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2009fermi
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6. Benchmarking of the stand alone space charge
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3
On the benchmarking of the space charge algorithm
Subsections
6
. Benchmarking of the stand alone space charge algorithm without rotation
6
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1
Fields for a cylindrical distribution
6
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1
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1
Theoretical expression of the potential
6
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1
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2
Theoretical expression of the Fields for the cylinder
6
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1
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3
Graphical comparisons
6
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2
Fields for an ellipsoidal distribution
6
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2
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1
Theoretical expression of the potential for a spheroid
6
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2
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2
Theoretical expression of the Fields for a spheroid and an ellipsoid
6
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2
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2
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1
Analytical derivation of the potential for a spheroid
6
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2
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2
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2
General ellipsoid - Introducing a form factor
6
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2
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3
Graphical comparisons of the fields
7
. Rms field values - Simulation vs. theory
7
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1
On the RMS definition
7
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2
Spheroidal distribution
7
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3
Ellipsoidal distribution
7
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4
Cylindrical distribution
7
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5
Results summary
7
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5
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1
Fields calculation
7
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5
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2
RMS calculation
8
. Benchmarking of the stand alone space charge algorithm with rotation
8
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1
Testing method
8
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1
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1
Principle
8
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1
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2
Method used
8
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1
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3
Technical details
8
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2
Overview of different comparisons performed
8
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2
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1
Exemple of a coin-shape cylinder
8
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2
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2
Exemple of an ellipsoid at high energy
9
. Including our algorithm in Astra - Modifications done and problem encountered
9
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1
Astra conventions
9
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2
Organizations of the source files
9
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3
Learning from my mistakes
9
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4
Note on the sigma matrix outputed by Astra
9
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4
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1
Analysing the previous algorithm without the source code
9
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4
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2
Modifying the source code to output a standard sigma matrix
Next:
6. Benchmarking of the stand alone space charge
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Up:
Report
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Previous:
5.3 Resolution of poisson screened equation with the
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Emmanuel Branlard
http://emmanuel.branlard.free.fr/