This paper theoretically investigates the coherent phase control in electron-argon scattering assisted by a bichro- matic laser field. The laser field is composed of a fundamental component and its second harmonic. The incoming and out going states of electron are described by the Volkov wave functions, and the electron-target interaction is treated as a screening potential. Numerical results for differential cross section of multiphoton processes vs the phase difference between the two components of laser field are discussed for several scattering angles and impact energies.
As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 （2005）], we investigate the Apell-Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.
The positron impact-ionisation of atomic hydrogen in the presence of a linearly polarised bichromatic field is investigated in the first Born approximation. The field is composed of a fundamental frequency and its second harmonic. The state of positron in the field is described by the Volkov wavefunction, and the continuum state of the ejected electron is described by the Coulomb-Volkov wavefunction. The dressed ground state of target is a first order time-dependent perturbative wavefunction. The triple differential cross sections and their dependencies on laser field parameters are discussed and compared with the results modified by a monochromatic field. Numerical results show that the coherent phase control is significant and the laser-assisted ionisation cross sections caused by positron and electron are different.
