Mark Hess

Confinement criterion for a highly bunched beam

The nonrelativistic motion is analyzed for a highly bunched beam propagating through a perfectly conducting cylindrical pipe confined radially by a constant magnetic field parallel to the conductor axis. In the present analysis, the beam is treated as either a thin rod distribution representing a continuous (unbunched) beam or periodic collinear point charges representing a highly bunched beam. Use is made of a Green’s function to compute the electrostatic force on the beam due to the induced surface charge in the conductor wall. By analyzing the Hamiltonian dynamics, a criterion is derived for the confinement of unbunched and bunched beams. It is shown that for the confinement of beams with the same charge per unit length, the maximum value of the effective self-field parameter is 2ωp2/ωc2≅2a/L for a highly bunched beam with a≪L. This value is significantly lower than the Brillouin density limit for an unbunched beam 2ωp2/ωc2=1. Here, a is the radius of the conducting cylinder, and L is the periodic spac...

Equilibrium and confinement of bunched annular beams

The azimuthally invariant cold-fluid equilibrium is obtained for a periodic, strongly bunched charged annular beam with an arbitrary radial density profile inside of a perfectly conducting cylinder and an externally applied uniform magnetic field. The self-electric and self-magnetic fields, which are utilized in the equilibrium solution, are computed self-consistently using an electrostatic Green’s function technique and a Lorentz transformation to the longitudinal rest frame of the beam. An upper bound on the maximum value of an effective self-field parameter for the existence of a bunched annular beam equilibrium is obtained. As an application of the bunched annular beam equilibrium theory, it is shown that the Los Alamos National Laboratory relativistic klystron amplifier experiment is operating slightly above the effective self-field parameter limit, and a discussion of why this may be the cause for their observed beam loss and microwave pulse shortening is presented. The existence of bunched annular ...

Beam Confinement in Periodic Permanent Magnet Focusing Klystrons

Abstract The confinement of a tightly bunched electron beam is studied in a periodic permanent magnet (PPM) focusing klystron. By analyzing the Hamiltonian dynamics of a train of collinear periodic point charges interacting with a conducting drift tube, an rf field, and an applied PPM focusing field, a space-charge limit is derived for the radial confinement of slightly bunched electron beams, and is shown to be significantly below the well-known Brillouin density limit for an unbunched beam. Several state-of-the-art PPM klystrons developed at SLAC are found to operate close to this limit, shedding some light on the origin of observed beam losses.

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.

Formation of a self-magnetic cusp in a highly bunched relativistic annular electron beam

The formation of a self-magnetic cusp that develops in a highly bunched, relativistic, annular electron beam as the beam current approaches a critical current limit is demonstrated. The self-magnetic cusp is calculated within the framework of a fluid equilibrium model for a beam of periodic, azimuthally symmetric, relativistic bunched annular disks propagating in a perfectly conducting cylindrical pipe with a uniform magnetic focusing field. Magnetic cusp formation may play an important role in determining the operational current limit of high-current bunched relativistic annular beam experiments.

Self-magnetic cusp limit of a finite sized bunched relativistic annular electron beam

Summary form only given. We show the existence of a self-magnetic cusp which forms in a highly bunched (zero bunch length) annular electron beam as the average beam current approaches a critical current limit. The self-magnetic cusp is calculated within the framework of a fluid equilibrium model for periodic azimuthally symmetric relativistic bunched disk beams propagating in a perfectly conducting cylindrical pipe with a uniform magnetic focusing field. In certain parameter regimes, magnetic cusp formation plays an important role in determining the operational current limit of high-current bunched annular beam experiments. We also discuss how finite bunch length affects the formation of the self-magnetic cusp.

Confinement criterion for a finite sized bunched beam

Summary form only given. A confinement criterion for a finite sized azimuthally symmetric relativistic bunched electron beam propagating through a perfectly conducting cylindrical pipe with a slight off-axis displacement while in the presence of either a uniform or periodic solenoidal field is studied. We compute the center-of-mass force on each off-axis beam bunch due to the induced surface charges on the pipe using a Greens function technique. By analyzing the center-of-mass dynamics of each bunch due to magnetic focusing and its interaction with the pipe, a space-charge limit for beam confinement is derived. A comparison of the theory to high-current periodic permanent magnet (PPM) klystron experiments is established.

Determination of current limits in bunched annular electron beams using Green's function techniques

Summary form only given, as follows. Three-dimensional Greens functions, which solve Maxwells equations, can be utilized for modeling space charge effects of bunched annular electron beams in high-power microwave (HPM) sources, such as relativistic klystron amplifiers (RKA), relativistic klystron oscillators (RKO), and backward wave oscillators (BWO). We model bunched annular beams as periodic annuli of charge with negligibly small longitudinal thickness in a perfectly conducting drift tube, and use Greens functions to solve for the space-charge interactions of the beams with appropriate boundary conditions. We present both theoretical and computational analysis of the beam equilibrium based on the three-dimensional Greens function technique. In particular, we show the existence of an annular beam confinement limit, and demonstrate that the limit agrees with the observed current limit for pulse shortening in the 1.3 GHz; RKA experiment at the Los Alamos National Laboratory. We also present beam simulation results of the LANL RKA experiment using PFB3D, a newly developed Greens function code.

Confinement of bunched beams

The non-relativistic motion is analyzed for a highly bunched beam propagating through a perfectly conducting cylindrical pipe confined radially by a constant magnetic field parallel to the conductor axis, using a Green’s function technique and Hamiltonian dynamics analysis. It is shown that for the confinement of beams with the same charge per unit length, the maximum value of the effective self-field parameter for a highly bunched beam is significantly lower than the Brillouin density limit for an unbunched beam.

Bunched annular beam equilibrium and confinement

The azimuthally invariant fluid equilibrium is obtained for a periodic strongly bunched charged annular beam with arbitrary radial density profile inside of a perfectly conducting cylinder and an external constant magnetic field. The electric and magnetic fields, which are utilized in the equilibrium solution, are computed self-consistently using an electrostatic Greens function technique in the longitudinal rest frame of the beam. An upper bound on the maximum self-field parameter, which allows beam equilibrium is obtained. As an application of the model, we find annular beam equilibrium for the Relativistic Klystron Oscillator experiment at Phillips Laboratory and the Backward Wave Oscillator experiment at the University of New Mexico. In addition, we compare the self-field parameters of these with the maximum theoretical values.