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Beam Sizes

by Stefan Hild — last modified 2008-06-25 21:43

Preliminary calculations for determining the beam size in the core interferometer.


A detailed analysis of the beam size for Advanced Virgo can be found in the following Virgo note:

VIR-038B-08"Advanced Virgo Design: Preliminary Revision of the Beam Size and the Test Mass Curvatures",Stefan Hild and Andreas Freise

In Addition a brief and simplified summary is given on this wiki page (see below).


Current working set of Beam sizes and mirror curvatures


The following numbers give a consistent, but still preliminary set of beam sizes and mirror curvatures:

  • Beam radius (1/e^2 in power) at the main test masses = 6.0 cm
  • Radius of curvature of main mirrors (IMX, IMY, EMX, EMY) = 1531 m
  • Radius of curvature of recycling mirrors = 1068 m
  • Beam waist (radius 1/e^2 in power) inside the main arm cavities = 8.5 mm


The calculations in more detail


As state above this is a brief and highly simplified description of the beam size analysis. To get the full documentation, please have a look at the Virgo note mentioned above. If you only need a short version, please go ahead reading this page.

The image below shows the geometry of an Advanced Virgo test mass including its coating (green area). The size of the coating is limited by two factors: First there need to be flats at th side of the mirror (for suspension) and second there needs to some space (x) between the edge of the coating and the im of the mirror.

beamsize3




















Using the following equation to determine the maximum size of the coating

beamsize1





We can derive the following beam radii in dependence of the the flat size. The second row shows the beam radii for a coating radius to beam radius ratio of 2.5, while the last row is for a bit safer ratio of 3.

beamsize2






From the table above we see, that possible beam radii range from about 5.5 to 6.5 cm. The corresponding radii of curvature for the main test masses as well as for the recycling mirrors are displayed in the table below:

beamsize5






For the time being we use a beam radius of 6.0 cm as a working-value.

The corresponding size of the beam waist inside the main arm cavities is 8.5 mm (radius 1/e^2 in power).



Documentation of Simulation files

The actual simulations persented here made use of:

  • Finesse 0.99.7
  • FinesseTools 0.3.1
  • The OSD-Tool-function: OSD_ROC.m
  • A parameter set derived from: advirgo_base_14062008.kat