Dynamics of shielding of a moving charged particle in a confined electron plasma

Abstract

Dynamics of shielding of a moving charged particle in a confined plasma, which represents a realistic model of an electron beam in accelerators, is studied. This is a longstanding problem in plasma physics with important applications in accelerator physics. However, only solutions for an infinite unrealistic plasma are available. We developed a novel method to solve this problem, which consists of transformation of the Vlasov-Poisson differential equations to an integral equation for the Laplace image of the electron density perturbation created by an external charge. The integral equation is then solved numerically via the piecewise polynomial collocation method and the fast Fourier transform. We present thorough analysis of the results obtained and their physical interpretation.

Simulation studies of modulator for coherent electron cooling

“…It is also the most likely reason of the expanding wave responsible for the oscillating wing in the density modulation. This phenomenon has similarity with the presence of waves in shielding of a moving charged particle in a confined electron plasma [8].…”

“…There is an analytic solution to the modulator problem involving an ion moving in a cloud of electrons with uniform spatial distribution [7]. For a system with spatially nonuniform electrons, numerical approaches are employed that either solve the Vlasov equation [8] directly or use macroparticle simulations [9]. One of the difficulties in a macroparticle simulation originates from the fact that the signal due to the modulation is too weak compared to the shot noise resulting from the discreteness of macroparticles.…”

Cooling rate for microbunched electron cooling without amplification

“…A considerable effort has been devoted to theoretical and computational analysis of various aspects of coherent cooling [4,8,[10][11][12]. However, to our knowledge, the theory is still lacking a simple formula that would allow to predict the cooling rate and its scaling with the main parameters of the cooling system, similar to simple formulas available for the traditional electron cooling [13].…”