1. VACCALC: A Program to find Beam pipe Pressure Profiles M. Sullivan Nov. 3, 2011 JLAB, CASA, MEIC

2. Outline Introduction Program –Method –Features Examples Writeup Disadvantages Advantages Summary

3. Introduction Calculating pressures in vacuum beam pipes is relatively straightforward The second order differential equation one gets when the viscosity is zero for low pressures is:

4. VACCALC The Program VACCALC uses the method of finite differences to solve this equation One divides each input pipe element into a uniform subdivision of equal length pieces and then forms a tri-diagonal matrix that one can solve The resolution of the program is controlled by the length of the slices the elements are divided into Pipe elements with lengths not matching a multiple of the slice size are truncated

5. VACCALC (2) The input deck is a list of pipe elements for each input pipe In addition, the program is capable of joining various pipes together into a system of pipes Each input list for a pipe has a pipe title line that also indicates a value for each end of the pipe Then the program looks for ends of pipes with the same value and requires the pressure and flow at pipes with the same end values all be the same

6. Examples The writeup uses a very simple example that can be checked analytically I have the input deck and results of a PEP- II interaction region

7. PEP-II input deck Conductance Outgassing Pumping Name (4 chars) Total or per (m) Length (m) These units are either total or per meter. If the L is present in column 9 then the entry is the total for the element. Title Min unit of length (m) Pipe Title Flow specs for each end Node # for each pipe end

8. PEP-II Output IP beam pipe 5.6 m long pipe Pressure profile Elements Pump locations and speeds Outgas rates

9. HER downstream beam pipe 35 m long pipe

10. LER upstream beam pipe 60 m long pipe

11. HER upstream beam pipe 38 m long pipe

12. LER downstream beam pipe 65 m long pipe

13. Writeup The writeup describes the math used It also describes the input deck of an example file in great detail

14. Some Disadvantages Code is FORTRAN –Need a compiler Output file is a TOPDRAW file –A File of text commands for TOPDRAW –Easily portable but need the TOPDRAW program to convert to a PS file –Need to know TOPDRAW commands to modify the picture –TOPDRAW has awkwardnesses and limited capabilities

15. Some Advantages Code is very fast –Complicated PEP-II baseline design takes seconds to converge Easy to modify the input deck and do another run I have PC EXE files as well as source code I have a pdf file of the TOPDRAW manual I have a pdf file of the VACCALC writeup

16. Crib sheets Conductance calculations [liters / s] – c = 12  D 3 / L D = diameter in cm L = length in cm – c = 120000  D 3 / L D = diameter in m L = length in m

17. Crib sheets (2) Outgas calculations [nTorr ( liters / s)] –Inside area of beam pipe in cm 2 –Multiply by 0.1 nTorr (l/s) / cm 2 –This should give one the total outgassing rate of a pipe element at room temperature –References Chen, Liu, “Thermal Outgassing from Stainless Steel Vacuum Chambers”, Chinese Journal of Physics, vol. 24, No. 1, pg. 29, (1986) Bowden, G., “RF Accelerator Pressure Profile by Monte Carlo”, SLAC-TN-03-055, May 2002* *Gordon quotes an outgassing pressure of 0.01 nTorr (l/s) /cm 2 for well scrubbed RF bombarded Cu. This is 10 times lower than the number used above but the case if interest is where we do not have any scrubbing.

18. Summary The program VACCALC is a good, easy way of calculating the pressure in the interaction region where pumping will be difficult and limited Once an input deck is constructed one can make changes and quickly see what sort of effect one obtains with new the pressure profile There are disadvantages to using this rather “old” code but once installed I think it could be quite helpful