THE PLASMA DOUBLE LAYER (Part I)

 

Pyotr Leonidovich Kapitsa (1894–1984): The 1978 Nobel Lecture

Pyotr Leonidovich Kapitsa was awarded the Nobel Prize in Physics 1978 “for his basic inventions and discoveries in the area of low-temperature physics.” 1 Whereas Kapitsa had actually left the field of low-temperature physics about 30 years prior, he chose the Nobel lecture2 platform to discuss his then current research in “plasma phenomena at those very high temperatures that are necessary for the thermonuclear reaction to take place.” 3

In terms of (thermonuclear) plasma confinement, Kapitsa initially reviews the two fundamental approaches of (a) magnetic confinement, and (b) inertial confinement, most of his review being focussed on the (pulsed) magnetic Tokamak method4 that by 1978, had been “under development in the [former] Soviet Union for more than a decade.” 5,6 He then briefly describes the (laser implosion) inertial method.7,8 While not excluding eventual solutions to the problems associated with each method, Kapitsa does raise doubts about their overall practicality.

That brings us to Kapitsa’s description of a “third approach to a thermonuclear [fusion] reactor based on continuously heating the plasma” — the method having being under development (at least at that time) exclusively at his institute, i.e., the Institute for Physical Problems of the Academy of Sciences, Moscow, USSR.9,10

Kapitsa begins by explaining that a “hot plasma phenomenon,” in the form of a “luminiscent [sic] discharge with well defined boundaries” was accidentally discovered during their development of a high power CW microwave generator, the observations leading to an hypothesis that (natural) ball lightning may result from “high frequency waves, produced by a thunderstorm after the conventional lightening [sic] discharge,” the requisite energy to sustain “the extensive luminosity” being delivered via the high frequency (electromagnetic) waves.11

Two statements from Kapitsa’s referenced paper titled, “ON THE NATURE OF BALL-LIGHTNING” 12 are quoted here as follows, more or less encapsulating Kapitsa’s definitive position on his hypothesis concerning the cause of ball lightning:

     Thus, the hypothesis that ball-lightning is due to the high-frequency electromagnetic oscillations can not only resolve the basic contradiction with the energy conservation law, but can also account for a number of other known and incomprehensible phenomena associated with the phenomenon of ball-lightning, such as: its fixed size, immobile position, existence of the chains, blast-shock accompanying its disappearance, and also its penetration into a room.13

[...]

... Finally, as another possible trend of experimental verification of the suggested hypothesis we should point to a possibility to produce under laboratory conditions a discharge similar to ball-lightning. For this, obviously, one has to dispose of a strong source of radiowaves of a continuous intensity in the decimetre range, and to be able to focus them in a small space. At a sufficient strength of the electrical field there should arise conditions necessary for a breakdown without electrodes which by means of the ionisation resonant absorption by the plasma should develop into a luminescent sphere of a diameter approximately equal to ¼ of the wavelength.14

Kapitsa explains that by March 1958 (three years after publishing the ball-lightning hypothesis), they resumed experiments, obtaining a “free gas discharge, oval in form” ... and began “to study this type of discharges where the plasma was not in direct contact with the walls of the resonator.” He further states: “The plasma discharge has a cord-like form 10 cm long, equal to half the wavelength [of the microwave oscillations].” 15,16

Kapitsa concludes his decription of the experiments stating:

... At low powers the discharge did not have a well defined boundary and its luminosity was diffuse. At higher power the luminosity was greater and the diameter of the discharge increased. Inside the discharge a well defined filamentary cord-like nucleus was observed. In our initial experiment, the power dissipated in the discharge was up to 15kW and the pressure reached 25 atm. The higher the pressure the more stable was the discharge with a well defined shape. ... we could firmly establish that the central part of the discharge had a very high temperature — more than a million K. So at the boundary of the plasma cord in the space of a few millimeters we had a disconinuity of temperature more more than a million K. This meant that at the surface there was a layer of very high heat isolation. ... It is easy to show that at these high temperatures electrons scattered at the boundary and freely diffusing into the surrounding gas [if indeed this were the case] will carry away a power of hundreds of kW. The lack of such a thermal flux may be explained by assuming the existence of electrons reflected without losses at the boundary of a double layer.17 ...

After explaining the mechanism for the well-known formation of a double-layer in the case of “hot plasmas surrounded by dielectric walls, say, of glass or ceramics,” 18 Kapitsa states:

... We assume that at a sufficiently high pressure a similar mechanism of heat insulation may take place in our hot plasma. The existence of a double layer in the plasma on the boundary of the cord discharge as a discontinuity in density was experimentally observed by us. This mechanism for a temperature discontinuity may obviously exist only if the ion temperature is much lower than the electron temperature and not much above the temperature at which the plasma is noticeably ionised. But this is only necessary at the boundary of the discharge. In the central part of the discharge the ion temperature inside the core may reach high values. ... the difference in temperatures inside the core and at the surface is determined by the value of the thermal flux and the heat conductivity of the ion gas. Usually the heat conductivity is high, but in a strong magnetic field the transverse heat conductivity may become very small. Thus we may expect that in a strong magnetic field the ion temperature may be sufficiently high to obtain in a deuterium or tritium plasma reaction. This is the basis for designing a thermonuclear reactor to produce useful energy, and this has been worked out (8).19 The general outlay and the description of the reactor are shown in fig. 4.20

After providing an overview of the thermonuclear reactor design,21 Kapitsa devotes the balance of his lecture to addressing what he refers to as “unresolved difficulties” that could preclude the possibilty of practical thermonuclear fusion with the design described, stating: ... “The main problem is to heat the ions to the same temperature [as the electrons], for although the electron gas interacts with the ions in the entire volume of the discharge, it is not easy to raise this temperature in such a way.” 22

Kapitsa continues:

     The temperature equalisation proceeds in two steps. In the first step the energy is passed from the electrons to the ions. This is simply due to the collisions of electrons with ions, and in this case it is obvious that the heat transfer will be proportional to the volume. The next stage is the transfer of energy from the ion gas to the surrounding media. This flux will be proportional to the surface of the plasma cord. At a given thermal conductivity of the ion gas the temperature will increase for larger sizes of the cross section o[f] the plasma cord. Thus at a certain heat conductivity there will be a critical size for the diameter of the plasma cord, when the ion temperature will reach a value close to that of the electrons and the required D + D or D + T reaction can take place. If we know the heat conductivity of the plasma, then it is easy to calculate the critical dimension. If, for example, we make this calculation for ordinary ion plasma in the absence of a magnetic field, when the heat conductivity is determined by the mean free path, we will find that the plasma must have an unrealizably large size of many km. One can lower this cross section only by decreasing the heat conductivity of the ion gas by placing it in a magnetic field as it is done in the reactor shown in fig. 4. The heat conductivity of an ion gas in a magnetic field is markedly decreased and it is determined not by the mean free path but by the radius of Larmor orbits the size of which is inversely proportional to the magnetic field. The thermal conductivity of ion gas in a magnetic field is easy to calculate.
     It is thus seen that the critical diameter of the cord is inversely proportional to the magnetic field and at a field of a few tesla the diameter of the cord to get thermal neutrons will be 5-10 cm, that can be readily provided for.23 ...

But then Kapitsa raises “yet another factor that could eventually make the whole process unfeasible.” 24 He describes this factor — convection — as follows:

We determined the heat conductivity of the ion gas by considering the mean free path of the ion, assuming it to be equal to the Larmor orbit radius, having not taken into account the effect of convection [emphasis added] fluxes of heat in the gas. It is well known that even in ordinary gases the convection heat transfer is much larger then [sic] the heat conduction due to molecular collisions. It is also known that unfortunately it is virtually impossible to calculate theoretically the heat transfer by convective currents even for the simple case of random turbulent motion in an ordinary gas. In this case we usually can, by dimensional considerations, estimate the thermal conductivity in a similar case and then generalise it for a special case, determining the necessary coefficients empirically. In the case of plasma the process depends on many more parameters and the problem of determining the convectional thermal conductivity is even more complicated than in an ordinary gas. [emphasis added] But theoretically we may estimate, which factors have most influence on the rate of convection. To sustain convection one must supply energy. In a gas this energy is drawn from the kinetic energy of flow and leads to loss of heat.25
     In a quiescent plasma there is no such source of energy. But in an ionized plasma there may be another source of energy that will excite convection. This source is connected with temperature gradients and some of the thermal energy flux could produce convection. Quantitatively this process is decribed by internal stresses and was first studied by Maxwell (9).26 Maxwell had shown that internal stresses are proportional to the square of viscosity and derivative of the temperature gradient. In an ordinary gas they are so small that up to now they have not yet been experimentally observed. This is because the viscosity, which is proportional to the mean free path, at normal pressures equals ~ 10-5 cm and so at low temperature gradients, the stresses are small.
     In the plasma the mean free path of electrons and ions is of the order of cm and the temperature gradients are high. In this case the internal stresses following Maxwell’s formula are ten orders of magnitude greater than in a gas and we may expect both convection currents and turbulence. The presence of a magnetic field certainly can have effect of this phenomenon, and with additional effect of an electric field on convection it makes even a rough theoretical approach to estimating the magnitude of convection very unreliable. In this case there is only one alternative: to study the process experimentally ...
     In any case convectional thermal conductivity will lower the heating of ions and will lead to a greater critical cross section for the thermonuclear plasma cord. Correspondingly the size of the reactors for useful energy production will be greater.
      If this size will be out of our practical reach, then we should consider methods to decrease convectional heat transfer. This may be done by creating on the boundary of the plasma a layer without turbulance, as it happens in fluids where we have the Prandtl boundary layer. This possibility has been theoretically considered /(4) page 1002/.27,28

The essential significance of the plasma double layer is clear in a simple statement by Kapitsa in the Conclusion of his (June) 1970 paper:

... The possibility of the existence of a plasma of such a high [> 1 million degrees] temperature is explained by us by analogy with gas discharge tubes in terms of the appearance at the boundary of the plasma of a double layer which reflects electrons elastically [emphasis added].29 ...


In THE PLASMA DOUBLE LAYER (Part II) — in progess — we will review a patent for a thermonuclear reactor based upon the application and further development of Kapitsa’s plasma double layer.


— FINIS —


  1. See THE NOBEL PRIZE — Nobel Prize in Physics 1978 — Pyotr Kapitsa — Facts.↩️

  2. See THE NOBEL PRIZE — Nobel Prize in Physics 1978 — Pyotr Kapitsa — Nobel Lecture, December 8, 1978 — Plasma and the Controlled Thermonuclear Reaction (PDF from Nobel Lectures, Physics 1971–1980, Editor Stig Lundqvist, World Scientific Publishing Co., Singapore, 1992, pp. 424–436).↩️

  3. Ibid., p. 424.↩️

  4. Ibid., pp. 426–429.↩️

  5. Ibid., p. 426.↩️

  6. Ibid., p. 436, Kapitsa’s ref. 1., i.e., F.L. Ribe, “Fusion reactor systems,” Rev. Mod. Phys. 47, 7 (1975) (DOI: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.47.7). See the Abstract.↩️

  7. Ibid., pp. 429–430.↩️

  8. Ibid., p. 436, Kapitsa’s ref. 1., F.L. Ribe, “Fusion reactor systems.” See the Abstract.↩️

  9. Ibid., pp. 430–436.↩️

  10. Ibid., p. 436, Kapitsa’s ref. 4., i.e., P.L. Kapitsa. “Free plasma filament in a high frequency field at high pressure,” Sov. Phys. JETP, 30, 6 (June 1970) pp. 973–1008. (see http://jetp.ras.ru/cgi-bin/dn/e_030_06_0973.pdf). The abstract of Kapitsa’s paper reads as follows:
    The main experimental results obtained in the course of an investigation of plasma in a filamentary high frequency discharge floating in the middle of a resonator are presented. An experimental arrangement for obtaining a stable discharge is described; stabilization is obtained by rotation of the gas. The investigations are carried out primarily in an atmosphere of deuterium at a pressure of several atmospheres. For an input power up to 20 kW the length of the discharge attains a value of 10 cm. Spectrometric investigations and their theoretical interpretation lead to the conclusion that the discharge consists of an internal cylindrical region filled with hot plasma at an electron temperature of the order of 106 °K and of a cloud of partially ionized plasma (T = (7–6) x 103 °K) surrounding it. It is shown that the existence of such a high temperature is possible due to a temperature discontinuity at the plasma boundary; an explanation is proposed that this discontinuity arises as a result of a double layer [emphasis added] at the boundary. The effective heating of the filament by HF current takes place due to the anomalous skin effect.
         Such an interpretation of plasma processes is experimentally confirmed by experiments on the effect on the discharge of a constant magnetic field (up to 25 kOe). A study is made of the ion temperature. The observed emission of neutrons is insufficient for the determination in terms of them of this temperature and cannot even be sufficiently reliably investigated in order to establish its thermonuclear nature. Other methods so far also do not give a reliable result for determining the ion temperature. The problem is considered as to how one could by means of magnetoacoustic oscillations and magnetic thermal insulation raise the ion temperature up to the level required for the production of a reliable thermonuclear reaction. Some preliminary experiments in this direction are described.
         The investigations reported here have been carried on for over ten years by the staff of the Physics Laboratory of the Academy of Sciences of the U.S.S.R.    ↩️

  11. Ibid., p. 430.↩️

  12. Ibid., p. 436, Kapitsa’s ref. 7., i.e., P.L. Kapitsa, No. 50. “ON THE NATURE OF BALL-LIGHTNING” in Collected Papers, Vol. 2 (Oxford: Pergamon Press, 1965) pp. 776–780 (see https://archive.org/details/p-l-kapitza-collected-papers-vol-2/mode/2up, digital pages 290/516–294/516). Note: As stated on p. 430 of the Nobel Lecture, “This paper was published in 1955” ... .↩️

  13. Ibid., p. 436, Kapitsa’s ref. 7., No. 50. “ON THE NATURE OF BALL-LIGHTNING”, p. 779 (digital p. 293/516).↩️

  14. Ibid., p. 436, Kapitsa’s ref. 7., No. 50. “ON THE NATURE OF BALL-LIGHTNING”, p. 780 (digital p. 294/516).↩️

  15. Ibid., p. 430.↩️

  16. Ibid., p. 436, Kapitsa’s ref. 4., “Free plasma filament in a high frequency field at high pressure.”↩️

  17. Ibid., p. 431.↩️

  18. Ibid., pp. 431–432.↩️

  19. Ibid., p. 436, Kapitsa’s ref. 8., i.e., P.L. Kapitsa. “A thermonuclear reactor with a plasma filament freely floating in a high frequency field,” Sov. Phys. JETP, 31, 2 (August 1970) pp. 199–204. (see http://jetp.ras.ru/cgi-bin/dn/e_031_02_0199.pdf).↩️

  20. Ibid., pp. 432–433.↩️

  21. Ibid., pp. 433–434.↩️

  22. Ibid., p. 434.↩️

  23. Ibid., pp. 434–435.↩️

  24. Ibid., p. 435.↩️

  25. Ibid.↩️

  26. Ibid., p. 436, Kapitsa’s ref. 9., i.e., J.C. Maxwell. “On Stresses in Rarified Gases arising from Inequalities of Temperature,” Philosophical Transactions of the Royal Society, 170 (1879) pp. 231–246. (see https://archive.org/details/philtrans09463079/mode/1up?view=theater).↩️

  27. Ibid., pp. 435–436.↩️

  28. Ibid., p. 436, Kapitsa’s ref. 4., “Free plasma filament in a high frequency field at high pressure,” p. 1002.↩️

  29. Ibid., p. 1006.↩️

 
Edwin Wright