Envelope Dynamics and Stability with non-linear Space-Charge Forces

Michael Holz; Volker Ziemann

doi:10.1016/j.nima.2019.163045

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arXiv · 1905.00660

Envelope Dynamics and Stability with non-linear Space-Charge Forces

Michael Holz·Volker Ziemann

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Abstract

We developed a model to calculate the stability of Gaussian beam distributions with non-linear space-charge forces in the presence of random and skew-quadrupole errors. The effect of the space-charge force on the beam matrix is calculated analytically including full cross-plane coupling in 4D phase space, which allows us to perform fast parameter studies. For stability analysis, we find the fixed points of the beam including the space-charge forces and construct a Jacobi-matrix by slightly perturbing the periodic solution. The stability of envelope oscillations is inferred by eigenvalue analysis. Furthermore, we employ envelope tracking as a complementary method and compare the results of the eigenvalue analysis with FFT data from the tracked envelope. The non-linearity of the space-charge force in combination with lattice errors and beam coupling opens up for envelope-lattice resonances and envelope coupling resonances. Hitting these resonances leads to envelope blow-up, causing an effective beam mismatch. Therefore, we finally examine the effect of beam mismatch on the envelope tune-shift and its stability.

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Michael Holz, Volker Ziemann. 2019-11-04. Envelope Dynamics and Stability with non-linear Space-Charge Forces. https://doi.org/10.1016/j.nima.2019.163045

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