Particle beam
A particle beam is a directed stream of charged or neutral subatomic particles, such as electrons, protons, ions, or positrons, that have been accelerated to high velocities and focused into a narrow path using specialized equipment known as particle accelerators.[1] These beams are generated from particle sources—such as thermal or photoemission for electrons and radioactive decay for positrons—and propelled by electric fields, either direct current (DC) or radiofrequency (RF), while magnetic and electric components guide and focus the particles to maintain low divergence and controlled energy spread.[1] Key properties include beam current (measuring particle flow rate), emittance (a measure of the beam's phase space volume, which remains invariant under acceleration), and brightness (indicating current density in phase space), all of which determine the beam's utility for precise applications.[1] Particle beams serve as essential tools in high-energy physics, where they enable the study of fundamental particles and forces by colliding beams at facilities like CERN's Large Hadron Collider (LHC), which accelerates protons to nearly the speed of light in bunches traveling through ultrahigh-vacuum pipes and steered by superconducting magnets.[2] In such colliders, beams are injected from sources like hydrogen gas ionized to produce protons, accelerated in stages (e.g., linear accelerators followed by synchrotrons), and collided either with fixed targets or counter-rotating beams to probe subatomic interactions.[2] Beyond research, particle beams have transformative applications in medicine, particularly in radiation therapy for cancer, where proton or heavy-ion beams exploit the Bragg peak—a sharp energy deposition at a specific depth—to target tumors with minimal damage to surrounding healthy tissue, as enabled by cyclotrons or synchrotrons.[3] In industry and materials science, particle beams facilitate nanofabrication, such as helium ion microscopy for creating sub-10 nm features, and surface modification for applications like superconducting coatings or X-ray production.[4] They also support space weather studies, where simulated beams help map Earth's magnetic field and predict impacts on telecommunications.[5] Ongoing advancements, including denser electron beams via controlled distortions and optical cooling techniques as of 2022, continue to enhance beam quality for probing rare phenomena and enabling compact accelerators; as of September 2025, new diagnostic techniques for measuring ultra-short particle beams further advance compact accelerator development.[6][7][8]Fundamentals
Definition and Properties
A particle beam is a directed stream of charged or neutral particles, excluding photons, that travel through a vacuum or medium with velocities ranging from thermal speeds to approaching the speed of light.[9] These beams consist of massive particles such as electrons, protons, ions, or neutrons, forming bunches or continuous flows with directed momentum and energy that require confinement to counteract thermal expansion and maintain coherence during transport.[9] Unlike photon beams, which are massless electromagnetic waves propagating at the speed of light, particle beams involve rest mass and can be manipulated via electromagnetic fields due to their charge (for charged variants) or other means.[10] Fundamental properties of particle beams include particle flux, quantified as the number of particles per unit area per unit time and often expressed through beam current I \approx n e \langle v_z \rangle, where n is the particle density, e is the charge, and \langle v_z \rangle is the average velocity component along the beam direction.[9] Beam divergence characterizes the angular spread of the particles, determining how tightly the beam remains focused over distance and influenced by initial conditions and external forces.[9] These properties are essential for assessing beam quality and transport efficiency in applications. For beams at relativistic speeds, effects from special relativity dominate, including the Lorentz factor\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}},
where v is the particle velocity and c is the speed of light, which quantifies length contraction, time dilation, and increased effective mass./27%3A__Special_Relativity/27.3%3A_Relativistic_Quantities) Time dilation, in particular, extends the proper lifetime of unstable particles in the beam frame, enhancing stability and allowing longer propagation distances in laboratory frames.[9] Interactions of particle beams with matter primarily involve ionization, elastic and inelastic scattering, and energy deposition, leading to excitation or disruption of atomic structures.[11] The mean energy loss per unit path length for charged particles is described by the Bethe-Bloch formula, approximated proportionally as
-\frac{dE}{dx} \propto \frac{Z^2}{\beta^2},
where Z is the particle's charge number and \beta = v/[c](/page/c), highlighting the dependence on charge squared and inverse velocity squared for non-relativistic to moderately relativistic regimes.[11] This energy loss mechanism underlies detection, attenuation, and biological effects in various media.