[Kryptid]

This will release 1 GJ of kinetic energy into the target each second .

Here is the part of my post that you are ignoring:

You want all of the electrons to be accelerated at once, but the problem is that there simply aren't enough photons coming in fast enough to get the job done. You could get more photons either by lowering the energy available for each photon while keeping the laser power constant (which will make each electron move slower) or you can increase the total power of the laser instead.

If you want all 0.17 kilograms (1.866 x 10²⁹) of electrons to be accelerated to 99.876% the speed of light in one second, then the laser will need to provide 10 MeV photons at a rate of 1.866 x 10²⁹ per second. That requires a total laser power of 298,966,149 gigawatts.

There is a hard upper limit on how many electrons you can accelerate to 99.876% of light speed in one second when you only have a gigajoule per second of power to work with.

That mass happens to be 0.583 micrograms of electrons.

So you want to accelerate a mass of electrons up to 99.876% of light speed in one second when you apply a gigajoule of energy in that one second? Sure, you can do that. However, you are limited to that tiny 0.583 micrograms. Any more mass than that and you'll have to wait more than one second to get the amount of energy you need. Even a human egg cell is more than six times more massive than such a cluster of electrons.

[Professor Mega-Mind (OP)]

................Simple Logic .
It doesn't matter if it's called one King Kong Ball , it's "one electron for one H.E.X-ray photon" ! The the photons bounce back as visible light , the electrons bounce forward as relativistic electrons .  Impact at the target is .99 GJ ( 278kw.hr. ) , per second .
Note-In practice , a longer "tube" will allow for more complete energy transfer .
P.M.

[Kryptid]

"one electron for one H.E.X-ray photon"

Which is why you're limited to moving 0.583 micrograms per second.

[Professor Mega-Mind (OP)]

.....................OOOOOR !
 25 micrograms accelerated to.9c.
There are many ways to skin this cat .  Bottom line , 1GJ thermal energy  ( HEX-ray ) in , 1GJ kinetic energy ( relativistic electrons ) out.
This actually crushes the "Epstein Drive" , and gives us "Interstellar" .
Ain't group-minds grand ?
P.M.   

[Kryptid]

25 micrograms accelerated to.9c.

If that impacted the receiver over a period of one second, the resulting force would be about 7 pounds. Hardly the stick of dynamite you keep going on about. You'd also have to have a laser with a power a bit over 5 gigawatts to get it up to that speed in a single second. I'm not going to bother showing you the calculations, since you'd ignore them anyway.

[Professor Mega-Mind (OP)]

...............Your own crud !
.583 micrograms at .9c gives a kinetic energy of 21,250,350 joules
That's 21 sticks of dynamite , but ; it SHOULD be 999 .  Read Replies number 221&223 again , and reconfigure your calculations . 
Get 'em Scotty's nephew !
P.M.

[Kryptid]

.583 micrograms at .9c gives a kinetic energy of 21,250,350 joules

You used a Newtonian equation when you should have used a relativistic one instead.

That's 21 sticks of dynamite

Energy is not force.

[Bored chemist]

What happens to the track of the centre of the ball?

BTW, I'm going to keep asking that question until you actually answer it.

[Professor Mega-Mind (OP)]

Let’s drop the photon energy down to 1MeV , go ahead and raise the # of photons to #×10th 30th .  What-ever # you use , Reply # 223 must apply .  The electrons soak up 1GJ per second , and impact with 1GJ per sec.  Triiiick !
P.M.

[Kryptid]

Let’s drop the photon energy down to 1MeV , go ahead and raise the # of photons to #×10th 30th .  What-ever # you use , Reply # 223 must apply .  The electrons soak up 1GJ per second , and impact with 1GJ per sec.  Triiiick !
P.M.

Actually, it would only be 0.7965 gigajoules per second because electrons can only absorb 79.65% of the photon's energy when the photon is at 1 MeV.

[Professor Mega-Mind (OP)]

Fine , dump the reflected ~20% EMR energy out the back .  1 MeV is a much easier energy for labs to work with .
P.M.

[Bored chemist]

What happens to the track of the centre of the ball?

BTW, I'm going to keep asking that question until you actually answer it.

[Professor Mega-Mind (OP)]

...........Mosquito Bite Itch .
The answer was veiled in # 216 !
It launches the ball , instead of the baby !
By the way , the electrons won't be exploding !
P.M.

[Bored chemist]

What happens to the track of the centre of the ball?

[Kryptid]

Let’s drop the photon energy down to 1MeV , go ahead and raise the # of photons to #×10th 30th .

By the way, dividing the energy of each photon by ten will only increase the number of photons per second ten-fold as well. So the actual number is on the order of 10²¹ photons per second, not 10³⁰.

Fine , dump the reflected ~20% EMR energy out the back .  1 MeV is a much easier energy for labs to work with .
P.M.

Okay, you now have ten times as many electrons per second flowing through the engine since you have 1 MeV photons instead of 10 MeV. However, each electron now has less energy (and a lower relativistic mass) than when there were 10 MeV photons. The laser light reflected back will also hit harder than before when it returns to the laser. All of these factors come together to make the thrust exactly the same as in my first calculation: 3.3356 newtons.

You have neither gained nor lost anything by modifying the photon energy.

[Professor Mega-Mind (OP)]

PRACTICALITY for research .  By the way , you can now change the quantity to 1 Godzilla Ball of electrons .
Note-You don't let the reflected EMR "hit" , you let it escape out of the exhaust .
P.M.

[Kryptid]

PRACTICALITY for research .  By the way , you can now change the quantity to 1 Godzilla Ball of electrons .

Godzilla Ball meaning what, exactly?

Note-You don't let the reflected EMR "hit" , you let it escape out of the exhaust .
P.M.

Then what you now have is a reaction engine, since you are letting propellant (in the form of the reflected light) out of the ship.

[Bored chemist]

What happens to the track of the centre of the ball?

[Professor Mega-Mind (OP)]

L-A-B W-O-R-K !
The point is to make it easy to create the dang thing in the first place !
P.M.

[Bored chemist]

L-A-B W-O-R-K !
The point is to make it easy to create the dang thing in the first place !
P.M.

No
Before you do the lab work, you check to see if it is already known to be impossible.
"A couple of months in the laboratory can frequently save a couple of hours in the library."
From
https://en.wikiquote.org/wiki/Frank_Westheimer

What happens to the track of the centre of the ball?