3.12.1.2 - Thermionic Emission of Electrons

Thermionic emission

A metal contains mobile electrons, but attraction to the metal prevents most of them from escaping its surface. Thermionic emission is the release of electrons from a sufficiently hot metal. Heating changes their energy distribution so that a larger fraction can overcome the surface energy barrier, called the work function.

A current in a filament supplies energy by electrical heating. The filament may itself be the emitting cathode, or it may heat a separate cathode. Increasing its temperature increases the emission rate: it releases more electrons per second, rather than increasing the charge on each electron. Positive ions are not the emitted beam particles.

The electron gun

An electron gun combines a heated cathode, a positive anode with an aperture, and an evacuated or low-pressure enclosure. Two supplies have separate roles. A low-voltage heater supply, for example $6\,\mathrm{V}$, drives current through the filament; both filament terminals must be connected. A larger accelerating supply, for example $1.0\,\mathrm{kV}$, makes the anode positive relative to the cathode.

The electric field between cathode and anode exerts a force on the electrons towards the anode. Some pass through its small hole and form a narrow beam. The aperture selects a narrow part of the beam; an aperture alone does not explain precise focusing, which real guns achieve with shaped electrodes. Low gas pressure reduces collisions that would scatter electrons or remove their kinetic energy.

[DIAGRAM: asset_name: D.1.2 - Thermionic Emission of Electrons - Diagram 1; asset_slug: D.1.2 - Thermionic Emission of Electrons - Diagram 1; caption: A heated cathode supplies electrons to a positive apertured anode; description: Simplified electron-gun geometry. The two filament leads connect to a low-voltage heating supply, omitted here. V labels a separate cathode-to-anode accelerating supply, not current arrows.]

This sketch shows the gun geometry rather than the complete supply circuits. Both free filament leads connect to the heater supply, which is omitted; the lower $V$ label marks the separate accelerating potential difference. Its arrows are not electron-flow arrows.

After the anode, electrons travel at constant velocity only where the resultant force is negligible. An aperture does not automatically make every nearby electric field zero: this is an idealisation for the field-free region beyond it. Later electric or magnetic fields can change the beam's motion.

Work done by the accelerating field

Potential difference is energy transferred per unit charge. Write $e$ for the positive magnitude of an electron's charge; the electron itself has charge $-e$. When it moves to an anode at a potential $V$ higher than the cathode, its potential-energy change is $(-e)V=-eV$. The electric field therefore does positive work $eV$ on it.