[mmaimcal] antenna stations

[Simon Radford]

Mark,

How many antenna stations? 

At present, the ALMA plan is n = 64 antennae in m = 5 configurations
with (approximate) diameters of 150 m, 450 m, 1.1 km, 3 km, and 10 km.
If each configuration reuses a fraction, alpha, of the stations in the
next smaller configuration, then the total number of stations 
     N = n * (1 + (m-1) * (1-alpha)) = n * beta.
Here are a few examples: 

 alpha    N    beta   example
   0     320    5     no reuse, upper limit
  10%    295    4.6   area reuse
  1/3    235    3.7   linear reuse  

Each ALMA configuration is roughly three times larger than the next
smaller one. By 'linear reuse,' I mean the station reuse scales as the
relative configuration diameter. I think the VLA scales like this.
'Zoom' configurations, as suggested by Conway (Memos 216 & 260) and
Webster (Memos 214, 233, & 239) might achieve this reuse factor for some
configurations. By 'area reuse,' I mean scaling by the relative areas.
'Filled' configurations would scale like this. Concentric ring
configurations would have little or no reuse. 

It's my impression station reuse has not had high weight in the
configuration studies to date (but see Memos 265 & 260 & references).
These issues will be thrashed out in future configuration work.

Simon