On-line monitoring of beam quality for high-intensity particle beams requires non-invasive transverse phase space diagnostics. Such diagnostics are in high demand for use in heavy ion accelerators and free-electron lasers (FELs). A technique to measure emittance using multi-turn resonant excitation of the quadrupole envelope mode has been demonstrated at the University of Maryland Electron Ring (UMER).

The rms Kapchinsky-Vladimirsky (KV) equations predict the time-evolution of particle beam envelopes. Linear perturbations to the matched envelope solution of these equations excite normal modes at space-charge-dependent natural frequencies. This experiment employs periodic, impulsed perturbations to drive resonant excitations of these modes. Steady state resonance structure in the form of a lattice is predicted using analytic solutions of a delta-kicked simple harmonic oscillator (SHO). Numerical simulations of this SHO along with simulations from the WARP envelope solver and particle-in-cell (PIC) codes are documented.

This dissertation presents the first proof-of-principle experimental resonant excitation of the quadrupole envelope mode in a high-intensity particle beam. To excite the mode experimentally, an rf-driven electric quadrupole is constructed and installed in UMER. The quadrupole fields are driven by a tunable resonant tank circuit designed and built for this experiment. After resonant excitation, the knockout imaging method is used to collect 3 ns synchronized transverse time slice images of the beam. Image moments are analyzed and show good agreement with simulation. Emittance can then be inferred from the measured natural frequencies of the envelope modes utilizing a conversion obtained through simulation. A direct emittance measurement is performed using a conventional pinhole scan at injection as an experimental validation of the envelope resonance method.