AcademyParticles and Cosmology
Academy
Accelerators and Detectors
Level 1 - Physics topic page in Particles and Cosmology.
Principle
Accelerators use electric fields to give charged particles energy, while detectors use ionization, curvature, timing, and deposited energy to infer particle properties.
Notation
\(q\)
particle charge
\(\mathrm{C}\)
\(V\)
accelerating potential difference
\(\mathrm{V}\)
\(K\)
kinetic energy
\(\mathrm{J,\;eV}\)
\(B\)
magnetic flux density
\(\mathrm{T}\)
\(r\)
track radius
\(\mathrm{m}\)
\(p\)
momentum
kg m s^{-1}, eV/c
Method
Derivation 1: Energy gain from voltage
An electric field does work on a charged particle when it moves through a potential difference.
Work by field
\[W=qV\]
Kinetic-energy gain
\[\Delta K=qV\]
Derivation 2: Track curvature gives momentum
A magnetic force perpendicular to velocity supplies centripetal acceleration.
Magnetic force
\[F=|q|vB\]
Centripetal force
\[|q|vB=\frac{mv^2}{r}\]
Momentum
\[p=|q|Br\]
Derivation 3: Detector signatures
Momentum, charge sign, and energy deposition are combined because one measurement rarely identifies a particle uniquely.
Curvature relation
\[r=\frac{p}{|q|B}\]
Speed from time of flight
\[v=\frac{L}{\Delta t}\]
Rules
Energy gain
\[\Delta K=qV\]
Magnetic rigidity
\[p=|q|Br\]
Track radius
\[r=\frac{p}{|q|B}\]
Examples
Question
A proton is accelerated through
\[2.0\,\mathrm{MV}\]
Find its kinetic energy.Answer
\[K=eV=2.0\,\mathrm{MeV}\]
Checks
- Electric fields change kinetic energy.
- Magnetic fields bend charged tracks but do no work.
- Curvature direction gives charge sign.
- Momentum, energy, and lifetime evidence should be combined.