Status and Challenges in Beam Crystallization

During the past several decades, beam crystallization has been studied both theoretically and experimentally. Theoretical investigations have been numerical, mainly using computer modeling based on the method of molecular dynamics (MD), and analytical, based on phonon theory. Experimental investigations involve both ion storage rings and ion traps using both electron and laser beam cooling. Topics of interests include crystal stability in various accelerator lattices and under different beam conditions, colliding crystalline beams, crystalline beam formation in shear-free ring lattices with both magnets and electrodes, experimental simulation of alternating-gradient conditions with an ion trap, tapered cooling and coupled cooling, and beam dynamics at different temperature regime as the beam is cooled from high to low temperature. In this paper, we first review theoretical approaches and major conclusions pertaining to beam crystallization. Then, we analyze conditions and methods of the various major experiments. Finally, we discuss, both theoretically and experimentally, some improvements, open questions, and challenges in beam crystallization.