  Conventional magnetic transverse focusing in conventional linear accelerators
represents a high fraction of their cost and complexity. Both transverse and
longitudinal focusing can be obtained from the radio frequency field by using
the technique known as Alternating Phase Focusing. The design of suitable
sequences has been difficult, without direct theoretical support, inhibiting
Alternating Phase Focusing adoption. Synthesis of reported details and new
physics and technique result in a new, general method for designing practical
Alternating Phase Focusing linear accelerators. Very long sequences with high
energy gain factors are demonstrated, motivated by the desire to accelerate
particles over a factor of 500-600 energy gain. The method is demonstrated with
simple dynamics and no space charge, later incorporation of space charge and
more accurate elements is straight forward. Alternating Phase Focusing can now
be another practical approach in the linear accelerator designer repertoire.
Alternating Phase Focusing can be used in addition to conventional magnetic
focusing, and could be useful in minimizing the amount of additional magnetic
focusing needed to handle a desired amount of beam current.
