The LIDOS.RFQ.Designer code package gives users the possibility to proceed successfully from input data up to RFQ channel design and space-chargedominated beam simulation. The code main feature is a maximum of scientific visualization for each calculation step. The package contains codes with three levels of mathematical model complexity. The first-level codes make not only a preliminary choice of the main parameter arrays on the basis of a simplified physical model but also chosen design optimization. In the case of high-current CW RFQ radiation purity (minimum of lost particles) is considered as the main optimization criteria. The secondlevel codes are used for RF field calculations taking into account the real shape of the RFQ vanes. The third-level codes are based on complex PIC-models that are needed for beam simulation in the chosen channel version.

Conventional approach to the designing of controlled systems is to start with calculation of program motion and to continue afterwards by examining perturbed motions using equations in deviations. It does not always, however, result in desirable outcomes. Thus, while analysing perturbed motions, which depend significantly on the program motion, it can happen, that dynamical characteristics of obtained perturbed motions are not satisfactory.This paper suggests new mathematical models, which allow joint optimization of program motion and an ensemble of perturbed motions. These mathematical models include description of controlled dynamical process, choice of control functions or parameters of optimization as well as construction of quality functionals, which allow efficient evaluation of various characteristics of examined control motions.This optimization problem is considered as the problem of mathematical control theory. The suggested approach allows to develop various methods of directed search and to conduct parallel optimization of program and perturbed motions. Suggested approach is applied to the optimization of RFQ channel. Simple model for description of beam longitudinal motion in the equivalent running wave is suggested. For the estimation of beam dynamics corresponding functionals are suggested.

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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...

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