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Tim McDaniel (tim)
New member
Username: tim

Post Number: 2
Registered: 04-2007
Posted on Tuesday, May 08, 2007 - 06:53 am:   

Hello,

I am trying to model the deposition and diffusion of thermal energy in silica glass by femtosecond laser pulses. The laser pulses are about 100e-15 s long. I want to see how the temperature diffuses as a function of distance and repitition rate.

To model the amount of thermal energy deposited into the glass I am using the equation ..

{energy and temperature of pulse}
Ep = 30e-6 {pulse energy, J/pulse }
a = 1 {absorption factor}
E = ( (a*Ep) / ( (w^3)*SQRT(pi^3) ) ) * exp (-(r^2)/(w^2)) {absorbed energy density, J/m^3}
tempd = E/(C*p) {temperature due to energy absorption, K}

and so the heat source term in the diffusion equation would be ..

{heat source}
delta = cos ( pi * tau / t_r )
Pulse = USTEP ( cos ( 2 * pi * ( t - tau / 2 ) / t_r ) - delta )

Q = (tempd) * Pulse {laser pulse as heat source, K} {using step function}

OR

! Q = (tempd) * SUM( i, 0, 1, exp( -( t - i*t_r )^2 / (tau)^2 ) ) {laser pulse as heat source, K} {Gaussian time distribution}

I've read through the forums and it seems like there have been some similar problems, but they were for slightly more complicated situations than mine. I am only interesed in 1D, ie radial position from the heating source.

The problem that I am running into is that the temperature jump in the material at each pulse depends on the duration of the pulse. If my absorption factor is set to 100% ( a = 1 ) shouldn't the temperature jump to the max temperature regardless of the pulse duration?

For the above listed parameters, the heat source should be about 1.5e6 K. I expect to see a rise in temperature in the material on that scale, but I have found that the shorter the pulse duration the less the temperature rise. For example, i get less than 1 degree K for a 100 femtosecond pulse. For a longer pulses (greater than 1 ns) I get temperature increases greater than the original amount in the pulse.

I have tried two forms of the heat source, an exponential time distribution, and a USTEP form, both have the same outcome.

Am I confused with the physics or is this an artifact of FEA? I believe it's the latter, since in the experiment, for a pulse energy 30e-6 J I was able to create plasma in the glass.

Also, I am concerned with femtosecond pulses, but also the temperature behavior on the scale of 1 ms, ie, for a pulse repitition rate down to 1kHz. Is this huge difference in time scales causing errors in my output, ie another artifact of FEA?

Also, how careful do I need to be with boundary conditions? I have set my region to be 100e-6 in size, where the heat source distribution is 1e-6. I figured that since the region was large and I am only concerned with distances around 10e-6 that I could just set the value at the far end of the region to 300K (the initial value for temp). Do I need to take into account flux at distances that far away?

Any help or explanation to point me in the right direction would be greatly appreciated. Thanks in advance. I have attached the pde file.

Thanks,
Tim

application/octet-streamLaser pulse heat diffusion
thesis heat diffusion - pulse energy absorption UPULSE.pde (2.0 k)
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 846
Registered: 06-2003
Posted on Wednesday, May 09, 2007 - 12:05 am:   

1.
You have specified an initial timestep of 1e-9, 10000 times the length of your pulse. On this timescale, the pulse is unseen, and is ignored.
Start with a timestep smaller than the pulse length, so FlexPDE will have a chance of seeing it. I suggest 1e-14.

2.
You have specified a THRESHOLD of 1e7. This tells FlexPDE that variations less than this amount need not be held to the specified error. Since the first pulse raises the temperature to only 350, the first pulse is five orders of magnitude below your requested resolution threshold. Use THRESHOLD=1. Later in the run the error scaling will be dominated by the actual temperature variation, and this number will be ignored.

3.
In 1D, boundary conditions must be POINT conditions - in your case POINT VALUE(temp)=300.

4.
With the outer boundary so close and held at Temp=300, all the energy deposited by the pulse leaks out the outer boundary by about t=1e-6, long before the second pulse.

5.
A 10000:1 duty cycle is a bit of a problem. With nothing going on for a millisecond, FlexPDE will scale the timestep up and completely miss the second pulse. You can control this by putting print times at the beginning, middle and end of each pulse. This will guarantee that the pulses are seen by the numeric sampling.

See attached.

application/octet-stream
heatpulse.pde (2.0 k)

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