How dangerous would a Stelaser be?

Question

So assuming the following, a Stelaser is build that can, at max, push a Ship with a Mass of 3 Megatons at 2G for several weeks if need be.

Needless to say, that's a stupidly powerful and concentrated Laser. Due to this, the current version of everything puts the launch points for the ITV´s far away from Earth on its own orbit, where there is nothing in-between the ship and the laser. At least for the acceleration phase.

Thus the question becomes just how much damage such a laser could do if it, by accident or as an attack, is used to burn stuff on Earth or anywhere else for that matter ?

My own thoughts

Considering just how much light you need to capture and focus on a more or less small point, I cant see any structure surviving this for any amount of time. At least as long as it isn't built to do so. The sails on the ship itself obviously do handle it pretty well. I am pretty sure that the heat, radiation and brightness together are well above what you need to just melt your way across, or through, anything you want. But the scale is kind of out there. If we for example say that the Main Mirror somehow shifts a fraction of a degree, the beam itself would pretty much rampage across Earth at light speed. Entire cities would be there one moment and then gone the next. More or less like a chain of nukes.

But yeah, let me hear what would happen and how much damage it would do :D

Thanks for the help !

Answer 1

Let's run some back of the envelope calculation.

The momentum carried by a photon is given by $p=h/\lambda$.

If your laser is emitting $n$ photons in a time interval $\Delta t$, it will be giving an acceleration equal to $m \Delta v/\Delta t = p/\Delta t = n h/\lambda \Delta t$

Knowing that your $m \Delta v/\Delta t$ is $3\cdot 10^9 [kg]\cdot 20 [ms^{-2}]=60\cdot 10^9 \ N$, we get that the photon emission rate $n /\Delta t$ has to be equal to n $60 \cdot 10^9 \lambda/h$.

Considering for simplicity emission at 500 nm, it would mean that the emission rate should be $4.55\cdot 10^{37} \ s^{-1}$.

Considering that a photon at 500 nm has an energy of $3.9\cdot 10^{-19} \ J$, it would mean the emitted power would need to be about $10^{18} \ W$.

Several weeks of exposures to that amount of power would turn into plasma anything smaller than a planet.