Richard Rhodes: X-Ray Flux has Mass?

Aaronvan

On pp. 459 of Dark Sun: The Making of the Hydrogen Bomb Richard Rhodes writes:
He is talking about soft-x-rays in that quote. I understand that X-rays are massless so their weight is zero regardless of the density of the flux. Is this not correct? Is there a better comparison he could have used to describe the density of the X-ray flux?

mfb

Photons as particles do not have mass, but if you consider the total energy of a box at rest (with radiation inside), it has a mass equivalent to its energy content (divided by c^2).
In the same way, a proton has a mass of ~940 MeV/c^2, while its (valence) quarks inside just have mass of ~10 MeV/c^2.

Astronuc

Nuclear detonations release energy in a broad EM spectrum. One sees the bright visible portion of the spectrum, but there is infrared, visible, UV, X-ray and gamma ray. The nuclear fission produces prompt gamma rays, and some of the fission products release gammas and beta particles. The high energy fission products, gammas, betas and X-rays then ionize atoms in the plasma and atmosphere, and these in turn release infrared, visible, UV and X-ray.

Perhaps Rhodes is referring to the equivalent-mass of the energy as indicated by mfb, or perhaps he is thinking of the momentum of the photons.