TCS Radiative Cooling

Simulation n.00

Values of the used parameters:

Power of the laser	125W
Finesse FP AdVirgo	885
Emissivity cold surface	1.0
Emissivity covering and substrate	0.89
Inner beam cold surface	0.150m
Beam of the mirror	0.175m
Thickness cold surface	0.025m
Distance cold surface from the coating	0.010m
Length cold surface	0.300m
Temperature cold surface	200K
Temperature mirror	295K
Angle between axis mirror and cold surface	0.0°

Scheme base of the simulation:



Course of the temperature in 3D:



The used data belong to the file “ss.txt” produced from ANSYS.

Course of the temperature along the beam:



"Yi" (depth) is the coordinate of the "nodes" of the ANSYS elements.
Every curve represents the course of the temperature to varying of the beam of the mirror.
Every curve belongs to a fixed coordinate "Yi". This generates of the just discontinuities between the succession of curves.

The curve more low corresponds to the course of the temperature on the surface of the mirror interacting with the laser.
We can notice a not favorable course. In fact, considering the surface of the mirror hit from the laser, the
temperature value smaller is not found to the center of the surface.
This could depend from the temperature of the surface of base of the cold surface.

Course of the temperature along the depth:



In this case every curve has like fixed parameter coordinate "Xi".
Not there are unfavorable courses, to the center of the mirror and on
the surface of the mirror hit from the laser the temperature is more
low.
To increasing of beam ("Xi") the temperature increases with an acceptable course.

Successive steps of simulation:

1. Reduction of the disturbance of the temperature of the surface of base of the cold surface.
   
2. Control of the points of the diagram 3D.
   

Simulation n.01

Values of the used parameters:

Power of the laser	125W
Finesse FP AdVirgo	885
Emissivity cold surface	1.0
Emissivity covering and substrate	0.89
Inner beam cold surface	0.175m
Beam of the mirror	0.175m
Thickness cold surface	0.005m
Distance cold surface from the coating	0.010m
Length cold surface	0.300m
Temperature cold surface	200K
Temperature mirror	295K
Angle between axis mirror and cold surface	0.0°

Scheme base of the simulation:



Course of the temperature in 3D:



The used data belong to the file “ss.txt” produced from ANSYS.
Not there are improvements.

Course of the temperature along the beam:



The course remains not favorable.
Al center of the mirror on the surface of the mirror hit from the
laser, in the Sim01, the temperature turns out greater regarding that
of the Sim00.

Course of the temperature along the depth:



Observations:

1. The cooling effect is smaller of about 1K.
   
2. The temperature of the base of the cold surface has a negligible effect in the Sim00 and the Sim01.
   

Successive steps of simulation:

1. Variation of the angle between axis mirror and cold surface.
   

My opinion is that the next steps should follow this order:
1) Optical Path Lenght calculation
2) Coupling Losses calculation
3) Structural analisys (calculation of the TM ROC)

Setting Sim00.
Variation of the parameter T of the cooling system.
The minimum values for the OPL are in bold.

T(K)	|Diff-OPL(m)| max	Increase-OPL(m) max/min
230	0.4500e-5	(-1.50/-1.90)e-5
260	2.0000e-6	(-8.50/-10.60)e-6
280	1.0000e-6	(-3.80/-4.50)e-6
284	2.6016e-7	(-2.70/-3.20)e-6
285	2.7011e-7	(-2.45/-2.86)e-6
286	2.9049e-7	(-2.15/-2.55)e-6
287	3.1301e-7	(-1.90/-2.20)e-6
288	3.3810e-7	(-1.53/-1.85)e-6
290	4.0000e-7	(-8.00/-12.00)e-7
292	4.5000e-7	(-0.50/-5.00)e-7

Presence of the laser.
Room temperature.

T(K)	Diff-OPL(m) max	Increase-OPL(m) min/min
295	7.4e-7	(3.6/11.0)e-7

Estimation of ROC:
T is the temperature of the cooling system

Formula used in this fit: F(x) = a*X^2 + b*X + c
(the values of b are negligible)

Formula for calculating the ROG: ROC = 1/(2a)

T(K)	Setting	ROC (m)
	No - Laser No-Cooling	1416.029
	Yes - Laser No-Cooling	1413.227 (-2.802)
284	Sim00: Yes - Laser Yes-Cooling	1395.478 (-20.551)
292	Sim00: Yes - Laser Yes-Cooling	1314.405 (-101.624)

For a T = 292K, the variation of ROC is too high!

Ok Alessandro. It seems you are converging.
Three things:

1. it is ROC (Radius Of Curvature), not ROG
   
2. the function used to evaluate the ROC is wrong: there must be no linear term F(x)=aX²+c
   
3. Coupling losses!
   

Alessandro wrote:

T(K)	Setting	ROC (m)
	No - Laser No-Cooling	1416.029
	Yes - Laser No-Cooling	1413.227 (-2.802)
284	Sim00: Yes - Laser Yes-Cooling	1395.478 (-20.551)
292	Sim00: Yes - Laser Yes-Cooling	1314.405 (-101.624)

I gave a better look at this table. There is something strange. The ROC should increase when the YAG only is on (row 3). How can it be that the ROC is smaller when the cooling system is less cold(rows 4 and 5)?

The problem was the linear term of the formula used in the fit.

Here are the correct values:

T(K)	Setting	ROC (m)
	No - Laser No-Cooling	1416.029
	Yes - Laser No-Cooling	1422.879 (+6.850)
284	Sim00: Yes - Laser Yes-Cooling	1406.074 (-9.955)
292	Sim00: Yes - Laser Yes-Cooling	1418.037 (+2.008)

Now the change in the ROC is more acceptable.

With TM: T=295K and Cylinder: T0=294K I noticed that:
- If we exclude the laser the effect of cooling has an acceptable performance!
- The ROC (fit: 1415.23 m) is good!

Conclusion:
- The method of cooling is functional;
- The temperature has a parabolic distribution over the surface of the mirror, but it is not Gaussian!

Next Steps:
- New simulations with successive increments of the power of laser;
- see the limit of operation of the cooling system, depending on the laser power;
- Possible application of the method of directional cooling.