Space-charge transport limits of ion beams in periodic quadrupolefocusing channels Page: 2 of 13
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The maximum transportable current density of an ion beam with high space-
charge intensity propagating in a periodic focusing lattice is a problem of
practical importance[1,2]. Accelerator applications such as Heavy Ion Fusion
(HIF), High Energy Density Physics (HEDP), and transmutation of nuclear
waste demand a large flux of particles on target. A limit to the maximum cur-
rent density can result from a variety of factors: instability of low-order mo-
ments of the beam describing the centroid and envelope, instability of higher
order collective modes internal to the beam, growth in statistical phase-space
area (rms emittance growth), excessive halo generation, and species contam-
ination associated with issues such as the electron cloud problem. Simula-
tions were first used to analyze the maximum current density transportable in
quadrupole channels[3,4] and provided guidance beyond initial heuristic esti-
mates. Experiments later obtained results consistent with simulations[1,2].
The present work describes a promising new approach toward predicting the
maximum transportable current density in a periodic quadrupole lattice due
to intrinsic space-charge limits. Previous studies to predict space-charge
related transport limits in the absence of focusing errors and species contam-
ination have not proved fully successful beyond a moment level description of
low-order beam instabilities. Although moment-based centroid and envelope
descriptions reliably predict regions of parametric instability where machines
cannot operate[8,7], such models are overly optimistic when compared to sim-
ulations and experiments which observe degraded transport due to emittance
growth and particle losses where the moment models predict stability[1-4]. On
the other hand, higher-order collective mode theories based on the equilibrium
KV distribution predict broad parametric regions of instability where sta-
bility is observed in simulations with more realistic distributions[3,4] and in
experiment[1,2]. The space-charge limit model proposed is based on parti-
cles oscillating outside, but near the beam edge exchanging energy with the
oscillating space-charge field of a envelope matched beam core leading to in-
creased particle oscillation amplitude, emittance blow-up, and particle losses.
This model can be applied to a wide range of matched core distributions and
does not require an equilibrium core - which circumvents the practical problem
of no smooth core equilibrium distribution being known. The increased un-
derstanding the origin of the observed limits obtained promises more reliable
design of optimal intense beam transport channels.
We denote the phase advance of particles oscillating in a periodic focusing
lattice in the presence and absence of beam space-charge by a and ao (both
measured in degrees per lattice period)[7,8]. The undepressed phase-advance
ao provides a measure of the strength of the linear applied focusing forces
of the lattice that is relatively insensitive to the details of the lattice. ao
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Lund, S. M. & Chawla, S. R. Space-charge transport limits of ion beams in periodic quadrupolefocusing channels, article, February 23, 2006; United States. (digital.library.unt.edu/ark:/67531/metadc887941/m1/2/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.