Infinite ISP for a first stage launch system

Speculation alert:  This is an idea.

During the Cold War, there was a program to use a nuclear reactor to power an airplane. The benefits of such a design were meant to keep the plane flying indefinitely using the energy from the reactor in order to heat the atmosphere so as to produce thrust in order to keep the plane airborne.

It was thought to be an impractical idea and scrapped. There is another possibility that would not require the nuclear reactor to be onboard, but rather to supply energy to the plane's engines so as to keep it airborne. That is, to use Kevin Parkins' design of microwave energy for a horizontal liftoff and horizontal lander launch vehicle that would use atmospheric air as reaction mass in a first stage rocket plane.

There are some practical considerations to implementing this design. One thing is how to get the energy to the heat exchangers? I figured that the thing may need a boost from a catapult that are used on aircraft carriers. This catapult may need to be much larger though as it will be pushing something much bigger and heavier. Anyway, the catapult would fling the spacecraft forward at a speed close to what it would need to remain airborne while furnishing energy to the heat exchanger which produces the rest of the thrust needed to remain airborne after the catapult releases the spacecraft.

Such a design would not need to carry fuel as the atmosphere will supply that. Its payload would be similar to a Falcon 9 second stage with a capsule attached. I'm guesstimating, because I don't know, that this would be about 100k lbs of mass. The airframe that is carrying this payload would probably look a little like the shuttle.

It would have the heat exchanger located underneath with the payload perched on top of it. I'm guessing its mass would be less than the Falcon 9 first stage, since it doesn't have to carry fuel onboard. Its mass would entail the heat exchangers and plumbing and airframe to make it all work.

The ISP of this first stage would be infinity because there is no fuel. The reaction mass would be the atmosphere itself. It would liftoff to an alititude and achieve an airspeed equivalent to a Falcon 9 first stage and then release its payload which would then proceed to orbit.

Elon Musk intends his second stage to be reusable. Therefore, the entire system could be reusable.

The first stage would have flyback capability. It would not have to get outside the range of the beamed microwave energy source. It would use a corkscrew trajectory to gain altitude, then a short sprint after getting sufficient altitude that would be enough velocity so that the second stage can take over.

Update:

In order to answer the question about mass of the second stage Falcon 9, I merely took the ratio of the  entire rocket and its thrust.  Given the thrust of the second stage, I calculated the mass using the same ratio.  That number is actually less than 100k pounds.  It is about 70k.

A fully loaded Super Hornet that operates off aircraft carriers weighs in at about 66k lbs.  So, the final mass of the rocket plus airframe shouldn't be all that much more than a Super Hornet.

There are other possibilities for obtaining the necessary lift to enable a horizontal liftoff.

You could send the spacecraft down a ski jump type arrangement with the engines providing the rest of the velocity.  Once it got airborne, the microwave beam would take over.

Update:

Scaled Composites' White Knight Two can carry 37k lbs to 50k feet.   Now, what if you replaced the Falcon 9 second stage with a LH/LOX type rocket with a higher ISP?  That'll reduce the weight.  Now, the Falcon 9 is going to weigh in at more 70k that I had above.  I'm thinking 140k.  If you use LH2 instead of RP1 rocket fuel, the weight can be brought down to slightly north of 100k pounds depending upon how much delta v you needed to get to orbit.

This is all pure speculation, of course.  You would need a version of White Knight that can go supersonic and carry about 3 times as much weight.  Is this even possible?  The service ceiling for the White Knight as is, is about 70k feet.  You need another 30k feet plus about Mach 2 in acceleration, or a bigger rocket.

The design of the carrier plane would have to be much different, of course.