Experiments to Control Atom Number and Phase-Space Density in ...

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Figure 4.3: Helicoflex seal. (a) The narrow ridges along the top and bottom concentrate
the compression load. (b) A metal jacket surrounds a helical spring. During compression
the spring deformes, creating a vacuum seal.
4.2 Magnetic Systems
Electro-magnets create magnetic fields serving multiple purposes during the course
of the experiment. These fields can be calculated using the Biot-Savart-law
d B = µ0I d L× Ir
4πr 2 . (4.1)
The exact expression for the magnetic field of a circular loop of wire, through which a
current I is flowing, can be derived from this equation. The axial and radial magnetic
fields of a loop with radius R placed a distance D away from the origin are given by
Bz = µI 1
2π(R+ρ)
2 +(z −D) 2
K(k 2 )+ R2 −ρ2 −(z −D) 2
(R−ρ) 2 +(z −D) 2E(k2
) (4.2)
Bρ = µI z −D
2πρ(R+ρ)
2 +(z −D) 2
−K(k 2 )+ R2 +ρ2 −(z −D) 2
(R−ρ) 2 +(z −D) 2E(k2
) , (4.3)
where
k 2 =
4Rρ
(R+ρ) 2 +(z −D) 2.
(4.4)
K(k 2 ) andE(K 2 ) are the complete elliptical integrals of the first and second kind. Useful
approximations to this exact expression can be found in [68].
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