Envelope dynamics and stability with non-linear space-charge forces

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 skewquadrupole 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 nonlinearity 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.

Improved Algorithms for Calculating the Space-Charge Field in Vacuum Devices

“…The space-charge field (SCF) [1][2][3][4][5][6] is an important physical factor in electronic vacuum devices, particle accelerators [7][8][9][10][11][12], free electron lasers (FEL) [13] and plasma systems [14][15][16][17][18]. It is generated by electrostatic interaction between charged particles.…”