VASCO (VAcuum Stability COde) : multi-gas code to calculate gas - PowerPoint PPT Presentation

VASCO (VAcuum Stability COde) : multi-gas code to calculate gas density lti d t l l t d it profile and vacuum stability in a UHV system Adriana Rossi • General equation q • 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 installation VASCO documentation and installation

Equation q • 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 depends on � Sources : � Net contribution from diffusion α q th � Thermal desorption. p e - η e � Beam induced phenomena: p + η i ion, electron and photon induced AD AD η ph molecular desorption. SR � � Localised sources Localised sources � Sink: dx � Localised pumps � Distributed pumps (NEG or cryo) p p ( y ) 2

Equation describing the gas density for each gas species for each gas species ⎛ ⎞ 2 ∂ ∂ ⋅ n n { } A v • • I ∑ ⎜ ⎟ g g g b = ⋅ ⋅ + η σ ⋅ − ⋅ α + ⋅ + η ⋅ Γ + η ⋅ Γ + ⋅ V a D n C n A q ⎜ ⎟ ph e + g i , j j g g g ph , g e , g g 2 → j g ∂ ∂ ⎝ ⎠ t x e 4 j 123 14243 1442443 14424443 123 123 123 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 α α q th Single gas model e - η e p ⎛ ⎞ + I σ η i AD AD b n ⎜ ⎜ ⎟ ⎟ η ph η η , e σ ⋅ n + i ⎝ g g ⎠ g → g SR dx 3

VASCO code ( ) = n n x , t • Cylindrical symmetry g g � Average density across the area ( ( ) ) • Time invariant parameters Time invariant parameters ∂ ∂ n n x x , , t t g ≈ V 0 (snapshot in time at steady state) ∂ t � Surface parameters (sticking and desorption coefficients) constant (not dependent on dose , selected for a specific incident energy) • Maxwell-Boltzmann distribution ⋅ 8 k T = B v g of molecular velocity π ⋅ m g � Assumption of uniform � Assumption of uniform Dg = 2 2 3 vg ⋅ r ( x ) D ( ) diffusion coefficient distribution in space A ⋅ v average number of particle g hitting the surface area 4 4

VASCO input file p • 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 ) G k G k+1 G 1 G 1 k+1 G N+1 • C Continuity of the density function: ti it f th d it f ti ⎧ − k 1 k = n ( x ) n ( x ) at the segment boundary x k the solution ⎪ k k ⎨ − k k 1 = ∂ ∂ k 2 , N n n from segment (k-1) must equal the − k k k k 1 k = − + S n ( x ) c c G ⎪ k spec spec ∂ ∂ ∂ ∂ solution from segment (k) g ( ) x x x x ⎩ ⎩ x x k k • Continuity of the flow function : ∂ the sum of flow of molecules coming n 1 1 1 1 = 1 + S n ( x ) c G from the two side of one boundary must from the two side of one boundary must 1 spec p ∂ ∂ x x equal the amount of molecules pumped 1 N (S) or generated by a local source (g) ∂ n + + N 1 N N N 1 = − + S n ( x ) c G + N 1 spec • Ends of segment sequence ∂ x x x N N + 1 1 6

Solution [ ] ′ • Density vector (per each segment k ) . . . . . . . . k = n n n n n H CH CO CO 2 2 4 4 2 2 ⎡ ⎤ • Coefficient vectors or matrices η η η η + + + + H − H CH − H CO − H CO − H ⎢ ⎥ 2 2 4 2 2 2 2 η η η η examples: ⎢ ⎥ + + + + H − CH CH − CH CO − CH CO − CH k η = 2 4 4 4 4 2 4 ⎢ ⎢ ⎥ ⎥ i η η η η η η η η – Ion stimulated desorption yield . . . . . . . . + + + + ⎢ ⎥ H − CO CH − CO CO − CO CO − CO 2 4 2 η η η η ⎢ ⎥ ⎣ ⎦ + + + + H − CO CH − CO CO − CO CO − CO 2 2 4 2 2 2 2 [ ] ′ – Electron SDY . . . . . . . . . . . . . . . . . . . . . . . k η = η η η η − − − − e e H e CH e CO e CO 2 4 2 ⎡ ⎤ α 0 0 0 H ⎢ ⎥ 2 – Sticking coefficient . . . . . . . . . . . . . . . . . . . α 0 0 0 ⎢ ⎥ CH k α = 4 ⎢ ⎥ α 0 0 0 ⎢ CO ⎥ ⎢ ⎢ α α ⎥ ⎥ ⎣ ⎣ 0 0 0 0 0 0 ⎦ ⎦ CO CO ⎧ 2 k = y n ⎪ 1 , k ⎨ • Change of variables • ⎪ = ⎩ y n k 2 , k ( ( ) ) { } z ∫ ∫ ( ) ( ) = + − τ τ Y z exp M z Y exp M z b d k k 0 , k k k 0 7

“Single-gas model” against “Multi-gas model” g g g g Gas density as a function of the beam current for single-gas model - multi-gas model a) b) 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 - MC p 1E-10 torr.l/s/cm 2 outgassing 2.5 variable sticking coefficient over 4m (80mm diameter) tube i bl ti ki ffi i t 4 (80 di t ) t b MC, stick=0 VASCO, stick=0 2 MC, stick=1E-3 VASCO, stick=1E-3 10 l/s 0 /s 10 l/s 10 l/s d gas density y MC, stick=1E-2 VASCO, stick=1E-2 MC, stick=1E-1 VASCO, stick=1E-1 1.5 MC, stick=1 VASCO, stick=1 Series11 Series11 Series12 Series12 normalised 1 0.5 0 0 0 1 2 3 4 5 distance (m) Thanks to Pedro Costa-Pinto for running MC simulation Thanks to Pedro Costa-Pinto for running MC simulation 9

VASCO with localised source 1E-3 torr.l/s 7m chamber - Ø 80, NEG coated 7m chamber Ø 80 NEG coated 1.E+00 stick=5E-3 stick=1E-2 stick=1E-1 stick=5E-1 1 E 01 1.E-01 5.00E-03 1.00E-02 density 1.00E-01 5.00E-01 1.E-02 normalised 1.E-03 Transmission 1.E-04 probability as from Smith & Lewin – JVST 3 (92)1966 JVST 3 (92)1966 1 E 05 1.E-05 0 1000 2000 3000 4000 5000 6000 7000 distance from source (mm) 10

Photon Induced gas Desorption g p [ Gröbner et al. Vacuum, Vol 37, 8-9, 1987] [ Gómez-Goñi et al., JVST 12(4), 1994] Energy dependence Evolution with dose 11

Electron Induced Gas Desorption p J. Gómez-Goñi et al., JVST A 15(6), 1997 G. Vorlaufer et al., Vac. Techn. Note. 00-32 Copper baked at 150º C Copper Unbaked 1 10 0 10 −1 10 η / (molec./e − ) −2 −2 10 10 −3 10 C2H6 Evolution with dose Evolution with dose CH4 CO CO CO2 H2 H2O Fit −4 10 0 50 100 150 200 250 300 350 E / eV E Evolution with dose Energy dependence l ti ith d E d d 12

NEG properties p p [ P . Chiggiato, JVC-Gratz-06-2002] [ P . Chiggiato, JVC-Gratz-06-2002] -2 ] [molecules cm 10 13 10 14 10 15 10 16 3 10 10 0 10 1 Heating duration 24 hours TiZrV/ St. Steel CO heated at 200°C TiZrV on rough Cu TiZrV on rough Cu ing speed [ l s -1 m -1 ] coated at 300 °C TiZrV/ Al -1 cm 2 ] heated at 200°C 10 -1 10 0 Sticking facto g Speed [ l s 2 10 200°C TiZrV on smooth Cu Pumping or coated at 100 °C 2 pump 10 -2 10 -1 TiZrV/ Al H heated at 180°C beam pipe diameter = 80 mm 10 -3 1 10 -2 10 10 10 0 5 10 15 20 10 -7 10 -6 10 -5 10 -4 10 -3 -2 ] Number of heating/venting cycles CO Surface Coverage [Torr l cm Pumping speed Aging 13

H 2 CH 4 CO CO 2 penning ion gauges o gauges N 2 equivalent N equivalent 1.E+ 16 mbar a Q1-Q2-Q3 Q1-Q2-Q3 293K 293K 1 E+ 15 1.E+ 15 MKI MKI MSI MSI recom b. es/ m 3 ) ch. Q7 Q6 Q5 D2/ Q4 D1 D1 D2/ Q4 Q5 Q6 Q7 1.E+ 14 molecule TCTH 1.E-09 TCLI B VGPB.623.4L8.R 1.E+ 13 Density ( 1.E-10 TDI VGPB.123.4L8.X 1.E+ 12 leak 2E-6 torr.l/ s 1.E-11 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 y C:\ drive • From your START menu go to CONTROL PANEL -> SYSTEM -> ADVANCE -> ENVIRONMENT VARIABLES 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) 16