Simulating Electron Clouds in Heavy-Ion Accelerators Page: 4 of 30
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volumetric source such as is obtained by ionization of neutral gas filing the beam pipe, and
electron desorption from ion beam scrape-off at the beam pipe. Section V is a summary and
discussion of the results.
II. SIMULATION MODEL
Modeling electron cloud effects in heavy-ion accelerators (and, we believe, other accel-
erators as well) requires self-consistent solution of electrons and ions. This is because the
dominant sources of electrons are associated with loss of beam ions, and (as shown in Ref.
[4]) the interaction of electrons with ions alters the ion beam propagation in such a way
as to alter ion beam loss. Furthermore, the electron dynamics depends on the ion distri-
bution becaue of its high space charge potential. Hence, a one-way chain of calculations is
insufficient.
Our approach to self-consistent electron and ion simulation has been to extend the WARP
code. WARP at its core is a multi-species three-dimensional electrostatic particle-in-cell
(PIC) code, with specialized capabilities to include the applied magnetic and electrostatic
fields and bounding conductors found in particle accelerators. To this core, we have added
modules for secondary electron emission and ion-induced electron desorption [from the
Computational Modules for Electron Effects (CMEE) library[7], derived from routines in
the POSINST high-energy-physics accelerator code[8]), first-cut models for ion reflection at
walls and ionization source terms, and the large-timestep electron mover described below.
We have, in development off-line, models for neutral-gas desorption and transport, charge
exchange, and improved models of ion reflection and ionization.
Self-consistent simulation of electrons and ions requires simulation of electrons in the
quadrupole magnets as well as in the gaps between magnets, and running the simulation
long enough to simulate the passage of the ion beam. This results in a broad range of time
scales, ranging from the electron cyclotron period (10-10 - 10-41 s) through the ion beam
transit time (10-5 - 10-7 s). The shortest electron cyclotron period is typically one to two
orders of magnitude shorter than the next-shortest timescale, usually the electron bounce
time in the combined beam-potential and magnetic wells.
We have developed a mover for electrons that interpolates between full electron dynamics
and drift kinetics. The algorithm is briefly mentioned in Ref. [4]. The algorithm builds upon4
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Cohen, R. H.; Friedman, A.; Kireeff Covo, M.; Lund, S. M.; Molvik, A. W.; Bieniosek, F. M. et al. Simulating Electron Clouds in Heavy-Ion Accelerators, article, April 7, 2005; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc788548/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.