[en] The low-energy-beam transport (LEBT) system for the Low-Energy Demonstration Accelerator (LEDA) transports the beam from the ion-source plasma surface to the LEDA RFQ entrance. The code PARMELA performed these simulations of the beam transport through the LEBT. This code can simultaneously transport three particle types of different charge-to-mass ratio. Electrostatic fields, magnetic fields, and space charge influence the beam particles in this simulation. The electrostatic fields exist in the ion-source extractor. The magnetic field exists in the ion source and in the solenoid lenses. The e^- particles, introduced into the beam of H⁺ and H₂⁺, simulate the space charge neutralization by the residual gas in the LEBT. The H⁺ and H₂⁺ ions leaving the source emerge from a longitudinal magnetic field, which causes the beam to rotate