with the following parameters, just to play around with some numbers

• heater (H3) on liquefier refrigerator was not running during operation of H4 (which induces large circulation), normal operating condition for H3 is 30%, it is a 12.5 Watt heater. This is equivalent to 4.1e-3 mol/s. heat of vaporization for hydrogen is 0.904 kJ/mol

• we have close to 600 mol of H2, ce at 70K is 46% for ortho• big assumption here, time constant for large c at beginning

period of decay is 1 day.

• this gives a c=21.5%, unacceptable

• better assumption, line is extremely dirty (magnetic dirt everywhere, not really possible), so up conversion in line is just as the same as down conversion in OPC. Instead, we have

• c = 3.14e-6• now, we can multiply this (1-c) to equilibrium

(1-ce) to obtain new para concentration

Conclusion

• we need to still think of other up-converting mechanisms.

• if line conversion is largest, then we are done. new steady state is only 3e-6 smaller

• rate for ortho to para conversion drops out in this estimation.