Non-Coulomb perturbations influence on beam dynamics in extended accelerating/focusing channels

Abstract

It is generally taken that the main source of particle losses in extended linac channel is the Coulomb field of space charge dominated beam. However there are the non-Coulomb effects concerned with external field perturbations (external perturhations) and their influence on beam dynamic is comparable with the action of space charge.It is convenient to split external perturbations into two groups: constructive (regular) perturbations caused by distinction of a real structure from an ideal one and perturbations caused by random parameter deviations within given tolerances. In the last case only the probability that the beam size would be no more than given value can be found. In connection with strict requirements for channel transparent and also with the complex procedure for channel retuning and readjustment, the confidence level must be chosen sufficiently large.The calculation of the acceleratinglfocusing channel.always based on the specific mathematical model involving description of external accelerating and focusing forces.In this model as a rule, the focusing field linear dependence an transverse coordinates and accelerating field axis distribution is used. The channel based on such models will be called ideal. Of course, there are no unprojected losses in the ideal channel. Output beam parameters degradation including transverse size and emittance growths is caused hy channel and beam parameter perturbations (not always small). The influence of perturbations upon the beam output parameters determines by qnantity, which have come tn be known as the channel sensitivity. The goals of beam dynamics investigations are:-knowledge about channel sensitivity -each petnybing factor influences output beam parameters, -perturbing factors compensation possibilities, -redundant factor determination guaranteed the beam passing throughout the real channel without losses.From strategy standpoint, the major goal of the investigation is determination of the generalized parameters whose numerical values permit to judge about channel sensitivity as well as about beam parameter degradation. The confidence level must be sufficient for intolerable beam loss estimation. The cardinal problem is to choose the channel with minimum sensitivity in order to minimize the beam losses during the process of accelerating.Mathematical foundation and the main ITeatments are given in the works [1-6] as well as the tolerance estimation for various types of focusing and accelerating channel. Below we will investigate the parameters determining the sensitivity of long channel to external perturbations.Let us consider as example motion of particles in focusing channel with random errors in focusing field gradients X,+ E@) ' X = 0 Let us consider G(z) as d ( z ) = G ( z ) . (I + a(=)),where C(z) is non-perturbed field gradient, a(z) is function for perturbation description.As is shown in above cited works we need to do transformation of variables x, &/dz to phase variables r,q.? is quadric in x,&dz, describing the ellipses matched with the ideal per...

Perturbation of Channel Parameters as a Source of Beam Loss in High-Power Linacs

“…[1][2][3][4][5][6] as well as the estimation of tolerances for various types of focusing and accelerating channels. [1][2][3][4][5][6] as well as the estimation of tolerances for various types of focusing and accelerating channels.…”

Monte-Carlo simulation module for Lidos.RFQ.designer code

“…The part Advisor offers the supplementary visual information for tolerance estimation. In [6] we define parameter S -sensitivity of period to perturbations. In this case this parameter is determined by relation…”

“…Visual information presents the plot of sensitivity versus number of cell as well as statistic estimation of effective emittance growth and beam center transverse displacement. The error integrals are calculated in according with relations given in [6]: if σ 2 is mean square value of focusing field gradient relative error then the probability that effective emittance growth would be no more than x is determined by function…”