Propagation of a cloud of hot electrons in the regime of fast relaxation

The propagation of a cloud of hot electrons and generation of Langmuir waves are investigated using numerical simulation of the quasilinear equations and analytical gas-dynamic theory. The validity of the gas-dynamic theory is investigated and the accuracy of Ryutov and Sagdeev's gas-dynamic equations is explored. It,is found that inclusion of spontaneous emission terms in the gas-dynamic equations is necessary for self-consistency of analytical solutions. Results of numerical simulations show that the electron distribution function relaxes to a plateau state and excites Langmuir waves. Evolution of the upper boundary and the height of the plateau are investigated and it is found - at a given time and location there are three different regions in the electron beam distribution which correspond to unrelaxed, partially relaxed, and completely relaxed states. In the completely relaxed region there is a good agreement between the results of numerical simulation and the predictions of gas-dynamic theory. As the beam propagates at. a given location slower electrons arriving later excite Langmuir waves at lower velocities and reabsorb the waves generated at slightly higher velocities. Hence the upper boundary of the plateau is not constant,and moves to lower, velocities with time. Results of numerical simulations show there is an abrupt change in reabsorption of waves near the upper boundary such that damping is maximal near this velocity and decreases very rapidly for higher velocities. The coordinate extent of the beam and waves increases with time but their profiles remain similar at all times and this situation enables a self-similar solution to be used. For the total. wave energy density good consistency is found between the numerical results and gas-dynamic theory. In the case of an initially unstable beam distribution function, Langmuir wave pile-up near the injection site is observed and it is found that its efficiency depends on temperature and the mean injection velocity of the beam distribution function. These piled-up waves are slowly damped out due to weak Landau damping at the tail of cold background distribution function and propagate very slowly at their group velocity. (c) 2005 American Institute of Physics.