VACCALC: A Program to find
Beam pipe Pressure Profiles
M. Sullivan
Nov. 3, 2011
JLAB, CASA, MEIC
Outline
• Introduction
• Program
– Method
– Features
•
•
•
•
•
Examples
Writeup
Disadvantages
Advantages
Summary
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:
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
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
Examples
• The writeup uses a very simple example
that can be checked analytically
• I have the input deck and results of a PEPII interaction region
Title
PEP-II input deck
Min unit of length (m)
Pipe Title
Conductance
Flow specs for each
end
Outgassing
Node # for each pipe
end
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.
PEP-II Output
IP beam pipe
Pressure profile
Elements
Pump locations
and speeds
Outgas rates
5.6 m long pipe
HER downstream beam pipe
35 m long pipe
LER upstream beam pipe
60 m long pipe
HER upstream beam pipe
38 m long pipe
LER downstream beam pipe
65 m long pipe
Writeup
• The writeup describes the math used
• It also describes the input deck of an example
file in great detail
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
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
Crib sheets
• Conductance calculations [liters / s]
c = 12  D3 / L
–
•
•
D = diameter in cm
L = length in cm
c = 120000  D3 / L
–
•
•
D = diameter in m
L = length in m
Crib sheets (2)
• Outgas calculations [nTorr ( liters / s)]
– Inside area of beam pipe in cm2
– Multiply by 0.1 nTorr (l/s) / cm2
– 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) /cm2 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.
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