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 PEP-II interaction region

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

PEP-II Output IP beam pipe

5.6 m long pipe

Pressure profile

Elements

Pump locations and speeds

Outgas rates

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