Transverse centroid oscillations in solenoidially focused beam transport lattices Page: 1 of 20
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Transverse centroid oscillations in solenoidially focused
beam transport lattices
Steven M. Lund
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
Christopher J. Wootton and Edward P. Lee
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
Linear equations of motion are derived that describe small-amplitude cen-
troid oscillations induced by displacement and rotational misalignments of the
focusing solenoids in the transport lattice, dipole steering elements, and initial
centroid offset errors. These equations are analyzed in a local rotating Larmor
frame to derive complex-variable "alignment functions" and "bending functions"
that efficiently describe the characteristics of the centroid oscillations induced
by mechanical misalignments of the solenoids and dipole steering elements. The
alignment and bending functions depend only on properties of the ideal lattice
in the absence of errors and steering and have associated expansion amplitudes
set by the misalignments and steering fields. Applications of this formulation
are presented for statistical analysis of centroid deviations, calculation of actual
lattice misalignments from centroid measurements, and optimal beam steering.
Key words: solenoid, transport, centroid, steering, alignment
PA CS: 29.27.Bd, 41.75.-i, 41.85.-p, 52.59.Sa
Solenoidal focusing is employed in a variety of ion and electron beam trans-
port applications such as ion beam driven experiments in warm dense matter,
intense electron beams for driving flash x-ray radiography, and electron cool-
ing for hadron beams[3, 4]. Such applications typically require precise control of
the beam centroid to: control the placement of the beam spot on target, main-
tain alignment of the beam with the field in cooling applications, and control a
variety of deleterious processes that are enhanced with increasing amplitude of
centroid oscillations in the machine. Effects enhanced include nonlinear image
charges and currents, applied field nonlinearities, and corkscrew effects[5, 6].
Email addresses: SMLund@llnl.gov (Steven M. Lund)
Preprint submitted to Elsevier
8 August, 2008
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Lund, Steven M.; Wootton, Christopher J. & Lee, Edward P. Transverse centroid oscillations in solenoidially focused beam transport lattices, article, August 1, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc894569/m1/1/: accessed November 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.