Improving the specularity of magnetic mirrors for atoms

European Physical Journal D

Volumn 7, Issue 3, 1999, Pages 351-359

  Zabow, G ^a   Drndic M ^a   Thywissen, J H ^a   Johnson, K S ^a,b   Westervelt, R M ^a   Prentiss, M ^a  

^a HARVARD UNIVERSITY   (United States)

^b Igen International Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MAGNETIC FIELDS; NUMERICAL METHODS; WIRE;

ANGULAR DEVIATIONS; ANTI-PARALLEL CURRENTS; CURRENT CARRYING WIRE; INHOMOGENEOUS MAGNETIC FIELD; NEUTRAL ATOMS; OPTIMAL TURNING; SPECULAR REFLECTIONS; SPECULARITIES;

MIRRORS;

EID: 0033473138     PISSN: 14346060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s100530050578     Document Type: Article

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20. Recent experiments conducted at the Institut d'Optique (Orsay, France) have since verified the predictions made here of an optimal turning height and an even/odd parity effect.
21. The B-field above a mirror of circular cross-sectional wires is easily calculable by noting that it is the same as that for a mirror of delta-function point wires - the surrounding Amperian loops map identical fields for both systems.
22. We also assume atoms with sufficiently large magnetic moments/small incident energies such that required reflecting field strengths are small and the potential depends only linearly on the B-field magnitude (linear Zeeman regime). Quantitative changes to results quoted here may be needed if stronger reflecting B-fields are required.
23. An alternative transition height is the start of the second region (rather than its middle) and can be approximated as that where the additional line's contribution is of similar magnitude to the B-field roughness, rather than to the B-field magnitude itself. This implies equating the current line B-field to the second term in (2) (normally the leading roughness term). The exact transition height can then vary substantially through its dependence on the wire profiles.
24. 2 mirror (L = 1 cm, a = 200 μm)) the curvature at all heights of interest can be shown negligible compared to other roughness contributions.
25. 5, limiting any spatial variations in resistivity/current density accordingly.
26. As Sidorov et al. note, second order endcap correction is achieved by placing the endcap wires at precisely a/4, instead of the mirror wire spacing a/2, from the mirror edge.
27. In this paper we assume perfect mirror manufacture. However, imperfections in mirror manufacture can also be modeled as additional intrinsic stray/error fields interfering with the infinite mirror harmonics. Fortunately, the same total current flows everywhere in the series mirror circuit, reducing effects of manufacture error.
28. J.H. Thywissen, M. Olshanii, G. Zabow, M. Drndić, K.S. Johnson, R.M. Westervelt, M. Prentiss, Eur. Phys. J. D 7, 361 (1999).
29. Recently, E. Hinds has independently suggested an alternative means, combining magnetic and electric forces, to create a similar series of waveguides: E.A. Hinds, in New Directions in Atomic Physics, edited by C.T. Whelan (Plenum, in press).
30. RMS of 0.1 mrad could be further reduced if a larger holding field were applied, or if higher order correcting endcaps were used. Second order (x-edge) endcap correction can reduce ORMS to a few μrad. However, we show only first order endcap calculations, since other, previously negligible, higher order effects dominate before reaching this μrad level.