Longitudinal dynamics for electrons in the thermal wave model for charged particle beams

Author(s):  
R. Fedele ◽  
G. Miele ◽  
L. Palumbo
2014 ◽  
Vol 80 (2) ◽  
pp. 133-145 ◽  
Author(s):  
Renato Fedele ◽  
Fatema Tanjia ◽  
Dusan Jovanović ◽  
Sergio De Nicola ◽  
Concetta Ronsivalle

AbstractThe standard classical description of non-laminar charged particle beams in paraxial approximation is extended to the context of two wave theories. The first theory that we discuss (Fedele R. and Shukla, P. K. 1992 Phys. Rev. A45, 4045. Tanjia, F. et al. 2011 Proceedings of the 38th EPS Conference on Plasma Physics, Vol. 35G. Strasbourg, France: European Physical Society) is based on the Thermal Wave Model (TWM) (Fedele, R. and Miele, G. 1991 Nuovo Cim. D13, 1527.) that interprets the paraxial thermal spreading of beam particles as the analog of quantum diffraction. The other theory is based on a recently developed model (Fedele, R. et al. 2012a Phys. Plasmas19, 102106; Fedele, R. et al. 2012b AIP Conf. Proc.1421, 212), hereafter called Quantum Wave Model (QWM), that takes into account the individual quantum nature of single beam particle (uncertainty principle and spin) and provides collective description of beam transport in the presence of quantum paraxial diffraction. Both in quantum and quantum-like regimes, the beam transport is governed by a 2D non-local Schrödinger equation, with self-interaction coming from the nonlinear charge- and current-densities. An envelope equation of the Ermakov–Pinney type, which includes collective effects, is derived for both TWM and QWM regimes. In TWM, such description recovers the well-known Sacherer's equation (Sacherer, F. J. 1971 IEEE Trans. Nucl. Sci.NS-18, 1105). Conversely, in the quantum regime and in Hartree's mean field approximation, one recovers the evolution equation for a single-particle spot size, i.e. for a single quantum ray spot in the transverse plane (Compton regime). We demonstrate that such quantum evolution equation contains the same information as the evolution equation for the beam spot size that describes the beam as a whole. This is done heuristically by defining the lowest QWM state accessible by a system of non-overlapping fermions. The latter are associated with temperature values that are sufficiently low to make the single-particle quantum effects visible on the beam scale, but sufficiently high to make the overlapping of the single-particle wave functions negligible. This lowest QWM state constitutes the border between the fundamental single-particle Compton regime and the collective quantum and thermal regimes at larger (nano- to micro-) scales. Comparing it with the beam parameters in the existing accelerators, we find that it is feasible to achieve nano-sized beams in advanced compact machines.


2021 ◽  
Vol 141 ◽  
pp. 106518
Author(s):  
Marijke De Saint-Hubert ◽  
Fabio Castellano ◽  
Paul Leblans ◽  
Paul Sterckx ◽  
Satoshi Kodaira ◽  
...  

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Robert Zimmermann ◽  
Michael Seidling ◽  
Peter Hommelhoff

AbstractElectron and ion beams are indispensable tools in numerous fields of science and technology, ranging from radiation therapy to microscopy and lithography. Advanced beam control facilitates new functionalities. Here, we report the guiding and splitting of charged particle beams using ponderomotive forces created by the motion of charged particles through electrostatic optics printed on planar substrates. Shape and strength of the potential can be locally tailored by the lithographically produced electrodes’ layout and the applied voltages, enabling the control of charged particle beams within precisely engineered effective potentials. We demonstrate guiding of electrons and ions for a large range of energies (from 20 to 5000 eV) and masses (from 5 · 10−4 to 131 atomic mass units) as well as electron beam splitting for energies up to the keV regime as a proof-of-concept for more complex beam manipulation.


Physics Today ◽  
1995 ◽  
Vol 48 (6) ◽  
pp. 59-59
Author(s):  
Martin Reiser ◽  
Edward P. Lee

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