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The cluster size is an important parameter in the study on the interaction of intense laser pulse with cluster jet produced by the gas adiabatic expansion through a nozzle into vacuum. The Hagena scaling law is usually used to estimate the average cluster size. However, there is the deviation of average cluster size from the prediction by the scaling law in the case that the conical nozzle is used at the high gas backing pressure. In this work, firstly the equivalent diameter of conical nozzle is re-calculated in detail, and then the relation between deq and the radial dimension of the cluster jet is obtained. As an example, the images of Rayleigh scattering light by argon cluster jet at different backing pressures are recorded to investigate the dimensions of cluster jet. And then the corresponding theoretical dimensions based on the idealized straight streamline model in the scaling law are compared with the experimental dimensions. It is found that the experimental dimension is larger than the theoretical one, and is related to the gas backing pressure. This under-estimation of theoretical cluster jet dimension leads to the over-estimation of the equivalent diameter of conical nozzle which is responsible for the cluster size deviation in Hagena scaling laws.
[1] Shao Y L, Ditmire T, Tisch J W G, Springate E, Marangos J P, Hutchinson M H R 1996 Phys. Rev. Lett. 77 3343
[2] Ditmire T, Tisch J W G, Springate E, Mason M B, Hay N, Smith R A, Marangos J, Hutchinson M H R 1997 Nature 386 54
[3] McPherson A, Thompson B D, Borisov A B, Boyer K, Rhodes C K 1994 Nature 370 631
[4] Zweiback J, Cowan T E, Hartley J H, Howell R, Wharton K B, Crane J K, Yanovsky V P, Hays G, Smith R A, Ditmire T 2002 Phys. Plasmas 9 3108
[5] Ditmire T, Zweiback J, Yanovsky V P, Cowan T E, Hays G, Wharton K B 1999 Nature 398 489
[6] Fukuda Y, Faenov A Ya, Tampo M, Pikuz T A, Nakamura T, Kando M, Hayashi Y, Yogo A, Sakaki H, Kameshima T, Pirozhkov A S, Ogura K, Mori M, Esirkepov T Zh, Koga J, Boldarev A S, Gasilov V A, Magunov A I, Yamauchi T, Kodama R, Bolton P R, Kato Y, Tajima T, Daido H, Bulanov S V 2009 Phys. Rev. Lett. 103 165002
[7] Kumarappan V, Kim K Y, Milchberg H M 2005 Phys. Rev. Lett. 94 205004
[8] Mohamed T W, Chen G L, Kim J, Geng X T, Ahn J, Kim D E 2011 Opt. Express 19 15919
[9] Chen G L, Geng X T, Mohamed T W, Xu H X, Mi Y M, Kim J, Kim D E 2012 Opt. Commu. 285 2627
[10] Hagena O F 1992 Rev. Sci. Instrum. 63 2374
[11] Hagena O F 1981 Surf. Sci. 106 101
[12] Pauly H 2000 Atom Molecule and cluster Beams I (Springer-verlag Berlin Heidelberg New York) p81-85
[13] Scoles G 1988 Atomic and Molecular Beam Methods (New York: Oxford University Press) p22
[14] Smith R A, Ditmire T, Tisch J W G 1998 Rev. Sci. Instrum. 69 3798
[15] Kim K Y, Kumarappan V, Michberg H M 2003 Appl. Phys. Lett. 83 3210
[16] DeArmond F M, Suelzer J, Masters M F 2008 J. Appl. Phys. 103 093509
[17] Dorchies F, Blasco F, Caillaud T, Stevefelt J, Stenz C, Boldarev A S, Gasilov, V A 2003 Phys. Rev. A 68 023201
[18] Lu H Y, Ni G Q, Li R X, Xu Z Z 2010 J. Chem. Phys. 132 124303
[19] Chen G L, Kim B, Ahn B, Kim D E 2010 J. Appl. Phys. 108 064329
[20] Fu P T, Han J F, Mou Y H, Han D, Yang C W 2011 Acta Phys.Sin. 60 053602 (in Chinese) [付鹏涛, 韩纪锋, 牟艳红, 韩丹, 杨朝文 2011 60 053602]
[21] Gao X, Wang X, Shim B, Arefiev A V, Korzekwa R, Downer M C 2012 Appl. Phys. Lett. 100 064101
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[1] Shao Y L, Ditmire T, Tisch J W G, Springate E, Marangos J P, Hutchinson M H R 1996 Phys. Rev. Lett. 77 3343
[2] Ditmire T, Tisch J W G, Springate E, Mason M B, Hay N, Smith R A, Marangos J, Hutchinson M H R 1997 Nature 386 54
[3] McPherson A, Thompson B D, Borisov A B, Boyer K, Rhodes C K 1994 Nature 370 631
[4] Zweiback J, Cowan T E, Hartley J H, Howell R, Wharton K B, Crane J K, Yanovsky V P, Hays G, Smith R A, Ditmire T 2002 Phys. Plasmas 9 3108
[5] Ditmire T, Zweiback J, Yanovsky V P, Cowan T E, Hays G, Wharton K B 1999 Nature 398 489
[6] Fukuda Y, Faenov A Ya, Tampo M, Pikuz T A, Nakamura T, Kando M, Hayashi Y, Yogo A, Sakaki H, Kameshima T, Pirozhkov A S, Ogura K, Mori M, Esirkepov T Zh, Koga J, Boldarev A S, Gasilov V A, Magunov A I, Yamauchi T, Kodama R, Bolton P R, Kato Y, Tajima T, Daido H, Bulanov S V 2009 Phys. Rev. Lett. 103 165002
[7] Kumarappan V, Kim K Y, Milchberg H M 2005 Phys. Rev. Lett. 94 205004
[8] Mohamed T W, Chen G L, Kim J, Geng X T, Ahn J, Kim D E 2011 Opt. Express 19 15919
[9] Chen G L, Geng X T, Mohamed T W, Xu H X, Mi Y M, Kim J, Kim D E 2012 Opt. Commu. 285 2627
[10] Hagena O F 1992 Rev. Sci. Instrum. 63 2374
[11] Hagena O F 1981 Surf. Sci. 106 101
[12] Pauly H 2000 Atom Molecule and cluster Beams I (Springer-verlag Berlin Heidelberg New York) p81-85
[13] Scoles G 1988 Atomic and Molecular Beam Methods (New York: Oxford University Press) p22
[14] Smith R A, Ditmire T, Tisch J W G 1998 Rev. Sci. Instrum. 69 3798
[15] Kim K Y, Kumarappan V, Michberg H M 2003 Appl. Phys. Lett. 83 3210
[16] DeArmond F M, Suelzer J, Masters M F 2008 J. Appl. Phys. 103 093509
[17] Dorchies F, Blasco F, Caillaud T, Stevefelt J, Stenz C, Boldarev A S, Gasilov, V A 2003 Phys. Rev. A 68 023201
[18] Lu H Y, Ni G Q, Li R X, Xu Z Z 2010 J. Chem. Phys. 132 124303
[19] Chen G L, Kim B, Ahn B, Kim D E 2010 J. Appl. Phys. 108 064329
[20] Fu P T, Han J F, Mou Y H, Han D, Yang C W 2011 Acta Phys.Sin. 60 053602 (in Chinese) [付鹏涛, 韩纪锋, 牟艳红, 韩丹, 杨朝文 2011 60 053602]
[21] Gao X, Wang X, Shim B, Arefiev A V, Korzekwa R, Downer M C 2012 Appl. Phys. Lett. 100 064101
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