Focusing Intense Charged Particle Beams with Achromatic Effects for Heavy Ion Fusion

Final focusing systems designed to minimize the effects of chromatic aberrations in the Neutralized Drift Compression Experiment (NDCX-II) are described. NDCX-II is a linear induction accelerator, designed to accelerate short bunches at high current. Previous experiments showed that neutralized drift compression significantly compresses the beam longitudinally ($\sim$60x) in the z-direction, resulting in a narrow distribution in z-space, but a wide distribution in p$_z$-space. Using simple lenses (e.g., solenoids, quadrupoles) to focus beam bunches with wide distributions in p$_z$-space results in chromatic aberrations, leading to lower beam intensities (J/cm$^2$). Therefore, the final focusing system must be designed to compensate for chromatic aberrations. The paraxial ray equations and beam envelope equations are numerically solved for parameters appropriate to NDCX-II. Based on these results, conceptual designs for final focusing systems using a combination of solenoids and/or quadrupoles are optimized to compensate for chromatic aberrations. Lens aberrations and emittance growth will be investigated, and analytical results will be compared with results from numerical particle-in-cell (PIC) simulation codes.