Beam Envelope Equation Research Articles

Numerical Simulation of Autoresonant Ion Acceleration

Computational and analytic studies of the Autoresonant Acceleration proposal for collective ion acceleration are presented. Linear theory is reviewed, the electrostatic well depth is estimated nonlinearly, and an electron beam envelope equation is derived and solved. Two-dimensional numerical simulation results are given. Together, these calcualtions demonstrate unneutralized electron beam equilibrium in a diverging magnetic guide field, the behaviour of large amplitude slow cyclotron waves in the beam, and the acceleration of test ions over short distances in the wave troughs. In addition, the computer simulations point up the need for improved understanding of the linear theory of radially inhomogeneous noneutral beams and for methods of suppressing radial modulation at the diode-waveguide interface.

Optical and hydrodynamical approaches to charged particle beams

The optical paraxial ray equation for charged particles, including the effects of self fields, is discussed in both the laboratory and rotating Larmor frames. The corresponding beam envelope equation is derived, in the first instance for laminar flow but later for some non-laminar distributions. The equivalence between optical and hydrodynamical viewpoints is discussed in some detail, and the relation between pressure and emittance is explored. Finally, some of the characteristics of longitudinal energy spread in the beam are investigated.