Lasers for Relativistic Propulsion (Eventually)

It takes a whole lot of power to get any force from a beam of light. The momentum of a light beam p=E/c, where E is the light energy, p is momentum, and c is the speed of light (3x10^8 m/s).
https://en.wikipedia.org/wiki/Radiation_pressure
You can divide by time to equate power versus force. And there is a factor of 2 (if that helps) because the light changes direction when it hits the sail and bounces off.So, 150 MW will generate 1 newton of force (about .225 lb for us Yanks). That comes out to about 666 MW per pound of force. (This is laser output power, laser input power would likely be considerably higher.)
A 1 kg mass could be sent to Neptune in 5 days with a 70 GW laser.http://www.deepspace.ucsb.edu/wp-content/uploads/2013/09/zhang_spie2015_SAIL-r815a.pdf
To put the power required into perspective, the electric energy generated in the US in 2012 was 4048 TWh or an average power of 462 GW, so the laser output would be about 15% of the average total US power production.
https://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=2&pid=2&aid=12

And another thing, the sail had better be very, very reflective or that 70 GW is going to do some damage!

Wouldn't that laser energy be better off used to vaporize and superheat solids into a super heated plasmas that can be ejected out the back to provide thrust?

As far as I know even a few KW's of laser energy being used to plasmadize most any solid that can be found anywhere would be able to provide a far greater energy to thrust ratio than simply pointing a laser at a sail or out the back.

Basically put a space rock on the back and blast the rear facing surface off of it with a laser creating a cloud of superheated plasma debris and you should get thrust in return.

Or is my understanding of basic plasmas and blowing them out the back of something to make thrust incorrect?

The power to thrust ratio is much better if you use the energy to eject mass at high velocity. But the problem is carrying that extra mass. For example, the saturn v weighs about 23 times the weight of the payload.

The mass ratio for accelerating a rocket by a given amount (Δv) is a function of the propellant exhaust velocity:

So accelerating a rocket to relativistic velocities with achievable exhaust velocities would require an enormous mass ratio. Laser propulsion, however inefficient, is a way around this.

No.

The advantage of the laser is that it is not bound by propellant speed, which would be much lower with a solid fuel.

The space craft's maximum velocity is limited by the exhaust velocity of the propellant.

Even with laser propulsion, a large reflector is required which will have some weight. A way around this is to use the sun's energy. One technique which has been proposed is to create a weightless magnetic sail and trap ions from the solar wind (M2P2).

https://en.wikipedia.org/wiki/Magnetic_sail