title: Universal instabilities of radio-frequency traps.
abstract: Using standard tools of nonlinear dynamics we analyze recently discovered instabilities of radio-frequency charged-particle traps. In the cw-driven cylindrical Kingdon trap the instabilities occur at the two values eta*(3) =3.6130467...and eta*(4) =4.4311244...of the trap's control parameter eta. Analytical estimates based on the theory of Mathieu functions predict eta*(3) =pi square root of [(363-32 pi(2))/(66 pi square root of (6-48 pi(2))]=3.6923922...and eta*(4) = [(square root of pi)/2) x [(363-32 pi(2))/(square root of (1089+48 pi(2))-12 pi)](1/2) =4.4965466... The kicked Kingdon trap, an analytically solvable model, predicts eta*(3) = 1/3 square root of 105=3.4156502...and eta*(4) = square root of 17=4.1231056... We show that similar instabilities occur in the two-particle Paul trap and the cw-driven spherical Kingdon trap.
authors.affiliation: MIT Center for Space Research, Cambridge, Massachusetts 02139, USA.
authors.forename: I
authors.initials: I
authors.lastname: Garrick-Bethell
authors.forename: Th
authors.initials: T
authors.lastname: Clausen
authors.forename: R
authors.initials: R
authors.lastname: Blümel