Abstract

We propose a novel scheme to generate a cw cold molecular beam by optically guided buffer-gas-cooled molecules around an S-shaped integrated fiber bundle. First we calculate the two-color evanescent field around the fiber bundle and its optical potential for I2 molecules. Then we estimate the guiding efficiency of the output molecular beam and its transverse and longitudinal temperatures based on a classical model. Finally, we study the dynamic process of the molecular guiding by using a classical Monte Carlo simulation, by which we obtain some simulated results consistent with the theoretically calculated results. Our study shows that when the power of the input CO2 laser is 10W and the curvature radius of the fiber bundle is 0.2cm, a cw cold molecular beam with a longitudinal and transverse temperature of 57mK and 0.29mK can be generated by our scheme. It is clear that such a cold molecular beam has some important applications in molecular optics and other fields.

© 2011 Optical Society of America

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  1. K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
    [CrossRef]
  2. T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
    [CrossRef]
  3. E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
    [CrossRef] [PubMed]
  4. J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
    [CrossRef]
  5. D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
    [CrossRef]
  6. H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
    [CrossRef]
  7. Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17, 10706–10717 (2009).
    [CrossRef] [PubMed]
  8. E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
    [CrossRef]
  9. J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
    [CrossRef] [PubMed]
  10. R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
    [CrossRef]
  11. T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
    [CrossRef]
  12. H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
    [CrossRef]
  13. Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
    [CrossRef] [PubMed]
  14. D. Patterson and J. M. Doyle, “Bright, guided molecular beam with hydrodynamic enhancement,” J. Chem. Phys. 126, 154307(2007).
    [CrossRef] [PubMed]
  15. V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
    [CrossRef]
  16. H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
    [CrossRef]
  17. H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
    [CrossRef]
  18. H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
    [CrossRef]
  19. U. Hohm, “Analysis of the vibrationally resolved polarizability spectrum of I2 in the range of the B3Πu+←X1Σg+ transition,” Mol. Phys. 96, 7–13 (1999).
    [CrossRef]
  20. L. Chen, W. Cheng, and J. Ye, “Hyperfine interactions and perturbation effects in the B0u+(Πu3) state of I2127,” J. Opt. Soc. Am. B 21, 820–832 (2004).
    [CrossRef]
  21. A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
    [CrossRef]
  22. W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.
  23. M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
    [CrossRef]
  24. H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
    [CrossRef]
  25. S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
    [CrossRef] [PubMed]

2010

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

2009

D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
[CrossRef]

Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17, 10706–10717 (2009).
[CrossRef] [PubMed]

2008

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

2007

D. Patterson and J. M. Doyle, “Bright, guided molecular beam with hydrodynamic enhancement,” J. Chem. Phys. 126, 154307(2007).
[CrossRef] [PubMed]

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

2006

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
[CrossRef] [PubMed]

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

2004

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

L. Chen, W. Cheng, and J. Ye, “Hyperfine interactions and perturbation effects in the B0u+(Πu3) state of I2127,” J. Opt. Soc. Am. B 21, 820–832 (2004).
[CrossRef]

2002

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

2000

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

1999

H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
[CrossRef]

U. Hohm, “Analysis of the vibrationally resolved polarizability spectrum of I2 in the range of the B3Πu+←X1Σg+ transition,” Mol. Phys. 96, 7–13 (1999).
[CrossRef]

1998

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

1997

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

1995

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Adams, A. W.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Anderson, D. Z.

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Balykin, V. I.

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Barker, P. F.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

Barnett, A. H.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Bell, M. T.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

Berden, G.

H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
[CrossRef]

Bethlem, H. L.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
[CrossRef]

Bishop, A. I.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

Blair, D. E.

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

Chandler, D. W.

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
[CrossRef] [PubMed]

Chavez, I.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Chen, L.

Cheng, W.

Chuska, R. F.

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

Claussen, N. R.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Constant, E.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

Corkum, P. B.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

Cornell, E. A.

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Danilov, J.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

deCarvalho, R.

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

Deng, L.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17, 10706–10717 (2009).
[CrossRef] [PubMed]

Donley, E. A.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Doyle, J. M.

D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
[CrossRef]

D. Patterson and J. M. Doyle, “Bright, guided molecular beam with hydrodynamic enhancement,” J. Chem. Phys. 126, 154307(2007).
[CrossRef] [PubMed]

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

Ellert, C.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

Even, U.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Friedrich, B.

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

Fulton, R.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

Gingell, A. D.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

Goral, K.

T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Guillet, T.

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

Hakuta, K.

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Hohm, U.

U. Hohm, “Analysis of the vibrationally resolved polarizability spectrum of I2 in the range of the B3Πu+←X1Σg+ transition,” Mol. Phys. 96, 7–13 (1999).
[CrossRef]

Ito, H.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Jhe, W.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Johnson, K. S.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Jones, K. M.

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

Julienne, P. S.

T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

Junglen, T.

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Kajita, M.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

Kanamori, H.

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

Kien, F. L.

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Kohler, T.

T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Lett, P. D.

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

Liang, J. Q.

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Libson, A.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Liu, Y.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Meijer, G.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
[CrossRef]

Morinaga, M.

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

Nakata, T.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Narevicius, E.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Narevicius, J.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Ohtsu, M.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Okuda, Y.

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

Olshanii, M.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Ott, M. N.

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

Parthey, C. G.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Patterson, D.

D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
[CrossRef]

D. Patterson and J. M. Doyle, “Bright, guided molecular beam with hydrodynamic enhancement,” J. Chem. Phys. 126, 154307(2007).
[CrossRef] [PubMed]

Pinkse, P. W. H.

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Prentiss, M.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Procter, S. R.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

Raizen, M. G.

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

Ramirez-Serrano, J.

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
[CrossRef] [PubMed]

Rangwala, S. A.

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Rasmussen, J.

D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
[CrossRef]

Rempe, G.

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Renn, M. J.

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Rieger, T.

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Sakai, H.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

Sakaki, K.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Sartakow, B.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

Sekiguchi, T.

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

Shneider, M. N.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

Smith, S. P.

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

Softley, T. P.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

Stapelfeldt, H.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

Strecker, K. E.

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
[CrossRef] [PubMed]

Switzer, R. C.

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

Tarasevitch, A.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

Thomes, W. J.

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

Thompson, S. T.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Tiesinga, E.

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

Tsuji, H.

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

Ubachs, W.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

Weinstein, J. D.

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

Wieman, C. E.

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

Willitsch, S.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

Xia, Y.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17, 10706–10717 (2009).
[CrossRef] [PubMed]

Ye, J.

Yin, J.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Y. Yin, Q. Zhou, L. Deng, Y. Xia, and J. Yin, “Multistage optical Stark decelerator for a pulsed supersonic beam with a quasi-cw optical lattice,” Opt. Express 17, 10706–10717 (2009).
[CrossRef] [PubMed]

Yin, Y.

Yip, R. W.

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

Yun, M.

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Zhou, Q.

Zozulya, A. A.

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Chem. Phys. Lett.

H. Tsuji, Y. Okuda, T. Sekiguchi, and H. Kanamori, “Velocity distribution of the pulsed ND3 molecular beam selected by a quadrupole Stark velocity filter,” Chem. Phys. Lett. 436, 331–334 (2007).
[CrossRef]

Eur. Phys. J. D

T. Junglen, T. Rieger, S. A. Rangwala, P. W. H. Pinkse, and G. Rempe, “Slow ammonia molecules in an electrostatic quadrupole guide,” Eur. Phys. J. D 31, 365–373 (2004).
[CrossRef]

Eur. Phys. J. Spec. Top.

H. L. Bethlem, M. Kajita, B. Sartakow, G. Meijer, and W. Ubachs, “Prospects for precision measurements on ammonia molecules in a fountain,” Eur. Phys. J. Spec. Top. 163, 55–69 (2008).
[CrossRef]

J. Chem. Phys.

D. Patterson and J. M. Doyle, “Bright, guided molecular beam with hydrodynamic enhancement,” J. Chem. Phys. 126, 154307(2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Mol. Phys.

U. Hohm, “Analysis of the vibrationally resolved polarizability spectrum of I2 in the range of the B3Πu+←X1Σg+ transition,” Mol. Phys. 96, 7–13 (1999).
[CrossRef]

Nat. Phys.

R. Fulton, A. I. Bishop, M. N. Shneider, and P. F. Barker, “Controlling the motion of cold molecules with deep periodic optical potentials,” Nat. Phys. 2, 465–468 (2006).
[CrossRef]

Nature

E. A. Donley, N. R. Claussen, S. T. Thompson, and C. E. Wieman, “Atom–molecule coherence in a Bose–Einstein condensate,” Nature 417, 529–533 (2002).
[CrossRef] [PubMed]

J. D. Weinstein, R. deCarvalho, T. Guillet, B. Friedrich, and J. M. Doyle, “Magnetic trapping of calcium monohydride molecules at millikelvin temperatures,” Nature 395, 921 (1998).
[CrossRef]

New J. Phys.

D. Patterson, J. Rasmussen, and J. M. Doyle, “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. Phys. 11, 055018 (2009).
[CrossRef]

Opt. Commun.

H. Ito, K. Sakaki, T. Nakata, W. Jhe, and M. Ohtsu, “Optical potential for atom guidance in a cylindrical-core hollow fiber,” Opt. Commun. 115, 57–64 (1995).
[CrossRef]

Opt. Express

Phys. Chem. Chem. Phys.

J. Ramirez-Serrano, K. E. Strecker, and D. W. Chandler, “Modification of the velocity distribution of H2 molecules in a supersonic beam by intense pulsed optical gradients,” Phys. Chem. Chem. Phys. 8, 2985–2989 (2006).
[CrossRef] [PubMed]

Y. Liu, M. Yun, Y. Xia, L. Deng, and J. Yin, “Experimental generation of a cw cold CH3CN molecular beam by a low-pass energy filtering,” Phys. Chem. Chem. Phys. 12, 745–752 (2010).
[CrossRef] [PubMed]

Phys. Rev. A

V. I. Balykin, K. Hakuta, F. L. Kien, J. Q. Liang, and M. Morinaga, “Atom trapping and guiding with a subwavelength-diameter optical fiber,” Phys. Rev. A 70, 011401 (2004).
[CrossRef]

E. Narevicius, A. Libson, C. G. Parthey, I. Chavez, J. Narevicius, U. Even, and M. G. Raizen, “Stopping supersonic oxygen with a series of pulsed electromagnetic coils: a molecular coilgun,” Phys. Rev. A 77, 051401 (2008).
[CrossRef]

A. H. Barnett, S. P. Smith, M. Olshanii, K. S. Johnson, A. W. Adams, and M. Prentiss, “Substrate-based atom waveguide using guided two-color evanescent light fields,” Phys. Rev. A 61, 023608 (2000).
[CrossRef]

H. Sakai, A. Tarasevitch, J. Danilov, H. Stapelfeldt, R. W. Yip, C. Ellert, E. Constant, and P. B. Corkum, “Optical deflection of molecules,” Phys. Rev. A 57, 2794–2801 (1998).
[CrossRef]

M. J. Renn, A. A. Zozulya, E. A. Donley, E. A. Cornell, and D. Z. Anderson, “Optical-dipole-force fiber guiding and heating of atoms,” Phys. Rev. A 55, 3684–3696 (1997).
[CrossRef]

Phys. Rev. Lett.

S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, “Cold reactive collisions between laser-cooled ions and velocity-selected neutral molecules,” Phys. Rev. Lett. 100, 043203 (2008).
[CrossRef] [PubMed]

H. Stapelfeldt, H. Sakai, E. Constant, and P. B. Corkum, “Deflection of neutral molecules using the nonresonant dipole force,” Phys. Rev. Lett. 79, 2787–2790 (1997).
[CrossRef]

H. L. Bethlem, G. Berden, and G. Meijer, “Decelerating neutral dipolar molecules,” Phys. Rev. Lett. 83, 1558–1561 (1999).
[CrossRef]

Rev. Mod. Phys.

K. M. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, “Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering,” Rev. Mod. Phys. 78, 483–535 (2006).
[CrossRef]

T. Kohler, K. Goral, and P. S. Julienne, “Production of cold molecules via magnetically tunable Feshbach resonances,” Rev. Mod. Phys. 78, 1311–1361 (2006).
[CrossRef]

Other

W. J. Thomes, Jr., M. N. Ott, R. F. Chuska, R. C. Switzer, and D. E. Blair, “Fiber optic cables for transmission of high-power laser pulses in spaceflight applications,” presented at the International Conference on Space Optics, Rhodes, Greece, 4–8 October 2010.

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Figures (5)

Fig. 1
Fig. 1

(a) Structure of the fiber bundle. (b) Schematic diagram of the velocity filter. (c) Transformation of the two coordinates.

Fig. 2
Fig. 2

Casimir potential and 266 nm and 10.6 μm optical potentials for the I 2 molecule. The detailed part of the three potentials in the near field is displayed in the right inset.

Fig. 3
Fig. 3

(a) Transverse profile of the total potential. (b) Radial distribution of the effective total potential.

Fig. 4
Fig. 4

Dependence of the (a) guiding efficiency, (b) transverse temperature, and (c) longitudinal temperature of the guided molecular beam on the laser power P. The data points with error bars are the simulated results, and the curves are the theoretically calculated results.

Fig. 5
Fig. 5

(a) Radial position distribution. (b) Transverse velocity distribution. (c) Longitudinal velocity distribution of the guided molecular beam. The data points with error bars are the simulated results, the solid curves are the distributions of the input molecular beam, and the dotted curve (including the right inset) in (a) is a fit to the simulated result and in (b), (c) is the theoretically calculated result.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

E z core = A 1 J 1 ( U a r ) H z core = B 1 J 1 ( U a r ) E z cladding = A 2 K 1 ( W a r ) H z cladding = B 2 K 1 ( W a r ) ,
E r = 1 ( k 0 2 n i 2 β 2 ) ( i β E z r μ 0 ω r H z ) E φ = 1 ( k 0 2 n i 2 β 2 ) ( i μ 0 ω H z r β r E z ) H r = 1 ( k 0 2 n i 2 β 2 ) ( i β H z r + ε 0 ω n i 2 r E z ) H φ = 1 ( k 0 2 n i 2 β 2 ) ( i ε 0 ω n i 2 E z r β r H z ) .
I red ( r ) = C red 2 ( E r H φ * E φ H r * ) red ,
I blue ( r , φ ) = C blue 2 ( j = 1 124 E r ( j ) j = 1 124 H φ * ( j ) j = 1 124 E φ ( j ) j = 1 124 H r * ( j ) ) blue ,
U red = α 2 ε 0 c I red ,
U blue = α 2 ε 0 c I blue ,
U Cas = 3 8 π c α 4 π ε 0 l 4 ε 1 ε + ( 30 / 23 ) ε + 7 / 23 ,
U total = U red + U blue + U Cas .
f ( x , y ) = 1 π w 2 e x 2 + y 2 w 2 ,
f ( v x , y ) = 1 π v T m e v x , y 2 v T m 2 ,
f ( v z ) = 2 v z v L m 2 e v z 2 v L m 2 ,
x = x y = R [ 1 cos ( z / R ) ] + y cos ( z / R ) z = ( R y ) sin ( z / R ) ,
e x = e x e y = e y cos ( z / R ) + e z sin ( z / R ) e z = e y sin ( z / R ) + e z cos ( z / R ) ,
a = a x e x + [ a y + v z 2 R ] e y + [ a z 2 v y v z R ] e z .
J in = r 1 2 x 2 + y 2 r 2 2 f ( x , y ) d x d y v x 2 + v y 2 f ( v x , v y ) d v x d v y v z > 0 v z f ( v z ) d v z ,
J out = r 1 2 x 2 + y 2 r 2 2 ( f ( x , y ) s ( v x , v y , v z ) f ( v x , v y ) v z f ( v z ) d v x d v y d v z ) d x d y ,
1 2 M ( v x y + v y x ) 2 / r 2 1 2 M v x 2 1 2 M v y 2 + U ( r 2 ) U ( x , y ) C S M v z 2 R ( y + r 2 ) .
T T m = r 1 2 x 2 + y 2 r 2 2 ( f ( x , y ) s ( v x , v y , v z ) ( ε t ) x y k B f ( v x , v y ) f ( v z ) d v x d v y d v z ) d x d y r 1 2 x 2 + y 2 r 2 2 ( f ( x , y ) s ( v x , v y , v z ) f ( v x , v y ) f ( v z ) d v x d v y d v z ) d x d y ,
T L m = r 1 2 x 2 + y 2 r 2 2 ( f ( x , y ) s ( v x , v y , v z ) ( ε t ) z k B f ( v x , v y ) f ( v z ) d v x d v y d v z ) d x d y r 1 2 x 2 + y 2 r 2 2 ( f ( x , y ) s ( v x , v y , v z ) f ( v x , v y ) f ( v z ) d v x d v y d v z ) d x d y ,
a x = F x M , a y = F y M v z 2 R , a z = F z M + 2 v y v z R .

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