ICAP 2002 Abstracts and Posters
Accuracy analysis of a 2D and 3D Poisson-Vlasov PIC solver and estimates of the collisional effects in space charge dynamics
Abstract
We analyze the accuracy of a Poisson-Vlasov PIC integrator developed for a 2D high current beam, taking the KV as a reference solution for a FODO cell. The time evolution is symplectic and the Poisson solver is based on FFT. The numerical error is evaluated by comparing the moments of the distribution and the electric field with the exact solution. A linear error growth with number of particles $N$, whose slope depends on the number $K$ of Fourier components and the perveance, is observed for the emittance, electric field and rms radii. This effect is due statistical fluctuations of the density and can be modeled by a white noise in the envelope equations for the KV beam, whose analytical solution shows a linear growth of the emittance. The onset of linear KV instabilities also depends on $N$ and $K$. A similar code has been developed in the fully 3D case for a short bunch and applied to the linac ADS design at LNL (Italy).
In order to investigate the collisional effects we have integrated the Hamilton's equations for $N$ charged macro particles with a hard-core $r_H$, reducing the computational complexity to $N^{3/2}$. In the constant focusing case we observed that the beam relaxes to the Maxwell-Boltzmann self consistent distribution with a period, depending on $r_H$, which has a finite limit for $r_H\to 0$ . A comparison with Landau collisional integrals is being considered to select the appropriate stochastic process, we plan to include in the the Poisson-Vlasov equation in order to mimick the effect of collisions.
G. Turchetti, A. Bazzani, C. Benedetti, A. Franchi, S.
Rambaldi
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