What specific type of particle motion causes synchrotron radiation in strong magnetic fields, as opposed to the random thermal motion that causes bremsstrahlung?

Synchrotron radiation is specifically caused by the continuous centripetal acceleration of charged particles, typically electrons, moving at relativistic speeds (speeds approaching the speed of light) in a strong, uniform magnetic field. The magnetic field exerts a Lorentz force on the moving electron, which is always perpendicular to both the electron's velocity and the magnetic field direction. This force continuously deviates the electron from a straight path, compelling it into a circular or helical trajectory. The constant change in direction, which is a form of acceleration directed towards the center of the circular path (centripetal acceleration), is the specific type of particle motion that causes the emission of electromagnetic radiation known as synchrotron radiation. Because this acceleration is continuous, ordered, and uniform due to the structured magnetic field, the emitted radiation has distinct properties: it is highly collimated (emitted in a narrow cone), highly polarized, and has a broad, continuous spectrum extending to very high energies.

In contrast, bremsstrahlung, or "braking radiation," is caused by the random, impulsive deceleration or deflection of charged particles, typically electrons, as they interact with the electric fields of atomic nuclei. This interaction is a Coulomb interaction. When an electron passes near a positively charged nucleus, the nucleus's electric field exerts a force that changes the electron's velocity, causing it to slow down, change direction, or both. This erratic and unsynchronized acceleration (deceleration or deflection) is the direct cause of bremsstrahlung. The "random thermal motion" refers to the chaotic and unpredictable nature of these individual collision events and the resulting varying magnitudes and directions of acceleration. Unlike the highly ordered, continuous acceleration in a magnetic field that produces synchrotron radiation, the acceleration events in bremsstrahlung are sporadic and vary greatly depending on the electron's specific trajectory and proximity to a nucleus. This randomness in the acceleration events results in bremsstrahlung having a continuous energy spectrum without sharp peaks and generally being unpolarized.