# Vacuum: Rules of thumb

## Engineering Fundamentals

#### Introduction

This sheet will give some basics about a vacuum chamber itself and about mechanical setups that are placed in it.

ClassificationLevel [mbar]PumpsSensorsExamples
LVLow103 … 100 Dry/wetMechanicalFood seals, domestic vacuum cleaner
MVMedium100 … 10-3Dry/wetMechanicalLight bulb
HVHigh10-3 … 10-6+Turbo ElectronicThermos bottle insulation
VHVVery high10-6 … 10-9+Turbo ElectronicVacuum vessel LHC CERN (particle accelerator)
UHVUltra high10-9 … 10-12+Turbo ElectronicAtomic physics research (e.g. gravity wave)
EHVExtreme high< 10-12(Space)ElectronicSpace

#### Pressure conversion

$1MPa\ =1\frac{N}{mm^2}=145psi=10bar$
$1mbar={10}^{-4}MPa=0.0145psi=100\frac{N}{m^2}$

#### Gas law

$pV=nRT$ with $R=8.314JK^{-1}mol^{-1}$

#### Estimates for wall thickness ($p=1$ bar)

$\tau_{0.2}\approx0.4\cdot\sigma_{0.2}$ (JPE Estimate for metals), $t=$ thickness,
$\delta=$ deformation

 Welded flanges $$t=\sqrt{\frac{{3d}^2p}{2\sigma_{max}}}$$ $$\delta=\frac{d^4p}{32{\rm Et}^3}$$ $$t=\sqrt{\frac{{3pL}^2}{\sigma_{max}}}$$ $$\delta=\frac{{\rm pL}^4}{16{\rm Et}^3}$$ O-ring-sealed flanges $$t=\frac{dp}{2\tau_{max}}$$ $$\delta=\frac{d^4p}{8{\rm Et}^3}$$ $$t=\frac{pL}{\tau_{max}}$$ $$\delta=\frac{{\rm pL}^4}{4{\rm Et}^3}$$ Thin walled tubes ($r>20t$) $$t=\frac{pr}{2\sigma_{max}}$$ $$\delta=\frac{2\pi{\rm pr}^2}{Et}$$

#### Types of leakage

• Real leakage (holes, porous materials)
• Virtual leakage (pocket sealed with bolt)
• Desorption / outgassing (solvents)
• Diffusion (e.g. H-atoms from steel)
• Permeability (O-rings)
• Evaporation (finger prints, lubricants)
• Backflow pump (dry > wet > turbo)

#### Paschen’s law

This law states that the breakdown potential (necessary to start a discharge between 2 electrodes) is pressure dependent. JPE Rule: vacuum must be below ${10}^{-1}mbar$

#### In-vacuum-design rules of thumb

• Prevent virtual leakage: drill holes in bolts etc.
• Do not use lubricants
• Check outgassing spec’s from synthetic materials
• Be aware of high friction (dry environment)
• Use hybrid bearings
• Heat must be conducted through material (no convection)

#### Pumps (mbar)

• Dry: Diaphragm ${(10}^0)$, Screw $({10}^{-2})$
• Wet: Roots ${(10}^{-2})$, Rotary vane $({10}^{-4})$
• +Turbo: Molecular pump $({10}^{-10})$
• Ionization $({10}^{-11})$

#### Sensors (mbar)

• Mechanical:
• Bourdon ${(10}^1)$
• Diaphragm ${(10}^0)$
• Electronic:
• Piezo based ${(10}^0)$
• Capacitive ${(10}^{-3})$
• Thermal conductivity (Pirani) ${(10}^{-4})$
• Ionization
• cold: Penning ${(10}^{-8})$
• hot: Inverted magnetron ${(10}^{-12})$

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