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The magnetic field excited by the offset-pole periodic cusped permanent magnet （OPPCPM） used for focusing the sheet electron beam has been approximately expressed in two different forms for the convenience of future numerical calculation and theoretical analysis, respectively. Firstly, the surface-current-sheet model has been used to approximate the OPPCPM, and an accurate expression has been obtained using Biot-Savart law. This expression would rather be applied to numerical calculation than theoretical analysis because of the complication. The optimization of entrance taper of the OPPCPM has been performed as an example of application of the expression, implying the high efficiency of the calculation brought by the expression. Secondly, to obtain simple expression of the magnetic field for the convenience of future theoretical analysis, the OPPCPM field has been divided into two parts: the periodic cusped magnetic （PCM） field component and the side-focusing magnetic field component. The expressions of the PCM field component have been obtained using the method of undetermined coefficient, while the expressions of the other one have been obtained using two-magnetic-charge-sheet model. The results are useful to study the transportation of the sheet electron beam in the offset-pole PCM field.
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Keywords:
- offset-pole periodic cusped permanent magnetic field /
- surface-current-sheet model /
- two-magnetic-charge-sheets model /
- propagation of the sheet electron beam
[1] ［1］Read M E, Jabotinski V, Miram G, Ives L 2005 IEEE Trans. Plasma Sci. 33 647
[2] ［2］Cheng S, Destler W W, Granatstein V L, Antonsen T M, Jr., Levush B, Rodgers J, Zhang Z X 1996 IEEE Trans. Plasma Sci. 24 750
[3] ［3］Carlsten B E 2005 Nucl. Instrum. Meth. A 550 14
[4] ［4］Zhou J, Chen C 2006 Phys. Rev. ST -Accel. Beams 9 104201
[5] ［5］Burke A, Besong V, Graniund K, Jensen A J, Jongewaard E, Phillips R, Rauenbuehler K, Scheitrum G, Steele R 2006 IEEE IVEC 485
[6] ［6］Humphries S, Russell S, Carlsten B E, Earley L 2005 IEEE Trans. Plasma Sci. 33 882
[7] ［7］Yang J H, Wang Y, Wang S Z 2007 High Power Laser and Particle Beams 19 643
[8] ［8］Basten M A, Booske J H 1999 J. Appl. Phys. 85 6313
[9] ［9］Booske J H, McVey B D, Antonsen T M Jr. 1993 J. Appl. Phys. 73 4140
[10] ］Kyhl R L, Webster H F 1956 IRE Trans. Electron Devices ED-3 1720
[11] ］Webster H F 1955 J. Appl. Phys. 26 1386
[12] ］Davidson R C, Tsang K T, Uhm H S 1988 Phys. Fluids 31 1727
[13] ］Uhm H S, Shahar Ben-Menahem, Yu D 1994 Phys. Plasmas 1 3686
[14] ］Cheng S, Destler W W 1995 Nucl. Instrum. Meth. A 358 200
[15] ］Halbach K 1981 Nucl. Instr. and Meth. 187 109
[16] ］Tatchyn R 1996 Nucl. Instr. and Meth. A 375 500
[17] ］Tatchyn R, Cremer T 1997 Nucl. Instr. and Meth. A 393 114
[18] ］Mikhailichenko A 2001 Proc. Part. Accel. Conf. 3648
[19] ］Biallas G, Benson S, Hiatt T, Neil G, Snyder M 2005 Proc. Particle Accel. Conf. 4093
[20] ］Destler W W, Granatstein V L, Mayergoyz I D, Segalov Z 1986 J. Appl. Phys. 60 521
[21] ］Varfolomeev A A, Bouzouloukov Yu P, Gubankov V V, Ivanchenkov S N, Khlebnikov A S, Osmanov N S, Tolmachev S V 1995 Nucl. Instrum. Meth. A 359 85
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[1] ［1］Read M E, Jabotinski V, Miram G, Ives L 2005 IEEE Trans. Plasma Sci. 33 647
[2] ［2］Cheng S, Destler W W, Granatstein V L, Antonsen T M, Jr., Levush B, Rodgers J, Zhang Z X 1996 IEEE Trans. Plasma Sci. 24 750
[3] ［3］Carlsten B E 2005 Nucl. Instrum. Meth. A 550 14
[4] ［4］Zhou J, Chen C 2006 Phys. Rev. ST -Accel. Beams 9 104201
[5] ［5］Burke A, Besong V, Graniund K, Jensen A J, Jongewaard E, Phillips R, Rauenbuehler K, Scheitrum G, Steele R 2006 IEEE IVEC 485
[6] ［6］Humphries S, Russell S, Carlsten B E, Earley L 2005 IEEE Trans. Plasma Sci. 33 882
[7] ［7］Yang J H, Wang Y, Wang S Z 2007 High Power Laser and Particle Beams 19 643
[8] ［8］Basten M A, Booske J H 1999 J. Appl. Phys. 85 6313
[9] ［9］Booske J H, McVey B D, Antonsen T M Jr. 1993 J. Appl. Phys. 73 4140
[10] ］Kyhl R L, Webster H F 1956 IRE Trans. Electron Devices ED-3 1720
[11] ］Webster H F 1955 J. Appl. Phys. 26 1386
[12] ］Davidson R C, Tsang K T, Uhm H S 1988 Phys. Fluids 31 1727
[13] ］Uhm H S, Shahar Ben-Menahem, Yu D 1994 Phys. Plasmas 1 3686
[14] ］Cheng S, Destler W W 1995 Nucl. Instrum. Meth. A 358 200
[15] ］Halbach K 1981 Nucl. Instr. and Meth. 187 109
[16] ］Tatchyn R 1996 Nucl. Instr. and Meth. A 375 500
[17] ］Tatchyn R, Cremer T 1997 Nucl. Instr. and Meth. A 393 114
[18] ］Mikhailichenko A 2001 Proc. Part. Accel. Conf. 3648
[19] ］Biallas G, Benson S, Hiatt T, Neil G, Snyder M 2005 Proc. Particle Accel. Conf. 4093
[20] ］Destler W W, Granatstein V L, Mayergoyz I D, Segalov Z 1986 J. Appl. Phys. 60 521
[21] ］Varfolomeev A A, Bouzouloukov Yu P, Gubankov V V, Ivanchenkov S N, Khlebnikov A S, Osmanov N S, Tolmachev S V 1995 Nucl. Instrum. Meth. A 359 85
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