Physicists studying the structure of the atomic nucleus and of elementary particles usually use a device called a particle accelerator. The first practical particle accelerator, invented in the 1930s, was the cyclotron. Cyclotrons remain important for many applications of nuclear physics, such as the creation of radioisotopes for medicine.

A cyclotron, shown in FIGURE 29.40, consists of an evacuated chamber within a large, uniform magnetic field. Inside the chamber are two hollow conductors shaped like the letter D and hence called “dees.” The dees are made of copper, which doesn’t affect the magnetic field; are open along the straight sides; and are separated by a small gap. A charged particle, typically a proton, is injected into the magnetic field from a source near the center of the cyclotron, and it begins to move in and out of the dees in a circular cyclotron orbit.

FIGURE 29.40 A cyclotron.

The cyclotron operates by taking advantage of the fact that the cyclotron frequency $f_{\text{cyc}}$ of a charged particle is independent of the particle’s speed. An oscillating potential difference $\text{Δ}V$ is connected across the dees and adjusted until its frequency is exactly the cyclotron frequency. There is almost no electric field inside the dees (you learned in Chapter 24 that the electric field inside a hollow conductor is zero), but a strong electric field points from the positive to the negative dee in the gap between them.

Suppose the proton emerges into the gap from the positive dee. The electric field in the gap accelerates the proton across the gap into the negative dee, and it gains kinetic energy $e\text{Δ}V$. A half cycle later, when it next emerges into the gap, the potential of the dees (whose potential difference is oscillating at $f_{\text{cyc}}$) will have changed sign. The proton will again be emerging from the positive dee and will again accelerate across the gap and gain kinetic energy $e\text{Δ}V$.

This pattern will continue orbit after orbit. The proton’s kinetic energy increases by $2e\text{Δ}V$ every orbit, so after N orbits its kinetic energy is $K=2Ne\text{Δ}V$ (assuming that its initial kinetic energy was near zero). The radius of its orbit increases as it speeds up; hence the proton follows the spiral path shown in Figure 29.40 until it finally reaches the outer edge of the dee. It is then directed out of the cyclotron and aimed at a target. Although $\text{Δ}V$ is modest, usually a few hundred volts, the fact that the proton can undergo many thousands of orbits before reaching the outer edge allows it to acquire a very large kinetic energy.