1. Midwest Accelerator Physics Meeting. Indiana University, March 15-19, 2004. ORBIT Electron Cloud Model Andrei Shishlo, Yoichi Sato, Slava Danilov, Jeff Holmes, SNS/ORNL

2. ORBIT E-Cloud Model Development Why another electron cloud model? To study the effect of electron clouds on the dynamics of the proton beam. Present status: The ORBIT E-Cloud Module is a collection of C++ classes. It is now fully implemented in ORBIT. Benchmarking of the secondary electron emission model and of electron-proton dynamics in preparation for application to PSR and SNS is underway. In addition to the rest of ORBIT, the simulation model includes: A 3D grid carrying the potential and density of the proton bunch. An electron bunch containing the 6D coordinates of the electrons. A 3D grid carrying the potential and density of the electron bunch. A transverse boundary defined by the beam pipe. Primary electrons generated by user specification or by protons grazing the vacuum chamber or by residual gas ionization. A secondary electron emission model which is our implementation of M. Pivi and M. Furman’s model. Electron tracking routines including electron and proton space charge as well as external magnetic and electrostatic fields. Accumulation of electron space charge forces on protons.

3. Computational Approach As with all ORBIT physics models, the electron cloud model takes the form of an ORBIT node. This node –supports the capabilities describe on the previous slide, –has a length, and –can be placed anywhere in the node sequence that makes up the beamline. Each node’s interface with the rest of ORBIT is its rectangular 3D proton grid. This grid –covers the proton distribution at the node over an entire turn, –consists of many transverse slices, –contains the proton beam densities, binned to the grid points, and the proton space charge potential on the grid. The electrons and the proton beam “see” each other only through this grid. Proton beam 3D SC potential grid

4. Computational Approach The electron cloud bunch consists of macroparticle electrons with six phase space coordinates. –The number of macroparticles varies as electrons are added to or removed from the cloud. –Primary electrons can be directly specified by the user or generated by routines simulating protons grazing the vacuum chamber and residual gas ionization. –Secondary electrons are produced by electrons striking the vacuum chamber boundary. The electron cloud node supports the electron cloud space charge forces through a 3D electron cloud grid. –The electron density is binned to this grid and the electron space charge potential is calculated on the grid. –The boundary condition for the space charge potential is conducting wall on the vacuum chamber boundary. –At present, only a few transverse slices are used in the grid. Electron Cloud Grids with few (perhaps only one) longitudinal slices

5. Computational Approach The electrons are tracked by solving their nonrelativistic equations of motion, turn by turn, with time as the independent variable. –During the turn, as time progresses the proton grid is moved through the electron cloud region at the beam velocity. –At each time the space charge forces on the protons due to the electrons are interpolated at the proton grid points from the electron grid, where they are accumulated throughout the turn as kicks. –The space charge forces on the electrons due to the protons and to the electrons are interpolated at the electron positions from the proton and electron grids, respectively. –These space charge forces are combined with any external forces to integrate the electron motion. Electron motion –can be integrated symplectically using a leapfrog method, or –can be integrated analytically, using a constant local field approximation, or –can be integrated by other methods, such as guiding center approximation.

6. Computational Approach Following each time step: –Each electron must be tested to determine whether it remains in the electron cloud region  If an electron crosses the beam pipe boundary, the Pivi-Furman electron- wall interaction routines must be run for that electron.  If an electron leaves the longitudinal node end, its longitudinal velocity is reflected, i.e. it bounces off the end. –The electrons must be rebinned onto the electron grid, and the electron space charge potential recalculated. –The proton grid must be moved to its position at the new time. –The next step is then ready to begin. Electron-wall interaction model: –Physics is an implementation of Pivi-Furman (backscattering, rediffused, and true secondary contributions). –Statistics can be used to produce macroparticles of enhanced weight in order to limit the number of macroparticles produced. Following the entire turn, the accumulated electron space charge kicks are applied to the proton beam by interpolation from the proton grid. This is the last operation performed by the electron cloud node.

7. Tracker Benchmark This is the test for 2D solver and the tracker.

8. Proton Bunch Field Source Benchmark Uniform proton bunch: L = 109 [m] N = 1.0*10^14 protons R = 20 [mm] The class pBunch instance reads coordinates of the protons, bins them, calculates field, defines pBunchFieldSource. One electron is moved by tracker inside this bunch with zero initial velocity and x_ini=10 [mm]. We have to see oscillations.

9. E-cloud Benchmark with p-Bunch fields The real proton bunch from ORBIT was used. Np = 10^14 Pipe Electron Cloud Region Proton Bunch

10. Benchmark Status 1.The whole new e-cloud module has been integrated in the ORBIT simulation code. The new module includes the following features: M. Pivi and M.Furman’s SEY surface model The full p-bunch and e-cloud dynamics including interactions between them External magnetic and electric fields in the e-cloud region Two sources of initial electrons: produced by (1) proton losses at the surface of vacuum chamber; (2) residual gas inonization 2.The benchmark of the code with the two stream instabilities example is in progress. The quantitative agreement is the final goal 3.Some initial benchmarks with simplest models that can be solved analytically have been done The example: p-bunch passing through the uniform e-cloud p-bunch e-cloud The change in the transverse momentum of protons are in perfect agreement with analytical calculations

11. E-Cloud Development (ORBIT Simulation)