As the demand for high-power radio-frequency (RF) applications continues to rise, modern-day technology is becoming increasingly prone to multipactor breakdown. Multipactor is a pernicious electron discharge driven by secondary electron emission (SEE) that plagues microwave components, particle accelerators, space-borne systems, and other related electronics. It occurs when electrons in a vacuum are accelerated by electromagnetic fields and impact device walls, resulting in the emission of secondary electrons from the surfaces. Under certain conditions, this process repeats and the number of electrons grows exponentially, potentially disrupting device operation or even causing component failure. Despite several decades of study, multipactor continues to be a longstanding engineering problem with no comprehensive theoretical solution.

This dissertation presents a novel theoretical approach for the understanding, prediction, and assessment of multipactor discharge. Drawing upon techniques from chaos theory, this new theory models multipactor as a complex dynamical system, where iterative maps track the RF phases at the surface impacts with no a priori assumptions on the electron trajectories. By systematically applying these maps and scanning system parameters, bifurcation diagrams are constructed that recover a plethora of multipacting modes. This information is combined with the SEE properties of the surface material to compute the multipactor exponential growth rate throughout parameter space.

The theory is first illustrated for a parallel-plate geometry driven by RF and DC fields. Here, the system attractor form is found to manifest in the exponential growth rate, where high-periodicity and chaotic modes suppress multipactor growth. Conventional multipactor regions are recovered but new parameter spaces susceptible to the discharge are also identified. These theoretical predictions are verified with particle-in-cell simulations and industrial design standards. Next, the theory is expanded to a coaxial system and validated against published simulation and experimental results. Finally, the theory is generalized to multicarrier operation, where several RF carriers (each with a separate amplitude and frequency) coexist, as employed in modern space communication systems. This is demonstrated for the lowest-order system in a parallel-plate geometry, namely two-carrier operation. These results are verified with particle-in-cell simulations. This model serves as the first comprehensive theoretical solution for multipactor in multicarrier systems.