2017/11/13 MolFlow simulation setup General information Gas sheet - - PowerPoint PPT Presentation

2017/11/13

MolFlow simulation setup

General information

Geometries in MolFlow are obtained and estimated by the these 2 figures. Gas sheet system

So far, the simulation only consider nozzle chamber, outer chamber, differential pumping chamber, and interaction chamber. 3 skimmers are included. Supersonic free expansion is not considered. Electrodes and MCP are not included in the interaction chamber yet. Simulation focus

Geometries

Simulation geometries

1st skimmer (z = 0 cm): 1 sided, opaque 3rd skimmer (z = 36.5 cm): 2 sided, opaque Skimmers 45o rotated 2nd skimmer (z = 2.5 cm): 2 sided, opaque y z x

Nozzle chamber: 2 sided, opaque In current setup, particles are travelling outside the nozzle chamber. No particle is existed inside the chamber. Nozzle chamber

Outer chamber: 1 sided, opaque Outer chamber

Differential pumping chamber: 1 sided, opaque Differential pumping chamber

Short pipe between outer and differential pumping chambers: 1 sided, opaque 1 mm This short pipe section is used to prevent particle travels from outer chamber to differential pumping chamber directly without going through the 2nd skimmer. Short pipe connection 1

Interaction chamber: 1 sided, opaque Interaction chamber

Short pipe connection 2 1 mm Short pipe between differential pumping chambers and interaction chamber: 1 sided, opaque This short pipe section is used to prevent particle travels from differential pumping chamber to interaction chamber directly without going through the 3rd skimmer.

Boundary conditions

Outgassing Outgassing boundary @ 1st skimmer arbitrary

Pumping speed 690 L/s 67 L/s 270 L/s

Gas dumping surface Sticking factor = 1 All particles reach this surface will be absorbed, which is used as gas beam dump.

Results

Des: 7033688 for outgassing boundary Number of outgassing particles More particles can be released by increasing the simulation time for reducing statistical noise.

General result

Gas beam density profile a b c d e 2 cm

(beam interact location)

a

z = 38.6 cm Hits: 13125

b

z = 45.16 cm Hits: 13082

c

z = 58.3 cm Hits: 13066

d

z = 71.44 cm Hits: 13059

e

z = 77.8 cm Hits: 13067

Transparent facets for visualization

2017/11/28

General information

Geometries in MolFlow are obtained and estimated by the these 2 figures. Gas sheet system

So far, the simulation only consider nozzle chamber, outer chamber, differential pumping chamber, interaction chamber, and dumping chambers. 3 skimmers are included. Supersonic free expansion is not considered. Electrodes and MCP are not included in the interaction chamber yet. Moveable pressure gauge is not included in the dumping chamber. Simulation focus

Geometries

Simulation geometries

Gas dumping chambers The gas dumping surface assumption from previous slide is no longer used. Gas dumping chambers: 1 sided, opaque

Boundary conditions

Pumping speed 270 L/s 67 L/s

Results

Des: 7242666 for outgassing boundary Number of outgassing particles More particles can be released by increasing the simulation time for reducing statistical noise.

General result

a

z = 38.6 cm Hits: +13738

• 31

b

z = 45.16 cm Hits: +13747

• 75

(beam interact location)

c

z = 58.3 cm Hits: +13721

• 81

d

z = 71.44 cm Hits: +13734

• 103

e

z = 77.8 cm Hits: +13722

• 142

Transparent facets for visualization f

z = 142 cm Hits: +14603

• 1279

2 cm a b c d e f Gas beam density profile

Forward Backward

2017/12/06

Design for gas sheet beam requirement

Gas jet and proton beam parameters

jet thickness 0.2 mm jet width 10 mm jet number density 4e11 /cm^3 (10% effect) background vacuum 1e-10 torr beta function 1.5 m sig_x,y 0.7 mm KE 2.5 MeV proton number 9.00E+10 bunch length 0.37 us (bunched) 1.8 us (injected) jet gas nitrogen and helium inclination angle 45 degrees detedtor distance 20 cm electric field 1e4 V/m

Current concern So far, we only concern about the gas sheet beam dimension at the interaction location

2nd/3rd skimmer 1st skimmer Interaction location z Particle flow direction Gas source center projection Gas source area projection Assume the gas particle paths are straight lines Gas sheet beam dimension calculation

skimmer 1 skimmer 2 skimmer 3 gas sheet (interaction location) diameter 180 µm 400 µm width 57.91 µm length 6.193 mm z 0 mm 25 mm 365 mm 583 mm

Skimmers’ dimensions & Locations: Obtain from calculation

Projection from 3rd skimmer (at interaction location)

• 5
• 4.98
• 4.96
• 4.94
• 4.92
• 4.9
• 4.88
• 4.86
• 4.84

x 10

• 3

2 4 6 8 10 x 10

• 5

x [m] y [m]

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5 x 10

• 3
• 1.5
• 1
• 0.5

0.5 1 1.5 x 10

• 4

x [m] y [m]

Top left corner Gas source center projection Gas source area projection 0.2 mm 10 mm

Projection from 2nd skimmer (at interaction location)

• 8
• 6
• 4
• 2

2 4 6 8 x 10

• 3
• 6
• 4
• 2

2 4 6 x 10

• 3

x [m] y [m]

Gas source center projection Gas source area projection 3rd skimmer projection Gas beam that pass through the 2nd skimmer covers the entire 3rd skimmer

Result gas beam profile (at interaction location) Each cell is (0.05 mmm)2, by pixel counting, the gas beam dimensions are 10 mm *0.2 mm Hits (forward/backward): 4622/0 Des: 12,519,166 from

• utgassing boundary

*Simulation should be ran longer to get better statistical result

Change of particle density along propagation

In the case of free propagation

Gas source: Diameter = 180e-6 m Particle density = 6.37e20 1/m3 z = 0 cm Distribution: [cos(θ)]100 Virtual surface: z = 5 cm Area = (1 cm)2

• 5

5 x 10

• 3
• 5

5 x 10

• 3

2 4 6 8 10 12 x 10

16

x [m] y [m] particle density [1/m3]

Result particle density

z = 5 cm

• 5

5 x 10

• 3
• 5

5 x 10

• 3

3 4 5 6 7 8 9 10 11 x 10

16

y [m] x [m] particle density [1/m3]

Analytical approximation

   

2

, , ,

s s

n A f n R R      Particle density:

With respect to gas source Distance from gas source Source particle density Source area Distribution function:    

100

101 , cos 2 f     

 

2 2 0 0

, sin 1 f d d

 

     

 

(solid angle for entire hemisphere)

• 5

5 x 10

• 3
• 5

5 x 10

• 3

3 4 5 6 7 8 9 10 11 x 10

16

x [m] y [m] particle density [1/m3]

Basically overlap with MolFlow result In this simple case of free propagation, without the interference of skimmers, downstream particle density can be analytically approximated if the simple gas source properties is known.

2017/12/13

Simulation result after long running time

MolFlow simulation 1st skimmer Outgassing profile: (cos θ)1000 In simulation: Desorbed particle #: 4.06e9 Run time: 3~4 days on desktop Virtual transparent surfaces (6 in total): For visualizing gas sheet beam profile

Particle density profile

5 10 15 20 25 30 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01 5.00E-01 6.00E-01 7.00E-01 8.00E-01 200 400 600 800 1000 1200 1400 1600

Length [mm] Width [mm] z [mm]

Width [mm] Length [mm] forward backward forward - backward 6 1420 7.46E-01 24.4 1.527E+06 41490 1.485E+06 5 778 3.11E-01 13.3 1.496E+06 1208 1.495E+06 4 714.4 2.86E-01 12.2 1.496E+06 621 1.495E+06 3 583 2.00E-01 9.93 1.496E+06 312 1.495E+06 2 451 1.14E-01 7.68 1.496E+06 133 1.496E+06 1 386 7.16E-02 6.55 1.496E+06 63 1.496E+06 Hits Virtual Surface # z [mm] Width [mm] Length [mm]

length width Interaction location

Particle density profile

• 1.5
• 1
• 0.5

0.5 1 1.5 x 10

• 4

2 4 6 8 10 12 14 16 18 x 10

16

z = 386 mm along width [m] number density [1/m3]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 x 10

• 4

1 2 3 4 5 6 7 8 9 10 x 10

16

z = 451.6 mm along width [m] number density [1/m3]

• 3
• 2
• 1

1 2 3 4 x 10

• 4

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10

16

z = 583 mm along width [m] number density [1/m3]

• 5

5 x 10

• 4

0.5 1 1.5 2 2.5 3 x 10

16

z = 714.4 mm along width [m] number density [1/m3]

• 5

5 x 10

• 4

0.5 1 1.5 2 2.5 x 10

16

z = 778 mm along width [m] number density [1/m3]

• 1.5
• 1
• 0.5

0.5 1 1.5 x 10

• 3

1 2 3 4 5 6 x 10

15

z = 1420 mm along width [m] number density [1/m3]

Particle density profile

• 4
• 3
• 2
• 1

1 2 3 4 x 10

• 3

2 4 6 8 10 12 14 16 18 x 10

16

z = 386 mm along length [m] number density [1/m3]

• 4
• 3
• 2
• 1

1 2 3 4 x 10

• 3

2 4 6 8 10 12 x 10

16

z = 451.6 mm along length [m] number density [1/m3]

• 6
• 4
• 2

2 4 6 x 10

• 3

1 2 3 4 5 6 7 x 10

16

z = 583 mm along length [m] number density [1/m3]

• 8
• 6
• 4
• 2

2 4 6 8 x 10

• 3

0.5 1 1.5 2 2.5 3 3.5 4 x 10

16

z = 714.4 mm along length [m] number density [1/m3]

• 8
• 6
• 4
• 2

2 4 6 8 x 10

• 3

0.5 1 1.5 2 2.5 3 x 10

16

z = 778 mm along length [m] number density [1/m3]

• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 1 2 3 4 5 6 x 10

15

z = 1420 mm along length [m] number density [1/m3]

Particle density profile

Simulation only with skimmers’ aperture 1st skimmer Outgassing profile: (cos θ)1000 In simulation: Desorbed particle #: 4.31e9 Run time: 1~2 hours on laptop Virtual transparent surfaces (6 in total): For visualizing gas sheet beam profile In this simplified simulation, only skimmers’ apertures and virtual transparent surfaces are remain from the original model. The sticking factors of all other surfaces are set to be 1, so all the particles will be absorbed without reflection.

• 1.5
• 1
• 0.5

0.5 1 1.5 x 10

• 4

2 4 6 8 10 12 14 16 18 x 10

16

z = 386 mm along width [m] number density [1/m3]

• 2
• 1.5
• 1
• 0.5

0.5 1 1.5 2 x 10

• 4

2 4 6 8 10 12 x 10

16

z = 451.6 mm along width [m] number density [1/m3]

• 3
• 2
• 1

1 2 3 4 x 10

• 4

1 2 3 4 5 6 x 10

16

z = 583 mm along width [m] number density [1/m3]

• 5

5 x 10

• 4

0.5 1 1.5 2 2.5 3 3.5 x 10

16

z = 714.4 mm along width [m] number density [1/m3]

• 5

5 x 10

• 4

0.5 1 1.5 2 2.5 x 10

16

z = 778 mm along width [m] number density [1/m3]

• 1.5
• 1
• 0.5

0.5 1 1.5 x 10

• 3

1 2 3 4 5 6 x 10

15

z = 1420 mm along width [m] number density [1/m3]

Particle density profile *Green curves represent the simplified model. The simplified model provides good approximation of the original model.

• 4
• 3
• 2
• 1

1 2 3 4 x 10

• 3

2 4 6 8 10 12 14 16 18 x 10

16

z = 386 mm along length [m] number density [1/m3]

• 4
• 3
• 2
• 1

1 2 3 4 x 10

• 3

2 4 6 8 10 12 x 10

16

z = 451.6 mm along length [m] number density [1/m3]

• 6
• 4
• 2

2 4 6 x 10

• 3

1 2 3 4 5 6 7 x 10

16

z = 583 mm along length [m] number density [1/m3]

• 8
• 6
• 4
• 2

2 4 6 8 x 10

• 3

0.5 1 1.5 2 2.5 3 3.5 4 x 10

16

z = 714.4 mm along length [m] number density [1/m3]

• 8
• 6
• 4
• 2

2 4 6 8 x 10

• 3

0.5 1 1.5 2 2.5 3 x 10

16

z = 778 mm along length [m] number density [1/m3]

• 0.015
• 0.01
• 0.005

0.005 0.01 0.015 1 2 3 4 5 6 x 10

15

z = 1420 mm along length [m] number density [1/m3]

Particle density profile The simplified model provides good approximation of the original model. *Green curves represent the simplified model.