The branch of physics concerned with the motion of charged particles under the influence of electric and magnetic fields.
Acceleration of charged particles
A positively charged particle that moves in an electric field experiences a force in the direction of this field. If the particle falls in the field from a potential of U volts to a potential zero, its energy gain, measured in electronvolts, is equal to the product of U and the particle's charge. For example, if a singly and a doubly charged particle are accelerated by a potential drop of 100 V, the two particles will gain energies of 100 eV and 200 eV, respectively. If both particles were initially at rest, they would have final velocities proportional to the square root of K/m, where K is the energy increase and m is the mass of the particle. This relation describes the velocities of energetic particles accurately as long as these velocities are small compared to the velocity of light c ≈ 300,000 km/s (186,000 mi/s), a speed that cannot be exceeded by any particle. See also: Electric field; Electrostatics
If an ensemble of ions of equal energies but of different masses is accelerated simultaneously, the ion masses can be determined from their arrival times after a certain flight distance. Such time-of-flight mass spectrometers have successfully been used, for instance, to investigate the masses of large molecular ions, up to and beyond 350,000 atomic mass units. See also: Time-of-flight spectrometers
Deflection of charged particles
If a homogeneous electric field is established between two parallel-plate electrodes at different potentials, a charged particle in the space between the electrodes will experience a force in the direction perpendicular to them. If initially the particle moved parallel to the electrodes, it will be deflected by the electric force and move along a parabolic trajectory. Magnetic fields also deflect charged particles. In contrast to electrostatic fields, however, magnetic fields change only the direction of a particle trajectory and not the magnitude of the particle velocity. A charged particle that moves perpendicular to the field lines of a homogeneous magnetic field moves through a circular path (Fig. 1) whose radius is determined from the balance between the centrifugal force along this circle and the magnetic force.
Charged particles that enter a magnetic field thus move along circles whose radii increase with the products of their velocities and their mass-to-charge ratios, m/q. If initially all particles start at the same potential U and are accelerated to the potential zero, they will move along radii that are proportional to the square root of U(m/q). Thus, particles of different mass-to-charge ratios can be separated in a magnetic sector field (Fig. 1).
In the plane of deflection, charged particles that diverge from a point in some source are focused back to a point of the image (Fig. 1). In the perpendicular direction, however, the particles remain divergent. A straight line that connects the source and the image also passes through the center of curvature of the trajectory of the reference particle. The images of particles of different mass-to-charge ratios all lie in a plane that is usually inclined with respect to the particle beam.
A sector-field mass analyzer can be used to determine the masses of atomic or molecular ions in a cloud of such ions. Such systems can also be used to purify a beam of ions that are to be implanted in semiconductors in order to fabricate high-performance transistors and diodes. Finally, such magnetic sector fields are found in large numbers in all types of particle accelerators. See also: Ion implantation; Mass spectroscope
Axially symmetric lenses
An Einzel lens consists of three cylindrical tubes, the middle one of which is at a higher potential than the outer two. Positively charged particles entering such a device are first decelerated and then accelerated back to their initial energies. Since the decelerations and accelerations are perpendicular to the eqipotential surfaces, the particles experience forces that drive them toward the optic axis in some regions and away from it in others. However, the focusing actions are always stronger than the defocusing actions since they occur in regions in which the particles are moving more slowly, that is, in the center regions. Defocusing lenses cannot be built in this fashion unless potential-defining metal grids distort the equipotential surfaces. This statement also holds for axially symmetric lenses in which the potential on the center electrode has been chosen such that the charged particles are not decelerated but accelerated while passing through the lens. See also: Electrostatic lens
Axially symmetric magnetic lenses have also been constructed. Such lenses, also called solenoids, consist mainly of a coil of wire through which an electric current is passed. The charged particles are then constrained to move more or less parallel to the axis of such a coil. Steel tubes with rotationally symmetric geometries can be used to surround the coil to increase the magnetic field strength. See also: Magnetic lens; Solenoid (electricity)
Axially symmetric electric and magnetic lenses are used extensively to focus low-energy particle beams. Particularly important applications are in television tubes and in electron microscopes. See also: Cathode-ray tube; Electron microscope; Picture tube
By passing charged particles through electrode or pole-face arrangements (Fig. 2), a particle beam can also be focused toward the optic axis. In such quadrupole lenses the electric or the magnetic field strengths, and therefore the forces that drive the charged particles toward or away from the optic axis, increase linearly with the distance from the axis. This is the main property of the lens. In quadrupoles the focusing occurs in one direction only, while there is a defocusing action in the perpendicular direction. Focusing in both directions thus requires a combination of at least two quadrupole lenses. In quadrupole lenses the particle trajectories are bent toward the optic axis by the main field, while in axially symmetric lenses such a focusing action is achieved by the much weaker fringing fields. Quadrupole lens systems thus have much stronger focusing abilities than other types of lenses, and smaller field strengths can be used to focus more rigid particle beams.
While quadrupole lenses are found in systems in which low-energy particle beams must be focused, for instance, in mass spectrometers, such lenses have become indispensable for high-energy beams. Consequently, quadrupole lenses, especially magnetic ones, are found in many types of particle accelerators used in research in, for example, nuclear and solid-state physics, as well as in cancer irradiation treatment facilities. See also: Charged particle interactions; Electron lens; Electron motion in vacuum; Particle accelerator