Summary form only given, as follows. In order to satisfy the drive profile requirements for inertial confinement fusion implosions, the beam current is a function of time. Since the beam current is high (kiloampere) and the pulse duration is short (10 ns), it is not practical to change the current in the final focusing quadrupoles. One can focus a beam with variable current using constant strength quadrupoles by realizing the following conditions: (1) the beam radius is proportional to the square root of the line-charge density; (2) the beam density profile remains uniform after radial expansion even in the presence of longitudinal compression; and (3) the beam can be formed into any reasonable pulse shape with the simultaneous removal of longitudinal velocity tilt. These predictions were confirmed by CONDOR particle-in-cell simulations. Beam line designs using the TRACE envelope code show that these are windows in parameter space where spot size remains relatively constant as current varies.
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