Particle Physics and Cosmology: Particle Accelerators and Detectors

Citation: The content below is based on the most recent edition of University Physics with Modern Physics.

Important Formulas

Relativistic Energy:
$E^2 = (pc)^2 + (m_0c^2)^2$
Magnetic Rigidity of a Particle:
$B \rho = \frac{p}{q}$
Time-of-Flight Measurement:
$t = \frac{d}{v}$
Cross Section for Particle Interaction:
$\sigma = \frac{N}{\mathcal{L}}$
Energy Loss due to Synchrotron Radiation:
$P \propto \frac{q^4 \beta^4 \gamma^4}{r^2}$

Key Terms and Definitions

Particle Accelerators: Machines designed to accelerate charged particles to high energies, enabling the study of fundamental particles and forces.
Linear Accelerator (LINAC): A type of accelerator where particles are accelerated in a straight line using electric fields.
Synchrotron: A circular accelerator where magnetic fields guide particles along a closed path, and electric fields boost their energy.
Detectors: Instruments that observe and measure the properties of particles produced in high-energy collisions.
Time Projection Chamber (TPC): A detector that tracks charged particles by observing ionized gas in an electric field.
Cross Section ( $\sigma$ ): A measure of the probability of a specific particle interaction occurring, typically in units of barns.

Example

Calculate the momentum ( $p$ ) of a proton moving in a magnetic field of $B = 2 \, \text{T}$ with a radius of curvature $\rho = 5 \, \text{m}$ .

Using the formula for magnetic rigidity:

$B \rho = \frac{p}{q}$

Rearranging for $p$ :

$p = q B \rho$

Substituting values ( $q = 1.6 \times 10^{-19} \, \text{C}$ ):

$p = (1.6 \times 10^{-19}) (2) (5) \, \text{T m}$

$p = 1.6 \times 10^{-18} \, \text{kg m/s}$

Result:

The momentum of the proton is $1.6 \times 10^{-18} \, \text{kg m/s}$ .

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