Outboard (X1A1) toroid vertical focus

The inboard branch toroidal mirror manipulator is shown in Fig. 3.7. The outboard (X1A1) branch toroidal mirror has a major radius of 70.6 m, and a minor radius of $R=0.509$ m. It has a focal length for vertical focusing of

$$f={R \over 2 \sin \theta_{g}},$$ (3.1)

where $\theta_{g}$ is the grazing incidence angle. Using $L_{2}$ as the distance from the toroid to the vertical focus, the change in $L_{2}$ as $\theta_{g}$ is changed is given by

$$\Delta L_{2} = -2 {L_{2}^{2} \over R} \Delta\theta.$$ (3.2)

Since $L_{2}$ is about 7.1 m, to change the $z$ position of the vertical focus point by 100 mm one must adjust the toroid angle by 0.5 mrad. Since the yaw adjustments on the toroid are about 0.3 m apart (check this carefully first!), this corresponds to an adustment of about 150 $\mu$m (or 0.006'') on one of the three adjusters (though of course this will also affect the toroid position in $x\ldots$).

Figure 3.7: Manipulator (McPherson) used to adjust the inboard branch toroidal mirror.