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I asked this question due to my lack of knowledge in what our scientific front-line can achieve, but what methods have we used to create temperatures around the billions? Is there anyway we can maintain this temperature for longer than seconds?

Chin Ho Kua
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  • My casual google search suggested that we can't really right now; but I would be interested to see an answer. For example, I saw a reference to a fusion reactor (possibly) sustaining ~100 million degrees for maybe 6 seconds; which falls below both your criteria. – JMac Nov 26 '19 at 20:02
  • Highest artificial temperature achieved so far is 5.5 trillion degrees: https://www.guinnessworldrecords.com/world-records/highest-man-made-temperature?fb_comment_id=962551457091594_2189957824350945 – Allure Nov 26 '19 at 20:12
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    A previous question about the beam temperature of the LHC: https://physics.stackexchange.com/q/165071/123208 – PM 2Ring Nov 26 '19 at 20:18
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    Related: https://physics.stackexchange.com/a/114138/44126 – rob Nov 26 '19 at 22:42

2 Answers2

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Anything with a temperature radiates electromagnetic radiation with power per unit area:

$$ P/A = \frac{2\pi^5k^4}{15c^2h^3}T^4 = \sigma T^4 = 5.67\,\times\,10^{-8}\, W/m^2/T^4$$

The fourth power of temperature is significant, so a billion is a trillion times more power than a million.

Keeping something the size of a virus (20 nm) at 1 GK requires:

$$ P =\sigma \cdot(10^9/K)^4 \cdot 4\pi(10^{-9}/m)^2\approx 70 TW $$

which is currently a few times larger than the power output of Mankind.

So even if we could do it, would we want to? At $0.12/kWh, that's 2.4 million dollars per second, and that doesn't include peak-pricing.

JEB
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  • Out of curiosity, what would be left of a virus at 1 GK? – Winston Nov 26 '19 at 22:16
  • @Exocytosis Hadron jets. – rob Nov 26 '19 at 22:39
  • @rob: I would have thought hadrons were transformed into a plasma of quarks and gluons at this temp range. – Winston Nov 26 '19 at 22:41
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    @Exocytosis Hadron jets are how quark-gluon plasmas cool off. Note that the expression in this answer is only for electromagnetic radiation and underestimates the radiated power above MeV temperatures. – rob Nov 26 '19 at 22:44
  • @rob: how large is the error? – Winston Nov 26 '19 at 22:50
  • @Exocytosis The statement that maintaining a virus-sized volume of GK temperature would require more than tens or hundreds of terawatts of power input is correct, but whether the 70 TW in this answer is low by a factor of 10% or a factor of 2 or a factor of 10 I don't know. – rob Nov 26 '19 at 22:59
  • @Exocytosis: Chemical binding energies are of the order of tens of $eV$, hence molecules surely don't exist at temperatures of $>100 eV$, correspnding to 1 MK. At 1 GK, there is nothing left that can form chemical structures. – AtmosphericPrisonEscape Nov 27 '19 at 00:51
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    @rob good point. RHIC(ollisons) radiate black body pions, and supernovae radiate thermal neutrinos. My answer was not comprehensive, as I was only addressing the last sentence and trying to emphasize the fact that hot (optically thick?) matter must radiate, and at giga-K's the power density is astronomical. – JEB Nov 27 '19 at 17:10
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At the moment top fusion temperatures are around 100 MK, so 'only' a factor of 10 shy of your 1 GK. The next generation, i.e. ITER or Wendelstein 7-X after the upgrade, should be able to reach 'steady state', aka plasma running times of about 30 minutes, while current max. running times are about 30 s.

The limits of the runtime are currently given by plasma instabilities and the skill in handling them (tokamak reactors) and frontier-level inexperience with running hotter plasmas which might damage the containment (true for stellarators). In principle, nothing stops us going above 100MK. However new physics starts to appear as plasma species start fusing, so people are careful to go there, as the (mainly) electromagnetic energy contained in a reactor volume is significant, and can damage the container if released spontaneously though an instability.

@JEB's answer is faulty insofar, as that an optically thin plasma of those temperatues has effective emission surfaces that are considerably smaller than a virus, this is why human civilization can build such machines. By JEB's calculation any modern fusion device would need around 7GW of power, which is 3-4 nuclear power plants, and that is certainly not the case. Be careful in the future to accept answers too quickly, before others can chime in.

AtmosphericPrisonEscape
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