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"Individual science fiction stories may seem as trivial as ever to the blinder critics and philosophers of today -- but the core of science fiction, its essence has become crucial to our salvation if we are to be saved at all."
- Isaac Asimov

Light-Sail Ship  
  A spacecraft that used a huge sail moved by light pressure.  

As far as I know, this is the first use of the phrase, but not the concept.

Earth could have kept her, but the new worlds needed her.

She had to go.

She went by light-sail ship. And she had to cross space—space, where the danger always waits.

...Most space offers no respite, no relay, no rescue, no repair. All dangers must be anticipated; otherwise they become mortal.

From Think Blue, Count Two, by Cordwainer Smith.
Published by Galaxy Publishing in 1962
Additional resources -

By 1964, Smith was simply calling it a "sailship", as in Dead Lady of Clown Town:

It selected a fertilized human embryo, tagged it with the freakish name ‘Elaine,’ irradiated the genetic code with strong aptitudes for witchcraft and then marked the person’s card for training in medicine, transportation by sailship to Fomalhaut III and release for service on the planet.

The idea of a light sail was still unfamiliar when Niven and Pournelle wrote The Mote in God's Eye (1974):

What in Hannigan's Hell was a light sail?
...Blaine snapped up from his reverie and touched his screen controls again. The ship's course appeared on his screen as a pictorial diagram below tables of figures. Rod spoke with effort. "Approved." Then he went back to the impossibly large object on his view screen. Suddenly he took out his pocket computer and scribbled madly across its face. Words and numbers flowed across the surface, and he nodded.
Of course light pressure could be used for propulsion...
A reflecting mirror could use outside light as propulsion and get twice the efficiency. Naturally the mirror should be as large as possible, and as light, and ideally it should reflect all the light that fell on it.
Blaine grinned to himself. He had been nerving himself to attack a space going planet with his half-repaired battle cruiser! Naturally the computer had pictured an object that size as a globe. In reality it was probably a sheet of silvered fabric thousands of kilometers across, attached by adjustable shrouds to the mass that would be the ship proper.
In fact, with an albedo of one— Blaine sketched rapidly.
The light sail would need about eight million square kilometers of area. If circular, it would be about three thousand klicks across. . .
It was using light for thrust, so. . . Blaine called up the intruder's deceleration, matched it to the total reflected light, divided . . . so. Sail and payload together massed about 450 thousand kilograms.

Compare to the starlight sail from The Lady Who Sailed The Soul (1960) by Cordwainer Smith, the solar sail from Sail 25 (1962) by Jack Vance, which has a longer discussion of the topic, and the photonic sail from Think Blue, Count Two (1962) by Cordwainer Smith. Don't miss the solar yacht from Arthur C. Clarke's 1963 short story Sunjammer.

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Additional resources:
  More Ideas and Technology from Think Blue, Count Two
  More Ideas and Technology by Cordwainer Smith
  Tech news articles related to Think Blue, Count Two
  Tech news articles related to works by Cordwainer Smith

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