Energy loss and longitudinal wakefield of relativistic short proton bunches in electron clouds

Abstract

The aim of our study is the numerical computation of the wakefield and energy loss per unit length for relativistic, short (<10 ns) proton bunches interacting with an electron cloud inside the beam pipe. We present analytical expressions for the energy loss in the impulse kick approximation. For the simulation of the wakefields a 2D self-consistent, electrostatic particle-in-cell (PIC) code is employed. Results for the energy loss and for the wakefields are presented for the parameter scope of the CERN LHC and SPS. For selected parameters the results are compared to a three-dimensional (3D) electromagnetic PIC code.

Interaction of relativistic short proton bunches with space charge limited electron clouds

“…However, simulation results (Refs. [4,13]) show that a dense, thin (d ≪ R p ) electron layer develops near the wall. In a circular pipe between the bunches a ringlike electron cloud is formed near the pipe wall, together with a diluted homogeneous background density (see Fig.…”

“…In the CERN super proton synchrotron and in the LHC, one attributes the observed slow transverse emittance growth as well as the rf phase shift of individual bunches in the train to the effect of the electron cloud [3,4]. Both effects depend again on the wakefield induced by a short, relativistic bunch in the electron cloud.…”

“…The resulting density profile is far from being uniform. Moreover, it was shown [4] that the rf phase shift induced by a saturated electron cloud is smaller compared to an equivalent uniform electron cloud with the same total number of electrons. The effect of a saturated electron cloud profile on the transverse tune shift is the subject of the present study.…”

High-accuracy diagnostic tool for electron cloud observation in the LHC based on synchronous phase measurements

“…The e-cloud causes an energy loss of the proton beam since the electrons are accelerated by the electric field generated by the beam. The bunch energy loss has been calculated analytically and using simulations [6,7] and found to be dependent on the e-cloud density. Then, the e-cloud buildup can be observed as an increasing bunchby-bunch energy loss along the bunch trains.…”

Quantification of resistive wall instability for particle accelerator machines

“…Discontinuities of the beam pipe due to various technical accelerator components (RF cavities, collimators, kickers etc. ), existence of electron cloud effects, and the nonzero resistivity of the pipe wall are the main sources of impedances in particle accelerators and storage rings [1,2].…”