Guiding-center Vlasov-Maxwell description of intense beam propagation through a periodic focusing field - art. no. 104401

This paper provides a systematic derivation of a guiding- center kinetic mo del that describes intense beam propagation through a periodic focusing lat tice with axial periodicity length S, valid for sufficiently small phase ad vance (say, sigma < 60<degrees>). The analysis assumes a thin (a,b much les s than S) axially continuous beam, or very long charge bunch, propagating i n the z direction through a periodic focusing lattice with transverse focus ing coefficients kappa (x) (s + S) = kappa (x) (s) and kappa (y) (s + S) = kappa (y) (s) where S = const is the lattice period. By averaging over the (fast) oscillations occurring on the length scale of a lattice period S, th e analysis leads to smooth- focusing Vlasov- Maxwell equations that describ e the slow evolution of the guiding-center distribution function (f) over b ar (b) ((x) over circle, (y) over circle, (x) over bar', (y) over bar', s) and (normalized) self- field potential psi ((x) over bar, (y) over bar, s) in the four-dimensional transverse phase space ((x) over barx, (y) over bar , (x) over bar', (y) over bar'). In the resulting kinetic equation for (f) over bar (b) ((x) over bar, (y) over bar, (x) over bar', (y) over bar', s) the average effects of the applied focusing field are incorporated in const ant focusing coefficients kappa (x) (sf) > 0 and kappa (y) (sf) > 0, and th e model is readily accessible to direct analytical investigation. Similar s mooth-focusing Vlasov- Maxwell descriptions are widely used in the accelera tor physics literature, often without a systematic justification, and the p resent analysis is intended to place these models on a rigorous, yet physic ally intuitive, foundation.