Wave particle interaction and Hamiltonian dynamics investigated in a traveling wave tube

For wave-particle interaction studies, the 1D beam-plasma system can be advantageously replaced by a Traveling Wave Tube (TWT). This led to detailed experimental analysis of the self-consistent interaction between unstable waves and a small either cold or warm beam.\footnote{G. Dimonte and J.H. Malmberg, Phys. Fluids \underline {21}, 1188 (1978); S.I. Tsunoda, F. Doveil and J. H. Malmberg, Phys. Rev. Lett. \underline {58}, 1112 (1987); D.A. Hartmann, C.F. Driscoll, T.M. O'Neil and V.D. Shapiro, Phys. Plasmas \underline {2}, 654 (1995).} More recently a test electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is investigated with a trocho\"{\i}dal energy analyzer\footnote{D. Guyomarc'h, and F. Doveil, Rev. Sci. Instrum. \underline {71}, 4087 (2000).} which records the beam energy distribution at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed.\footnote{F. Doveil, Kh. Auhmani, A. Macor, and D. Guyomarc'h, Phys. Plasmas \underline {12}, 010702 (2005).} The resonant velocity domain associated to a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap.\footnote{F. Doveil, D.F. Escande, and A. Macor, Phys. Rev. Lett. \underline {94}, 085003 (2005). } This transition exhibits a ``devil's staircase'' behavior when increasing the excitation amplitude. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region is successfully tested.\footnote{C. Chandre, G. Ciraolo, F. Doveil, R. Lima, A. Macor, and M. Vittot, Phys. Rev. Lett. \underline {94}, 074101 (2005).} This work was done in collaboration with Dr. Kh. Auhmani, Dr. D. Guyomarc'h, and A. Macor for the experimental part.