TheThe USUS ParticleParticle AcceleratorAccelerator SchoolSchool VacuumVacuum FundamentalsFundamentals Lou Bertolini Lawrence Livermore National Laboratory June 10-14, 2002 USPAS June 2002 Vacuum Fundamentals Page 1 Your Instructor • Lou Bertolini —Mechanical Engineer —Accelerator Technologies Engineering Group − E-mail: [email protected] − Phone: (925) 422-9532 − FAX: (925) 423-1767 USPAS June 2002 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 June 2002 Vacuum Fundamentals Page 3 Kinetic behavior of gas molecules TheThe behaviorbehavior ofof aa collectioncollection ofof gasgas moleculesmolecules inin aa vesselvessel 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 June 2002 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 June 2002 Vacuum Fundamentals Page 5 Charles’s Law TheThe volume volume of of a a fixed fixed amount amount of of gas gas at at a a fixed fixed pressurepressure will will vary vary proportionally proportionally with with 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 June 2002 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 June 2002 Vacuum Fundamentals Page 7 Finding volume of a vessel with Boyle’s Law V = ? liters V1 = 1.5 liters TC1 2 TC2 P1 = 760 Torr Vacuum Vessel 1 Vacuum Vessel 2 P2 = 20 Torr USPAS June 2002 Vacuum Fundamentals Page 8 Combined Gas Law ProvidesProvides relationshiprelationship betweenbetween pressure,pressure, volume,volume, andand temperaturetemperature forfor aa fixedfixed amountamount ofof gas.gas. PV = constant T P1V1 P2V2 = T1 T2 USPAS June 2002 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 June 2002 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 June 2002 Vacuum Fundamentals Page 11 Ideal Gas Law ProvidesProvides 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 June 2002 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 June 2002 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 June 2002 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 bebe oneone uniformuniform velocity.velocity. 3 2 -mv m 2 2kT N = 4πN v2e 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 June 2002 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 June 2002 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 June 2002 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 June 2002 Vacuum Fundamentals Page 18 Mean Free Path Equation kT λ = i π 2 2 Pd i λ cm i = 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 June 2002 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 λ a = mean free path a = characteristic dimension of flow channel (typically a pipe radius) USPAS June 2002 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 June 2002 Vacuum Fundamentals Page 21 Viscous Flow • Viscous Flow – Molecules travel in Process Chamber uniform motion toward lower pressure – Random motion 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 June 2002 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 June 2002 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 June 2002 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 u = particle flux density (molecules/sec cm2) P = pressure (Torr) M = molecular weight of gas (g/mole) T = absolute temperature (K) USPAS June 2002 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 = residence time (sec) Q = activation energy T = temperature (K) USPAS June 2002 Vacuum Fundamentals Page 26 Vapor Pressure Psat Pv < Psat In this case, the gas above the In this case, there is not sufficient bulk bulk is considered to be saturated. material to support a saturation vapor pressure • Vapor pressure is an important concept as it relates to cryopumps. • At thermal equilibrium the net flux of particles at the surface of bulk material is zero. • Each element has a specific saturation pressure for a given temperature. The saturation pressure is also referred to as the saturation vapor pressure, equilibrium vapor pressure, or just vapor pressure. USPAS June 2002 Vacuum Fundamentals Page 27 Vapor Pressure Curve USPAS June 2002 Vacuum Fundamentals Page 28 Pumping Speed DefinedDefined asas aa measuremeasure ofof volumetricvolumetric displacementdisplacement (liters/sec,(liters/sec, cu.feet/minute,cu.feet/minute, cu.meters/minute)cu.meters/minute) • It is the volume of gas flowing past a point per unit time. • Pumping speed is independent of pressure. • Pumping speed is an abstract concept used to describe the behavior of gas in a vacuum system. dV S = dt USPAS June 2002 Vacuum