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2009fermi
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4. On the implementation of a 3D algorithm
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2
Implementation of the space charge algorithm
Subsections
4
. On the implementation of a 3D algorithm in Astra
4
.
1
Wider prospects for the algorithm
4
.
1
.
1
The need to adapt the meshing
4
.
1
.
2
No momentum direction favorised
4
.
2
General description of the method
4
.
3
Detailled description of the method
4
.
3
.
1
Frame definitions
4
.
3
.
2
Boosting the distribution to the rest frame
4
.
3
.
3
Rotation of the bunch to its principal axis
4
.
3
.
4
Diagonalization algorithm
4
.
3
.
5
Space charge calculation
4
.
3
.
6
The 3d space charge algorithm
4
.
3
.
7
Solving the equations of motion
5
. Space Charge calculation
5
.
1
Poisson equation
5
.
2
Resolution of poisson screened equation with the use of Fourier transform
5
.
3
Resolution of poisson screened equation with the use of Green function
Next:
4. On the implementation of a 3D algorithm
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3.2 Beam matrix and phase space
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Emmanuel Branlard
http://emmanuel.branlard.free.fr/