Strategy for O/P from thermodynamics

1. Strategy for O/P from thermodynamics

2. 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

3. 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.

4. 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 ceis 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

5. 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

6. 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

7. 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

8. 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.