Breakeven conditions for a deuterium-tritium mixture of prescribed temperature evolution in a spherical pinch configuration

Summary form only given. For 37 years, since Lawson in 1957, the plasma physics community has been guided in its quest for fusion by the directions provided by the so-called 'Lawson criteria' for energy breakeven conditions. These are general criteria, applicable to an idealized situation where a plasma of particle density n is brought instantaneously to a temperature T, which is maintained for a time t after which it is allowed to cool to the original temperature. The criteria state that for breakeven, the temperature has to be above 30 million degrees and the product nt must exceed 10/sup 14/ cm/sup 3/.sec in deuterium-tritium reactions. The reaction products are not retained in the plasma of the Lawson analysis, and conduction losses are neglected during the plasma burning time. These criteria apply to the so-called 'scientific breakeven', in which the energy supplied to heat the plasma and maintain the bremsstrahlung losses is returned to the system, together with the reaction energy, with a recovery efficiency /spl eta/ of 1/3. No allowance is made for the fact that the energy used to heat the plasma and supply the bremsstrahlung losses must come from a conventional source, and that the transfer efficiency is normally much less than 100 percent. In the present work, we examine in detail the complete system, i.e., source of energy and plasma sink, and consider various energy transfer efficiencies from the first to the second, as well as from the second to the first. The energy from the source is deposited in the plasma in a pulse of prescribed temporal power evolution. In order to ease the inclusion in the energy balance equation of conduction losses, the geometry considered here is the spherical one. More specifically, it is the spherical pinch geometry.