#### Introduction

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

Classification | Level [mbar] | Pumps | Sensors | Examples | |
---|---|---|---|---|---|

LV | Low | 10^{3} … 10^{0} | Dry/wet | Mechanical | Food seals, domestic vacuum cleaner |

MV | Medium | 10^{0} … 10^{-3} | Dry/wet | Mechanical | Light bulb |

HV | High | 10^{-3} … 10^{-6} | +Turbo | Electronic | Thermos bottle insulation |

VHV | Very high | 10^{-6} … 10^{-9} | +Turbo | Electronic | Vacuum vessel LHC CERN (particle accelerator) |

UHV | Ultra high | 10^{-9} … 10^{-12} | +Turbo | Electronic | Atomic physics research (e.g. gravity wave) |

EHV | Extreme high | < 10^{-12} | (Space) | Electronic | Space |

#### 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 ${(10}^{-12})$