GaussianSpaceCharge

This repository contains the implementation, with some bugs, of an Analytic Space-Charge Model for Gaussian Beams with cross-plane coupling, based on the research paper by M. Holz and V. Ziemann (link to the paper).

Installation

To install the package, follow the instructions:

$ git clone https://github.com/isavoj/GaussianSpaceCharge.git
$ cd GaussianSpaceCharge

(Optional step, but recommended:) Create and activate a virtual environment:

$ python -m venv env
$ source env/bin/activate  # On Windows, use 'env\Scripts\activate'

Now,

$ python setup.py install

Run the main script:

$ cd gaussian_space_charge
$ (env) python main.py

---

Project Overview

The project contains 1 module called GaussianSpaceCharge, within which you'll find 4 files:

• main.py
• space_charge_calc.py
• elements.py
• beam.py

All space charge (SC) calculations are handled within the space_charge_calc.py file,containing:

• NonLinearSc Class
• calculate_T_components_linear Function
• calculate_matrix_T Function

All relevant Parameters are changed in main() in main.py

Except for :

1. Perveance: Change beam parameters for perveance by modifying the beam_perveance function in beam.py.
2. SC -T matrix: Adjust the T matrix in space_charge_calc.py, there are 2 now, 1 uncommented that includes the problematic x4_f3 and x2_f1 terms

Overview

When you run main.py, the main() function is invoked, which in turn calls the function propagate_beam_through_lattice(). This function iterates over each sliced element (divided by 2 to apply Space Charge (SC) more accurately) in a series of FODO cells and calculates the space charge effects for each slice.

+------------------------------------------------------+
|                        main()                        |
|  +-----------------------------------------------+   |
|  | Define lattice configuration and properties  |    |
|  | Set up Twiss parameters                      |    |
|  | Configure SD and cutoff for Gaussian dist.   |    |
|  | Calculate initial covariance matrix (sigma)  |    |
|  | * Propagate beam through lattice             |    |
|  | Plot resulting beam envelope                 |    |
|  +-----------------------------------------------+   |
+------------------------------------------------------+
                     |                                 | 
                     v                                 |
          +-----------------------------------+        |
          | * propagate_beam_through_lattice() |       |
          |   +---------------------------+    |       |
          |   | Iterate over elements     |    |       |
          |   |   + Calculate transport   |    |       |
          |   |   + **Apply space charge  |  |       |
          |   |   + Complete step         |    |       |
          |   +---------------------------+    |       |
          +-----------------------------------+        |
                     |                                 |
                     v                                 |
         +----------------------------+                |                                          
         | **space_charge_calc.calculate_matrix_T()    |
         +----------------------------+

---

Issue:

The x4_f3 and x2_f1 terms in the T- matrix seem to cause problems for me.

Because when I run with homogenous space charge terms, hence space-charge matrix for KV-distrbution, I get something similar to the gaussian-SC-model without these two terms:

PLOTS WITHOUT x4_f3 and x2_f1 terms (with homogenous linear space-charge matrix and non-homogenous linear space-charge terms)

KV distribution

Gaussian distribution for 2 different intensities:

PLOTS WITH x4_f3 and x2_f1 terms (with homogenous linear space-charge matrix and non-homogenous linear space-charge terms)

Gaussian distribution for 2 different intensities: