u03b8 l 0 u03bc l g ue89e ue89e 2 eq ue89e 9 equations 9 and 10 can be combined to obtain an expression relating the field b 2 with the air gap l g2 and the field b 1 with initial air gap l g1 b 2 b 1 ue89e l 0 u03bc l g ue89e ue89e 1 l 0 u03bc l g ue89e ue89e 2 u2245 b 1 ue89e l g ue89e ue89e 1 l g ue89e ue89e 2 eq ue89e 10 ue89e thus eq ue89e 11 f 1 f 2 b 1 2 b 2 2 eq ue89e 12 f 2 f 1 ue89e b 2 2 b 1 2 eq ue89e 13 f 2 f 1 ue89e b 1 ue89e l g ue89e ue89e 1 l g ue89e ue89e 2 2 b 1 2 eq ue89e 14 which can be simplified to obtain the lsm force as a function of lsm gap f 2 l g ue89e ue89e 1 l g ue89e ue89e 2 2 ue89e f 1 eq ue89e 15 a similar analysis can be conducted for the eds system the peak magnetic field at the surface of halbach array b 0 is b 0 b r ue8a0 1 e kd ue89e sin ue89e u03c0 m u03c0 m eq ue89e 16 where b r is the residual permanent magnet flux density p y b 0 2 u03bc ue89e 1 1 u03b1 2 ue89e e 2 ue89e ky eq ue89e 17 where a is.