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VASCO (VAcuum Stability COde) : multi-gas code to calculate gas density profile and vacuum stability in a UHV
system Adriana Rossi
• General equation• VASCO code assumptions and solution• Comparison between Single and Multi-Gas models• Comparison between VASCO and MC (Pedro Costa-Pinto)• Discussion on input parameters and example of IR8 results (with real
data)• VASCO documentation and installation
2
Equation
• Level of water in a sink depends on:– Flow of water from the tap = source– Flow of water through the drain = sink
• After transient level stabilises only if source = sink
dx
+p
i
e- e
ph
qth
ADAD
SR
Pressure (density) in a vacuum tube depends on
Sources : Net contribution from diffusion Thermal desorption. Beam induced phenomena:
ion, electron and photon induced molecular desorption.
Localised sources
Sink: Localised pumps Distributed pumps (NEG or cryo)
3
Single gas model
Equation describing the gas density for each gas species
gegephgphgggg
jj
bjgji
gg
g qAnCvA
ne
I
x
nDa
t
nV
,,,2
2
4
Time variation Diffusion Ionisation by beam Distributed pumping Desorption of 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
dx
+p
i
e- e
ph
qth
ADAD
SR
gbgggi n
e
I ,
4
VASCO code
• Cylindrical symmetry
Average density across the area
• Time invariant parameters (snapshot in time at steady state)
Surface parameters (sticking and desorption
coefficients) constant (not dependent on
dose , selected for a specific incident energy)
• Maxwell-Boltzmann distribution of molecular velocity
Assumption of uniform
distribution in space
txnn gg ,
g
Bg m
Tkv
8
Dg 23vg r (x)
4gvA
diffusion coefficient
average number of particle hitting the surface area
0
,
t
txnV g
5
VASCO input file
• Vacuum chamber divided in segments:
– Geometry (length and diameter)
– Temperature
– Distributed and localised pumps
– Distributed and localised sources
• Thermal outgassing
• Ion, electron, photon stimulated desorption
6
Boundary conditions (steady state)
• Continuity of the density function: at the segment boundary xk the solution
from segment (k-1) must equal the solution from segment (k)
• Continuity of the flow function :
the sum of flow of molecules coming 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 sequence
11
1
1111
11
1
1
)(
)(
N
x
NNspecN
NN
xspec
Gx
ncxnS
Gx
ncxnS
N
GkG1Gk+1
GN+1
NG
x
nc
x
ncxnS
xnxn
k
x
kkspec
x
kkspeck
kk
kk
kk
kk
,2k )(
)()(1
1
1
7
Solution
• Density vector (per each segment k) . . . . . . . .
• Coefficient vectors or matrices examples:
– Ion stimulated desorption yield . . . . . . . .
– Electron SDY . . . . . . . . . . . . . . . . . . . . . . .
– Sticking coefficient . . . . . . . . . . . . . . . . . . .
• Change of variables
242 COCOCHH
k nnnnn
2222422
242
4244442
2222422
COCOCOCOCOCHCOH
COCOCOCOCOCHCOH
CHCOCHCOCHCHCHH
HCOHCOHCHHH
ki
242 COeCOeCHeHeke
2
4
2
000
000
000
000
CO
CO
CH
H
k
kk
kk
ny
ny
,2
,1
dbzMYzMzY kk
z
kkk exp exp0
,0
8
“Single-gas model” against “Multi-gas model”
a) b)
Gas density as a function of the beam current for
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)
9
Comparison VASCO - MC
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5
distance (m)
no
rma
lised
gas
den
sity
MC, stick=0 VASCO, stick=0
MC, stick=1E-3 VASCO, stick=1E-3
MC, stick=1E-2 VASCO, stick=1E-2
MC, stick=1E-1 VASCO, stick=1E-1
MC, stick=1 VASCO, stick=1
Series11 Series12
variable sticking coefficient over 4m (80mm diameter) tube
10 l/s 10 l/s
1E-10 torr.l/s/cm2 outgassing
Thanks to Pedro Costa-Pinto for running MC simulation
10
VASCO with localised source
1E-3 torr.l/s7m chamber - Ø80, NEG coated
Transmission probability as from Smith & Lewin – JVST 3 (92)19661.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 1000 2000 3000 4000 5000 6000 7000
distance from source (mm)
no
rma
lis
ed
de
ns
ity
stick=5E-3 stick=1E-2
stick=1E-1 stick=5E-1
5.00E-03 1.00E-02
1.00E-01 5.00E-01
11
Photon Induced gas Desorption
[Gröbner et al. Vacuum, Vol 37, 8-9, 1987] [Gómez-Goñi et al., JVST 12(4), 1994]
Evolution with dose Energy dependence
12
Electron Induced Gas DesorptionJ. Gómez-Goñi et al., JVST A 15(6), 1997
Copper baked at 150ºCG. Vorlaufer et al., Vac. Techn. Note. 00-32
Copper Unbaked
Evolution with dose
Evolution with dose Energy dependence
13
NEG properties
[P. Chiggiato, JVC-Gratz-06-2002] [P. Chiggiato, JVC-Gratz-06-2002]
10-2
10-1
100
101
10-7 10-6 10-5 10-4 10-3
10-3
10-2
10-1
1001013 1014 1015 1016
Pum
pin
g S
pe
ed
[ s-1
cm
2 ]
CO Surface Coverage [Torr cm-2] S
ticking
facto
r
[molecules cm-2]
TiZrV on smooth Cucoated at 100 °C
TiZrV on rough Cucoated at 300 °C
CO
101
102
103
0 5 10 15 20
H2 p
um
pin
g s
pe
ed
[
s-1 m
-1]
Number of heating/venting cycles
200°C
Heating duration 24 hours
beam pipe diameter = 80 mm
TiZrV/Alheated at 180°C
TiZrV/Alheated at 200°C
TiZrV/St. Steelheated at 200°C
Pumping speed Aging
14
1.E+10
1.E+11
1.E+12
1.E+13
1.E+14
1.E+15
1.E+16
-280 -210 -140 -70 0 70 140 210 280
IR8 red beam - B2 (distance from IP8 - m)
Den
sity
(m
ole
cule
s/m
3)
H2 CH4 CO CO2
D1 D2/Q4
Q1-Q2-Q3
Q5 Q6
recomb.ch.
1.E-09
mbar at 293K
1.E-10
1.E-11
1.E-12
TCTH
Q7
penning
ion gauges N2 equivalent
MKI MSI
TDIleak 2E-6
torr.l/ s
TCLI B
D1
Q1-Q2-Q3
D2/Q4Q5Q6Q7
VGPB.623.4L8.R
VGPB.123.4L8.X
15
VASCO documentation
Code description in VASCO_brief1.pdf
\\Srv2_div\div_lhc\VACUUM\Rossi\VASCOInput file in manual.xls
16
Installation
• To install the program, copy the whole VASCO directory onto your C:\ drive
• From your START menu go to CONTROL PANEL -> SYSTEM -> ADVANCE -> 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)
17
Example of input file
H2 CH4 CO CO2 H2 CH4 CO CO221 0 0 0 22 0 0 0
212.7 0 0 0 212 0 0 0400 0 0 0 500 0 0 0
77233 0 0 0 77633 0 0 0300 0 0 0 300 0 0 0
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 00 0 0 0 0 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 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
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
0.00E+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 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
VMBGA.C4R8.X VCTCN.4R8.XH2 CH4 CO CO2 H2 CH4 CO CO2 H2 CH4 CO CO2
23 0 0 0 24 0 0 0 26 0 0 0212 0 0 0 212 0 0 0 212 0 0 0
1350 0 0 0 1350 0 0 0 1350 0 0 078133 0 0 0 79483 0 0 0 82183 0 0 0
300 0 0 0 300 0 0 0 300 0 0 00 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 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
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
0.00E+00 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 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 00 0 0 0 0 0 0 0 0 0 0 0
_TDI .4R8%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] %
%%%
in_alpha = [ %%%%
in_alpha_p = [ %%%%
in_eta_ i = [ %%%%
in_eta_p_ i = [ %%%%
in_eta_e = [ %in_eta_p_e = [ %in_eta_ph = [ %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) %[l/s] (CO2) %
in_g_Nplus1 = [[torrl/ s] %
