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10.2 Influence of the space charge in a drift

The same plots than before will be shown for a distribution without correlation between $ x$ and $ x'$, excepts that here, the space charge forces are taken into account.
Figure 10.5: Evolution of the transversal space charge for a drift with space charge forces. From left to right : $ z=0$m, $ z=2$m and $ z=4$m. This time, the dispersion $ x'$ is no longer constant. The space charge forces induce an expension of the bunch in more directions
Image drift4m_cylinder1104-Ek15-Q025-Ez2-Ex5-10000_1_z=00_phase_space_x_tim2white_3d
Figure 10.6: Evolution of the longitudinal space charge for a drift with space charge forces. From left to right : $ z=0$m, $ z=2$m and $ z=4$m. This time, the longitudinal phase space is modified during the drift. Remembering that the distribution is a cylinder, and remembering the shape of the longitudinal space charge field for a cylinder, one can understand why the following shape is found.
Image drift4m_cylinder1104-Ek15-Q025-Ez2-Ex5-10000_1_z=00_phase_space_z_tim2white_3d

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Emmanuel Branlard