15lerg~.-I.mlallCC arotllllellls are combined wilh Ihe s(ochaslic-growth theory of type II[ radio sources to determine the properties of line source ill average dynamical equilibliuttl wilh Ihe beam, and Ihe beam's hmg-term evolution. Purely linear stoclnastic-growlh theory has pre.iously emphasized that the beam evolves to a slate close Io marginal stability. Small mean residual deviations from marginal stability are present at dynanlical equilibrimn and lhese lead to residual energy' flows that feed Ihe waves observed in .situ and by remote receivers; consequentl 5, the beam energy is depleled.
Here. dynalnical equilibrium bealn alld wave levels al-e estimated for Ihc [irsl lime and it is fotmd that the main sink of beam-driven Langtnuir waves is either via clcclrostatic decay iJllO product Langmuir and ion-sound waves or via scattering by shorl-.wavelength density fluctuations, depending on line conditions, hnproved estimates of eneley hranchirlo ratios imply' thai, at I AU from the Sun, typically 20% of the beam energy is con\erled n.~ l,anglnuir waves thai are scattered off low-flequenc 5. density Ilucluatior~s and then dissipated, with ahnost all the renmining waves undergoing electrostatic decay, althoueh as liu.le as one-third of the Langmuir waves lnay decay in atypical circumstances. (.)f order 10 -~ of the bean1 energy is converted into SOUlld Wl.l\Cs, which are mostly dissipated, and of order 10 -+ is converted into potentially observable electrornagnelic waves. The inean lifetime of the Langnluir waves at I ,.{+7 is 1-40 s, while that of the beatn is of order 1000 s. The beanl density decreases relative to that of the background as Ihc beam propagales. For most parameters, analysis of energy losses fronl the bealll to the waves shov,s that the heam velocil,., decreases at roughly lhe same rate as the thermal velocity of the hackground plasnla. lt is argued froln these considerations, and front in situ observations at I AU, that these trends imply that only the densest and fastest type 11I beams will be able to penetrate mucl+l past I At; frorn the Sun. This imlflies a Iove-fiequency. cutoff to type III emission at roughly. 10 kHz, in good agreement with ,ecent Ulysses remote observalions, showing their consislency v+.Jth it+ silu measurements.