Transcript Astra Klaus Flöttmann DESY A Space Charge Tracking Algorithm

Astra
A Space Charge Tracking Algorithm
Klaus Flöttmann
DESY
Zeuthen 18.08.03
General
• Program development started in ’96
based on a precursor by Ch. Stolzenburg
• written in Fortran 90, runs on:
– Windows PC
– LINUX PC
– SUN UNIX
– MAC OS
• ~ 50 -100 users
Astra design philosophy
• the program is user oriented, i.e. it is
designed
– to be easy to use
– to be robust against user errors
– to avoid ambiguous parameters
• Astra supports parameters scans.
• Astra is complemented by graphics and
analysis tools.
Astra design philosophy
• in order to avoid the development of
diverging versions only executables are
distributed.
• to give the user insight into what is
going on in the code a number of tools
are provided. Examples will be shown in
the following.
Space Charge Calculation
- a grid consisting of rings
(transversely) and slices
(longitudinally) is set up for
the space charge calculation.
- the grid size matches the
dimensions of the bunch,
with some additional grid
cells added automatically
outside of the bunch.
Space Charge Calculation
- the space charge field is calculated in
the average rest frame of the bunch
assuming a constant charge density inside
the ring elements.
- remaining non-relativistic velocity
components in the average rest frame can
be taken into account.
- in the center of the bunch statistical
problems may arise due to the small cell
volume despite the higher charge density.
Example: radial electric space charge field of a bunch as
calculated by Astra, plotted with fieldplot
uniform charge
density,
grid lines
1000 macroparticles,
10x10 grid cells
bunch extension
Example: radial electric space charge field of a bunch as
calculated by Astra, plotted with fieldplot
uniform charge
density,
1000 macroparticles,
10x10 grid cells
increased cell
size in the center
Example: radial electric space charge field of a bunch as
calculated by Astra, plotted with fieldplot
uniform charge
density,
5000 macroparticles,
10x10 grid cells
adjusted cell size
Space Charge Calculation
The grid and the space
charge field are scaled as
the bunch propagates
through the beam line
according to varying
bunch dimensions, charge
and energy.
When the scaling factor exceed a user defined limit a new
space charge calculation is automatically initiated.
Example: development of electric space charge field as
seen by probe particles. (Calculation with Astra, plotted with
lineplot.)
L-band rf gun
5000 macroparticles,
10x10 grid
cells
Example: development of electric space charge field as
seen by probe particles. (Calculation with Astra, plotted with
lineplot.)
L-band rf gun
5000 macroparticles,
10x10 grid
cells
Example: development of space charge scaling factors in
Astra.
L-band rf gun
5000 macroparticles,
10x10 grid
cells
Cavity shape
Example: development of time steps.
L-band rf gun
5000 macroparticles,
10x10 grid
cells
Emission of particles
from the cathode
Emission of particles from the cathode
Random
distribution
with
clusters
and voids.
Emission of particles from the cathode
Regular
distribution
with mismatched
grid.
Emission of particles from the cathode
Quasi
random
distribution
based on a
Hammersley
sequence.
Emission of particles from the cathode
Particles are sorted w. r. t. their emission
time. After the emission of a single particle
the space charge field is scaled with:
When a complete time step is fulfilled a
new space charge field calculation is
initiated.
Some resolution below a time step.
Emission of particles from the cathode
The grid is set up
successively as the
particles come out
of the cathode.
Equivalently a
mirror charge
bunch is generated
Example: Space Charge field at the cathode during
emission.
1 nC,
3.0 mm dia.
Plate capacitor:
Example: Space Charge field at the cathode during
emission.
space charge
limited emission:
5 nC launched
2.3 nC emitted
3.0 mm dia.
Emission of particles from the cathode
In Astra it is not necessary to assign
the same charge to all macro particles.
This allows to simulate the emission
self-consistently, e.g. when the quantum
efficiency of the cathode depends on
the applied accelerating field, so-called
Schottky effect.
Example: Charge vs. phase of an rf gun.
1 nC, 40 MV/m
Example: Charge vs. phase of an rf gun.
1 nC, 40 MV/m
with strong
Schottky effect
Example: Charge vs. phase of an rf gun.
1 nC, 40 MV/m
Ekin = 0.0 eV
Ekin = 0.25 eV
Ekin = 0.5 eV
Ekin = 1.0 eV
without space
charge
Astra graphics tools
• for the data visualization and analyses
three graphics programs are provided
– fieldplot
– lineplot
– postpro
• the plot programs are menu controlled
Some menu pages of graphic programs
Slice emittance plot
Core emittance plot
Acknowledgement
Thanks to all colleagues who
contributed to the program
development, especially: Christoph
Stolzenburg, Phillipe Piot, Bagrat
Grigorian and Sven Reiche.