Bunched beam envelope equations including image effects from a cylindrical pipe

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 6, 1997, Pages 7591-7605

  Allen, Christopher K ^a   Reiser, Martin ^b  

^a TECHNO SCIENCES INC   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGED PARTICLES; DIFFERENTIAL EQUATIONS; ELECTRIC SPACE CHARGE; FOURIER TRANSFORMS; GREEN'S FUNCTION; INTEGRATION; LIGHT PROPAGATION; NUMERICAL METHODS; PIPE; PROBABILITY DENSITY FUNCTION;

BESSEL SERIES EXPANSION; BUNCHED BEAM ENVELOPE EQUATIONS; CONVOLUTION THEOREM; CYLINDRICAL PIPE; MAXWELL-BOLTZMANN DISTRIBUTION;

PARTICLE BEAMS;

EID: 0031168919     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.7591     Document Type: Article

References (17)

1. O D. Kellogg, Foundations of Potential Theory (Dover, New York, 1953), pp. 192–194.
2. R L. Gluckstern, Fermilab Internal Report No. TM-1402, 1986 (unpublished).
3. T D. Newton, Can. J. Phys.44, 3137 (1966).
4. D. Neuffer, IEEE Trans. Nucl. Sci.NS-26, 3031 (1979).
5. C K. Allen, N. Brown and M. Reiser, Part. Accel.45, 149 (1994).
6. C K. Allen and M. Reiser, Phys. Rev. E54, 2884 (1996).
7. C K. Allen and M. Reiser, Part. Accel.48, 193 (1995).
8. F R. Sacherer, IEEE Trans. Nucl. Sci.NS-18, 1105 (1971).
9. I M. Kapchinskij and V V. Vladimirskij, Proceedings of the International Conference on High-Energy Accelerators and Instrumentation (CERN, Geneva, 1959), pp. 274–288.
10. For details of these derivations, see C. K. Allen, Ph.D. disseration, University of Maryland, 1996, Secs, 1.4.4, 3.7.3, and 3.8.3.
11. Martin Reiser, Theory and Design of Charged Particle Beams (Wiley, New York, 1994), Sec. 4.4.
12. These equations are found using a derivation similar to that of Sacherer in Ref. 5.
13. The derivation is similar to that done for the Helmholtz equation by I. Stakgold, Green’s Function and Boundary Value Problems (Wiley, New York, 1979), pp. 459–462.
14. For a broad description of Fourier transform properties see R N. Bracewell, Fourier Transform and its Application, 2nd ed. (McGraw-Hill, New York, 1978).
15. F. Oberhettinger, Table of Fourier Transforms and Fourier Transforms of Distributions (Springer-Verlag, Berlin, 1990), p. 95.
16. This transform is computed directly using the residue theorem, for details of this calculation see Ref. 10, Sec. 3.5.4.
17. This transform is computed by comparing the two alternate expression for the Green’s function; for details of this calculation, see Ref. 10, Sec. 3.5.4.