VASCO (VAcuum Stability COde) : lti d t l l t d itmulti-gas code to calculate gas density

profile and vacuum stability in a UHV systemAdriana Rossi

• General equationq• VASCO code assumptions and solution• Comparison between Single and Multi-Gas models• Comparison between VASCO and MC (Pedro Costa-Pinto)Comparison between VASCO and MC (Pedro Costa Pinto)• Discussion on input parameters and example of IR8 results (with real

data)• VASCO documentation and installationVASCO documentation and installation

Equationq• Level of water in a sink depends on:

Flow of water from the tap = source– Flow of water from the tap = source– Flow of water through the drain = sink

• After transient level stabilises only if source = sink

Pressure (density) in a vacuum tube depends on

αqth

depends onSources :

Net contribution from diffusionThermal desorption.

+p

ηi

e- ηe

ηph

ADAD

SR

pBeam induced phenomena:ion, electron and photon induced molecular desorption. Localised sources

dx

Localised sourcesSink:

Localised pumpsDistributed pumps (NEG or cryo)

2

p p ( y )

Equation describing the gas density for each gas speciesfor each gas species

{ } gegephgphgggg

jj

bjgji

gg

g qAnCvA

neI

xn

Dat

nV ⋅+Γ⋅+Γ⋅+⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛+⋅

⋅−⋅+

∂∂

⋅⋅=∂

∂ ••

→∑ + ,,,2

2

4 ηηαση

123 14243 1442443 14424443 123 123 123Time variation Diffusion Ionisation by beam Distributed pumping Desorptionof particles in through and desorption by by NEG or by photons by electron thermal

volume V surface a the ions by beam screen

Multi gas model

α

Single gas model+

pη

i

α

e- ηe

ηph

qth

ADAD⎟⎞

⎜⎛ ⋅b nI ση

dx

SR⎟⎠

⎜⎝→+ ggggi n

eση ,

3

VASCO code

• Cylindrical symmetry ( )txnn gg ,=

Average density across the area

• Time invariant parameters ( ),∂ txnTime invariant parameters(snapshot in time at steady state)

Surface parameters (sticking and desorption

( )0

,≈

∂∂

ttxn

V g

coefficients) constant (not dependent on dose , selected for a specific incident energy)

• Maxwell-Boltzmann distribution of molecular velocity

Assumption of uniform

g

Bg m

Tkv⋅

⋅=π8

D 2 ( )Assumption of uniform distribution in space

Dg = 23 vg ⋅ r (x)

4gvA ⋅

diffusion coefficient

average number of particle hitting the surface area

4

VASCO input filep

• Vacuum chamber divided in segments:g

– Geometry (length and diameter)

– Temperature

– Distributed and localised pumps

– Distributed and localised sources

Thermal outgassing• Thermal outgassing

• Ion, electron, photon stimulated desorption

5

Boundary conditions (steady state)y ( y )

GkG1 Gk+1G1 k+1GN+1

C ti it f th d it f ti• Continuity of the density function: at the segment boundary xk the solution from segment (k-1) must equal the solution from segment (k)

NG

xnc

xncxnS

xnxn

kk

kspec

kkspeck

kk

kk

kk

,2k )(

)()(1

1

1

=⎪⎩

⎪⎨

⎧

+∂

∂−∂∂=

=−

−

−

g ( )

• Continuity of the flow function : the sum of flow of molecules coming from the two side of one boundary must

1111

11 )( +∂∂= spec GncxnS

xx xx kk⎩ ∂∂

from the two side of one boundary must equal the amount of molecules pumped (S) or generated by a local source (g)

• Ends of segment sequence1

11

1

1

)( ++

+ +∂

∂−=

∂

N

x

NNspecN

NN

xp

Gx

ncxnS

x

N

6

1+xN

Solution

• Density vector (per each segment k) . . . . . . . . [ ]′=242 COCOCHH

k nnnnn

• Coefficient vectors or matrices examples:

242

⎥⎥⎥⎤

⎢⎢⎢⎡

= −−−−

−−−−

++++

++++

4244442

2222422

CHCOCHCOCHCHCHH

HCOHCOHCHHH

ki ηηηη

ηηηηηηηη

η– Ion stimulated desorption yield . . . . . . . .

– Electron SDY . . . . . . . . . . . . . . . . . . . . . . .

⎥⎥⎥

⎦⎢⎢⎢

⎣ −−−−

−−−−

++++

++++

2222422

242

COCOCOCOCOCHCOH

COCOCOCOCOCHCOH

ηηηηηηηη

[ ]′= −−−− 242 COeCOeCHeHeke ηηηηη

– Sticking coefficient . . . . . . . . . . . . . . . . . . .

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

= 4

2

000000000000

CO

CO

CH

H

k

αα

αα

α

• Change of variables

⎥⎦⎢⎣ 2000 COα

⎪⎩

⎪⎨⎧

=

=•

kk

kk

ny

ny

,2

,1

( ) ( ) ( ){ } ττ dbzMYzMzY kk

z

kkk exp exp ,0 −+= ∫7

( )0∫

“Single-gas model” against “Multi-gas model”g g g g

Gas density as a function of the beam current for

a) b)

single-gas model - multi-gas model

The critical current calculated neglecting desorption by different ionised gas species is > twice bigger than what is estimated with the multi-gas model (with identical j-j coefficient)

8

Comparison VASCO - MCp

2.5

i bl ti ki ffi i t 4 (80 di t ) t b

1E-10 torr.l/s/cm2 outgassing

2

y

MC, stick=0 VASCO, stick=0

MC, stick=1E-3 VASCO, stick=1E-3

variable sticking coefficient over 4m (80mm diameter) tube

10 l/s 10 l/s

1.5

d ga

s de

nsity MC, stick=1E-2 VASCO, stick=1E-2

MC, stick=1E-1 VASCO, stick=1E-1

MC, stick=1 VASCO, stick=1

Series11 Series12

0 /s 10 l/s

1

norm

alis

ed

Series11 Series12

0

0.5

00 1 2 3 4 5

distance (m)

Thanks to Pedro Costa-Pinto for running MC simulation

9

Thanks to Pedro Costa-Pinto for running MC simulation

VASCO with localised source1E-3

torr.l/s7m chamber Ø80 NEG coated7m chamber - Ø80, NEG coated

1 E 01

1.E+00stick=5E-3 stick=1E-2

stick=1E-1 stick=5E-1

1.E-02

1.E-01

dens

ity

5.00E-03 1.00E-02

1.00E-01 5.00E-01

1.E-03

norm

alis

ed

Transmission probability as from Smith & Lewin –JVST 3 (92)19661 E 05

1.E-04

JVST 3 (92)19661.E-050 1000 2000 3000 4000 5000 6000 7000

distance from source (mm)

10

Photon Induced gas Desorptiong p

[Gröbner et al. Vacuum, Vol 37, 8-9, 1987] [Gómez-Goñi et al., JVST 12(4), 1994]

Evolution with dose Energy dependence

11

Electron Induced Gas DesorptionpJ. Gómez-Goñi et al., JVST A 15(6), 1997

Copper baked at 150ºCG. Vorlaufer et al., Vac. Techn. Note. 00-32

Copper Unbaked

0 50 100 150 200 250 300 35010

−4

10−3

10−2

10−1

100

101

E / eV

η / (

mol

ec./e

−)

C2H6CH4 CO CO2 H2 H2O Fit

0 50 100 150 200 250 300 35010

−4

10−3

10−2

10−1

100

101

E / eV

η / (

mol

ec./e

−)

C2H6CH4 CO CO2 H2 H2O Fit

0 50 100 150 200 250 300 35010

−4

10−3

10−2

10−1

100

101

E / eV

η / (

mol

ec./e

−)

C2H6CH4 CO CO2 H2 H2O Fit

Evolution with dose

0 50 100 150 200 250 300 35010

−4

10−3

10−2

10−1

100

101

E / eV

η / (

mol

ec./e

−)

C2H6CH4 CO CO2 H2 H2O Fit

Evolution with dose

0 50 100 150 200 250 300 35010

−4

10−3

10−2

10−1

100

101

E / eV

η / (

mol

ec./e

−)

C2H6CH4 CO CO2 H2 H2O Fit

E l ti ith d E d dEvolution with dose Energy dependence

12

NEG propertiesp p

[P. Chiggiato, JVC-Gratz-06-2002] [P. Chiggiato, JVC-Gratz-06-2002]

101100

1013 1014 1015 1016[molecules cm-2]

TiZrV on rough CuCO

103

Heating duration 24 hoursTiZrV/St. Steel

heated at 200°C

100 10-1

g Sp

eed

[ l s

-1 c

m2 ]

Sticking factoTiZrV on smooth Cu

TiZrV on rough Cucoated at 300 °C

102

ing s

pee

d [l

s-1 m

-1]

200°C

TiZrV/Alheated at 200°C

10-2

10-1

10-3

10-2

Pum

ping

or coated at 100 °C

101

H2 p

um

p

beam pipe diameter = 80 mm

TiZrV/Alheated at 180°C

1010-7 10-6 10-5 10-4 10-3

CO Surface Coverage [Torr l cm-2]

100 5 10 15 20

Number of heating/venting cycles

Pumping speed Aging

13

H2 CH4 CO CO2penning

ion gauges N equivalent

1 E+15

1.E+16

Q1-Q2-Q3mbar a293K

o gauges N2 equivalent

MKI MSIQ1-Q2-Q3

1.E+14

1.E+15

es/m

3)

D1 D2/Q4 Q5 Q6

recomb.ch.

293K

Q7

MKI MSI

D1D2/Q4Q5Q6Q7

1.E+13

mol

ecule

1.E-09TCTHTCLIB

VGPB.623.4L8.R

1.E+12

Den

sity

( 1.E-10

1.E-11

TDIleak 2E-6

torr.l/s

VGPB.123.4L8.X

1.E+11

D 1.E 11

1.E-12

1.E+10-280 -210 -140 -70 0 70 140 210 280

IR8 red beam - B2 (distance from IP8 - m)

14

VASCO documentation\\Srv2_div\div_lhc\VACUUM\Rossi\VASCO

Input file in manual.xls

Code description in VASCO_brief1.pdf

15

Installation

• To install the program, copy the whole VASCO directory onto your p g py y yC:\ drive

• From your START menu go to CONTROL PANEL -> SYSTEM -> ADVANCE -> ENVIRONMENT VARIABLESADVANCE -> ENVIRONMENT VARIABLES

– Select SYSTEM VARIABLES. • Select the line PATH and edit it. • At the end of the line add a semicolon, then the path name where you have

the Start-Multi-Gas.exe program + \bin\win32 (;C:\VASCO \bin\win32)

16

Example of input filep p

VMBGA.C4R8.X VCTCN.4R8.X _TDI.4R8H2 CH4 CO CO2 H2 CH4 CO CO2

21 0 0 0 22 0 0 0212.7 0 0 0 212 0 0 0

400 0 0 0 500 0 0 077233 0 0 0 77633 0 0 0

300 0 0 0 300 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

8 90E-23 0 0 0 8 90E-23 0 0 0

H2 CH4 CO CO2 H2 CH4 CO CO2 H2 CH4 CO CO223 0 0 0 24 0 0 0 26 0 0 0

212 0 0 0 212 0 0 0 212 0 0 01350 0 0 0 1350 0 0 0 1350 0 0 0

78133 0 0 0 79483 0 0 0 82183 0 0 0300 0 0 0 300 0 0 0 300 0 0 0

0 0 0 0 1900 0 0 0 509.1 0 0 00 0 0 0 0 900 0 0 0 129.8 0 00 0 0 0 0 0 700 0 0 0 200.4 00 0 0 0 0 0 0 560 0 0 0 161.90 0 0 0 0 0 0 0 0 0 2.00E-06 0

8 90E-23 0 0 0 8 90E-23 0 0 0 8 90E-23 0 0 0

%in_Segment = [ %in_d = [ [mm] %in_L = [ [mm] %in_dist_ref = [mm] %in_T = [ [K] %in_S = [ [l/s] (H2) %

[l/s] (CH4) %[l/s] (CO) %[l/s] (CO2) %

in_g = [ [torrl/s] %in sigma = [ [m2] % 8.90E 23 0 0 0 8.90E 23 0 0 0

0 6.36E-22 0 0 0 6.36E-22 0 00 0 5.50E-22 0 0 0 5.50E-22 00 0 0 8.58E-22 0 0 0 8.58E-22

1.00E-07 0 0 0 5.00E-03 0 0 00 0.00E+00 0 0 0 0.00E+00 0 00 0 1.00E-07 0 0 0 0.5 00 0 0 1.00E-07 0 0 0 0.50 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

8.90E 23 0 0 0 8.90E 23 0 0 0 8.90E 23 0 0 00 6.36E-22 0 0 0 6.36E-22 0 0 0 6.36E-22 0 00 0 5.50E-22 0 0 0 5.50E-22 0 0 0 5.50E-22 00 0 0 8.58E-22 0 0 0 8.58E-22 0 0 0 8.58E-22

1.00E-07 0 0 0 1.00E-07 0 0 0 1.00E-07 0 0 00 0.00E+00 0 0 0 0.00E+00 0 0 0 0.00E+00 0 00 0 1.00E-07 0 0 0 1.00E-07 0 0 0 1.00E-07 00 0 0 1.00E-07 0 0 0 1.00E-07 0 0 0 1.00E-070 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

in_sigma = [ [m2] %%%%

in_alpha = [ %%%%

in_alpha_p = [ %%%%

0.54 0.54 0.54 0.54 0.05 0.05 0.05 0.050.04 0.05 0.07 0.11 0 0.01 0.01 0.010.25 0.29 0.29 0.33 0.03 0.03 0.03 0.030.14 0.14 0.14 0.14 0.01 0.01 0.01 0.01

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1.77E-03 6.46E-05 4.52E-04 3.87E-04 3.33E-05 8.33E-07 1.67E-05 1.67E-050 0 0 0 0 0 0 0

1.50E-04 4.00E-06 1.50E-05 2.50E-05 2.50E-07 2.50E-09 1.25E-08 1.25E-080 0 0 0 0 0 0 0

0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.54 0.540.04 0.05 0.07 0.11 0.04 0.05 0.07 0.11 0.04 0.05 0.07 0.110.25 0.29 0.29 0.33 0.25 0.29 0.29 0.33 0.25 0.29 0.29 0.330.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

1.77E-03 6.46E-05 4.52E-04 3.87E-04 1.77E-03 6.46E-05 4.52E-04 3.87E-04 1.77E-03 6.46E-05 4.52E-04 3.87E-040 0 0 0 0 0 0 0 0 0 0 0

1.50E-04 4.00E-06 1.50E-05 2.50E-05 1.50E-04 4.00E-06 1.50E-05 2.50E-05 1.50E-04 4.00E-06 1.50E-05 2.50E-050 0 0 0 0 0 0 0 0 0 0 0

in_eta_i = [ %%%%

in_eta_p_i = [ %%%%

in_eta_e = [ %in_eta_p_e = [ %in_eta_ph = [ %in eta p ph = [ % 0 0 0 0 0 0 0 0

0.00E+00 0 0 0 0.00E+00 0 0 00 0.00E+00 0 0 0 0.00E+00 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1.00E-12 5.00E-15 1.00E-14 5.00E-15 5.00E-14 3.00E-17 1.00E-14 1.00E-140 0 0 0 0 0 0 0

1.20E+14 0 0 0 6.00E+13 0 0 03.00E+15 0 0 0 3.00E+15 0 0 0

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 00.00E+00 0 0 0 0.00E+00 0 0 0 0.00E+00 0 0 0

0 0.00E+00 0 0 0 0.00E+00 0 0 0 0.00E+00 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

5.00E-12 1.00E-13 1.00E-12 1.00E-12 5.00E-12 1.00E-13 1.00E-12 1.00E-12 5.00E-12 1.00E-13 1.00E-12 1.00E-120 0 0 0 0 0 0 0 0 0 0 0

1.20E+14 0 0 0 1.20E+14 0 0 0 1.20E+14 0 0 03.00E+15 0 0 0 3.00E+15 0 0 0 3.00E+15 0 0 0

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

in_eta_p_ph = [ %in_Cbs = [ [l/s/m] %

%%%

in_Qth = [ %in_n_e = [ %in_N_e = [ [e-/m/s] %in_Gamma_ph[ph/m/s] %in_S_Nplus1 [l/s] (H2) %

[l/s] (CH4) %[l/s] (CO) %

0 0 0 0 0 0 0 00 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0

[l/s] (CO2) %in_g_Nplus1 [torrl/s] %

17