ICARUS 58, 182-185 (1984) Alfven Drag for Satellites Orbiting in Jupiter's Plasmasphere* L. ANSELMO* AND P. FARINELLA? *CNUCE, Via S. Maria 36, 1-56100, Pisa, Italy, and ~;Scuola Normale Superiore e Dipartimento di Matematica dell' Universitd di Pisa, Piazza dei Cavalieri 2, 1-56100 Pisa, Italy Received November 28, 1983; revised February 13, 1984 According to a mechanism discovered by S. D. Drell, H. M. Foley, and M. A. Ruderman ((1965). J. Geophys. Res. 70, 3131-3145), a satellite orbiting around a planet having a strong magnetic field and a dense ionospheric plasma dissipates orbital energy via radiation of Alfvrn waves. The dissipation process is effective for objects larger than a minimum size and made of material exceeding a minimum electrical conductivity. It is shown that the corresponding drag effect could have influenced in a significant way the orbital evolution of the small natural moons orbiting inside or in proximity of Jupiter's ring. In particular this mechanism could explain the absence in the ring of objects in the size range from -0.1 to -10 km. The motion of a conductor across a mag- netic field B induces in the conductor itself an electric charge separation canceling the electric field E = (v × B)/c which is seen in the co-moving reference system (here v is the velocity of the conductor relative to the magnetic field and c is the velocity of light). If the body (e.g., a spacecraft or a natural satellite) is moving through a plasma (e.g., a planetary plasmasphere), then according to a physical mechanism described origi- nally by Drell et al. (1965) the charge can be conducted away via generation of Alfvrn waves. This implies that a dc current flows through the conductor and at the same time some mechanical energy is converted to that of Alfvrn radiation. In this note we in- tend to show that the corresponding drag effect could be relevant (and possibly mea- surable in the near future) for the small nat- ural satellites orbiting in the inner plasma- sphere of Jupiter. We recall that Alfvrn waves are mag- netohydrodynamic disturbances of fre- quency oJ much less than the ion cyclotron frequency f/i = eB/Mic, i.e., < i04B(Mp/Mi) Hz, (1) where B is the field strength in Gauss and * Paper presented at the "Natural Satellites Confer- ence," Ithaca, N.Y., July 5-9, 1983. 00~9-1035/84 $3.00 Copyright © 1984 by Academic Press,Inc. All rights of reproduction in any form reserved. Mp/Mi is the proton to ion mass ratio. Since a moving body of size D and velocity v radi- ates at frequencies of the order of v/D, the generation of Alfvrn waves is important only if D > 10 -4 U Mi. (2) BMp' for B = 1 G, o -- 104 m/sec, MJMp = 1 we obtain the condition D > 1 m (except where noted, we shall use Gaussian units). Thus, in the cases of interest for us, the mecha- nism discovered by Drell et al. is not effec- tive for dusty particles, but can be applied only to macroscopic objects. How much energy can be dissipated? If VA is the Alfv6n velocity VA = c 1 + (3) where P is the plasma mass density (note that the usual definition VA = B/4V~o is valid only in the limit VA < C; see Clemmow and Dougherty, 1969, p. 170), then Drell et al. derived that the energy dissipation rate is B 2 V 2 P = -- -- D 2. (4) 27r VA However, this dissipation occurs only pro- vided three assumptions are verified: (1) we 182