Eur. Phys. J. D (2014) 68: 198
https://doi.org/10.1140/epjd/e2014-50133-4

Regular Article

Low temperature high current ion beams and laminar flows^⋆

INFN-Laboratori Nazionali di Legnaro, Viale dell’Universitá N. 2, 35020 Legnaro ( PD), Italy

^a e-mail: cavenago@lnl.infn.it

Received: 20 February 2014
Received in final form: 14 April 2014
Published online: 24 July 2014

Abstract

Self-consistent Vlasov-Poisson equilibria for the extraction of ions with low temperature T_i are discussed, with comparison to the laminar flow case T_i = 0, in two dimensional diodes. Curvilinear coordinates aligned with laminar beam flow lines are extended to the low ion temperature case, with a reduced current density j_d, expressed with cathode integrals. This generalizes one-dimensional interpolation between rays along the cathode coordinate to multidimensional integrations, including also the momentum components, so that j_d is free from the granularity defect and noise, typical of standard ray tracing approach. A robust numerical solution procedure is developed, which allows studying current saturated extraction and drift tube effects. A discussion of particle initial conditions determines the emission angles and shows that temperature effect at beam edge is partly balanced by the focus electrode inclination. Results for a typical diode are described, with detail about normalized emittance, here taken strictly proportional to the x − p_x phase space area, for a beam with non uniform velocities.