# 5.3: What is a “Collider?”

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Describe the purpose of a collider.
• Describe what a collider is in a complete sentence.
• Describe the steering mechanism for directing the charged particles.
• Compare linear and ring designs.

## Overview

It is theorized that when the universe began the temperatures were so hot that protons and neutrons did not exist. Instead the building blocks of these particles, quarks, roamed in space by themselves. As the universe cooled down, the quarks began to regroup into protons and neutrons. Today, the universe in our location is too cool for quarks to float around by themselves. The collider will do two things to solve this. First, it will accelerate protons or electrons to such high speeds that the energy of the charges at impact will be converted into thermal energy. Second, the energy of the particles at impact will be converted into new particles.

To generate these high levels of energy, charged particles are accelerated into each other at speeds near the speed of light. Nothing can start out slower than the speed of light and then accelerate to a speed faster than the speed of light. However, large electric fields are used to accelerate charged particles to speeds near the speed of light. There are two basic design geometries.

The linear accelerator has charged particles that travel down a straight line. The particles can start at opposite ends of a long tunnel and collide into each other.

The linear accelerator works best with electrons because they are a thousand times lighter than protons. A high percentage of the energy put into the accelerator goes into speeding up the charge (Schwartz, 1997). But electrons generate large amounts of synchrotron radiation. Protons generate less radiation but cannot achieve the same velocities.

Synchrotron radiation is caused any time a charged particle accelerates. When a particle accelerates in a straight line it is called brehmsstrahlung radiation. The (simplified) formula for calculating the radiation's power is: \begin{align*}P = \frac{2 ke^2} {3c^3} \gamma^2 a^2,\end{align*} where \begin{align*}k\end{align*} is Coulomb’s constant, \begin{align*}e\end{align*} is the elementary charge’s value, \begin{align*}c\end{align*} is the speed of light, \begin{align*}\gamma =\sqrt{1- (v/c)^{2}}\end{align*} is a factor to account for relativistic speeds, and a is the acceleration. (When the speed is less than \begin{align*}10\end{align*}% the speed of light, \begin{align*}\gamma \simeq 1\end{align*}). This equation applies, for example, for the power radiated by a (radio-) antenna. When a particle accelerates in a circle or curve it is called synchrotron radiation. The same formula applies except the acceleration is found from: \begin{align*}a_c = \frac{\upsilon ^2} {r}\end{align*} This means for circular motion: \begin{align*}P = \frac{2 ke^2} {3c^3} \gamma^2 \frac{\upsilon^4} {r^2}\end{align*} Because the \begin{align*}\gamma\end{align*} varies with speed, the \begin{align*}\gamma\end{align*}-factor for an electron moving near the speed of light can be \begin{align*}10^{13}\end{align*} times greater than for a proton. This means that accelerating electrons is more difficult than the accelerating protons. In order to keep synchrotron radiation as small as possible protons are used and as the speed increases the radius must also increase.

If the charges were placed in an energized ring, then they could continually be pumped up with energy to reach relativistic speeds. Because the proton generates less synchrotron radiation, it would make for a more viable candidate for acceleration in a circular collider.

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