Particle accelerators and detectorsEdexcel A-Level Physics: Revision notes

Particle accelerators need a source of charged particles. For electrons this is a heated metal filament (the cathode) in a vacuum. Heating gives some conduction electrons enough energy to escape from the metal surface. This is thermionic emission.

The emitted electrons are accelerated by an electric field between the cathode and an anode. A charge $Q$ accelerated from rest through a p.d. $V$ gains kinetic energy $E_k = QV$. For an electron through 2.0 kV: $E_k = 1.60\times10^{-19}\times 2000 = 3.2\times10^{-16}$ J.

Accelerators are evacuated so particles do not collide with air molecules, lose energy or ionise the gas.

A linac has a line of hollow metal drift tubes connected alternately to the terminals of a high-frequency a.c. supply.

• Inside a tube there is no electric field, so charged particles drift at constant speed.
• The particles are accelerated across the gaps between adjacent tubes, where there is a p.d.
• The supply polarity reverses every half cycle so that, when a particle reaches a gap, the next tube has the opposite polarity and attracts it forwards.
• As the particles speed up they cover more distance in each half cycle, so the tubes get longer along the line.

Worked example. At 25 MHz, $T = 4.0\times10^{-8}$ s. A proton at $1.0\times10^{7}$ m s⁻¹ spends $2.0\times10^{-8}$ s in a tube, so $L = vt = 0.20$ m.

A cyclotron has two hollow D-shaped dees in a vacuum, with a uniform magnetic field perpendicular to the dees.

• The magnetic field makes the particles move in a semicircle inside each dee. It does no work, so it does not change their speed.
• An alternating p.d. between the dees gives an electric field in the gap that accelerates the particles every time they cross it.
• The p.d. must reverse each time the particles cross, so it must alternate in step with their motion.
• As the speed increases, the radius of the path increases, so the particles spiral outwards until they leave at the edge.

A particle of charge $Q$ and momentum $p = mv$ moving at right angles to a uniform field $B$ is acted on by a force $BQv$ perpendicular to its velocity. This is the centripetal force:

$BQv = \frac{mv^2}{r} \quad\Rightarrow\quad r = \frac{mv}{BQ} = \frac{p}{BQ}$

A particle with greater momentum travels in a path of greater radius, and a stronger field gives a smaller radius.

Worked example. A proton at $5.0\times10^{6}$ m s⁻¹ in a 1.2 T field: $r = \dfrac{1.67\times10^{-27}\times5.0\times10^{6}}{1.2\times1.60\times10^{-19}} = 0.043$ m.

Detectors use two principles:

• Ionisation. Charged particles ionise atoms along their path, leaving a visible track of ions, droplets or bubbles. Neutral particles do not ionise the medium directly and leave no track.
• Deflection. A magnetic field curves the tracks of charged particles into circles of radius $r = p/BQ$.

From the tracks:

• the direction of curvature shows the sign of the charge
• the radius shows the momentum (larger radius, larger momentum, for the same charge)
• tracks that spiral inwards show the particle losing energy by ionisation.