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Linked Article: Fusion: X-ray laser zaps solid to 2 million degrees

The quest to create nuclear fusion may have come a step closer when scientists heated solid matter to two million degrees with the world's most powerful X-ray laser, a study reported on Wednesday.

I don't see how is it possible that these scientists manage to measure two million degrees Celcius. Are there such measuring instruments that can measure extremely hot stuff without melting and still get a proper reading, or is it a theoretical deduction?

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Related: What does it mean a temperature of billions of degrees?. Community input on if this constitutes a duplicate is solicited. –  dmckee Jan 26 '12 at 2:46
@dmckee I checked the link, and the answer is not complete. –  anna v Jan 26 '12 at 5:21
@dmckee I would vote to treat it as a non-duplicate, because this question has a well-defined scope about measurement, which was peripheral to that prior question (which didn't even use the wording of measurement). On top of that, this should be a common hangup for laymen, who don't have the background into plasmas, radiation, etc. –  AlanSE Jul 9 '12 at 20:47
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3 Answers

up vote 5 down vote accepted

Fusion is plasma physics, and in plasma physics the temperature is defined by the average kinetic energy of the ions and electrons in the plasma.

Therefore the kinetic energy distributions have to be measured and they have developed ingenious methods of doing so. Fitting with the black body radiations curves allows an estimate of the temperature.

There are more ingenious methods developed, using Thomson scattering, which allow by scattering light on different ions accurate measurements of temperature.

Very high temperatures can be measured for the stars from their black body radiation and the spectral distribution of the light reaching us also.

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To measure such temperatures, one can observe and analyze the radiation of the "hot stuff", as the spectrum and intensity of such radiation depends on the temperature.

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this link which describes how one knows the temperature of the stars is useful zebu.uoregon.edu/~soper/Stars/color.html –  anna v Jan 26 '12 at 5:22
A blackbody at 1e5 K would have a spectrum peaked at 30 nm or so. This is how we know laser ablation temps. –  user27777 Aug 14 '13 at 2:23
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One method mention by Anna V is to use X-ray Thomson Scattering, which is also known as Compton scattering. I figured I would expand on how this works.

When x-rays scatter off of stationary free electrons, relativistic energy and momentum conservation requires that the scattered photon is shifted to lower energy (longer wavelength). The shift is known as the Compton shift, and is given by $\Delta E = \hbar^2 q^2 / 2m$ where $q$ is the momentum transferred to the electron (which can be determined from the scattering angle).

However, the electrons in any material, and in particular an extremely hot, dense plasma, are not stationary. Instead they have some momentum distribution, which is determined by the electronic wavefunctions (property of the material) and by the temperature. Scattering off of a moving electron gives (again by energy and momentum conservation) $\Delta E = \hbar^2 q^2 / 2m + \hbar \vec{q} \cdot \vec{p}/m$, where $\vec{p}$ is the momentum of the electron before scattering.

This Doppler effect causes, for a constant incident x-ray energy, a broad down-shifted peak to be present in the scattered x-ray spectrum. The center is at the standard Compton shift, while the shape of the peak can be used to extract the electronic momentum distribution. From that it is possible to extract a temperature.

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