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A numerical solution for the self-consistent differential equations describing the laminar-flow equilibrium in magnetically focused relativistic electron beams is given and proved to be available by comparison with analytical results of solid electron beam in the case of pθ=0 （magnetically shielded sources）. With the numerical method, the space-charge limited current and the externally applied magnetic field of both solid and annular electron beam in three cases of pθ=0,pθ=const and pθ∝r2 （magnetically immerged sources） are presented and compared. It is shown that the conditions at the source with respect to the canonical angular momentum pθ have little effect on the space-charge limited current and the externally applied magnetic field, but more intense annular electron beam generated by the source with pθ=const. can be transported in the same drift tube under lower guided magnetic field than solid ones.
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Keywords:
- relativistic electron beams /
- laminar-flow equilibrium /
- space-charge limited current /
- guided magnetic field
[1] ［1］Miller P B 1982 An Introduction to the Physics of Intense Charged Particle Beam （New York: Plenum）
[2] ［2］Freund H P, Antonsen Jr T M 1996 Principles of Free-electron Lasers （London: CHAPMAN & HALL）
[3] ［3］Reiser M 1977 Phys. Fluids 20477
[4] ［4］Pierce J R 1944 J. Plasma Physics 15 721
[5] ［5］Bennett W H 1934 Phys. Rev. 45 890
[6] ［6］Alfven H 1939 Phys. Rev. 55 425
[7] ［7］Lawson J D 1959 J. Nucl. Energy Pt. C 131
[8] ［8］Kirstein P T, Kino G S, Waters W E 1967 Space-Charged Flow （New York: McGraw-Hill）
[9] ［9］Stephens K F, Ordonez C A 2000 Phys. Plasmas 7 3108
[10] ］Sotnikov G V, Yatsenko T Y 2002 Tech. Phys. 47 535
[11] ］Uhm H S 1993 Phys. Fluids B 5 1919
[12] ］Liu J, Li Z Q 2008 17th International Conference On High-Power Particle Beams Xian, China
[13] ］Li J Q, Mo Y L 2007 Chin. Phys. 16 2716
[14] ］Hramov A, Koronovskii A, Morozov M 2008 Phys. Lett. A 372 876
[15] ］Benford J， Swegle J A 2007 Edi Schamiloglu High Power Microwaves （Second Edition） （Taylor & Francis Group，LLC）
[16] ］Kurkin S A, Hramov A E 2009 Tech. Phys. Lett. 35 23
[1] ［1］Miller P B 1982 An Introduction to the Physics of Intense Charged Particle Beam （New York: Plenum）
[2] ［2］Freund H P, Antonsen Jr T M 1996 Principles of Free-electron Lasers （London: CHAPMAN & HALL）
[3] ［3］Reiser M 1977 Phys. Fluids 20477
[4] ［4］Pierce J R 1944 J. Plasma Physics 15 721
[5] ［5］Bennett W H 1934 Phys. Rev. 45 890
[6] ［6］Alfven H 1939 Phys. Rev. 55 425
[7] ［7］Lawson J D 1959 J. Nucl. Energy Pt. C 131
[8] ［8］Kirstein P T, Kino G S, Waters W E 1967 Space-Charged Flow （New York: McGraw-Hill）
[9] ［9］Stephens K F, Ordonez C A 2000 Phys. Plasmas 7 3108
[10] ］Sotnikov G V, Yatsenko T Y 2002 Tech. Phys. 47 535
[11] ］Uhm H S 1993 Phys. Fluids B 5 1919
[12] ］Liu J, Li Z Q 2008 17th International Conference On High-Power Particle Beams Xian, China
[13] ］Li J Q, Mo Y L 2007 Chin. Phys. 16 2716
[14] ］Hramov A, Koronovskii A, Morozov M 2008 Phys. Lett. A 372 876
[15] ］Benford J， Swegle J A 2007 Edi Schamiloglu High Power Microwaves （Second Edition） （Taylor & Francis Group，LLC）
[16] ］Kurkin S A, Hramov A E 2009 Tech. Phys. Lett. 35 23
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