The adage natura non facit saltus (Nature eschews jumps) was cited repeatedly by Charles Darwin in his Origin of Species. He used it to support the notion that the evolution of organs, entire organisms and instincts is gradual and continuous, and, by implication, that the record appears patchy simply because it is incomplete. The maxim was previously used by Carl Linnaeus in his Philosophia Botanica of 1751 to underpin the notion that taxa have relations on every side and that there are no gaps in the botanical panorama. Alfred Marshall later made it the motto of his Principles of Economics (1890, 8th ed 1920).

The slogan hardly deserved to survive after 1900, the year when Planck proposed that energy is composed of packets or quanta and when Mendel’s work on particulate inheritance was validated. Indeed, at least since the days of Aristotle humanity has been familiar with a natural phenomenon characterised by dramatic jumps: metamorphosis, the sequence of distinct episodes by which an insect egg produces a caterpillar, which eventually turns into a pupa, which in due course becomes a butterfly.  Darwin interpreted metamorphosis as the development of different body forms of a single organism in response to changing selective pressures; modern workers appear to be more interested in the processes at issue. Advances in genetics, biochemistry and microscopy highlight the role of hormones in triggering or halting the changes in tissue and cell differentiation that are genetically programmed but if anything they highlight the jumps [43].

There are unsolved problems which can profit from explanations that are boldly discontinuous. The case study outlined here comes from solar physics. The corona’s elevated temperature – ≥ 1-2 10⁶ K compared with a mere ~4 10³ K at the upper photosphere – has been known for the best part of a century [9,30]. The explanatory models currently most in favour invoke heating primarily by magnetic reconnection, MHD waves or solar flares [1], and although they recognise such features as the transition region, where temperature jumps from 10⁴ K to 10⁶ K, and may identify magnetic structures, they implicitly view the solar atmosphere as a physical unit [1,15,42].

This paper avoids searching for periodicities by Fourier, wavelet and similar analyses to avoid the associated assumptions and data sacrifice, and it instead seeks major episodes within the various solar records. The discussion is based mainly on photospheric imaging, measurements by the EVE instrument on the SDO spacecraft which allow energy transfer to be traced at different thermal levels within the solar atmosphere, and a fall in solar wind speed 2 by 98 % in 10-12 May 1999. The suggestion here is that the accepted threefold structure of the solar atmosphere – namely chromosphere, transition region and corona (Fig 1) – is the outcome of differential heating rather than its cause. The analogy with holometabolous insect metamorphosis is that each of the three successive steps creates novel structures and is triggered and sometimes delayed by local controls.

Figure 1: Proposed heating episodes set against major subdivisions of the solar atmosphere, and plots of temperature (T) and plasma particle density (N). EM = electromagnetic energy, J-T = inverse Joule-Thomson effect. T and N after Peter (2004).

Experimental work in this field is focused on plasmas in tokamaks where temperatures of 1.5 10⁸ K are obtained through ohmic heating derived from an induced current supplemented by RF heating. A major hurdle in such laboratory studies is the need to confine the plasma, usually attained magnetically, but the solar environment may bring this about gravitationally.  Bearing in mind that any analogy between processes on the Sun and in terrestrial laboratories -- particularly fusion [31] -- is only approximate, there are instructive parallels between the first step in our model and the early stages of a conventional tokamak operation, especially as laboratory experiments for the solar conditions are not available. There a toroidal current serves the dual purpose of confining the plasma and heating it: as the main contours of the solar body represent the interplay between gravitational contraction and thermal expansion, the solar environment performs confinement effectively though imperfectly, thus freeing the available magnetic energy from this task. In fact, as indicated by the solar wind, there is a net surplus of plasma to sustain the chromosphere.

Plasma composition as well as induction heating shows qualified kinship between Sun and laboratory, although in a tokamak the currently favoured fuel – deuterium-tritium – is fully ionised at the temperatures required for fusion. The H: He ratio could dominate discussion of the influence of elemental abundance on chromospheric heating, with a photospheric bulk composition of H 90.965% and He 8.89% (NASA 2018). Sodium, magnesium, calcium, and iron are also present, a fact that is exploited in particular in the assessment of fractionation between the photosphere and different varieties of solar wind [40].  The impurities that have been detected during the ohmic heating phase of JET operation, such as reactor wall material (Ni, Cr, Fe), oxygen, carbon, molybdenum and chlorine, also lead to radiation losses and presumably do so in the solar reactor too [3].

Step 1: Photosphere - Chromosphere

In our model of the solar atmosphere, photospheric induction is by way of electromagnetic energy derived from spinning convective pseudoTaylor columns in the Rayleigh-Bénard setting of the convection zone -- pseudo in the sense that they may develop in a fluid subject to strong rotation and thermal forcing without the basal obstacle of the original definition [48,18,26].

Large-scale vortices are a possible outcome of rotating planar convection in an electrically conducting Boussinesq fluid [19]. The associated dynamos generate magnetic fields that are concentrated in the shear layers surrounding the vortices, although for Rayleigh numbers just above a critical value the convection takes the form of elongated columns with a small horizontal cross-section and aligned with the rotation axis [20]. Tangential (vortical) flows associated with the average photospheric supergranule outflow are indeed reported to reach about 10 m s⁻¹ [27]. The fluid in which they spin is partly ionised and therefore electrically conducting. The cylindrical support is irrelevant except insofar as it creates quasi-regular spacing of planar rotating discs at the photospheric surface, the structures that govern photospheric granulation [55], a pattern made familiar on the Internet by the Swedish telescope on La Palma and more recently transmitted by the Inouye telescope in Hawaii.

The columnar model evidently differs from the classic notion of a primarily convective mechanism for granulation (e.g. November 1994). The summit of the columns is manifested as mesogranulation and supergranulation; the surface flow field is accordingly in close agreement with the magnetic field [45]. The columns are free to spin, even if closely packed, because they are insulated mechanically by sheaths [47]. Indeed, Spacelab-2 white-light images illustrate both clockwise and anticklockwise spin; they also show that photospheric vorticities can twist a magnetic flux tube by 360° in < 3 hr, that is an average of >2°/min [45].

The dominant heating mechanism is resistive dissipation of the proton (Pedersen) currents driven by the convection electric field that we have visualised as spinning columns. Indeed, the modelling by Goodman (2004) leads to the proposition consistent with the theme of this paper that the chromosphere (away from flaring regions) is created by current dissipation. Even so Pedersen current dissipation is very inefficient when the plasma is fully ionized and strongly magnetised, whereas Joule dissipation due to dynamo action (Kan & Yamaguchi, 1989)  amounts in nonactive regions, on the basis of the classic quiet Sun model by Vernazza et al. (1981), to ~2.4 10⁷ erg cm^-2 s^-1 when the electromagnetic energy employed by induction may be approximated by the observed energy losses suffered, again during quiet Sun conditions, by the low chromosphere, which Withbroe & Noyes (1977) put at  2 10⁶ erg cm⁻² s⁻¹. 

Step 2: Chromosphere - Transition Region

In our proposed tripartite scheme the weakly ionised Hα of the chromosphere is also subject to ohmic (or Joule) heating. In accordance with the account by Spitzer (1958) the resistance and thus the efficacy of ohmic heating decrease in proportion to the electron temperature as Te^-3/2, so that there is a point at which heating stalls. Owing to operational constraints [35] ohmic heating at startup in most tokamaks can attain at most ~ 1 keV, say 10⁷ K, as is the case with the JET tokamak (ESA 2013).

Figure 2: Selection of Joule-Thomson coefficients to illustrate low inversion temperature for hydrogen and helium.

In the absence of experimental data for coronal temperatures we must rely on extrapolation of inversion curves [22]. (Fig, 2)), but to advance the discussion we note that at very high temperatures the Joule-Thomson coefficient μJT may be represented by – b/Cp [13], where b is of course one of the two constants that distinguish the van der Waals equation from the Real Gas Law and that vary according to the gas at issue, and Cp is the heat capacity. The negative result is consistent with the temperature increase obtained experimentally and by calculation. The radial elevation of the temperature maximum above the photosphere [28] provides a rough measure of the limits of J-T heating and it illustrates how astronomical observation can supplant the laboratory for evaluating thermochemical processes at extreme settings.   

 It has been suggested that the temperature of the chromosphere ‘steadfastly refuses to rise above 10⁴ K until hydrogen becomes fully ionized’ perhaps because ‘ionization of hydrogen leads to a high specific heat’ [23]. Operating experience from fusion research shows how Spitzer resistivity may render ohmic heating in the chromosphere self-limiting and serve to define the lower margin of the transition region.  Thus specific heat imposes an upper limit on the chromospheric temperature well below the Spitzer limit. Indeed, the temperature in the Sun, after a temporary reversal, increases only to ~ 2.10⁴ K some 3.10³ km above the photosphere.     

The issue of specific heat had previously been raised in a study of the Jovian atmosphere for which an atmospheric composition of hydrogen and helium was postulated (Nelson 1971). A nondimensional plot of specific heat against temperature at 1-6 10⁴ K for particle densities from 10^-10 to 10^-6 g cm^-3 and for hydrogen unit volumes of 0.333 and 1.0 (equivalent to 50 % and of 100 % hydrogen by volume) yields two prominent peaks. The greater is at 2.5-4 10⁴ K, which may be manifested as a heightened but shortlived response to ohmic heating when the transiting gas attains a critical temperature.    

Analogy with the H/He atmospheric evolution of young terrestrial planets [11] points to XUV radiation as a plausible supplementary heating source; XUV emission by the upper chromosphere and the TR was demonstrated by a slit spectrograph observation from Skylab [7]. Magnetic energy flux at the photosphere has been evaluated at active regions, such as NOAA 11158 [25], by modelling complemented by Hinode satellite observations. At one plage region the vertical Poynting flux had values of about 5±1 10⁷ erg cm^-2 s ^-1 [56].

Step 3: Transition Region - Corona

In a classic study [39] (Fig 1) the onset of the TR corresponds to a plasma particle density Ne (as distinct from ‘plasma density’ commonly used to signify electron density) of slightly more than 10¹⁶ m^-3. Photoionisation of hydrogen reduces its cooling efficiency by some six orders of magnitude so that at high temperatures (10⁴ -10⁸ K) neutral hydrogen cools at about 10^-18 erg cm³ s^-1 compared to 2 10^-24 erg cm³ s^-1 for ionised hydrogen, with a peak (to judge from the published data) at ~ 10³ K [14]. Photoionisation has a similar effect on helium [38], which when partially ionised cools very efficiently by blackbody radiation and direct coupling to the helium Lyman continuum. Once fully ionised by further heating, however, it no longer couples well to the continuum (the Lyman limit being 91.2 nm, 13.6 eV). This signals the end of radiative loss or, in other words, the onset of uninhibited heating, and temperatures of 10⁶ K are rapidly attained. In short the trigger is more in the nature of a safety catch which is released at the critical temperature.

A value of ~ 6.10³ K signals the region where cooling by radiation begins to nullify EUV heating as shown by very similar radiative cooling functions for 3HeH+ and 4HeH+ [4]. Here the rate of cooling attains between 10^-10 and 10^-9 erg/s. Indeed the calculated radiative cooling function (in erg cm^-3 s^-1) at temperatures >10⁴ K for plasmas at low densities with solar abundances in collisional ionisation equilibrium K drops rapidly from 10⁵ to 10^7.5 K [8].

In short, the third and last stage in the proposed scheme is expansion into the tenuous plasma of space, which leads to the acceleration of ions to high energies. The upper limit of the TR may be defined about 5.10⁶ m above the photosphere, where the solar plasma has attained a value of 2.5 10⁵ K, by a deceleration in the temperature increase then in progress. The onset of the TR corresponds to a plasma particle density N of slightly more than 10¹⁶ m^-3 (Peter 2004; Fig 1).

 Gurevich et al. (1966) and Gurevich & Pitaevsky (1975) were perhaps the first to show that the expansion of a plasma into a vacuum or a more tenuous plasma could result in the acceleration of ions to high energies (Samir et al. 1983), a process for which the self-similar solution indicates a logarithmic increase in velocity [6]. Plasma expansion has been investigated experimentally as well as theoretically [10] even though the circumstances that concern us here, viz. temperatures of 10⁶ K and coronal pressures of perhaps 1.3 10^-11 Pa, present even more serious laboratory limitations than does the ohmic heating of plasmas in the chromosphere. The bearing of this effect on space phenomena was made explicit by the interaction of an obstacle with a plasma: heating of He++ ions in the solar wind has long been recorded by spacecraft [36].

A relation between pressure fall and temperature in an astronomical context was assumed by Kothari (1938) when he showed that, for a relativistically degenerate gas (i.e. one nearing its ground state) undergoing Joule-Thomson expansion, the degree of heating per unit fall of pressure increased with the degree of degeneracy. Samir & Wrenn (1972) reported that ionospheric electron temperature measured by a Langmuir probe in the near wake of an artificial satellite (Explorer 31) was raised above that of the ambient electron gas by as much as 50 %. They referred to earlier work (Medved 1969) on the Gemini/Agena spacecraft in which wake temperature was 1700 K greater than the ambient temperature in one experiment and 764 K in another. The Moon’s wake provided scope for related work; the increase in the electron temperature in the lunar wake found by the SWE plasma instrument on the WIND spacecraft amounted to a factor of four although ion temperatures were little changed [37]. Laboratory investigations based on immersion of a plate in a single-ion, collisionless, streaming plasma, saw ‘early time expansion’ result in ion acceleration into the wake [44].

There is thus dynamic continuity all the way from the solar interior - the energy source for spinning columns in the Rayleigh–Benard setting of the convection zone - to the coronal exhalation of the solar wind, a finding which should benefit the analysis of space weather, witness the association between helium in the solar wind and the incidence of coronal mass ejections. An unusual and instructive reduction in the solar wind density by 98% and its speed by about a half occurred on 10-11 May1999. The geomagnetic value at Earth Kp also fell to zero (BGS 2016). The sunspot record for the same period, however, shows no reduction (SIDC 2016), and the values for F_10.7 [50] confirm a NASA report that, as observed by the SOHO spacecraft, there were no amomalies in the solar EUV flux. The prima facie case, therefore, is that fluctuations in the speed of the solar wind are largely independent of processes in the lower corona EUV represented by F _10.7 and the photosphere (sunspots), and are therefore a useful guide to energy transformation within the main body of the corona (Vita-Finzi 2016). A further clue to the route by which heat is transmitted through the corona to the solar wind is provided by the predominance of H and He in the Sun’s composition.

Figure 3: Irradiance oscillations during January-July 2012 for solar wind, corona, upper transi-tion region and photosphere. Sources in Vita-Finzi 2016.

The solar wind emerges as the preferred indicator of solar activity. Sunspot data are compromised by their indirect relation to the Sun’s irradiance: the rotation of active areas explains no more than 42% of its variation (Li et al. 2012). Moreover the secure sunspot record spans at most four centuries and says little about such matters as solar fluctuations during the Maunder and other sunspot minima. It remains to be seen whether the cosmogenic isotope record, which already spans 800,000 years [41], can provide the requisite link to the history of the solar wind on the grounds that it represents its modulating effect on the flux of galactic cosmic rays [2].

Contrary to the accepted puzzling notion that the transition region and even the chromosphere are heated inwards from the corona (NASA 2018), the temperature rise is cumulatively radial. What is more, structuring of the solar atmosphere into three major zones is not the source of our stepwise heating sequence but its outcome. The coherence between solar wind variations and sunspot activity (Fig 3) is consistent with our proposed tripartite heating scheme: induction heating, which brings temperatures up to 20,000 K and triggers Joule-Thomson heating, which in turn results in temperatures of 250,000 K at the TR, and thereafter plasma expansion into the near vacuum of space, which is here proposed as the mechanism by which temperatures of 1-2 million K are raised in the corona before it grades into interstellar space.

 The long-term record of the Sun’s activity, essential for robust interpretation of palaeoclimates as well as for assessing the solar factor in weather, requires detailed information on the source of EUV fluctuations. Measurements by the EVE instrument on the Solar Dynamics Observatory satellite combined with neutrino data suggest that the UV flux is modulated primarily by rotation of the solar interior (provisionally named the Dicke Cycle: Vita-Finzi 2009) rather than the passage of active areas across the solar disc. Thus periodicities recorded by cosmogenic isotopes such as ¹⁰Be, which respond to oscillations in the strength of the solar wind, are better guides to the solar factor than observed sunspot records and have the advantage of spanning >10⁵ yr rather than a mere 4 10² yr. The proposed scheme could help to explain heating in other bodies (such as Titan) which display a radial increase in temperature and a decrease in plasma density as well as sustained gas outflow. It may also bear on the stepwise evolution of other coronal stars.

Figure 4: The tripartite scheme for coronal heating. I: ohmic induction; J-T: inverse Joule-Thomson effect; PE: plasma expansion. N_e data points itemised in Vita-Finzi 2016.

 The hormonal analogy is of course very crude, not least by virtue of the subtleties revealed by decades of entomological field and laboratory investigation [51] when our simple aim is to highlight the qualitative and quantitative impact of our three discontinuities, namely Step 1, photosphere–chromosphere, powered by ohmic current dissipation; Step 2, chromosphere–transition region, Spitzer resistivity as limit; and Step 3, transition region–corona, plasma expansion into a near-vacuum.

Acknowledgments

I am grateful for the encouragement received from Kenneth J. H. Phillips over the years.

I have received no funding.

1. Amari T, Luciani JF, Aly JJ. Small-scale dynamo magnetism as the driver for heating the solar atmosphere. 2015; 522:188-191.
2. Bard E, Raisbeck GM, Yiou F, Jouzel J. Solar modulation of cosmogenic nuclide production over the last millennium: comparison between ¹⁴C and ¹⁰Be records. Earth Planet. Sci. Lett. 1997; 150, 453-462.
3. Behringer KH. et al. Impurity and radiation studies during the JET ohmic heating phase. Nucl Fusion. 1986; 26: 751-786.
4. Coppola CM, Lodi L, Tennyson J. Radiative cooling functions for primordial molecules. Mon Not R Astron Soc. 2011; 415: 487-493.
5. Solar and geomagnetic data. British Geological Survey, Keyworth UK. 2016.
6. Crow JE, Auer PL, Allen JE. The expansion of a plasma into a vacuum. J Plasma Phys. 1975; 14: 65-76.
7. Doscheck GA, Feldman U, Tousey R. Limb-brightening curves of XUV transition lines in the quiet sun and in a polar coronal hole observed from SKYLAB. Astrophys J. 1975; 202: 151-154.
8. Draine BT. Physics of the interstellar and intergalactic medium. Princeton Univ Press, Princeton NJ. 2011.
9. Edlén B. An attempt to identify the emission lines in the spectrum of the solar corona. Arkiv Matematik Astron Fys. 1941; 28B.
10. Elkamash, I. & Kourakis, I. Multispecies plasma expansion into vacuum: The role of secondary ions and suprathermal electrons. Phys Rev E.2016; 94: 053202.
11. Erkaev NV. et al. XUV-exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets. Part I: atmospheric expansion and thermal escape. 2013; 13: 1011-1029.
12. www.esa-tec.eu retrieved April 2019. 2013.
13. Gans PJ. Joule-Thomson expansion. 1993 tccc.iesl.forth.gr/education/local/Labs-PCII/JT.pdf.
14. Gnat O, Ferland GJ. Ion-by-ion cooling efficiencies ApJ Suppl. 2011; 199:
15. Golub L, Pasachoff JM. The Solar Corona. Cambridge, Cambridge Univ. Press. (2010, 2nd ed).
16. Goodman M.L. On the mechanism of chromospheric network heating and the condition for its onset in the Sun and other solar-type stars. Astrophys J. 2000; 533: 501-522
17. Goodman, M.L. On the creation of the chromospheres of solar type stars. Astr Astrophys. 2004; 424: 691-712l.
18. Grooms I. et al. Model of convective Taylor columns in rotating Rayleigh-Bénard convection. Phys Rev Lett. 2010; 104: 224-501
19. Guervilly C, Hughes DW, Jones CA. Large-scale vortices in rapidly rotating Rayleigh–Bénard convection. J Fluid Mech. 2014; 758: 407-435.
20. Guervilly C, Hughes DW, Jones CA. Generation of magnetic fields by large-scale vortices in rotating convection. 2015.
21. Gurevich AV, Pariiskaya LV, Pitaevskii LP. Self-similar motion of rarefied plasma. Soviet Physics JETP. 1966; 22: 449-454.
22. Hendricks RC, et al. Joule-Thomson inversion curves and related coefficients for several simple fluids. NASA Tech note D-6807. 1972; 1-62.
23. Judge PH. The structure of the chromosphere. Space Sci Rev. 1998; 85:187-202.
24. Kan JR, Yamaguchi M. Joule heating in the photosphere and chromosphere. J Geophys Res. 1989; 94: 6879-6886.
25. Kazachenko MD, et al. Photospheric electric fields and energy fluxes in the eruptive active region NOAA 11158. Astrophys J. 2015; 811: 16
26. King EM, Aurnou JM. Thermal evidence for Taylor columns in turbulent rotating Rayleigh-Bénard convection. Phys Rev E. 2012; 85: 016313.
27. Langfellner J, Gizon L, Birch A. Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking. Astron Astrophys. 2015; 581: A67.
28. Lemaire JF. Determination of coronal temperatures from electron density profiles. 2011; 112.
29. Maytal BZ, Pfotenhauer JM. The Joule-Thomson effect, its inversion and other expansions. In Miniature Joule-Thomson Cryocooling. Springer. 2013; 39-72.
30. Miyamoto S. Ionization theory of solar corona. Publ Astron Soc Jpn. 1949; 1: 10-13.
31. Morse E. Nuclear Fusion. Springer. Cham. 2018.
32. Sun fact sheet. Nssdc.gsfc.nasa.gov. Retr Nov 2019. 2018.
33. Nelson, H.F. Thermodynamic Properties of Hydrogen-Helium Plasmas. NASA, Washington DC. 1971.
34. November LJ. Inferring the depth extent of the horizontal supergranular flow. Solar Phys. 1994; 154:1-17.
35. O'Brien MR, Robinson DC. Tokamak experiments. In Dendy, R. (ed) Plasma Physics: an Introductory Course. Cambridge Univ Press, Cambridge. 1993; 189-208.
36. Ofman L, Viñas AF, Maneva Y. Two-dimensional hybrid models of H+ -H++ expanding solar wind plasma heating. J Geophys Res. 2015; 119: 4223-4238.
37. Ogilvie JW, et al. Observations of lunar plasma wake from the WIND spacecraft on December 27, 1994. Geophys Res Lett. 1996; 23:1255-1258.
38. Oppenheimer BD, Schaye J. AGN proximity zone fossils and the delayed recombination of metal lines. Mon Not Roy Astr Soc. 2013; 434: 1063-1078.
39. Peter H. Structure and dynamics of the low corona of the Sun. Rev Mod Astron. 2004; 17: 87.
40. Peter H, Marsch E. Hydrogen and helium in the solar chromosphere: a background model for fractionation. Astron Astrophys. 1998; 333, 1069-1081.
41. Raisbeck GM, Yiou F, Cattani O, Jouzel J. ¹⁰Be evidence of the Matuyama-Brunhes geomagnetic reversal in the EPICA Dome C ice core. 2006; 444: 82-84.
42. Ruderman MS. Nonlinear waves in the solar atmosphere. Phil Trans Roy Soc Lond A. 2005; 364:1839.
43. Ryan F. The Mystery of Metamorphosis. Chelsea Green, White River Junction. 2011.
44. Samir U, Wright KH, Stone NH. The expansion of the plasma into a vacuum. Rev Geophys Space Phys. 1983; 21: 1631-1646.
45. Simon GW, et al. Relation between photospheric flow fields and the magnetic field distribution on the solar surface. Astrophys J. 1988; 327.
46. Spitzer L. Jr. The Stellarator concept. Phys Fluids. 1958; 1, 253-264.
47. Sprague M et al. Numerical simulation of an asymptotically reduced system for rotationally constrained convection. J Fluid Mech. 2006; 551: 141-174.
48. Taylor GI. Experiments with rotating fluids. Proc R Soc London A. 1921; 100:114-121.
49. Thomson W, Joule JP. On the thermal effects of fluids in motion. Trans. Roy. Soc. London. 1853; 143: 357-365.
50. Tobiska WK, et al. The SOLAR2000 empirical solar irradiance model and forecast tool. J. Atmos. Sol-Terr. Phys. 2000; 62; 1233-1250.
51. Truman JW, Riddiford LM. The evolution of insect metamorphosis: a developmental and endocrine view. Phil Trans R Soc Lond. 2019;
52. Vernazza JE, Avrett EH, Loeser R. Structure of the solar chromosphere. III. Models of the EUV brightness components of the quiet Sun. Astrophys J. 1981; 45: 635-725.
53. Vita-Finzi C. The Dicke cycle: a ~27-day solar oscillation. J Atmos Solar-Terr Phys. 2009; 72:139-142.
54. Vita-Finzi C. The Contribution of the Joule-Thompson effect to solar coronal arXiv. 2016; 1612.
55. Vita-Finzi C. The Sun Today. Springer Cham. 2018.
56. Welsch BT. The photospheric Poynting flux and coronal heating. Publ Astron Soc Japan. 2015; 67: 18.1-18.17.
57. Withbroe GL, Noyes RW. Mass and energy flow in the solar chromosphere and corona. Annu Rev Astron Astrophys. 1977; 15: 363-387.  
58. Wright KH, Stone NH Samir U. A study of plasma expansion phenomena laboratory generated plasma wakes: preliminary results. J Plasma Phys. 1985; 33: 71-82.