Renato Pakter

Mechanisms and control of beam halo formation in intense microwave sources and accelerators

Halo formation and control in space-charge-dominated electron and ion beams are investigated in parameter regimes relevant to the development of high-power microwave (HPM) sources and high-intensity electron and ion linear accelerators. In particular, a mechanism for electron beam halo formation is identified in high-power periodic permanent magnet (PPM) focusing klystron amplifiers. It is found in self-consistent simulations that large-amplitude current oscillations induce mismatched beam envelope oscillations and electron beam halo formation. Qualitative agreement is found between simulations and the 50 MW 11.4 GHz PPM focusing klystron experiment at Stanford Linear Accelerator Center (SLAC) (D. Sprehn, G. Caryotakis, E. Jongewaard, and R. M. Phillips, “Periodic permanent magnetic development for linear collider X-band klystrons,” Proceedings of the XIXth International Linac Conference, Argonne National Laboratory Report ANL-98/28, 1998, p. 689). Moreover, a new class of cold-fluid corkscrewing elliptic...

Electron beam halo formation in high-power periodic permanent magnet focusing klystron amplifiers

Electron beam halo formation is studied as a potential mechanism for electron beam losses in high-power periodic permanent magnet focusing klystron amplifiers. In particular, a two-dimensional (2-D) self-consistent electrostatic model is used to analyze equilibrium beam transport in a periodic magnetic focusing field in the absence of a radio frequency (RF) signal, and the behavior of a high-intensity electron beam under a current-oscillation-induced mismatch between the beam and the periodic magnetic focusing field. Detailed simulation results are presented for choices of system parameters corresponding to the 50-MW, 11.4-GHz periodic permanent magnet (PPM) focusing klystron experiment performed at the Stanford Linear Accelerator Center (SLAC). It is found from the self-consistent simulations that sizable halos appear after the beam envelope undergoes several oscillations, and that the residual magnetic field at the cathode plays an important role in delaying the halo formation process.

Equilibrium and stability properties of self-organized electron spiral toroids

A cold-fluid model for a self-organized electron spiral toroid (EST) is presented. In the present model, the electrons are assumed to undergo energetic spiral motion along a hollow torus with a fixed ion background, the electron mean free path is assumed to be long compared with the torus size, and the minor radius of the EST is assumed to be small compared with the major radius. Using this model, the equilibrium and stability properties of the electron flow in the self-organized EST are analyzed. It is found that a class of self-organized EST equilibria exists with or without an externally applied toroidal magnetic field. It is shown that in the absence of any applied toroidal magnetic field, the EST equilibria are stable at high electron densities (i.e., at high toroidal self-magnetic fields), although they are unstable at low electron densities (i.e., at low toroidal self-magnetic fields).

Phase space structure for matched intense charged-particle beams in periodic focusing transport systems

Test particle motion is analyzed analytically and numerically in the field configuration consisting of the equilibrium self-electric and self-magnetic fields of a well-matched, thin, continuous, intense charged-particle beam and an applied periodic focusing solenoidal magnetic field. The self fields are determined self-consistently, assuming the beam to have a uniform-density, rigid-rotor Vlasov equilibrium distribution. Using the Hamilton–Jacobi method, the betatron oscillations of test particles in the average self fields and applied focusing field are analyzed, and the nonlinear resonances induced by periodic modulations in the self fields and applied field are determined. The Poincare surface-of-section method is used to analyze numerically the phase-space structure for test particle motion outside the outermost envelope of the beam over a wide range of system parameters. For vacuum phase advance σv=80°, it is found that the phase-space structure is almost entirely regular at low beam intensity (phase...

Ideal matching of heavy ion beams

Abstract A novel technique is developed, and demonstrated via simulations, which allows ideal matching of an ultrahigh-brightness heavy ion beam in a linear focusing channel with general magnetic focusing field profile. Unlike the conventional rms matching used in accelerator design, this technique is based on a new class of corkscrewing elliptic beam equilibria in a linear focusing channel consisting of uniform solenoidal fields, periodic solenoidal fields, and/or alternating-gradient quadrupole magnetic focusing fields in an arbitrary arrangement including field tapering. As an illustration of the effectiveness of this technique, a perfect matching of an ultrahigh-brightness heavy ion beam from an axisymmetric particle source into alternating-gradient quadrupole focusing channel is achieved without beam hollowing and beam halo formation. Discussions are made of how to implement such a perfect beam matching to avoid beam hollowing observed in the LBNL 2-MV Heavy Ion Injector Experiment.

Green's function description of space-charge in intense charged-particle beams

We present two- and three-dimensional models of space charge in intense charged-particle beams using Greens functions. In particular, we compute the electrostatic Greens function for a periodic collinear distribution of point charges located inside of a perfectly conducting drift tube. As applications of the Greens function description, we analyze the matching and transport of an initially axisymmetric beam into a quadrupole channel and the interaction of a particle with its induced surface charge.

Halo formation in intense electron beams in high-power klystron amplifiers

An important issue in the design of high-power microwave sources is how to prevent high-intensity relativistic electron beams from forming halos because they cause electron beam losses and radio-frequency pulse shortening. In this paper, we study the behavior of a high-intense electron beam under a current-oscillation-induced mismatch between the beam and the magnetic focusing field, using a 2D self-consistent electrostatic model. For high-intensity electron beams, it is found from the self-consistent simulations that sizable halos appear after the beam envelope undergoes several mismatched oscillations, depending on the amplitude of mismatched beam envelope oscillations. Detailed simulation results are presented for the choice of system parameters corresponding to the 50 MW, 11.4 GHz periodic permanent magnetic focusing klystron experiment at the Stanford Linear Accelerator Center. Moreover, it is found that the process of halo formation in a uniform-solenoidal focusing klystron is essentially the same as in the PPM focusing klystron with comparable system parameters.

Emittance growth and particle diffusion induced by discrete-particle effects in intense beams

We analyze particle diffusion and emittance growth induced by discrete-particle effects in two-dimensional self-consistent numerical simulation studies of beam dynamics. In particular, an analytical model is presented which describes the slow time-scale variation of edge emittance for a perfectly matched beam in a periodic solenoidal magnetic focusing field. A scaling law for edge emittance growth is obtained.

Stability of the envelope evolution of a cold-fluid corkscrewing elliptic beam in a uniform-focusing magnetic field

The envelope oscillations of a cold-fluid corkscrewing elliptic beam in a uniform-focusing magnetic field are studied. In particular, by linearizing the generalized beam envelope equations, the eigenmodes of small-amplitude envelope oscillations are calculated for a cold-fluid corkscrewing elliptic beam oscillating about its equilibrium. All of the eigenmodes are shown to be stable.

Electron-beam halo formation in periodic permanent magnet focusing klystron amplifiers

Electron beam halo formation is studied as a potential mechanism for electron beam losses in high-power periodic permanent magnet focusing klystron amplifiers. In particular, a 2D self-consistent electrostatic model is used to analyze equilibrium beam transport in a periodic magnetic focusing field in the absence of radio-frequency signal, and the behavior of a high-intensity electron beam under a current-oscillation-induced mismatch between the beam and the periodic magnetic focusing field. Detailed simulated results are presented for choices of system parameters corresponding to the 50 MW, 11.4 GHz periodic permanent magnet focusing klystron experiment performed at the Stanford Linear Accelerator Center. It is found from the self-consistent simulations that sizable halos appear after the beam envelope undergoes several oscillations, and that the residual magnetic field at the cathode plays an important role in delaying the halo formation process. Finally, a confinement criterion is obtained for a highly bunched beam propagating through a perfectly conducting drift tube in a uniform magnetic field.