Quadrupole mode perturbation in storage rings

Quadrupole mode oscillation (QMO) means the second moments of a system oscillating with time, or, the elliptical torus of the Hamiltonian rotating in phase space. We study the QMO in storage rings. In the transverse direction the QMO can be excited by an rf quadrupole. The strength of the rf quadrupole varies with time, and the oscillation frequency ω_m must be close to two times the transverse betatron oscillation frequency ω _y. The perturbation equation is solved with the Hamiltonian method and we found the beam satisfies Boltzmann distribution. Mathieu instability occurs when 2(ω_y − C ₁ω₀) < ω_m < 2(ω_y + C₁ω ₀), where C₁ is the effective strength of the rf quadrupole and ω₀ is the revolution frequency. When a nonlinear detuning term is included, the multi-particle system will bifurcate after passing through the thresholds. The QMO can be detected by a Beam Position Monitor (BPM), and the emittance of the beam can be derived from the signal. The other applications of quadrupole mode perturbation include mismatch correction and spin resonance overcoming.; In the longitudinal direction voltage modulation induces QMO. The Hamiltonian has the same form as the transverse nonlinear QMO Hamiltonian, therefore the beam dynamics and the properties are similar. QMO in the longitudinal direction can be used to compress the bunch in storage rings. Our research results show that the bunch can be compressed by a factor of 2∼3 in proton storage rings. This factor is smaller in electron storage rings due to radiation damping and quantum fluctuation. The more effective method, however, is using a harmonic cavity. Both methods are explored in the second part of this dissertation.