Abstract
Transverse dipole modes in bunches with space charge are simulated using the synergia accelerator modeling package and analyzed with dynamic mode decomposition. The properties of the first three space charge modes, including their shape, damping rates, and tune shifts are described over the entire range of space charge strength. The intrinsic Landau damping predicted and estimated in 2009 by one of the authors is confirmed with a reasonable scaling factor of $\ensuremath{\simeq}2.4$. For the KV distribution, very good agreement with PATRIC simulations performed by Kornilov and Boine-Frankenheim is obtained.
Highlights
The Landau damping effect, which provides an important mechanism for stabilizing beam propagation, is an important research topic in accelerator physics
For each mode the beam is excited with a shape proportional to the corresponding space charge harmonic calculated in Ref. [6]
We propose a formula for the intrinsic Landau damping of the 3D-G bunches that fits reasonably well over the entire range of space charge strengths, 0.4 mode 1 mode 2 mode 3
Summary
The Landau damping effect, which provides an important mechanism for stabilizing beam propagation, is an important research topic in accelerator physics. For Landau damping to take place, a continuous incoherent spectrum around the coherent frequency is required. Aside from nonlinear lattice elements, incoherent tune spread is provided by space charge. The damping mechanism caused by space charge is not fully known, especially for bunched beams and at intermediate space charge strength. Many high-intensity hadronic synchrotrons operate in the intermediate or strong space charge regimes (e.g., the Fermilab Booster and the CERN PS). The beam dynamics of a bunch is investigated over the entire range of the strength of the space charge effect, from no space charge to the strong space charge limit. A comparison between the modes’ properties between bunches with a transverse Gaussian distribution (3D-G) and bunches with a transverse Kapchinsky-Vladimirsky (KV-G) distribution, both with a longitudinally Gaussian profile, is presented
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