We investigate the gravitational instability which is indicated by the appearance of an imaginary mass proportional to the squared temperature. We show in the perturbative calculations that the time component of the graviton's self-energy IIm,m, which was calculated by Gross, Perry, and Yaffe, depends on the definitions of the graviton field, while IIw,oo-KI'lp,oo does not depend on them. However, the mass derived from it is found to differ from the one in the classical argument by a factor 3. The effect of space-time curvature on this instability is qualitatively studied. I. INTKODUCTIONRecent developments in grand unified theory combined with cosmology could provide a possible explanation, called the inflationary-universe to how our universe was created. The advantage of this scenario is that not only can it give solutions to the long-standing classical puzzles such as the horizon and flatness problems4-' but it can also explain the baryon-to-entropy ratios and the monopole problem.9 On the other hand, it is an unsatisfactory point that no dynamical effects of gravity are taken into account in this scenario. Only the effects of global structure of curved space-time have been investigated. lo Beyond the grand-unification mass scale gravity is thought to play important roles in the history of the early universe. One of them is the creation of particles by the rapidly changing gravitational field." Another example is the formation of primordial black holes12 and their evaporation.'3 Very recently it was suggestedl%hat the bigbang explosion itself might have been the result of a firstorder phase transition involving gravity. This investigation also suggests that gravity, especially its finitetemperature effects, would play the key role in our understanding of the universe.A remarkable property of gravity is its universally attractive nature which causes many instabilities. Even classical Newtonian theory involves Jeans instability,'' which is a close resemblance to the plasma o~cillation.~ With these instabilities, it is tempting to inquire about the instability (or stability) of the ground state of quantum gravity. Keeping the roles of quantum gravity in the early universe in particular in mind (although they are beyond the present investigations), we should investigate the ground state of quantum gravity at finite temperature. It may give a clue to understanding the very early universe. For this purpose, let us take quantized matter fields coupled to gravity and consider the analogy of the plasmon phenomenon in gauge theories such as Q E D and Q C D . '~? '~ In these theories, massless gauge bosons in a medium (i.e., in the hot vacuum) acquire masses proportional to temperature, which indicates the screening of charges. The work of Gross, Perry, and Yaffe18 is the first to investigate the one-loop thermal correction of fermions to the graviton propagator in flat space. They found that the time component of the graviton's selfenergy evaluated at zero four-momentum develops an imaginary mass, which is proportiona...

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The ion beams are produced by a cylindrical thermal contact-ionization plasma source with an electrostatic lens system. The source plasma is produced at the inside surface of a 5-mm-diam 20-mm-long Re foil cylinder protected with a W cylinder. The surface is heated up to 3000 K by electron bombardment. The material to be ionized is fed to the surface through a guide pipe from a reservoir. Generation of all alkaline metal ions have been tested and a beam current of hundreds of μA is obtained. The efficiency for Li+ production is 30%, while that for Cs+ is nearly 100%. Alkaline earth ion beams, except Mg, are generated. A current of Ba+ up to 200 μA is obtained, while a Tl+ beam of over 200 μA is achieved. Halogen negative ion beams, except F−, of the order of 10 μA are also obtained when alkali halides are used. Attempts to extract Li− from the source are also being made.