Long-term stability of nonlinear particle orbits

4 problems

• Rate of chaotic action diffusion in weakly nonlinear 4D maps

  Open

  Inside the region that looks stable, particles can still drift outward extremely slowly through thin chaotic layers; how fast is not known.

• Do short-time chaos indicators predict long-term orbit stability

  Open

  Quick tests of chaotic behavior over a few thousand turns could replace expensive long simulations if they reliably flag the orbits that eventually escape.

• Error tolerance of nonlinear integrable accelerator lattices

  Partially resolved

  Specially designed nonlinear magnets make orbits regular in theory; how much of that survives real magnet errors and energy spread is open.

• Extrapolating dynamic aperture from a million to a billion turns

  Partially resolved

  Computers can track particles for about a million turns, but colliders store beams for billions; the rule used to extrapolate the stable region is a conjecture.