TCS noise calculations

Go down

TCS noise calculations

Post  Alessio on Mon Nov 17, 2008 3:27 pm

The heating profile of the AXICON can be fitted with a finction of this kind:
I(r)=2r^2/w1^2*4*(w2^2-r^2)^2/w2^4*exp(-2r^2/w1^2)
with w1=0.099 and w2=0.0048 for our present telescope (see attached plot).



Considering that r^2=x^2+y^2, the above function can be rewritten as:
I(x,y)=8/(w1^2*w2^4)*(w2^4*(x^2+y^2)-2w2^2*(x^2+y^2)^2+(x^2+y^2)^3)*exp(-2(x^2+y^2)/w1^2)
As stated in LIGO-T060224-00-D, to compute the flexural noise it is necessary to consider the first derivative of I(x,y) in x and y. After some algebra (if the calculations are right), I get:
dI/dy=16y/(w1^2*w2^4)*exp(-2(x^2+y^2)/w1^2)*(w2^4-2w2^2*(x^2+y^2)*(2+w2^2/w1^2)+(x^2+y^2)^2*(3+4w2^2/w1^2)-2/w1^2*(x^2+y^2)^3)
but considering that w2^2/w1^2=2.5e-3, we can approximate the above expression to:
dI/dy=16y/(w1^2*w2^4)*exp(-2(x^2+y^2)/w1^2)*(w2^4-4w2^2*(x^2+y^2)+3*(x^2+y^2)^2-2/w1^2*(x^2+y^2)^3)
avatar
Alessio

Posts : 127
Join date : 2008-11-07
Age : 46
Location : Rome

View user profile

Back to top Go down

RIN requirements

Post  Alessio on Tue Nov 18, 2008 5:29 pm

Using dI/dy found in the previous topic, it is possible to evaluate the RIN requirements in case of direct application of the CO2 beam on the TM.

Applying 10W of CO2 on the HR face requires a RIN better than 5*10-9/Hz1/2 @ 50Hz (see figure below)



While if CO2 beam is applied on both faces of the TM (2.5W on HR and 7.5W on AR faces), the RIN requirement is relaxed to 2*10-8/Hz1/2 @ 50 Hz (see figure below)

avatar
Alessio

Posts : 127
Join date : 2008-11-07
Age : 46
Location : Rome

View user profile

Back to top Go down

Back to top

- Similar topics

 
Permissions in this forum:
You cannot reply to topics in this forum