AstraA 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

grid lines

uniform charge density,

1000 macro-particles,

10x10 grid cellsbunch extension

Example: radial electric space charge field of a bunch as calculated by Astra, plotted with fieldplot

uniform charge density,

1000 macro-particles,

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 macro-particles,

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 macro-particles,

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 macro-particles,

10x10 grid cells

Example: development of space charge scaling factors in Astra.

L-band rf gun

5000 macro-particles,

10x10 grid cells

Cavity shape

Example: development of time steps.

L-band rf gun

5000 macro-particles,

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 mis-matched grid.

Emission of particles from the cathode

Quasi random distribution based on a Hammersley sequence.

Emission of particles from the cathode

the space charge field is scaled with:

Particles are sorted w. r. t. their emission time. After the emission of a single particle

When a complete time step is fulfilled a new space charge field calculation is initiated.

Some resolution below a time step.

1 QQ

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:

20

16 /

QE

r

MV m

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

without space charge

Ekin = 0.0 eV

Ekin = 0.25 eV

Ekin = 0.5 eV

Ekin = 1.0 eV

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.