The Differential Algebra Based Multiple Level Fast Multipole Algorithm for 3D Space Charge Field Calculation and Photoemission Simulation
AbstractCoulomb interaction between charged particles inside a bunch is one of the most important collective
effects in beam dynamics, becoming even more significant as the energy of the particle beam is lowered
to accommodate analytical and low-Z material imaging purposes such as in the time resolved Ultrafast
Electron Microscope (UEM) development currently underway at Michigan State University. Space
charge effects are the key limiting factor in the development of ultrafast atomic resolution electron
imaging and diffraction technologies and are also correlated with an irreversible growth in rms
beam emittance due to fluctuating components of the nonlinear electron dynamics. In the short pulse
regime used in the UEM, space charge effects also lead to virtual cathode (VC) formation in which the
negative charge of the electrons emitted at earlier times, combined with the attractive surface field,
hinders further emission of particles and causes a degradation of the pulse properties. Space charge and
virtual cathode effects and their remediation are core issues for the development of the next generation
of high-brightness UEMs. Since the analytical models are only applicable for special cases,
numerical simulations, in addition to experiments, are usually necessary to accurately understand the
space charge effect. In this paper we will introduce a grid-free differential algebra (DA) based multiple
level fast multipole algorithm (MLFMA), which calculates the 3D space charge field for n charged
particles in arbitrary distribution with an efficiency of O(n), and the implementation of the DA
based MLFMA to a simulation code for space charge dominated photoemission process.
H. Zhang, J. Portman, Z. Tao, P. Duxbury, C.-Y. Ruan, K. Makino, M. Berz,
Microscopy and Microanalysis 21 Suppl. 4 (2015) 224
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