Session I. An introduction into vacuum system design · An introduction into vacuum system design...

Session I. An introduction into vacuum system design

Dr. Oleg B. Malyshev

ASTeC - Accelerator Science and Technology Centre

STFC Daresbury Laboratory, Warrington Cheshire WA4 4AD

United Kingdom

e-mail: [email protected]

2018 Training Course on Vacuum System Design and Maintenance

Mercure Chester Abbots Well, Chester, UK

12-14 June 2018

mailto:[email protected]

Outlook• Statement of the problem

• Ideal gas

• Materials in vacuum

• Vacuum “enclosures”

• Real things in vacuum

• Adsorption, absorption, desorption (thermally and particle bombardment induced), diffusion and permeation, sticking probabilities etc.

• Basics of vacuum gas dynamics

• Throughput, pumping speed and vacuum conductance

• Simple pump-down calculations

• Examples

O.B. Malyshev2018 Training Course on Vacuum System Design and Maintenance. Session I. An introduction into vacuum system design 2

Vacuum• Vacuum (from Latin “vacua”) means empty

• In practice, gas density n = 0 particles/m3 is an unreachable

• There is always some number of particles in any volume:

• Vacuum 0

• n > 0 particles/m3

• this means that everybody who needs “FULL VACUUM” is a dreamer!

• In the gas dynamics, Vacuum is the gas state when P < 1 bar

• As soon as gas from a closed volume is pumped out all that remains is called the vacuum

• In a realistic and scientific approach we define the level of vacuum: a vacuum range or a specific value of pressure (or gas density)

• Vacuum is a problem for many applications and researchers and it is a subject of

• Rarefied Gas Dynamics for studying gas flows, heat transfer, etc.

• Vacuum Science and Technology for applications and implementation.


Vacuum

There’s nothing in it!


Particles/m3

Atmosphere 2.5 x 1025

Vacuum Cleaner 2 x 1025

Freeze dryer 1022

Light bulb 1020

Thermos flask 1019

TV Tube 1014

Low earth orbit (300km) 1014

SRS/Diamond 1013

Surface of Moon 1011

Interstellar space 105

Pressure

• Pressure is a force, F [N], exerted by the substance per unit area, A [m2], on another substance. The pressure of a gas is the force that the gas exerts on the walls of its container or any surface in that gas.

• Pressure = Force per Unit Area

• SI pressure Unit – Pascal: Pa = N/m2

• 1 atm = 101325 N/m2 = 1.0332 kgf/cm2


atmosphere

Patm

Patm

Patm

Patm

Patm

Patm

Patm

Patm

FP

A


Magdeburg hemispheres

Guericke first demonstrated the

force atmospheric pressure in 1654

for the Emperor Ferdinand III.

30 horses, in two teams of 15, were

unable to pull apart the evacuated

22’’-diametre hemispheres!

Vacuum Units

• SI pressure Unit – Pascal (1 N/m2)

• Pa is used by all metrology labs, in Asia and Eastern Europe

• In Western Europe – mbar (= 100 Pa)

• In USA – Torr (= 133.322 Pa) <= this not SI unit!

• Atmosphere = 1.01325 bar = 760 Torr

• 1 bar = 105 Pa = 103 mbar = 750 Torr = 0.98692 atm.

• Gas density unit - particles/m3

where P [Pa] – pressure, n [m3] – gas density (number gas density),

kB – Boltzmann coefficient, T [K] – temperature.

BP nk T


Classification of Vacuum ranges

• For convenience, ‘to distinguish between various ranges or degrees of vacuum according to certain pressure intervals’, the ranges of vacuum are defined


Vacuum ranges Pressure

low (rough) vacuum: 105 Pa to 102 Pa

medium vacuum: 102 Pa to 10-1 Pa

high vacuum (HV): 10-1 Pa to 10-5 Pa

ultra-high vacuum (UHV): below 10-5 Pa

Vacuum ranges Pressure

low (rough) vacuum: 105 Pa to 102 Pa

medium vacuum: 102 Pa to 10-1 Pa

high vacuum (HV): 10-1 Pa to 10-4 Pa

very high vacuum (VHV): 10-4 Pa to 10-7 Pa

ultra-high vacuum (UHV): 10-7 Pa to 10-10 Pa

extremely high vacuum (XHV): below 10-10 Pa

ISO 3529-1:1981 Non-ISO vacuum ranges

Gas in a closed volume • Gas occupies entire volume

• Pressure in equal at every location

• Number gas density n = N/V

• Amount of gas

• where NA = 6.02214×1023 is the Avogadro constant is the number of constituent particles (atoms or molecules) that are contained in the amount of substance given by one mole.

• In vacuum technology we use

• where kB = 1.38065×10−23 J/K = 1.38065×10−23 Pa·m3/K is the Boltzmann constant


N molecules

in volume V

at temperature T

A

Nmole

N

[ ] BQ mbar l PV N k T

Ideal gas• For fixed amount of gas

• Boyle-Mariotte low for fixed temperature:

• where R0 = 8.3 J/(mole·K) is the universal gas constant

• The equation of state of ideal gas includes the gas temperature as well:

• Mixture of gases:

• Dalton law: “The total pressure, Ptot, is the sum of all the partial pressure, Pi ”:


0

.

or

PV const

PV R T

.PV

constT

.tot i

i

P P 1 2A A BPV P V V

P1, VA P=0, VB

(1) Initial sate,

valve is closed

P2, VA P2, VB

(2) After opening

the valve

Type of gas molecules

• In a container with

• a volume of 22.4 litre

• at the temperature of T = 0 °C = 273 K and

• pressure to P = 1013 mbar = 1 atm

• A mass of gas is


Gas H2 He CH4 H2O CO N2 O2 Ar CO2

M

[g/mol]

2.0159 4.0026 16.0425 18.0153 28.0101 28.0134 31.9988 39.9480 44.0095

RMM 2 4 16 18 28 28 32 40 44

Velocity of gas molecules

• Molecular velocity distribution (Maxwell-Boltzmann distribution):

• Most probable velocity, vmp :

• An average of absolute value of the velocity vector (also known as mean speed), ҧ𝑣 :

• The root-mean-square velocity, vrms, is defined as:


2 2

0 2 2

4exp

mp mp mp

v v vF

v v v

33 Brms

m m

k TRTv

M m

88 B

m m

k TRTv

M m

22 Bmp

m m

k TRTv

M m 1.085

mp

v

v 1.128rms

mp

v

v

T = 300 K

Mean speed of most common gases in a vacuum chamber at LHe, LN2 and room temperatures

Gas H2 He CH4 H2O CO N2 O2 Ar CO2

M [g/mol] 2.0159 4.0026 16.0425 18.0153 28.0101 28.0134 31.9988 39.9480 44.0095

ҧ𝑣[m/s]

T = 20 C 1755 1245 622.0 587.0 470.7 470.7 440.4 394.2 375.5

T = 77.2 K 900.5 639.0 319.2 301.2 241.6 56.14 226.0 202.3 192.7

T = 4.17 K 209.3 148.5 74.19 70.01 241.6 56.14 52.53 47.01 44.79


• Typical size of molecules:

d = ~3×10-8 cm

• – mean free path

•

impingement rate or flux

l

J

2

1

2m

d nl

2 4

nvJ

mole s

m

le

s

cu

A Useful Exercise

From the equation for impingement rate, if we assume that every gas

molecule which impinges on a surface sticks, prove that the time, ,

to form a monolayer of gas at a pressure P (mbar) on a surface (i.e.

where there is one gas atom for each atom in the surface) is given by


610( )

( )s

P mbar

9For 10P mbar

310 s

Impingement rate


J

J

J

J – a number of molecules per cm2 per second

- Hitting a real surface

- Passing through any virtual (imaginary) surface in both directions

J

J

area 1 cm2

Gas flow regimes

• Viscous gas flow regime

• molecule-molecule collisions dominate behaviour

• l << D or Kn < 0.01

• Transitional gas flow regime

• molecule-molecule collisions and molecule-wall collisions are equally important for the gas flow

• l ~ D or 0.01 < Kn < 10

• Free molecular gas flow regime

• molecule-molecule collisions dominate behaviour

• l >> D or Kn > 10

• Knudsen number, Kn defined as Kn = l /D

• Kn = mean free path at prevailing pressure / typical dimension


l

l >> D

D

l << D

Interaction with a wall• Molecules hitting rough technical surfaces are

• adsorbed at the surface for a very short time (sojourn time),

• fully thermalised with a wall (this is called as a complete accommodation),

• then desorbed with diffuse (cosine) low

• Practically, this means that a particle can be reflected to any direction independent of its velocity before the collision with a surface. Such an interaction is called as the complete accommodation

• Mirror reflections could be considered as negligible, i.e. molecules do NOT rebound like tiny snooker balls


In many practical

applications the diffuse

scattering is well

justified and provides

reliable results

Pressure, gas density, mean free path and

impingement rate for N2 at room temperature


P (mbar) Range n (m-3) l J (cm-2 s-1)

103 atm. 2.5×1025 66 nm 2.9×1023

1 LV 2.5×1022 66 mm ~

0.1mm2.9×1020

10-3 MV 2.5×1019 66 mm 2.9×1017

10-6 HV 2.5×1016 66 m 2.9×1014

10-10 UHV 2.5×1013 660 km 2.9×1010

l ~ a

a is a characteristic vacuum chamber size

l << a

l >> a

Gas Composition in the Atmosphere and in Vacuum

Atmosphere

(at sea level)

Unbaked vacuum

chamber

Baked vacuum

chamber

NEG coated

vacuum chamber

At cryogenic

temperatures (1

to 80 K)

N2 (78.1%) H2 H2 H2 H2

O2 (20.9%) H2O CO CH4 CO

H2O (0.1-5.0%) CO CO2 CxHy CH4

Ar (0.93%) CO2 CH4 CO CO2

CO2 (0.033%) CH4 CxHy


Atmospheric air is a mixture of gases with over 99% of nitrogen and oxygen, while the rest

of gas in UHV consist mainly of hydrogen.

The gas composition is varied depending on many factors: choice of material, cleaning, baking,

pumping system design, type of pumps, temperature, photon, electron or ion bombardment of

the surface and many others.

Sources of Gas in a Vacuum System


Schematic layout of a typical vacuum system


Vacuum chamber

Pump

Vacuum gauge

vent / gas

injectionAccess /

load lock Vacuum

process

Atmosphere

Residual gas

Mechanisms Contributing to Outgassing

Atmosphere

Vacuum

Thermal

Desorption

Recombination

To reduce outgassing,

one must inhibit or

reduce these processes

Vaporisation

Adsorption

Permeation

Surface DiffusionBulk

Diffusion

Real Leaks

Virtual

Leaks

Back-

streaming


Sources of Gas in a Vacuum System• Gas injection ── It is usually well controlled

• Residual gas from atmosphere ── It is not a source of gas for the most of UHV systems

• Leaks (from atmosphere or trapped volumes) ── there must be no leaks

• Thermal outgassing

• Vacuum chamber

• Components and samples inside the vacuum chamber

• Equilibrium vapour pressure

• H2O and Hg at RT,

• H2 at LHe, CO2 at LN2, etc.

• Products or by-product of a processing in vacuum

• Induced gas desorption

• Photon, electron and ion simulated desorption

• Cryogenic vacuum chamber: recycling and cracking

• Back streaming from the pump

The major

sources of gas

in UHV system


Sources of Gas in a Vacuum System: LeaksThe aim is to build a vacuum tight vessel, i.e. no gas from atmosphere

should be able to find its way into the vessel, there should be no leaks.

To minimise the possible leaks it is necessary:

• to engineer an appropriate design (both mechanical and vacuum)

• to use vacuum tight components (checked by vacuum support)

• to perform quality welding and careful assembly of components

• to use tested types of valves and flanges, only new gaskets

After the production of the vacuum vessel, assembly of components and installation, leak detection is needed to locate possible leaks and to guarantee the required pressure will be reached.


Sources of Gas in a Vacuum System: Thermal Desorption

Thermal desorption

(or thermal outgassing) means:

• Molecules adsorbed on the surface (initially or after the air venting) and desorbing when vacuum chamber is pumped

• Molecules diffusing through the bulk material of the vacuum chamber, entering the surface, (recombining) and desorbing from it

Outgassing rate depends on many factors: choice of material, cleaning procedure, baking, pumping time, etc...

Ex.: 316 LN (10-8 – 10-15) mbarlt/(scm2)

=> Input data for a gas dynamic model are very approximate

AirVacuum


Choice of Material for UHV System• The outgassing rates may vary in order of magnitudes depending on factors: choice

of material, cleaning procedure, history of material, pumping time, etc...

• Not all materials are compatible with UHV and XHV system!

• The example of the outgassing rates after one hour pumping:


Material t [mbarl /(scm2)]

Aluminium (fresh ) 910-9

Aluminium (20h at 150C) 510-13

Cupper (24h at 150C) 610-12

Stainless steel (304) 210-8

Stainless steel (304, electropolished) 610-9

Stainless steel (304, mechanically polished) 210-9

Stainless steel (304, electropolished, 30h at 250C ) 410-12

Perbunan 510-6

Pyrex 110-8

Teflon 810-8

Viton A (fresh) 210-6

What can be achieved for stainless steel?

• Experience shows that an outgassing rate of the order of 10-11 mbar l s-1 cm-2

can be obtained after bakeout to 250 °

• An outgassing rate of 10-13 mbar l s-1 cm-2 is achievable with conventional techniques

• Rates lower than 10-14 mbar l s-1 cm-2 are achievable with care, particularly in thin walled vessels, or on polished and vacuum fired surfaces


• Permeation:

• wall thickness

• barrier layer on surface

• coating, oxide, nitride, etc.

• internal or external

• preferred orientation of grains

• should be parallel to the surface (rolled sheets)

• forged flanges (to minimise normal to surface)

• Bulk diffusion :

• reduce dissolved hydrogen

• vacuum melt, vacuum firing, air bake, induce trapping states (bulk or surface)

• grain boundary density

• Recombination :

• reduce surface mobility by introducing surface trapping sites

Strategies for reducing of outgassing

• Desorption :

• reduce surface concentration

• surface cleaning and vacuum bakeout

• reduce physical surface area

• by design and by surface polishing

• Adsorption :

• reduce exposure to air and sorbing gases

• fill surface binding sites

• surface polishing, air-bake

References:

• R. Calder and G. Levin. Brit. J. Appl. Phys. 18 (1967) 1459.

• G. Chuste, CERN, unpublished results

• M Suemitsu et al. Vacuum 44 (1993), 425.

• DG Bills. J. Vac. Sci. Technol. 6 (1969), 166

• M. Bernardini et al. J. Vac. Sci. Technol. A16 (1988), 188.

• L. Westerberg et al. Vacuum 48 (1997), 771.

• JRJ Bennett and RJ Elsey. Vacuum 43 (1992), 35

• Y. Tito Sasaki. J. Vac. Sci. Technol. A25 (2007), 1309.

• C. Benvenuti. Proc. of PAC’01, p.602.


Sources of Gas in a Vacuum System:Equilibrium Vapour Pressure without pumping.

When liquid, condensed gas or a very porous material is present in a vacuum chamber the pressure is limited by the equilibrium vapour pressure:

There are two gas flows:

from and to liquid surface

4 4

eq

in out eq

B

P vvq q n

k T


Material Temperature,

T [K]

Equilibrium pressure,

Peq [mbar]

Mercury 293 210-3

Pump oil 293 10-6 to 10-8

Water 293 20

H2 4.2 810-7

CO2 77.8 210-8

surface

liquid

Vapour at P = Peq

qout

qin

Sources of Gas in a Vacuum System:Equilibrium Vapour Pressure with pumping.

When liquid, condensed gas or a very porous material is present in a vacuum chamber the pressure is limited by the equilibrium vapour pressure:

That means that there are two gas flow from and to liquid surface:

; ;4 4 4 4

eq

out eq in

B B

P vv v Pvq n q n

k T k T Peq and neq are equilibrium pressure and gas density;

P and n are the actual pressure and gas density in

vacuum chamber


Material Temperature,

T [K]

Equilibrium pressure,

Peq [mbar]

Mercury 293 210-3

Pump oil 293 10-6 to 10-8

Water 293 20

H2 4.2 810-7

CO2 77.8 210-8 surface

liquid

Vapour at P < Peq

qout qin

Photon stimulated desorption (PSD)


PSDPhoton stimulated desorption (PSD) is one of the most important sources of gas in

the presence of synchrotron radiation (SR) or any photons with E > 5-10 eV.

PSD can be considered as a two-step process:

• first, photons with energy >5-10 eV cause the photoelectron emission,

• then the photoelectron stimulate gas desorption.

O.B. Malyshev

Gas molecules may desorb from a surface when and where photoelectrons leave

and arrive at a surface


PSD yields

PSD yields are defined as a number of gas molecules desorbed from

the surface per incident photon, [molecules/photon]:

3

,B

Q Pamolecules

photon k T K photon

s

s

m


What PSD depend on?

Similarly to thermal desorption,

PSD depends on:

• Choice of material

• Cleaning procedure

• History of material

• Bakeout and vacuum firing

• Pumping time

Additionally it depends on

• Energy of photons

• Photon flux

• Integral photon dose

• Temperature


Photodesorption yields, (molecules/photon), as a function of accumulated

photon dose, D, for different materials measured up to certain doses, these results

are extrapolated for use in the design of new machines

PSD yield for CO for prebaked and in-situ baked stainless steel vacuum chambers.

Yields for doses higher then 1023 photons/m (1 to 10 Amphrs for diamond) are extrapolations.

165.0,00 <<

D

D

Photodesorption yield as function of

accumulated photon dose can be

described as:

PSD as a function of dose


PSD as a function of dose

aluminium vacuum chamber

(Vacuum 33, 397 (1983))

The PSD yield for various gas species as a function of the accumulated photon dose at c = 3.75 keV at DCI

stainless steel vacuum chamber

(Vacuum 60, 113 (2001)).


PSD yields from different materials as a function of photon dose

Photodesorption yields, (molecules/photon), as a function of

accumulated photon dose for different materials for vacuum chamber (A. Mathewson, AIP Conf. Proc. 236 (1), 313 (1991))


Amount of desorbed gas as a function of photon dose

The same data can be analysed differently, amount of desorbed gas :

0 0

t Dmbar l

Q t t dt D dDs

Stainless steel Aluminium Copper

This information is important when the sorption pumps are used such as NEG

cartridges or cryosorbers


PSD as a function of amount of desorbed gas

The same data can be plotted differently:

Stainless steel Aluminium Copper


PSD as a function of critical energy of SR

J. Gomez-Goni, O. Gröbner, and A. G. Mathewson, J. Vac. Sci.

Technol. A12, 1714, (1994)

• c = 10-1000 eV c = 0.1-1.4 MeV


PSD as a function of critical energy of SR

J. Vac. Sci. Technol. A 25(2007): 791-801


PSD: effect of bakeoutBakeout Impact Comment

In-situ at 150 C for 24 hrs reduction of H2O by 5-10 times; reduction of

initial PSD yields for other species by 2-4 times

Reducing bakeout temperature to 120 C

requires increasing of bakeout duration to a

few days.

In-situ at 300-350 C for 24 hrs: reduction of initial H2 by 10-20 times, for other

species by 7-15 times

-

Ex-situ at 250-300 C for 24 hrs reduction of initial H2 by 5-10 times, for other

species by 4-8 times

keep in vacuum; minimise vent to air during

installation; purge with dry air, N2 or noble

gases

Vacuum firing at 950 C for 1-2 hrs at P

< 10-5 mbar

hydrogen depletion in the bulk of vacuum

chamber material

Keep in vacuum or fill with N2 or noble gas.

No in-situ bakeout after vacuum firing reduction of H2 by ~1.5-2 times

In-situ bakeout after vacuum firing reduction of H2 by ~20-50 times


Effect of incident angle on PSD

PSD and PEY as a function of

absorber angle (90)

normalised to response at normal

incidence for copper surface[B. A. Trickett, D. Schmied and E. M.

Williams. Hard synchrotron radiation and

gas desorption processes at a copper

absorber J. Vac. Sci. Technol. A10 (1992)

217]


Electron stimulated desorption (ESD)


ESDElectron stimulated desorption (ESD) could be an important sources of gas in case of

electron beam bombardment, beam induced electron multipacting, or as a part of the PSD

process in the presence of SR.

Gas molecules may desorb from a surface when and where electrons arrive at a surface

H2

H2O

CO2

CH4

CO

e-

e- e-

e-

e-

e-

e-e-

e-

e- e-e-e-

e-

e-

ESD could also be an important sources of gas in case of measurements with an electron

beam, electron beam treatment, electron beam welding, and other processes with electrons.


ESD yields

ESD yields are defined as a number of gas molecules desorbed from the

surface per incident electron, e [molecules/e-]:

3

,emolecules

e

electrons B

Q Pa q CNmolecules

e N k T K I A

m s

where

• Q is a flux of molecules desorbed due to electron bombardment,

• I is the electron current,

• qe is the elementary charge


What ESD depend on?

Similarly to PSD and thermal

desorption, ESD depends on:

• Choice of material

• Cleaning procedure

• History of material

• Bakeout and vacuum firing

• Pumping time

Additionally it depends on

• Energy of electrons impinging the

surface

• Electron flux to the surface

• Integral electron dose

• Temperature


ESD yields of 316 LN stainless steel baked to 250 ºC for 24 hours as a function of electron dose at

electron energy Ee = 500 eV.O.B. Malyshev and C. Naran. Vacuum 86 (2012), 1363-1366.

00

D

D

ESD yield as function of

accumulated photon dose

can be described as:

ESD as a function of dose

the exponent lies between

0.5 a 1


ESD from different materialsESD yields of unbaked OFHC copper

after 24-hour pumping as a function of

electron dose at Ee = 300 eV

ESD yields of aluminium alloy baked to 220 ºC for

24 hours as a function of electron dose at

electron energy Ee = 500 eV

F. Billard et al, Some Results on the Electron Induced Desorption Yield of OFHC

Copper. Vacuum Technical Note 00-32, December 2000, CERN, Geneva.

O.B. Malyshev et al, Vacuum 85 (2011) 1063-1066.


ESD as a function of electron energyUnbaked OFHC copper at the dose D = 1.4 1014 e–/cm2

F. Billard et al, Vacuum Technical Note 00-32, December 2000, CERN, Geneva.

10 100 1 103

1 104

1 106

1 105

1 104

1 103

0.01

0.1

H2

CH4

CO

CO2

H2 fit

CH4 fit-1

CH4 fit-2

CO fit

CO2 fit

Energy [eV]

Yie

ld [

Mol

ecul

es/e

lect

ron]

Stainless steel baked at 250 C for 24 h

at the dose D = 7 1021 e–/cm2

Aluminium sample baked at 220 C for 24 h at the dose

D = 1.3 1022 e–/cm2

J. Vac. Sci. Technol. A12 (1994), 1714.

O.B. Malyshev et al, J. Vac. Sci. Technol. A 28 (2010) 1215.


ESD as a function of electron energy316LN stainless steel baked at 250 C for 24 h O.B. Malyshev et al, J. Vac. Sci. Technol. A 31 (2013) 031601.


ESD as a function of wall temperature

O.B. Malyshev, C. Naran. Vacuum 86 (2012) 1363.


Ion stimulated desorption (ISD)


Ion Induced Pressure Instability

H2+

COH2

CH4

CO2

+

where

Q = gas desorption,

Seff = effective pumping speed,

= ion induced desorption yield

= ionisation cross section,

I = beam current.

IIe

Q

e

IS

Qn

ceff

e

ISeff

eSI

eff

c

When I Ic (or )

then gas density (pressure) increases dramatically!

When the positive charged beam particles colliding with

residual gas molecules ionise them, these ions are

accelerated towards the vacuum chamber wall. This

causes ion induced gas desorption, the pressure rises and

more molecules will be ionised, accelerated and bombard

the wall…

ISD could also be an important sources of gas in case of measurements with an ion

beam, ion beam treatment, ion beam etching, and other processes with ions.


ISD

Ion stimulated desorption (ISD) can be a significant gas source in a vacuum system where the ion beam bombards the surface. There is very little data, most work has been done at CERN.

Similarly to thermal desorption, PSD and ESD, the ISD depends on: choice of material, cleaning procedure, history of material and pumping time.

It is also depends on:

• Mass, charge and energy of ions impacting the surface

• Ion flux to the surface

• Integral ion dose

• Temperature

O.B. Malyshev CAS on Vacuum for Particle Accelerators 2017

6-16 June, 2017, Glumslöv, Sweden55


ISD yields

ISD yields, defined as a number of gas molecules desorbed from the surface per

incident ion, (molecules/ion), :

3

,e qmolecules

ions B

Q q C nNmolecules

ion N k T K I

a m s

A

P

where

• Q is a flux of molecules desorbed due to ion bombardment,

• I is the ion current,

• qe is the elementary charge and

• nq is the ion charge number


ISD yields as a function of ion energy

A.G. Mathewson. Ion induced

desorption coefficients for titanium

alloy, pure aluminum and stainless

steel. CERN-ISR-VA/76-5 (1976).


The ISD yields as a function of accumulated ion dose from (a) as-

received and (b) baked aluminium and copper samples bombarded

with argon ions at 5 keV.

M.P. Lozano. Ion-induced desorption yield measurements from copper and

aluminium. Vacuum 67 (2002) 339.

ISD yield as function of

accumulated ion dose can

be described as:

ISD as a function of dose

the exponent lies

between 0.3 0.5 for as-

received samples and

between 0 1/3 for baked

samples

*

* ;i i

DD D

D


ISD as a function of ion mass

N. Hilleret. Influence de la nature des ions incidents sur les taux de desorption par bombardement ionique de

molécules adsorbées sur une surface d’acier inoxydable. CERN-ISR-VA/78-10 (1978).

ISD yield from (a) unbaked and (b) baked stainless steel sample as a function of incident ion mass


Throughput, pumping speed,

vacuum conductance


Throughput (Gas Load)

• Gas Load or Throughput – rate gas evolves within or enters the volume

• Pressure P in a vacuum vessel is defined by the total gas load, Q, and total Volume, V.

In the case of a simple vacuum chamber it is :

P

VQ

dP mbarmbar lQ V l

s dt s


Pumping speed

Pressure P [mbar] in a vacuum vessel is defined by the total gas load, Q [mbarl/s],and total pumping speed, S [l/s].

In the case of very simple vacuum chamber it is :

Vacuum Plumbers’ Formula 1

For Q = 10-6 mbarl/s and S = 100 l/s the pressure in vacuum chamber:

P = 10-8 mbar

S

PQQ

PS


Vacuum conductance

P1 P2C

1 2

QC

P P

P1 C P2

Tube

Thin aperture


Vacuum Plumbers’ Formula 2

Vacuum conductance of a tube

C

Tube


d

Viscous flow

4

136 d cmlC P mbar

s L cm

Free molecular flow

3

12.4 d cmlC

s L cm

LC

l >> d

l << d

l ~ d

Kn

Effective pumping speed

In general a pump will be attached to the vessel which has to be pumped with a tube of some sort. If this tube has a conductance C, then the net (or effective) pumping speed Seff at the vessel will be given by

I.e. pumping speed is reduced due to a connecting pipe: Seff < S

0

0

eff

CSS

C S

eff

QP

S

S

PQ

C


How to increase Seff?

To increase Seff when S >> C It is not efficient to increase S

=> increase C

To increase Seff when C >> S

it is not efficient to increase C

=> it is necessary increase S


effS C S S

effS C S C

Series connections

Vacuum conductance of series connection of various vacuum component is calculated as follows:

S

PQ

C1

C2

C3C4

1 1

1 1 1

i i

ieff i

C C

S S C


Initial very rough estimations

• Guess (or estimate) internal surface area

• A (m2)

• Assume an achevable outgassing rate

• qth (mbarl/(sm2))

• Determine total required pumping speed, S (l/s) to reach the base pressure, PB

• Since conductance was not considered here, this a lower limit estimate of total required pumping speed.

th th

B B

Aq QS

P P


• The antiproton decelerator recycling ring (AD-rec) is a small UHV ring a circumference of 8.16 m where up to 105 particles will circulate with energy on the range of 3-30 keV.

• Required vacuum:

• Preq = 10-11 mbar in 3 days from beginning of pumping.

• The total internal surface:

• Atot = 20 m2.

• Six locations for pumps:

• Spump ≤ 1000 l/s

• What specific outgassing rate must me achieved to meet vacuum specifications?

Example: initial vacuum calculations for AD-rec

𝒒𝒎𝒂𝒙 =𝑷𝒓𝒆𝒒 ∙ (𝟔 ∙ 𝑺𝒑𝒖𝒎𝒑)

𝑨𝒕𝒐𝒕𝒒 < 𝒒𝒎𝒂𝒙 = 𝟑 × 𝟏𝟎−𝟏𝟒

𝒎𝒃𝒂𝒓 ∙ 𝒍

𝒔 ∙ 𝒄𝒎𝟐


Rough Design of a simple vacuum system

• Vacuum Vessel (dv=0.5 m, Lv=1 m

with 2 ports (dp=0.15 m, Lp=0.1 m

and internal components

• Pumping port (d1=63 mm, L1=0.1 m

• Transition to a smaller diameter

d2=38 mm

• Tube (d3=38 mm, L3=0.15 m)

• Valve (C4=50 l/s for N2)

• Tube to the pump (d5=38 mm,

L5=0.5 m)S

P

C1

C4

C3

C5

C2


Rough Design of a simple vacuum systemTotal outgassing area A=2.5 m2

• H2 10-8 mbarl/(scm2)

• CH4 10-10 mbarl/(scm2)

• CO 10-9 mbarl/(scm2)

• CO2 310-10 mbarl/(scm2)

Vacuum conductance in a free molecular regime:

• CH2 30 l/s; CCH4 11 l/s

• CCO 8 l/s; CCO2 6.5 l/s

If S = 100 l/s then Seff C

Calculate:

PH2 = 8.3 10-6 mbar

PCH4 = 2.3 10-7 mbar

PCO = 3.1 10-6 mbar

PCO2 = 1.2 10-6 mbar S

P

C1

C5

C2

C4

C3


Rough Design of a simple vacuum systemIf the pump is connected directly to the

same vessel

• CH2 1370 l/s

• CCH4 480 l/s

• CCO 370 l/s

• CCO2 290 l/s

If S = 100 l/s then Seff ≲ C

Calculate Seff and partial pressures:

PH2 = 2.7 10-6 PCH4 = 3.0 10-8 mbar

PCO = 3.2 10-7 PCO2 = 1.0 10-7 mbar

S

P

C


Vacuum system with a turbo-molecular pump (TMP)

and a scroll pump


Vacuum system with TMP and a scroll pump

Total outgassing rate is Q

S is a pumping speed

K is a compression ratio

Scroll pump

S

Pv

C1

TMP

S, K

C2

P1

P2

P3

1

1

3

2

1

2

2

3

TMP

scroll

bg

o l

v

scr l

QP

C

PQ

S K

QP

C

P

P

S

P

PQ

P


Q


Total outgassing rate is Q

S is a pumping speed

K is a compression ratio

1

1

2

3

2

1 2

1

2

2

2

3

1 1 1 1

1 1 1

1 1

scroll

bg

v

TMP scroll

scroll

bg

TMP scrTMP

scroll

bg

s

oll

scroll

bg

c

scro

o l

ll

r l

PP Q

C S C K

QP

S K K

PP Q

S C K S K K

P Q PC S

C

PQ

S K

QP

C

QP

SP

Scroll pump

S

Pv

C1

TMP

S, K

C2

P1

P2

P3


Q


Calculate partial pressures.

Total outgassing rates Q from a previous example.

Sscrl[m3/h]

STMP[l/s]

KTMP Pv[mbar]

P1[mbar]

P2[mbar]

P3[mbar]

H2 10 50 104

CO 10 65 1010

CO2 10 60 1011

For a scroll pump Pbg = 0.01 mbar

Scroll pump

S

Pv

C1

TMP

S, K

C2

P1

P2

P3


Q

Optimising pumping system

This formula helps optimising choice of pumps for

Ultimate pressure vs. Minimising the cost

• Ultimate pressure at Q=0:

• Ultimate pressure at Q0:

• The lowest term between C1, STMP, C2K and SscrollK is the most limiting

• To study how any change can affect pressure in the vacuum system one can vary

• vacuum conductances: C1 and C2,

• TMP: S and K,

• Roughing pump: Pbg and S.

1 2

1 1 1 1scroll

bg

v

TMP scroll

PP Q

C S C K S K K

scroll

bgult

v

PP

K


Differential Pumping

A common requirement is to maintain part of a system at a relatively low pressure while another part is at a relatively high pressure (e.g. an ion gun and a target chamber). We need to calculate the pumping speed S2

required to maintain the pressure P2

Assume C is small, so

P1 >> P2

then 12

2 2 1

CP CQS

P P S

P1

S1

Q

S2

P2

Q1 Q2

C


Pumping down

• Initial pressure P0

• Gas from all sources: QT

• Pump has speed S at vessel


Vacuum chamber

Pump

Vacuum gauge

vent / gas

injectionVacuum

process

Residual gas

Pumping down• The equation of gas balance can be written as:

• Change of amount of gas in vacuum vessel, amount of pumped gas and desorbed/injected gas

• Hence equation of pumping:

• Ultimate pressure is defined as

• Solution is


TV dP S P dt Q dt

T

dPV S P Q

dt

u TP Q S

0 exp , where u

t VP t P P

S

time

Pre

ssure

Pumping down• To reach a specified pressure Ps

within time t requiredpumping speed S:


0 0ln 2.3 logs s

P PV VS

t P t P

• What time t is required toreach a specified pressure Ps

with a provided pumping speedS:

0 0ln 2.3 logs s

P PV Vt

S P S P

Example:

• V = 5 m3 , Ps = 10 mbar, t = 20 min

• Required pumping speed S:

3

0

3 3

5 102.3 log 2.3 log

20 10

m m1.15 69

min h

s

PVS

t P

Work out:

• V = 1 m3 , Ps = 10 mbar, pumpingspeed S = 60 m3/h

• Please find required t:

Pumping down

• Note that in real world QT slowly changes with time


( ) ( )u TP t Q t S

0 exp ( ), where u

t VP t P P t

S

Ideal pumping speed

• An ideal pumping speed Sid is defined then all impinged molecules are absorbed

• For nitrogen at room temperature

• Then the pump capture coefficient can be defined as:


3

4id

m vS A

s

id

S

S

11.8id

lS A

s

Transmission probability• Vacuum conductance of thin orifice

with area A

• Conductance of al other vacuum components can be defined in in respect to the entrance opening with area A with transmission probability, w:


11.8o id

lC S A

s

, where 1oC wC w

oC

Vacuum conductance for different gases• Conductance depends on the inverse square root of molecular mass

(theory)

• i.e. (basically this is because lighter molecules move faster)

• Therefore,

• Thus for hydrogen,

• In other words, the aperture transmits 3.74 times the quantity of H2 than it would N2 under the same pressure conditions.

• The corresponding factor is 2.64 for He, 1.32 for CH4, 0.94 for O2, 0.84 for Arand 0.8 for CO2 …


1C

M

2

28X

N X

C

C M

2 2 228 / 2 3.74H N NC C C

Pumping speed of a TMPs for various gases


Pumping speed of a TMPs for

various gases

How to find a

pumping speed for

gases that aren’t

shown in a

catalogue?


Pumping speed of a TMP for various gases

In TPMC the pump represented not by a pumping speed S but by a capture factor , i.e. the probability of the molecule entering the pump to be captured there:

where S(M) is the pumping speed at room temperature for the gas with mass M, v(M) is the molecular velocity at room temperature for this gas and A is the area of entrance to the turbo-pump.

4 ( )

( )TP

S M

v M A


Pumping speed of a

TMP for various gases

The calculated capture factor lies on very smooth (almost straight) line on the log-linear graph. Using this graph, the capture factor (M) can be easily obtained for any gas of molecular mass M. The pumping speed for that gas can be calculated as:

O.B. Malyshev. Vacuum 81 (2007) p. 752.

( )( ) ( )

4TP

v M AS M M


Pumping speed of a

TMP for various gases

Using these graphs for the capture factor (M) find the pumping speed of methane (M = 16) for the pump V2000 DN250:

( )( ) ( )

4TP

v M AS M M


Using TPMC results for pumping system optimisation


Test Particle Monte-Carlo (TPMC) code


• The first version of this program

was written by R. KERSEVAN

in 1990.

• Transfers CAD drawings into

programme readable file.

• Molflow+ allows calculating the pressure

in an arbitrarily complex geometry when

ultra-high vacuum condition is met.

• It is free!

• For more details look at http://test-

molflow.web.cern.ch/

Transmission probability and Seff

• Pumping port for DLS was modelled with TPMC. Transmission probability is w = 0.15,

• Entrance area is 23 mm 300 mm

• Effective pumping speed Seff: can be calculated for various gases and various pumps using only the w value:

𝐶 = 𝑤𝐴ത𝑣

4; 𝑆𝑒𝑓𝑓 =

𝑆∙𝐶

𝑆+𝐶


• (1) Direct modelling which includes:

• all gas load distribution (qi), 𝑄 = σ qi

• Pumping in terms of sticking probabilities (i)

• Outcome:

• pressure calculated from Mhiti:

• 𝑃𝑖 =4 𝑄 𝑀ℎ𝑖𝑡𝑖

𝑁 𝐴𝑖 ത𝑣𝑘𝐵𝑇

•(2) Superposition method:

• Each source of gas modelled in a separate TPMC run:

• Q1 and q1i for injection of gas (if any)

• Q2 and q2i for thermal outgassing

• Q3 and q3i for PSD in a beam chamber

• Q4 and q4i for PSD from SR absorber(s)

• Etc.

• Pumping in terms of sticking probabilities (i)

• Outcome:

• pressure calculated as a sum of all cases:

•𝑃𝑖 = 𝑃1𝑖 + 𝑃2𝑖 + 𝑃3𝑖 + 𝑃4𝑖 +⋯ =

•= 𝑄1𝑀1ℎ𝑖𝑡𝑖

𝑁1 𝐴𝑖 ത𝑣+

𝑄2𝑀2ℎ𝑖𝑡𝑖

𝑁2 𝐴𝑖 ത𝑣+⋯ 4𝑘𝐵𝑇

Three algorithms in TPMC

•(3) Superposition method with variable pumping:

• All pumping facets are set to a sticking probability i = 1

• Each source of gas which we want to vary sedately

should be modelled in a separate TPMC run:

• Q1 and q1i for thermal outgassing

• Q2 and q2i for PSD in the beam chamber

• Q3 and q3i for PSD from the SR absorber(s)

• Q4 - Q15 and q4i - q15i for a backflow from the pumps (these are

calculated from Q1-Q3 and transmission probability matrix W on the following pages)

• Outcome:

• pressure calculated as a sum of all cases:

• 𝑃𝑖 = 𝑃1𝑖 + 𝑃2𝑖 + 𝑃3𝑖 + 𝑃4𝑖 + 𝑃5𝑖 +⋯

Three algorithms in TPMC

DLS arc

vacuum chamber

O.B. Malyshev

Further resources and reading• Modern Vacuum Practice (3rd Edn), N Harris, (2005). ISBN 0955150116

• A User’s Guide to Vacuum Technology (3rd Edn), J F O’Hanlon, Wiley- Interscience,

2003. ISBN 0-471-27052-0

• Basic Vacuum Technology (2nd Edn), A Chambers, R K Fitch, B S Halliday, IoP

Publishing, 1998, ISBN 0-7503-0495-2

• Modern Vacuum Physics, A Chambers, Chapman & Hall/CRC, 2004, ISBN 0-8493-

2438-6

• Handbook of Vacuum Technology, Ed. K Jousten , Wiley- VCH, 2008. ISBN

3527407235

• F. Sharipov, Rarefied Gas Dynamics. Fundamentals for Research and Practice.

Wiley- VCH, 2016. ISBN 978-3-527-41326-3

• Vacuum Science and Technology, Pioneers of the 20th Century, AIP, 1994, ISBN 1-

56396-248-9

• Manufacturers’ data

Session I. An introduction into vacuum system design · An introduction into vacuum system design...

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