# **Stochastic Space Charge GPT Tool**

### Project Outline:

As we move to ultra-high brightness photocathodes and ultra-cold beams, we may become more sensitive to stochastic, point-to point effects such as disorder induced heating and the Boersch effect, given the failure of Debye screening. In modern beam dynamics codes, point to point interactions are often approximated by a potential created by smoothing the charge over space, removing sensitivity to these effects. The beam dynamics code, General Particle Tracer(GPT) provides a faster method for including these stochastic effects, but does not allow for the inclusion of effects from the cathode. This work aims to make a GPT tool to quickly simulate the effects of stochastic space charge in the context of photoinjectors.

### Current Collaborators:

- At Cornell University: Jared Maxson
- At University of Chicago: Matthew Gordon, Young-Kee Kim

### Barnes Hut Tree Algorithm:

Brute force calculation of the coulomb interaction in simulation scales as the number of particles squared. This makes simulations with a large number of interacting particles computationally prohibitive. The major difference between smooth and discrete treatment of space charge come from the interactions of particles which are very close together. Thus a good approximation for the field acting on an individual particle can be made by grouping farther away charges and exactly calculating the field from close by particles. The exact method of grouping the charges is called the Barnes Hut Tree Algorithm which you can learn more about here.

### Including the Cathode:

The effect of the cathode is included through the method of image charges. In order to prevent divergent fields for electrons at the cathode the idea of the Plummer smoothing radius is used. In point like interaction simulations, the Plummer radius acts as a minimum separation between particles for field calculation. When a particle is more than the Plummer smoothing radius from the cathode, an image charge for the particle is created. It should be noted that this choice is not physical, however a minimal image charge distance can be justified.

### Syntax:

The custom algorithm is called with the following syntax:

Imsctree(Theta,Cathode_z,Max_Image_dist, Min_Image_dist);

Theta: Barnes Hut Theta, controls the accuracy of the Barnes Hut Algorithm by determining minimum distance to cell:cell size ratio

Cathode_z: determines the location of the cathode in z

Max_Image_dist: Farthest distance image charge is created from the cathode

Min_Image_dist: Minimum distance from cathode image charges are created, if not given, defaults to 1fm

##### Checks:

225 keV DC Photocathode