Vacuum in Particle Accelerators, by Oleg B. Malyshev

Vacuum in Particle Accelerators

Modelling, Design and Operation of Beam Vacuum Systems

Oleg B. Malyshev

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Author

Dr. Oleg B. Malyshev

ASTeC

STFC Daresbury Laboratory

Keckwick Lane

WA4 4AD Daresbury, Cheshire

United Kingdom

Cover Image: Courtesy of Mr. Clive Hill, STFC Daresbury Laboratory

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Print ISBN: 978‐3‐527‐34302‐7

ePDF ISBN: 978‐3‐527‐80916‐5

ePub ISBN: 978‐3‐527‐80914‐1

oBook ISBN: 978‐3‐527‐80913‐4

Acknowledgements

The editor hereby acknowledges with deepest appreciation and thanks the support of many people who helped at different stages of writing and editing this book from its original idea to final polishing.

First of all, I would like to thank Dr. Vincent Baglin (CERN, Switzerland) for providing me the greatest support in discussing a structure and a content of the book, for helping to build a team of co‐authors, and for being my co‐author in three chapters.

Great thanks to my co‐authors who worked hard aiming to write a book that would be useful to particle accelerator vacuum community and keeping consistency from chapter to chapter. Dr. Olivier Marcouillé (SOLEIL, France) worked on describing synchrotron radiation in terms required for a vacuum system designer (this information is usually hard to find in other books), Dr. Junichiro Kamiya (J‐PARC, Japan) made a detailed overview of thermal outgassing of materials used in particle accelerators and methods of measurements, Dr. Erik Wallén (LBNL, USA) kindly agreed to review theoretical cryosorption models and results of cryosorption experiments, Dr. Adriana Rossi (CERN, Switzerland) worked with me on the ion‐induced pressure instability analysis, and Dr. Markus Bender (GSI, Germany) summarised a present state of problem solving for heavy ion‐induced pressure instability.

I would also like to thank many colleagues from different research centres around the world for useful suggestions, corrections, reviewing different parts of the book, and following feedback. I would also acknowledge my colleagues from the STFC Daresbury Laboratory for providing necessary information, images, and graphs, for useful suggestions, and for support. My Great thanks are to Mr. Clive Hill for the cross‐sectional view of EMMA accelerator shown on a cover of this book.

I would also wish to give a special thanks to my wife Larisa and my children Dmitry and Daria for the daily support, interest to a progress, reading and making corrections, and great patience when I was spending my free time with a computer instead of a family.

And finally, many thanks to Wiley teams for the great help with the book production: to Dr. Martin Preuss for setting up the process of publishing and for answering my numerous questions, to Ms Shirly Samuel for assistance with the submission process, to the production team lead by Mr. Ramprasad Jayakumar for careful reading and corrections and for being responsive to author's concerns and suggestions.

Dr. Oleg B. Malyshev

Editor

Nomenclature

A [m2] Vacuum chamber cross section area or volume per unit of axial length
A(r, t) [W/m3] Source term of energy input on the electrons
a [m] Vacuum chamber or channel height or width
a A constant in equations
B [T] Magnetic field
B(r, t) [W/m3] Source term of energy input on the lattice
b [m] Vacuum chamber or channel width or height
C [m2/s] Distributed pumping speed of pumping holes or slots per unit axial length
C e/a [J/(kg·K)] Specific heat of the electronic/lattice system
c [m2/s] Distributed pumping speed per unit axial length
D [m2/s] Knudsen diffusion coefficient
D Accumulated dose of particle bombarding a surface
  1. – D or D γ
Photon dose
  1. ○ D or D γ [photons]
Total photon dose
  1. ○ D or D γ or D L [photons/m]
Photon dose per unit of axial length
  1. ○ D or D γ or D A [photons/m2]
Photon dose per unit of area
  1. – D or D e
Electron dose
  1. ○ D or D e [electrons]
 Total electron dose
  1. ○ D or D e or D L [electrons/m]
 Electron dose per unit of axial length
  1. ○ D or D e or D A [electrons/m2]
 Electron dose per unit of area
  1. – D or D i
Ion dose
  1. ○ D or D i [ions]
Total ion dose
  1. ○ D or D i or D L [ions/m]
Ion dose per unit of axial length
  1. ○ D or D i or D A [ion/m2]
Ion dose per unit of area
d [m] Tube or orifice diameter
E Energy of charged particles
  1. – E [MeV, GeV, TeV]
 Energy of particles in the beam
  1. – E 0
Rest energy, e.g. E 0 = 0.511 MeV for electron and E 0 = 938.27 MeV for proton
  1. – E e or E [eV, keV]
 Energy of test electron in ESD and SEY measurements
  1. – E i or E [eV, keV]
 Energy of test ion in ISD
  1. – E des [eV]
 Desorption energy
ℰ [V/m] Electric field
F [m] Vacuum chamber cross section circumference or surface area per unit axial length
f Fraction of beam ions (0 < f < 1)
g [W/(m3·K)] Electron–phonon coupling
H (index) [ions/s] or [ions/(s·m)] Ion flux
I [A] Charged particle beam current
  1. – I e [mA]
 (Photo)electron current
  1. – I i [mA]
 Ion current
I [J] Mean ionization potential
J [molecules/(s·m2)] An impingement rate
K e/a [W/(m·K)] Thermal conductivity of the electronic/lattice system
Kn Knudsen number
K q Charge state of ions
L [m] Length of vacuum chamber
M [kg/mol] or [amu] Molecular molar mass
Mh i A number of hits on facet i′ in TPMC model
Mp i A number of particles pumped by facet i in TPMC model
m [kg] (molecular) mass
N [molecules] A number of molecules in a volume
N A number of generated molecules in TPMC model
n [molecules/m3] Number density of gas
n e [molecules/m3] Thermal equilibrium gas density (in Chapters 7 and 9)
n e [electrons/m3] Electron density (in Chapters 8 and 10)
P [Pa] Pressure
images [W/m] Power dissipation per unit axial length
R [m] Bending radius of dipole magnet
R or ρ Photon reflectance (reflectivity coefficient)
R z [μm] Mean surface roughness
r [m] Radius
Q [molecules/s] or Q* [Pa·m3/s] Local gas flux
q [molecules/(s·m2)] or q* [Pa·m/s] Specific outgassing rate
q [molecules/(s·m)] or q* [Pa·m2/s] Gas desorption flux per unit axial length
S [m2/s] Distributed pumping speed per unit axial length
S eff [m3/s] Effective pumping speed
images [m3/s] Ideal pumping speed
S p [m3/s] Pumping speed of a lumped pump
images [m3/s] Ideal wall pumping speed of accelerator vacuum chamber of length L
S A [m/s] Specific pumping speed (pumping speed per unit of surface area)
s [molecules/m2] Surface molecular density, a number of adsorbed molecules
s 0 [molecules/m2] A number of adsorption sites
T [K] Temperature of gas or walls of vacuum chamber
t [s] Time
U = u/L [m3/s] The vacuum chamber conductance
u = AD [m4/s] Specific vacuum chamber conductance per unit axial length
V [m3] Vacuum chamber volume
v [m/s] Bulk velocity
images [m/s] Average molecular velocity
v rms [m/s] Root‐mean‐square molecular velocity
W Transmission probability matrix
w Transmission probability
x and y [m] Transversal coordinate
Z Atomic number
Z eff Effective charge of projectile ion, screened by electrons
z [m] Longitudinal coordinate along the beam vacuum chamber
α Sticking probability of molecules on vacuum chamber walls
α Exponent in Eqs. (4.29), (4.34), and (4.35) for η(D)
β Capture coefficient
Γ Photon flux
  1. – Γ [photons/s]
Total photon flux
  1. – Γ or Γ L [photon/(s·m)]
Linear photon flux (photon flux per unit of axial length)
  1. – Γ or Γ A [photon/(s·m2)]
Photon flux per unit surface area
  1. – Γmrad [photon/(s·mrad)]
Photon flux from the beam in dipole magnetic field into 1 mrad bend
γ The Lorentz factor: γ = E/E 0
δ Secondary electron yield
ε Photon energy
ε c Critical energy of SR
η or η e or ξ [molecules/electron] ESD yield
η or η γ [molecules/photon] PSD yield
η t [molecules/(s·m2)] or [Pa·m] Specific thermal outgassing rate
η′ or η e ′ or ξ′ [molecules/electron] ESD yield from cryosorbed gas (secondary ESD)
η′ or η γ ′[molecules/photon] PSD yield from cryosorbed gas (secondary PSD)
Θ Electron flux (surface bombardment intensity)
  1. – Θ [electron/s]
Total electron flux
  1. – Θ or Θ L [electron/(s·m)]
Electron flux per unit axial length
  1. – Θ or Θ A [electron/(s·m2)]
Electron flux per unit surface area
Θ [mrad or °] Incidence angle of bombarding particles
θ = s/s 0 Normalised surface coverage
ν 0 [s−1] Oscillation frequency of bound atom/molecule
ρ A pump capture efficiency (or a capture coefficient), pump mesh or beam screen transparency
ρ(x, y) [C/m3] Beam charge density
τ [s] Beam lifetime, an average residence time of sorbed molecule on a surface
σ [m2] An ionisation cross section of the residual gas molecules by beam particles, an interaction cross section (in Chapter 1)
σ x and σ y [m] Transverse r.m.s. beam sizes
χ [molecules/ion] ISD yield
χ′ [molecules/ion] ISD yield from cryosorbed gas (secondary ISD)

Physical Constants

c Speed of light in vacuum c = 299 792 458 m/s
k B Boltzmann constant k B  = 1.380 650 4(24) × 10−23 J/K
= 1.380 650 4(24) × 10−23 Pa·m3/K
h Plank's constant h = 6.626 069 57 × 10−34 m2·kg/s
q e Elementary charge q e  = 1.602 176 46 × 10−19 C
N A Avogadro constant N A  = 6.022 140 76 × 1023 mol−1
R Ideal gas (Regnault) constant R = 8.314 459 8(48) J/(mol·K) or Pa·m3/(mol·K) or kg·m2/(mol·K·s2)

List of Abbreviations

AC
angular coefficient method
ESD
electron‐stimulated desorption
ISD
ion‐stimulated desorption
NEG
non‐evaporable getter
PEE
photoelectron emission
PEY
photoelectron yield
PSD
photon‐stimulated desorption
RGA
residual gas analyser
SEE
secondary electron emission
SEY
secondary electron yield
SIP
sputter ion pump
SR
synchrotron radiation
TD
thermal desorption
TPMC
test particle Monte Carlo method
TMP
turbo‐molecular pump
TSP
titanium sublimation pump
UHV
ultra‐high vacuum
XHV
extreme high vacuum

Frequently Used Vacuum Units and Their Conversion

Vacuum Units

Pa mbar Torr bar Atmosphere at sea level
Pa 1 10−2 7.500 62 × 10−3 10−5 9.869 2 × 10−6
mbar 100 1 0.750 062 10−3 9.869 2 × 10−4
Torr 133.322 1.333 22 1 1.333 22 × 10−3 1.315 8 × 10−3
bar 105 103 750.062 1 0.986 92
atm 1.013 25 × 105 1.013 25 × 103 760 1.013 25 1

Conversion of Frequently Used Units

Amount of gas PV images images images
Units Pa·m3 = 10 mbar·l molecules mol kg
Gas flow images images images images
Units Pa·m3/s = 10 mbar·l/s molecules/s mol/s kg/s
Specific outgassing rate images images images images
Units Pa m/s = 105 mbar·l/(s·cm2) molecules/(s·cm2) mol/(s·cm2) kg/(s·m2)

Monolayer (ML)

A monolayer (ML) is a one‐molecule thick layer of closely packed molecules of gas on a geometrically flat surface.

In practical estimations for the gases present on rough surface of accelerator vacuum chamber, an approximate value of 1 ML ≈ 1015 molecules/cm2 can be used.