Synchrotrons and Particle Accelerators: Light From Speeding Electrons

A Charged Particle in a Magnetic Field

By Abhishek Thakur · Science faculty, The Cavalier · 15 years teaching NDA and CDS Science

Every accelerator rests on two facts about a charge q moving at speed v. An electric field pushes along its own direction, so it can speed the particle up. A magnetic field exerts the force F = qvB sin θ, always at right angles to the motion. A force at right angles does no work, so a magnetic field changes a particle's direction but never its speed. That is why accelerators use electric fields to give energy and magnets to steer.

If the particle enters the field at right angles (θ = 90°), the magnetic force acts as the centripetal force, and the path is a circle. Setting qvB = mv²/r gives:

The second line is the surprise: the time for one lap does not depend on how fast the particle goes. A faster particle moves on a bigger circle, but exactly in step. Lawrence's cyclotron uses this fact. If the velocity has a component along the field, the path becomes a helix. Our page on circular motion covers the centripetal-force idea.

Linac, Cyclotron, Synchrotron: Three Ways to Add Energy

To push a particle to high energy, you must keep pushing it with an electric field. The three classic machines differ in how they keep the particle in the pushing field.

Lawrence won the 1939 Nobel Prize in Physics for the cyclotron. Cyclotrons are still working machines: hospitals use them to produce short-lived isotopes such as fluorine-18 for PET scans (see our radioactivity article). In India the Variable Energy Cyclotron Centre at Kolkata runs one for nuclear research. The synchrotron idea was worked out independently by Vladimir Veksler and Edwin McMillan in the mid-1940s. It replaced the huge solid magnet of the cyclotron with a thin ring of magnets, which made much higher energies affordable.

Light From Bending Electrons: Synchrotron Radiation

Any charged particle that is accelerated gives off electromagnetic radiation, and bending counts as acceleration, since the direction of velocity changes. A slow electron radiates very little. An electron travelling at almost the speed of light (a "relativistic" electron) radiates strongly, and the light comes out as a thin beam along the tangent to the circle, like water off a spinning wheel. It was first seen in 1947 as a glow from a small synchrotron at General Electric in the USA, and was at first a nuisance that drained the beam's energy. Today it is the product.

Why do electrons give out so much more than protons? For the same energy and ring radius, the energy radiated per lap is inversely proportional to the fourth power of the particle's mass. A proton is about 1,836 times heavier than an electron, so an electron radiates roughly 10¹³ times more. A ring of electrons is a natural light source. A ring of protons, as at the LHC, loses little.

A modern light source is really a storage ring. Electrons are speeded up in a linac and a booster ring, then stored in the main ring at fixed energy. They lose energy at every bend, and a radio-frequency cavity tops it up each lap. Along the straight sections, undulators make electrons zig-zag and give even brighter beams, and each beam goes down a beamline to its own experiment. For where this light sits on the spectrum, see our electromagnetic spectrum page.

What the Light Does, and India's Machines

X-rays have a wavelength of about 1 Å (10⁻¹⁰ m), the same as the spacing between atoms. So a crystal diffracts them, as described by Bragg's law, nλ = 2d sin θ. For example, for λ = 1 Å and a plane spacing d = 2 Å, the first-order reflection (n = 1) comes at sin θ = 1 ÷ 4 = 0.25, so θ ≈ 14.5°. By recording the pattern, scientists can work out where each atom sits. The uses follow:

• Protein crystallography. Most protein structures are solved with synchrotron X-rays. The 2009 Nobel Prize in Chemistry (Venkatraman Ramakrishnan, Thomas Steitz and Ada Yonath) for the structure of the ribosome relied on these beams.
• Materials and chemistry. Batteries, catalysts and metals are scanned while they work, and samples are squeezed under high pressure.
• Cultural heritage. X-ray fluorescence from the beam identifies pigments and inks without damaging a painting or manuscript. It was used to read the erased text of the Archimedes Palimpsest.

India's own national facility at Indore (Indus-1 and Indus-2) runs round-the-clock for researchers from universities, IITs and national laboratories. At Elettra, Indian groups have sent more than 1,100 proposals, second only to Italy's, and about 50–60 Indian scientists travel to Trieste each year. Ring machines are one kind of mega-science. India's work on another, the FAIR accelerator in Germany, is covered in our beam-catcher article.

Bigger Rings: The LHC and the Higgs Boson

The Large Hadron Collider (LHC) at CERN, near Geneva, is a synchrotron for protons, in a tunnel about 27 km round and roughly 100 m underground. It is the largest machine ever built. It began running in 2008. Two proton beams circle in opposite directions and are made to collide at four points. Because protons radiate little, they can be taken to enormous energy: the machine was designed for 7 TeV per beam. Its bending magnets are superconducting electromagnets cooled by liquid helium to about 1.9 K (−271 °C), with a field of about 8.3 T. The same ideas of electromagnet and field appear on our induction page.

The higher the energy, the bigger the ring, unless the magnets are stronger. That is the answer to "why so large?" On 4 July 2012 the ATLAS and CMS experiments at the LHC announced the discovery of a new particle with a mass of about 125 GeV, matching the Higgs boson. It is the particle linked to the Higgs field, through which other fundamental particles acquire mass. Peter Higgs and François Englert shared the 2013 Nobel Prize in Physics.

India has long supplied magnets, electronics and software to CERN's experiments, and became an Associate Member State of CERN on 16 January 2017. Associate membership lets India take part in the CERN Council, but without a vote.

How UPSC Has Asked It: Past Papers Solved

The questions fall into three groups: the force on a moving charge, properties of X-rays, and big-science facts (the Higgs). UPSC repeats the X-ray deflection question almost every year.

Practice MCQs (with answers)

1. A charged particle enters a uniform magnetic field at right angles to it. Its path is
   1. a straight line
   2. a parabola
   3. a circle
   4. a widening spiral
2. The frequency of revolution of a charged particle in a uniform magnetic field depends on
   1. its speed
   2. its charge, mass and the field only
   3. the radius of its path
   4. its kinetic energy
3. Which machine raises the magnetic field as the particles gain momentum, to keep the orbit radius fixed?
   1. Linear accelerator
   2. Cyclotron
   3. Van de Graaff generator
   4. Synchrotron
4. India's Indus-2 synchrotron is located at
   1. Indore
   2. Mumbai
   3. Kolkata
   4. Hyderabad
5. Synchrotron radiation from a ring of electrons leaves
   1. along the magnetic field
   2. backwards along the beam
   3. along the tangent to the orbit
   4. equally towards the centre
6. The Large Hadron Collider is operated by CERN near
   1. Hamburg
   2. Geneva
   3. Trieste
   4. Darmstadt
7. The LHC accelerates protons rather than electrons mainly because
   1. electrons lose far more energy as synchrotron radiation
   2. protons are neutral
   3. electrons are heavier
   4. protons cannot be bent by magnets
8. India became an Associate Member State of CERN in
   1. 1998
   2. 2004
   3. 2012
   4. 2017

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