Vacuum Technology

Vacuum Generation

Vacuum systems are categorized by pressure range:

Pressure Measurement

The mean free path of gas molecules relates to pressure:

$\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$

where $d$ is the molecular diameter and $P$ is pressure.

Cryogenics

Gas Liquefaction

The Joule-Thomson coefficient determines whether a gas cools or heats upon expansion:

$\mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H$

For gases below their inversion temperature, $\mu_{JT} > 0$ and expansion causes cooling.

Superfluidity

Liquid helium-4 undergoes a phase transition at the lambda point ($T_\lambda = 2.17 \, \text{K}$), entering a superfluid state with zero viscosity.

Thermometry

Resistance Thermometers

The resistance of platinum follows the Callendar-Van Dusen equation:

$R(T) = R_0 \left[1 + A T + B T^2 + C(T-100)T^3\right]$

for $T < 0°\text{C}$, where $R_0 = 100 \, \Omega$ for a Pt100 sensor.

Optics & Spectroscopy

Laser Fundamentals

Population inversion is the key condition for lasing:

$N_2 > N_1$

where $N_2$ and $N_1$ are populations of the upper and lower laser states.

Atomic Spectra

The energy levels of hydrogen-like atoms:

$E_n = -\frac{13.6 \, \text{eV}}{n^2} \cdot Z^2$

Particle & Photon Detection

Photomultiplier Tubes

PMTs achieve single-photon detection through cascading secondary electron emission. The gain is:

$G = \delta^n$

where $\delta$ is the secondary emission coefficient per dynode and $n$ is the number of dynode stages (typically 8–14).

Source

Notes structured as an Obsidian vault with cross-linked concepts. Available on GitHub.