Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation.

In typical numerical simulations, the space-charge force is calculated by slicing a beam into many longitudinal segments and by solving the two-dimensional Poisson equation in each segment. This method neglects longitudinal leakage of the space-charge force to nearby segments owing to its longitudinal spread over 1/γ. By contrast, the space-charge impedance, which is the Fourier transform of the wake function, is typically calculated directly in the frequency-domain.

Resistive wall impedance and tune shift for a chamber with a finite thickness.

Since the resistive wall impedance for a beam pipe of a nonround cross section depends on the coordinates of a witness particle, the witness particle receives an incoherent tune shift. When the expression for the impedance of an infinitely thick chamber is applied to the calculation of this tune shift, it becomes infinite. We have derived the resistive wall impedance for a chamber with a finite thickness and calculated the tune shift.

Heating rate of hadron beams during crystallization.

A theory concerning the relation between the heating rate and temperature of hadron beams is formulated from a quantum point of view. This theory predicts that the heating rate can be reduced by increasing the lattice periodicity of the accelerator with its fixed tunes and circumference. This prediction is quite consistent with simulation results.