The Simulation Of Ionic Radial Density In High Intensity Ion Beam

The principle of chaos control and its control methods, halo-chaos formation mechanism andits control methods and ion-density distribution in high intensity beam are summarized in thispaper. The ionic radial density of high intensity ion beam whose halo-chaos is controlled or isn'tin K-V distribution is simulated based on those. It is shown that halo-chaos is removed by chaoscontrol methods, as long as the proper parameters are chosen, the beam distribution may becontrolled, and the application may be carried out in the future. People study chaos and sum up many chaos control methods. The phylogeny ofchaos control, understanding and use on chaos control are not only reviewed, butOGY control, delay feedback control, control of spatiotemporal chaos etc. areselected as typical examples to give a further description. High intensity ion beam is used diffusely. But halo-chaos is noticed andbecomes a critical problem gradually in real world. Firstly, the features and physicalmechanisms of halo-chaos are stated; secondly, control strategy and methods ofhalo-chaos are described, and investigation of ion density distribution is introduced;finally is halo-chaos study summarized in this paper. The halo-chaos will cause damage to accelerator etc, so it is necessary to removehalo-chaos. Researcher. Fang Jin-qing in China institute of Atomic Energy hasproposed the nonlinear control strategy; the approach is to apply a nonlinear feedbackcontroller G to the right-hand side of the single ion forced equation, that is, Fr = ?q?Φs (x, y,s) + G (1)Halo-chaos is controlled in terms of controller G. About the halo-chaos control, peoplehave proposed some methods, moreover, the reference [1] gives the filling factorregion that halo-chaos is controlled well. But the character of ion beam isn't knownwhen halo-chaos is controlled or isn't in any other papers. By applying the PICprocedure and delay feedback control, the controller G is selected in this paper. G = g[rrms (s ? S) ? rrms (s)] (2)Ionic radial density is simulated when halo-chaos is controlled or isn't in K-V beam.With numerical simulation and statistical method, we solve the single ion equation(3),(4) by combining equation (1), (2). We can study the beam character whenhalo-chaos is controlled isn't. 3广西师范大学硕士研究生学位论文——摘要翻译 d 2x q ?Φs(x, y,s) = 0 (3) ds2 + kz(s)x + γbβb mc2 3 2 ?x d 2 y q ?Φs(x, y,s) = 0 (4) ds2 + kz(s)y + γbβb mc2 3 2 ?y The two works are done base on that theory: ○ Ionic radial density is simulated when halo-chaos is controlled or isn't by 1delay feedback control in periodically interrupted focusing channel. We chose fillingfactor 0.4,0.64,0.8 respectively, the numerical simulation exhibits, before halo-chaosis controlled, there is a little difference on ion beam density when the filling factor isdifferent. However, in spite of any filling factor, the ionic transverse area not onlyincreases, but also ionic radial density on cross section becomes nonuniform incontrast to the initial K-V distribution. The rough result is that there are a lot of ionsin beam's center, there are a few ions at the beam edge, the density curve isn'tmonotonous, there is a maximum in density figure. It is well known that the ionmotion is complicated in beam's center, using the particle-core model, an ion isaffected by linear space charge force inside the core; outside the core, an ion isaffected by nonlinear space charge force, and in periodic-focusing channel, amismatch beam is affected by magnetic force, because the ionic action is complicated,the density fig...