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Submitted on 1 Jan 1969
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SUPERCONDUCTIVITY OF JUPITER ?
P. Pincus
To cite this version:
P. Pincus. SUPERCONDUCTIVITY OF JUPITER ?. Journal de Physique Colloques, 1969, 30 (C3), pp.C3-19-C3-20. �10.1051/jphyscol:1969303�. �jpa-00213680�
JOURNAL DE PHYSIQUE Colloque C 3, supplt3ment au Tio 11-12, Tome 30, Nov.-D&c. 1969, page C 3 - 19
SUPERCONDUCTIVITY OF JUPITER ?
P. PINCUS
Physique des Solides (*), FacultC des Sciences, 91-Orsay
Rksumk. - Ashcroft a suggkrk que, si une phase mktallique d'hydrogkne solide (sous pres- sion > 1 mkgabar) existe, elle peut Etre supraconductrice avec une tempkrature critique t r b Bevk.
Ici on examine les ordres de grandeur des propriktks supraconductrices (Tc, Hc, k, etc ...) suivant les conditions ambiantes de la planhie Jupiter. On discutera la possibilitk que le champ magnktique de Jupiter soit cr% par les supracouranfs.
Abstract. - It has been suggested by Ashcroft that, if solid hydrogen has a metallic phase (under a pressure > 1 megabar), such a phase could be a supraconductor with very high critical temperature. Orders of magnitude for its supraconductive properties (Tc, Hc, k, etc ...) are considered in relation with the physical conditions in the planef Jupiter. The possibility that supracurrents create Jupiter's magnetic field is discussed.
Several workers [l] have suggested that under sufficient pressure (- 1 megabar) solid hydrogen (normally a molecular crystal) undergoes a phase transition to a close packed (hcp or fcc) metallic phase. This hypothetical phase is calculated to have a zero pressure density corresponding to r, = 1,6 where the electron density n is given by :
a , is the Bohr radius.
Recently Ashcroft [2] has predicted that if metallic hydrogen exists it is probably a superconductor with a high transition temperate Tc given by the BCS [3]
expression
where 8, is the Debye temperature and N(0) V, the BCS coupling constant. The Debye temperature of solid hydrogen is elevated because of the extremely light nuclear mass.
In fact, the free electron gas result for the velocity of sound v,, is
( m = electron mass, M = proton mass, v, = Fermi velocity) corresponding to r, = 1,6 is 3,5 x lo6 cm/s, or about an order of magnitude greater than is typical of solids. A more sophisticated compressibility calcu-
(*) Laboratoire associk au C . N. R. S. Ph. Sol. 69/49.
lation by Ashcroft [2, 41 taking into account band effects, exchange, and correlation effects gives a sound velocity of about one-half this value. Thus we may expect that the Debye temperature (OD av, r,'I3) to be significantly higher than in a more typical metals.
Indeed, Ashcroft finds 8, = 3,5 x lo3 OK, again about one order of magnitude greater ,than most metals.
The coupling constant N(0) V describing the net electron-electron attractive energy arising from the exchange of virtual phonons in competition with the Coulomb repulsion has also been computed in ref. 2 and is found to be at least 0,25.
When these results are inserted into (2), one finds Tc 2 100 OK. Then the thermodynamical critical field Hc can be determined from [5]
~ , 2 = 4 nN(0) (k, Tc) (4) (N(0) is the density of states at the Fermi surface for the Normal metal), and it is found that Hc 6 kg.
Similarly the London penetration depth
This leads to a Landau-Ginsburg parameter, of the order of unity implying that this is a type I1 super- conductor.
One possible astrophysical consequence of the pre- dicted superconductivity of solid hydrogen concerns cool planets ( T < Tc) whose composition is mainly hydrogen and thus, at least in the interior, under
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1969303
C 3 - 2 0 P. PINCUS considerable gravitational pressure. Jupiter, in fact, may be such a case. Radio observations [6] show that Jupiter has a magnetic field. However its order of magnitude depends on the model chosen for the origin of the decimetric radiation. For cyclotron radiation the surface polar field would have to be
- lo5 Oe
while synchrotron radiation would require
-
lo2 Oe.It is therefore not inconceivable that some portion of Jupiter is hydrogen is in a superconducting state-?
Furthermore, one may pose the possibility that the magnetic field arises from supercurrent flow. Since states of finite current density are only metastable this would require relaxation times on the order of the planetary age, which seems rather unlikly. A rather less for fetehed origin for Jupiter's magnetic field has recently been proposed by Hide [7].
References
[I] WIGNER (E.) and HUNTINGTON (H. B.), J. Chem. Phys., 1935, 3 , 764, KRONIG (R.), DE BOER (J.) and KORRINGA (J.), Physica, 1946, 12, 245, DE MARCUS (W. C.), Astron. J., 1958, 63,2.
[2] ASHCROFT (N. W.), Phys. Rev. Letters, 1968, 21, 1748.
[3] BARDEEN (J.), COOPER (L. N.) and SCHRIFFER (J. R.), Phys. Rev., 1957, 108, 1175.
[4] ASHCROFT (N. W.) and LANGRETH (D. C.), Phys. Rev., 1967. 155, 682.
[5] For a ieview of superconductivity see P. G . de Gennes, Superconductivity of metals and alloys (BENJAMIN (W. A.), Ins. New York, 1966).
[6] MICHEUX (G. M.), Handbook of the Physical Properties of the Planet Jupiter, N . A. S. A., Publication No SD-3031 (U. S. Goverment Printing Office Washington, D. C., 1967).
[7] HIDE (R.), paper in S. K. Runcorn, Magnetism and the Cosmos (Oliver and Boyd, Edinburgh, 1966).
