Non-modal analysis of the diocotron instability: Plane geometry

The comprehensive investigation of the temporal evolution of the diocotron instability of the plane electron strip on the linear stage of its development is performed. By using the method of Kelvin of the shearing modes, the role of the initial perturbations of the electron density is elucidated, which is connected with the problem of the continuous spectrum. The linear non-modal evolution process detected by the solution of the initial value problem, leads toward convergence to the phase-locking configuration of the mutually growing normal modes.