KAHIBARO
Table of Contents
Basic Idea
A LINAC, or linear accelerator, is a machine that accelerates charged particles along a straight path. The word "linear" means that the particles move through a line of accelerating sections instead of going around in a circle.
In a LINAC, electric fields give energy to the particles. Because a charged particle feels a force in an electric field, it can be pushed forward again and again as it passes through a sequence of accelerator structures. Each stage adds a little more kinetic energy, and the total energy can become very large after many stages.
A LINAC is especially useful when particles need to reach high speeds without being bent into circular motion. It is used in research, medicine, and industry.
How a LINAC Works
A charged particle source first produces particles such as electrons, protons, or ions. These particles enter the accelerator with some initial speed. Inside the LINAC, they pass through regions where an oscillating electric field is arranged so that the particle is pushed forward at the correct moment.
If a particle with charge $q$ moves through a potential difference $V$, the gain in energy is
$$
\Delta E = qV
$$
This is the basic energy principle behind all linear accelerators. A positive charge gains energy when it moves through a drop in electric potential in the right direction. A negative charge, such as an electron, must be accelerated with the field arranged appropriately for its sign.
The key challenge is timing. The electric field changes direction repeatedly, so the particle must arrive at each accelerating gap when the field points the correct way.
Important rule:
For a particle crossing an accelerating gap, the energy gain is
$$
\Delta E = qV
$$
A LINAC works only if the particle reaches each gap at the right phase of the oscillating electric field.
Main Parts of a LINAC
A LINAC usually contains a particle source, accelerating gaps or cavities, a vacuum system, and focusing elements. The vacuum reduces collisions with air molecules. The focusing system keeps the beam narrow and prevents particles from spreading too much.
For low speed particles, the accelerator geometry often changes from one section to the next because the particle speed increases significantly during acceleration. For particles already moving near the speed of light, the structure can become more regular because their speed changes less.
The table below shows the main parts and their roles.
| Part | Function |
|---|---|
| Particle source | Produces charged particles |
| Accelerating cavity or gap | Increases particle energy |
| Vacuum tube | Reduces collisions with gas |
| Focusing magnets | Keep the beam concentrated |
| Beam diagnostics | Measure beam position, intensity, and energy |
Drift Tubes in Proton and Ion LINACs
One common linear accelerator design for heavier particles uses drift tubes. The particle passes through a gap where the electric field accelerates it, then enters a metal tube. Inside the tube, the electric field is effectively shielded, so the particle is not slowed down when the field reverses.
While the particle is inside the drift tube, the radio-frequency field changes sign. When the particle reaches the next gap, the field is again in the accelerating direction.
As the particle speeds up, it travels farther in the same amount of time. Because of this, later drift tubes are usually longer.
Key idea:
Drift tubes protect the particle while the electric field reverses. Tube lengths are chosen so that the particle arrives at each gap when the field is accelerating it.
Electron LINACs
Electrons become relativistic very quickly, meaning their speed soon becomes close to the speed of light. Because of this, electron LINACs often use microwave cavities rather than long drift tube structures with greatly changing lengths.
In these machines, electromagnetic waves inside metal cavities create accelerating electric fields. The particle beam travels through the cavities and gains energy from the oscillating field. Since the electron speed soon changes only a little, the cavity spacing can be designed more uniformly.
Electron LINACs are widely used in particle physics and radiation therapy.
Why LINACs Are Useful
A linear accelerator has several advantages. Since particles move in a straight line, they do not continuously lose energy because of bending. This is especially important for electrons, which radiate strongly when forced into curved motion at high energy.
LINACs can also produce very well controlled beams. They are often used as injectors for larger accelerators, meaning they first accelerate particles and then send them into another machine.
Typical uses include medical treatment, material processing, and basic research.
Energy Gain Along the Machine
If a particle passes through many accelerating stages, the total energy gain is approximately the sum of the gains from each stage:
$$
\Delta E_{\text{total}} \approx \sum_i qV_i
$$
If all gaps provide about the same effective accelerating voltage $V$, and there are $N$ stages, then roughly
$$
\Delta E_{\text{total}} \approx NqV
$$
This simple relation shows why many repeated accelerating sections can produce very high final energies.
Important formula for a multistage LINAC:
$$
\Delta E_{\text{total}} \approx \sum_i qV_i
$$
If the stages are similar,
$$
\Delta E_{\text{total}} \approx NqV
$$
Beam Focusing
As particles travel down the accelerator, they tend to spread out because of small direction differences and repulsion between like charges in the beam. Focusing elements are placed along the LINAC to keep the beam narrow.
Magnetic quadrupoles are often used for this purpose. They do not accelerate the particles directly, but they shape the beam so that it stays useful for experiments or applications.
Without focusing, many particles would strike the walls of the accelerator and be lost.
Practical Limits
Although LINACs are powerful, they have an important drawback. To reach very high energy, they must become very long. Since each section adds only a limited amount of energy, higher final energy usually means a longer machine and greater cost.
For this reason, LINACs are excellent for many purposes, but for some very high energy applications, other accelerator types may be preferred.
Simple Picture of the Process
Summary
A LINAC accelerates charged particles in a straight line using timed electric fields. Each accelerating section gives the particles extra energy, with energy gain given by $qV$. In many proton and ion LINACs, drift tubes protect particles while the field reverses. In electron LINACs, microwave cavities are common. LINACs are important because they provide controlled high energy beams and serve in science, medicine, and technology.