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## Main Question or Discussion Point

I am doing some basic heat calculations about a CW laser illuminated tungsten tip (which should be used for photoemission) - I started to play with the tip geometry to try and find a way to get more flux Watts/metre^2 onto the tip with out it melting. I found that after solving the 1d heat equation for a cone and then including a rod on the other end (held at T=300K):

{dT=\frac{Q}{k*A(z)}dZ=\Dint{T_{facet}}{T_{shaft}}=\Dint{Z_{facet}}{Z_{shaft}} \frac{Q}{kz^{2}tan^{2}\theta\pi}dZ}

which comes out as

{Q=\frac{T_{facet}-300}{\frac{facetradius^{-1}-shaftradius{^-1}}{tan^{\theta\pi}k}+\frac{shaftlength}{shaftradius^2{\pi}k}}}

This assumes (wrongly of course) that all the laser power is absorbed on only the facet of the tip.

Now my calculations tell me that if I make the facet area around 10 nm i can apply 10^12W/m^2.

Is this possible? Am I not doing something that should ablate my tip immediatly ?

{dT=\frac{Q}{k*A(z)}dZ=\Dint{T_{facet}}{T_{shaft}}=\Dint{Z_{facet}}{Z_{shaft}} \frac{Q}{kz^{2}tan^{2}\theta\pi}dZ}

which comes out as

{Q=\frac{T_{facet}-300}{\frac{facetradius^{-1}-shaftradius{^-1}}{tan^{\theta\pi}k}+\frac{shaftlength}{shaftradius^2{\pi}k}}}

This assumes (wrongly of course) that all the laser power is absorbed on only the facet of the tip.

Now my calculations tell me that if I make the facet area around 10 nm i can apply 10^12W/m^2.

Is this possible? Am I not doing something that should ablate my tip immediatly ?