Recent developments in theoretical and numerical modeling of Langmuir
turbulence in space and laboratory plasmas are addressed Kinetic effec
ts, which have been missing from (fluid) traditional Zakharov equation
models are explored using Vlasov code simulations. These studies are
motivated by beam-driven Langmuir waves and particle distributions mea
sured in Earth's foreshock region, and by beam-driven Langmuir waves a
nd beams that underlie Type III solar radio emission in the solar wind
. The nonlinear physical processes studied in these 1-D Vlasov simulat
ions include bath wave-wave interactions and acceleration of particles
by waves-leading to electron-beam flattening. We study bump-on-tail i
nstabilities as boundary value problems, and determine the interplay i
n space and time between beam plateau formation, stimulated wave-wave
backscatter cascades, and strong turbulence wave-packet collapse.