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Message ID: 469     Entry time: Thu May 8 01:50:25 2008
Author: rana 
Type: Summary 
Category: ASC 
Subject: Arm Cavity HOM Resonances 
Nothing new, but I calculated the frequencies of the first 22 higher order transverse modes and thought I might as well list them here.

To do this I took formula (23) from page 762 of Siegmans book and put it into this form:
         f_fsr
dfmn =   ----- * (m+n) * acos(sqrt(g1*g2))
           pi

and then calculated them from m+n = 1..22 (22 is not a magic number).

I also used the 'mod' function of matlab to calculate the frequency mod FSR so that we would know how far away
from a cavity resonance it is. I took as parameters: Larm = 38.55 m, Ritm = 1e6 m, Retm = 57.1 m. Kirk measured
the arm length some time ago; we need to measure the arm g-factor...maybe we'll put Tobin on this when he comes
by for a visit.

1.1936 (TEM01, TEM10)
2.3871
3.5807
0.8859 (TEM22, TEM13, TEM31)
2.0795
3.2730
0.5782
1.7718
2.9654
0.2706 (TEM55, ...)
1.4641
2.6577
3.8512
1.1564
2.3500
3.5436
0.8488
2.0423
3.2359
0.5411
1.7347
2.9282
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