ABSTRACT
In Chapter 8, the formal theory of the production of an atomic beam by a beamforming impedance when it is a single tube has been presented. In Section 9.2 we provide easily applied relationships that allow the atomic beam properties to be predicted for any atom in practical circumstances. The limitations are that Γ should be sufciently large and that the gas pressure should be sufciently low that the beam shape is cusp shaped as shown in Figure 1.3 rather than approaching the cosine distribution of Figure 1.1. These limitations, which are normally achieved in practice for a well-collimated beam, mean that the equations are insensitive to tube end effects. Hence the gas density in the entrance plane of the tube ZP is assumed to be the same as that of the ambient gas in VP so that no allowance is made for the pressure drop due to the gas ow in the tube. However, the gas density in the tube exit plane ZV is not assumed to be the same as the zero of V0, since we are following Zugenmaier’s (1966) approach that is discussed in Section 8.5.4. The theoretical tube end effects are discussed in Section 8.5.3. Further discussion of them is deferred to Section 12.4, since their existence could be a source of a disagreement between experiment and theories that do not take them adequately into account. For simplicity the shape of the distribution is also expressed in terms of the halfwidth. If the detailed shape of the distribution is required, this must also be calculated.
