How can I calculate the relationship between power and acceleration for a beam driven photon sail? I am writing a novel, and although I have a background in physics, I am unsure of the exact equations to use.
Specifically:
For a photon-sail ship, how powerful would a driving laser need to be in order for the ship to reach an acceleration of ~0.5g?
Assuming we are only talking within the solar system here, and assuming that the ship is heavy enough to carry passengers.
Would such a thing ever be feasible? I am trying to strike the right balance between fun and feasibility for some method of regular interplanetary transport (think the space equivalent of commercial jets).
 A: Photons generate what we call Radiation Pressure. From wikipedia, http://en.wikipedia.org/wiki/Radiation_pressure, we get the equation:
$$
P_{absorb} = \frac{E_f} {c} cos\space\alpha\\
\text{and} \space P_{reflect}=\frac{2E_f} {c} cos^2\space\alpha
$$
Where:$P_{absorb}$ is the Radiation Pressure on an absorptive surface (in Pascals).
$P_{reflect}$ is the Radiation Pressure on a reflective surface e.g. mirror (in Pascals).
$E_f$ is the energy flux/intensity (in $\frac{W} {m^2}$) 
$c$ is the speec of light, and
$\alpha$ is the angle between the surface normal and the incident radiation. 
Assuming that the ship has a reflective sail and the sail is orthogonal the the laser beam, we get $P=\frac{2E_f} {c}$. From $F=ma$ and $F=PA$,
$$
\frac{2E_fA}{c}=ma
$$
I will stop here since there are parameters to be filled (namely, $m$ and $A$, which depends on your design of the ship.) After plugging in all the values, including  $a=0.5g$, you shall obtain $E_f$, which is proportional to the power of the laser.
