… 6 and 7 cover simulation techniques for bunched beams with … Section 6 treats the envelope
equations for bunched beams … beam envelopes, which is fundamental in much of the beam …

… The good agreement between the analytically predicted envelopes dashed lines and the
numerical simulation data solid lines gives a significant confirmation of the capability of the …

… to different beam envelopes. Substituting the obtained forces into the beam-envelope
equations establishes a set of six modified equations describing the beam dynamics using simple …

… To obtain further insight into the beam physics in the case of stable or unstable envelope
oscillations, we performed particle-simulation studies with the modified PARMILA code at GSI, …

… study on the envelope dynamics of space charge dominated beam in synchrotrons. We …
theories and discusses a multiparticle tracking technique. Envelope dynamics with simulation …

… the beam envelopes of an axisymmetric, bunched beam inside a perfectly conducting beam
… We simulate a simple beam transport system to demonstrate the application of these results. …

Linear beam-envelope theory of ionization cooling in 6D phase space has been systematically
established in the past few years. In this paper, we briefly review the general formalism …

… the beam envelope are constructed to explain oscillations in the beam envelope observed
in the PIG simulations but … A test particle analysis is also developed as a method to visualize …

… the beam envelope varying markedly under certain mismatched magnetic field configurations.
Initial simulations show that the electron beam envelope … Theoretical simulation work was …

… The research of this paper will provide a theoretical basis for the development and … distribution
of the Bessel beam array in the propagation process, we simulated the diffraction field of …