Effects of space charge in beams for heavy ion fusion
A new analytic model is presented that accurately estimates the radially averaged axial component of the space-charge field of an axisymmetric heavy-ion beam in a cylindrical beam pipe. The model recovers details of the field near the beam ends that are overlooked by simpler models, and the results compare well to exact solutions of Poisson`s equation. Field values are shown for several simple beam profiles and are compared with values obtained from simpler models. The model has been implemented in the fluid/envelope code CIRCE and used to study longitudinal confinement in beams with a variety of axial profiles. The effects of errors in the longitudinal-control fields are presented.
Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\omega=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small parameter. The exterior space-time of one family of solutions is arbitrarily close to the exterior Schwarzschild space-time. These nontopological solitons have some similarity with soliton stars, and are proposed as candidates for {\em approximate black holes} for the use in numerical relativity, in particular for treatment of horizon boundary conditions.