The phase velocity equations are derived analytically.
The phase velocity calculated from equation (6) was the average wave velocity.
The states are influenced by the average flow velocity, the size of DE droplet and carrier phase velocity.
Pukhov, A. et al. Phase velocity and particle injection in a self-modulated proton-driven plasma wakefield accelerator.
The phase velocity equations for surface acoustic waves are obtained.
The phase velocity (i.e. the effective phase velocity) of the superposed particle vibration is different from those of the modes.
Then the phase velocity of the wave42 was derived If the dispersion effect was not considered, the relation λ = 2π/k = 2πd02/h must be satisfied.
In this geometry, the fundamental harmonic has a phase velocity synchronous with an electron velocity of corresponding to an electron energy of 25 keV.
Using the scaling theory41 from the view of energy equilibrium, we derived the dispersion relation of the capillary wave to evaluate the phase velocity.
The phase velocities are then inverted for fundamental-mode Rayleigh phase velocity maps at a grid spacing of 0.3°, at periods from 10 to 100 s.
Schroeder, C. B., Benedetti, C., Esarey, E., Grüner, F. J. & Leemans, W. P. Growth and phase velocity of self-modulated beam-driven plasma waves.
