Diverse methods proposed for the acceleration of particles by means of collective fields are reviewed. A survey is made of the various currently active experimental programs devoted to investigating collective acceleration, and the present status of the research is briefly noted.

General expressions are given for the field and its expansion coefficients produced by a two dimensional conductor structure surrounded by iron with a circular inside boundary. Saturation effects are described in terms of the tangential field at that boundary. The effects of the following types of perturbations are discussed: displacement, rotation and error excitation of a conductor, change of conductor shape, and modification of the inside contour of the iron. A design criterion is given to minimize the error fields associated with a displacement of the iron shell relative to the conductor structure. Expressions for the force and torque acting on a conductor are derived both for the unperturbed and perturbed magnet. Formulae are presented that allow convenient and fast evaluation of pertinent quantities with a computer when the structure is too complicated for hand computations.