33.3 Accelerators Create Matter from Energy

Particle Accelerators

Particle accelerators use electric fields and magnetic fields to push charged particles to extremely high speeds and energies. At these energies, collisions between particles can actually create new matter, directly demonstrating Einstein's mass-energy equivalence ($E = mc^2$). Understanding how accelerators work connects the physics of electromagnetism you've already studied to the frontier of particle physics.

Acceleration in Cyclotrons

A cyclotron is one of the simplest circular accelerators. It uses a constant magnetic field and a cleverly timed electric field to spiral particles outward to higher and higher energies.

Here's how the process works:

1. Charged particles (typically protons) are injected at the center of the cyclotron.
2. A uniform magnetic field, applied perpendicular to the plane of the cyclotron, forces the particles into circular paths.
3. Inside the cyclotron sit two hollow, D-shaped electrodes called "dees." An alternating electric field is applied across the gap between them.
4. Each time a particle crosses the gap between the dees, the electric field accelerates it, increasing its kinetic energy.
5. With more kinetic energy, the particle moves faster and traces a larger circular arc. The result is a spiraling outward path.
6. The timing of the alternating field is synchronized to the particle's orbit so that the particle always gets a "push" in the right direction as it crosses the gap.
7. This repeats until the particle reaches the outer edge of the cyclotron at the desired energy, where it's extracted for use.

Cyclotrons are used in particle physics experiments and also in medical applications, such as producing radioactive isotopes for imaging.

Features of Synchrotrons

Synchrotrons are circular accelerators designed to reach much higher energies than cyclotrons. Instead of spiraling outward, particles in a synchrotron travel in a fixed-radius ring.

The key components of a synchrotron ring include:

• Dipole magnets that bend the particle beam, keeping it on a closed circular orbit.
• Quadrupole magnets that focus the beam, preventing it from spreading out.
• Radio frequency (RF) cavities that accelerate the particles each time they pass through. The RF frequency is synchronized with the beam's circulation frequency.

The critical difference from a cyclotron is that as particles gain energy, the magnetic field strength in the bending magnets is increased to match. This keeps the orbit radius constant even as the particles get faster. That's where the name "synchrotron" comes from: the magnets and the RF cavities stay in sync with the rising particle energy.

Because the orbit stays fixed, you can build a synchrotron as large as you need to reach very high energies. The Large Hadron Collider (LHC) at CERN, for example, is a synchrotron ring 27 km in circumference that collides protons at energies of 13 TeV.

Voltage Calculations for Accelerators

To figure out how much voltage is needed to give a particle a certain energy, you can use:

$V = \frac{E}{q}$

• $V$ = voltage (in volts)
• $E$ = desired kinetic energy (in electron volts, eV)
• $q$ = particle charge (in units of elementary charge, $e$)

Example: Suppose you want to accelerate a proton (charge = $+1e$) to an energy of 10 MeV.

$V = \frac{10{,}000{,}000 \text{ eV}}{1e} = 10{,}000{,}000 \text{ V} = 10 \text{ MV}$

So you'd need 10 million volts across the accelerating gap. In practice, this is why accelerators use repeated acceleration stages or RF cavities rather than a single enormous voltage.

Components of Fermilab's Accelerator Complex

Fermilab (near Chicago) uses a chain of accelerators, each one boosting particle energy before handing the beam off to the next stage. This step-by-step approach is how all major accelerator facilities reach very high energies.

1. Ion source produces negatively charged hydrogen ions ($H^-$).
2. Linear accelerator (Linac) accelerates the $H^-$ ions to 400 MeV.
3. Booster synchrotron strips the electrons from the $H^-$ ions, leaving bare protons, and accelerates them to 8 GeV.
4. Main Injector synchrotron accelerates protons from 8 GeV up to 120 GeV or 150 GeV.
5. Recycler Ring stores and cools antiprotons that were produced by slamming the 120 GeV proton beam into a target.
6. Tevatron (now decommissioned) was the final stage. It accelerated both protons and antiprotons to 980 GeV each, then collided them head-on at a total energy of 1.96 TeV.

The general principle is the same at every major facility: gradually ramp up particle energy through a series of connected accelerators until you reach the collision energy needed for the experiment.

Energy and Matter in Particle Accelerators

This is where accelerators connect directly to $E = mc^2$. When two particles collide at high enough energy, that kinetic energy can convert into the mass of entirely new particles. The collision doesn't just break things apart; it creates matter that wasn't there before.

For example, when a proton and an antiproton collide in an accelerator, their combined kinetic energy (plus their rest mass energy) can produce a shower of new particles, including exotic ones like W bosons, Z bosons, or top quarks. These particles are far more massive than the original proton and antiproton, and the "extra" mass comes from the kinetic energy of the collision.

A few key principles govern what happens:

• Conservation of energy still holds. The total energy before the collision (kinetic + rest mass) equals the total energy after (rest mass of new particles + their kinetic energy).
• Conservation of charge, baryon number, and lepton number restricts which particles can be produced.
• Accelerators use electromagnetic fields to control charged particles, whether they're hadrons (like protons) or leptons (like electrons).

The higher the collision energy, the more massive the particles you can create. That's why physicists keep building bigger accelerators: reaching higher energies opens the door to discovering heavier, rarer particles.