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Materials, Fabrication Techniques, and Joint Design 11 Accelerator Vacuum and Mechanical Engineering UCRL-MI-201847 Louis R. Bertolini Lawrence Livermore National Laboratory January 9, 2004 United States Particle Accelerator School @ The College of William & Mary Table of Contents 1. Vacuum Fundamentals 2. Estimating Gasloads 3. Vacuum System Design Calculations 4. Mechanical Vacuum Pumps 5. Ion Pumps 6. Non-evaporable Getter Pumps 7. Titanium Sublimation Pumps 8. Cryosorption Pumps and Compressors 9. Pressure Measuring Devices 10. Materials, Fabrication Techniques, and Joint Design 11. Vacuum Testing & Leak Detection 12. Vacuum Hardware 13. Material Preparation, Cleaning, and Processing 14. Supports and Alignment This work was performed under the auspices of the U. S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-Eng-48. TheThe USUS ParticleParticle AcceleratorAccelerator SchoolSchool VacuumVacuum FundamentalsFundamentals Lou Bertolini Lawrence Livermore National Laboratory January 19-24, 2004 USPAS January 2004 Vacuum Fundamentals Page 1 Your Instructor • Lou Bertolini —Mechanical Engineer − E-mail: [email protected] − Phone: (925) 422-9531 − FAX: (925) 422-4667 USPAS January 2004 Vacuum Fundamentals Page 2 Vacuum is a highly interdisciplinary subject Mechanical Fluid Engineering Mechanics Physics Simulation Heat Sciences Transfer Vacuum Electronics Technology Chemistry Surface Science Molecular Thermodynamics Mathematics Metallurgy USPAS January 2004 Vacuum Fundamentals Page 3 Kinetic behavior of gas molecules TheThe behaviorbehavior ofof aa collectioncollection ofof gasgas moleculesmolecules inin aa vesvessselel isis dependentdependent uponupon thethe pressure,pressure, temperaturetemperature andand compositioncomposition ofof thethe gas.gas. Velocity of gas molecules. Kr He Mean free path Impingement rate USPAS January 2004 Vacuum Fundamentals Page 4 Gas Laws Charles’ Law volume vs temperature Boyle’s Law pressure vs volume Combined or General Gas Law pressure vs temperature vs volume Avogadro’s Law volume vs amount Ideal Gas Law TheseThese lawslaws applyapply toto allall pressure vs temperature moleculesmolecules andand atomsatoms vs volume vs amount regardlessregardless ofof theirtheir sizesize USPAS January 2004 Vacuum Fundamentals Page 5 Charles’s Law TheThe v voolumelume of of a a fixed fixed amount amount of of gas gas at at a a fixed fixed pressurepressure w willill var varyy proportionall proportionallyy wi withth absolute absolute temperature.temperature. 10 8 V V ∝ T = constant T 6 4 ⎛ ⎞ ⎛ ⎞ Volume (liters) V1 V2 ⎜ ⎟ = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 2 ⎝ T1 ⎠ ⎝ T2 ⎠ 0 0246810 Temperature (C) USPAS January 2004 Vacuum Fundamentals Page 6 Boyle’s Law ForFor aa fixedfixed amountamount ofof gasgas atat aa fixedfixed temperature,temperature, itsits pressurepressure isis inverselyinversely proportionalproportional toto itsits volume.volume. 10 8 1 V ∝ PV = constant P 6 4 Volume (liters) P1V1 = P2V2 2 0 0246810 Pressure (Torr) USPAS January 2004 Vacuum Fundamentals Page 7 Finding volume of a vessel with Boyle’s Law V1 = 1.5 liters TC1 V2 = ? liters TC2 P1 = 760 Torr Vacuum Vessel 1 Vacuum Vessel 2 P2 = 20 Torr USPAS January 2004 Vacuum Fundamentals Page 8 Combined Gas Law ProvidProvideses relationshiprelationship betweenbetween pressure,pressure, volume,volume, andand temperaturetemperature forfor aa fixedfixed amountamount ofof gas.gas. PV = constant T P1V1 P2V2 = T1 T2 USPAS January 2004 Vacuum Fundamentals Page 9 Example of combined gas law P1 = 100 Torr P2 = 200 Torr V1 = 200 liters V2 = 80 liters T1 = 293 K T2 = ? K P1V1 P2V2 = T1 T2 ()100 Torr ()200 liters ()200 Torr ()80 liters = 293 K T2 T2 = 234 K USPAS January 2004 Vacuum Fundamentals Page 10 Avogadro’s Law TheThe VolumeVolume occupiedoccupied byby anyany gas,gas, atat aa fixedfixed temperaturetemperature andand pressure,pressure, isis proportionalproportional toto thethe numbernumber ofof molesmoles ofof thatthat gas.gas. V ∝ n 23 No = Avogadros’ Number = 6.02 x 10 particles = 1 mole USPAS January 2004 Vacuum Fundamentals Page 11 Ideal Gas Law ProvidProvideses relationshiprelationship betweenbetween pressure,pressure, volume,volume, Temperature,Temperature, andand amountamount ofof gas.gas. PV = nRT R = 0.08206 Atm-liter/ K-mole = 62.36 Torr-liter/K-mole USPAS January 2004 Vacuum Fundamentals Page 12 Units in Gas Law calculations GasGas lawlaw calculationscalculations maymay bebe performedperformed usingusing aa varietyvariety ofof pressurepressure unitsunits (Torr,(Torr, Bars,Bars, ATM,ATM, PSI,PSI, Pa,Pa, etc.)etc.) butbut thethe pressurepressure unitsunits mustmust remainremain consistentconsistent throughthrough thethe calculation.calculation. V P ⎛ Torr ⎞ t = ln 1 ⎜ ⎟ St P2 ⎝ Torr ⎠ TemperatureTemperature mustmust bebe inin absoluteabsolute unitsunits (K,R).(K,R). USPAS January 2004 Vacuum Fundamentals Page 13 Pressure unit conversions To convert from: Multiply by: To: Atm Torr 760 Pascal Torr 7.5 x 10-3 mBar Torr 0.750 PSI Torr 51.7 USPAS January 2004 Vacuum Fundamentals Page 14 Maxwell’s Distribution Law MaxwellMaxwell determineddetermined thatthat forfor aa largelarge populationpopulation ofof oneone typetype ofof molecule,molecule, therethere wouldwould bebe aa distributiondistribution ofof velocities.velocities. ThereThere isis notnot oneone uniformuniform velocity.velocity. 3 ⎛ 2 ⎞ ⎜ -mv ⎟ ⎛ m ⎞ 2 2 ⎜ 2kT ⎟ N = 4πN⎜ ⎟ v e⎝ ⎠dv v ⎝ 2πkT ⎠ where Nvdv = the number of molecules found in the velocity interval between v and v + dv v = velocity of the gas molecules (m/sec) N = the total number of gas molecules k = Boltzmann's constant (1.38 x 10-23 J/K) m = mass of the molecule (kg) T = Temperature (K) USPAS January 2004 Vacuum Fundamentals Page 15 A Typical Maxwell Velocity Distribution vrms = root mean square velocity 1 1 V p ⎛ kT ⎞ 2 ⎛ T ⎞ 2 V ≈ 1.7⎜ ⎟ ∝ ⎜ ⎟ avg ⎝ m ⎠ ⎝ M ⎠ Vrms vavg = average velocity of population ≈ 0.98vrms vp = most probable velocity ≈ 0.82vrms USPAS January 2004 Vacuum Fundamentals Page 16 Velocity of gas molecules TheThe velocityvelocity ofof gasgas moleculesmolecules isis independentindependent ofof thethe pressurepressure ofof thethe gas,gas, andand dependsdepends onlyonly onon thethe molecularmolecular weightweight ofof thethe gasgas andand itsits absoluteabsolute temperature.temperature. T V = 1.455 x 10 4 M V = average velocity (cm/sec) T = absolute temperature (K) M = molecular weight of gas, (g/mole) USPAS January 2004 Vacuum Fundamentals Page 17 Mean free path TheThe meanmean freefree pathpath isis thethe averageaverage distancedistance thatthat aa gasgas moleculemolecule cancan traveltravel beforebefore collidingcolliding withwith anotheranother gasgas molecule.molecule. Mean Free Path is determined by: - Size of molecule - Pressure - Temperature USPAS January 2004 Vacuum Fundamentals Page 18 Mean Free Path Equation kT λ = i 2 2π Pd i cm λi = mean free path of gas species “i” ( /sec ) k = Boltzmann’s constant (1.38 x 10-23 Joules/K) T = Temperature (K) P = Pressure (Pa) di = gas species diameter (cm) USPAS January 2004 Vacuum Fundamentals Page 19 Gas Flow TheThe flowflow ofof gasesgases inin aa vacuumvacuum systemsystem isis divideddivided intointo threethree regimes.regimes. TheseThese regimesregimes areare defineddefined byby specificspecific valuevalue rangesranges ofof aa dimension-lessdimension-less parameterparameter knowknow asas thethe KnudsenKnudsen numbernumber.. λ K = a n a λa = mean free path a = characteristic dimension of flow channel (typically a pipe radius) USPAS January 2004 Vacuum Fundamentals Page 20 Gas Flow λ Viscous Flow : Kn = a < 0.01 a Turbulent Laminar Transition Flow : 0.01 < Kn < 1.0 Molecular Flow : Kn > 1.0 Molecular USPAS January 2004 Vacuum Fundamentals Page 21 Viscous Flow • Viscous Flow – Molecules travel in Process Chamber uniform motion toward lower pressure – Random motmotionion of a Rough molecule is influenced Valve in the direction of the mass flow High P – Molecular motion Rough “against” mass flow Line unlikely Rough Pump Low P USPAS January 2004 Vacuum Fundamentals Page 22 Molecular Flow Process Chamber • Molecular Flow Molecules move randomly in either direction - to or away from rough pump and vacuum pump – Oil molecules will Backstream (move up Chamber the rough line) in this flow regime Oil Pump USPAS January 2004 Vacuum Fundamentals Page 23 Gas Flux Density incident on a Surface (impingement rate) 1 / 2 ⎛ kT ⎞ υ = N⎜ ⎟ ⎝ 2πm ⎠ PN where N = o RT = density of molecules per m3 1 / 2 PN ⎛ kT ⎞ υ = 103 o ⎜ ⎟ RT ⎝ 2πm ⎠ liters/m3 conversion USPAS January 2004 Vacuum Fundamentals Page 24 Gas Flux Density (Impingement rate) TheThe numbernumber ofof gasgas moleculemolecule collisionscollisions withwith thethe innerinner surfacesurface ofof aa containercontainer isis givengiven byby:: P υ = 3.5 x 1022 MT υ = particle flux density (molecules/sec cm2) P = pressure (Torr) M = molecular weight of gas (g/mole) T = absolute temperature (K) USPAS January 2004 Vacuum Fundamentals Page 25 Residence time ResidenceResidence timetime isis thethe averageaverage amountamount ofof timetime aa moleculemolecule staysstays onon aa surface,surface, andand isis aa functionfunction ofof thethe molecularmolecular weightweight ofof thethe gasgas andand thethe temperaturetemperature ofof thethe surface.surface. ⎛ Q ⎞ ⎜ ⎟ ⎝ RT ⎠ t = toe where tO = time of oscillation in the absorbed state (typically 10-12 to 10-13 sec) Q = activation energy T = temperature (K) USPAS January 2004 Vacuum Fundamentals Page 26 Composition of Atmosphere •• Nitrogen:Nitrogen: 78%78% •• Oxygen:Oxygen: 21%21% • Water: 1%
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