R & D Projects

1. Nonlinear beam dynamics expreriments at IUCF Cooler Ring
   
   • CE22 - Nonlinear beam dynamics experiments at the IUCF Cooler Ring.
   • CE34 - Cooler Modeling (completed)
   • CE37 - beam transfer function measurement in the Cooler Ring.
   • CE48 - Nonlinear beam dynamics experiments (completed)
   • CE63 - Nonlinear beam dynamics and beam manipulations.

2. Electron Cooling at the IUCF Cooler Ring
   Since 1994, we have been studying the effect of electron cooling on proton beams. We found that when the relative velocity between the proton beam and cooling electrons is larger than the velocity spread of cooling electrons, the proton beam will encounter Hopf bifurcation into a ring in the phase space. using this technique, we can measure the "effective electron temperature". We observe the co-existence of fixed point attractor and limit cycle attractor. This shows for the first time the evidence of two-component theory of electron cooling. (see Pub. 1994-1996).

3. Chaos and resonances in dynamcal systems: Longitudinal and Transverse beam dynamics:

4. Space charge dominated beam studies:
   We introduce KV-envelope phase space coordinates to express the KV envelope equation in Hamiltonian formalism. The effects of space charge force on envelope and particle Hamiltonian can be analyzed analytically. This method has been shown to agree well with results obtained from numerical simulations. Thus the effect of global chaos on the Hamo formation can be analyzed analytically. (see Pub. 1995) For periodic focusing systems, there are many structure resonances. (1995)

5. Cooler Injecter Synchrotron ( Injector) and Light Ion Spin Synchrotron(LISS)

6. RF dipole spin manipulation at AGS: Experimental Results

7. Spin dynamics experiments at AGS E880 .
   The snake experiment at the IUCF Cooler Ring
   A recent study on the overlapping synchrotron sideband resonances analyzes polarization data measured at the SPEAR and the IUCF Cooler Ring (see Pub. 1996). We find that (1) the synchrotron sideband spin resonances can only be corrected by correcting its principal resonance, and (2) the synchrotron sideband spin resonances for polarized proton can be summed to change the spin precession phase.

8. Particle dynamics of quasi-isochronous (QI) storage rings
   The equation of motion for particle in QI storage rings can be transformed into the universal Weierstrass equation. Sum rules for the resonance strength function are derived. Including synchrotron radiation damping and the rf phase modulation, the QI equation of motion becomes
   x''+Ax'+x-x²=B\omega_m \sin \omega_m t.
   This QI dynamical system exhibits global chaos and strange attractor in a region of the rf modulation tune. The stability of the QI dynamics is determined by the 2:1 and 1:1 parametric resonances. (see Pub. 1996)
   Our current effort is to study the quantum fluctuation and the multiparticle effects such as potential well distortion, intrabeam scattering etc.

9. Particle Diffusion Experiments:

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