# Presentation: 445862

## Strong-Strong Simulation of Long-Range Beam-Beam Effects at LHC and RHIC

- Ji Qiang

- LARP IR Workshop, Chicago, Oct 3-4.

- Work performed under the auspices of the
**DOE Advanced Computing for 21st Century Accelerator Science and Technology Project **using resources at the
**Center for Computational Sciences** and the
**National Energy Research Scientific Computing Center**

## Outline

**Introduction**
**Computational model**
**Strong-strong simulation of RHIC long range beam-beam effects (in collaboration with W. Fischer) (****preliminary results****)**
**Strong-strong simulation of LHC long range beam-beam effects (in collaboration with M. Furman and CERN beam-beam group)(****preliminary results****)**

## Introduction

**What factors could affect the long range beam-beam effects?**
**Tune? Crossing angle? Density variation? Beam size anisotropy? Beam size mismatch? Machine nonlinearity? etc**
**Can we compensate the long range beam-beam effects?**

## Particle-In-Cell (PIC) Simulation

**Particle-In-Cell (PIC) Simulation**

- Advance momenta using radiation damping and quantum excitation map

- Advance momenta using Hspace charge

- Field solution on grid to find beam-beam forces

- Charge deposition on grid

- Field interpolation at particle positions

- Setup for solving Poisson equation

- Initialize
- particles

- (optional)
- diagnostics

- Advance positions & momenta using external transfer map

## Two Beam Collision with Crossing Angle Alpha

**IP**

- Lab frame

- Moving frame: c cos(alpha)

- 2 alpha

**Two Beam Collision with Crossing Angle Alpha**

## Quadratic Deposition/Interpolation

- -1

- 0

- +1

## A Schematic Plot of the Geometry of  

- x

- y

- Particle Domain

- -R

- 2R

- R

- 2R

- 0

**A Schematic Plot of the Geometry of  **
**             ****Two Colliding Beams**

- Field Domain

## ;  r = (x, y)

- ;  *r = (x, y)*

- Direct summation of the convolution scales as N4 !!!!
- N – grid number in each dimension

## Green Function Solution of Poisson’s Equation (cont’d)

_*Hockney’s Algorithm*__:- __*scales as (2N)*__*2*__*log(2N)*_
- - Ref: Hockney and Easwood, ***Computer Simulation using Particles***, McGraw-Hill Book Company, New York, 1985.

_*Shifted Green function Algorithm*_*:*

## Ex

**Comparison between Numerical Solution and **
**Analytical Solution (Shifted Green Function)**

- Ex

- radius

- inside the particle domain

## Ey

**(Integrated Green Function)**

_*Integrated Green function Algorithm for large aspect ratio*__:_

- x (sigma)

- Ey

## BeamBeam3D:

**Parallel Strong-Strong / Strong-Weak Simulation Code**

- Multiple physics models:
- strong-strong (S-S); weak-strong (W-S)
- Multiple-slice model for finite bunch length effects
- New algorithm -- shifted integrated Green function -- efficiently models long-range parasitic collisions and large aspect ratio beams
- Parallel particle-based decomposition to achieve perfect load balance
- Lorentz boost to handle crossing angle collisions
- W-S options: multi-IP collisions, varying phase adv,...
- Arbitrary closed-orbit separation (static or time-dep)
- Independent beam parameters for the 2 beams

##                 RHIC Physical Parameters 

- Beam energy (GeV)                          26

-                 **RHIC Physical Parameters **
**for the Long-Range Beam-Beam Simulations**

- Protons per bunch                            19e10

- * (m)                                                20

- Rms spot size (mm)                         1.6/1.29

- Betatron tunes                             (0.7xx,0.7xx)

- Rms bunch length (m)                       3.6

- Synchrotron tune                               3.7e-4

- Momentum spread                            1.6e-3

- Beam-Beam Parameter                0.0077/0.0095

## RHIC Long-Range Experiment Scan 2

- Tunes (0.7351,0.7223) (0.7282 0.7233)

## RHIC Long-Range Experiment Scan 4

- Tunes (0.7394,0.7271) (0.7264 0.7388)

## RHIC Long-Range Simulation Scan 2 

- RHIC Long-Range Simulation Scan 2
-             (rms emittance vs. turn)

- 4.70 separation

- 5.54

- 7.15

- One million macroparticles for each
-  beam and 128 x128 grid points

- Beam 1 (blue beam)

- Beam 2 (yellow beam)

## RHIC Long-Range Simulation Scan 4

-             (rms emittance vs. turn)

- Beam 1

- Beam 2

## RHIC Long-Range Simulation Scan 2

- phase space (y-py) for some particles

## RHIC Long-Range Simulation Scan 4

-               phase space (y-py) for some particles

##        LHC Physical Parameters

- Beam energy (TeV)                         7

-        **LHC Physical Parameters**
** ****for the Beam-Beam Simulations**

- Protons per bunch                            10.5e10

- * (m)                                              0.5

- Rms spot size (mm)                         0.016

- Betatron tunes                             (0.31,0.32)

- Rms bunch length (m)                       0.077

- Synchrotron tune                               0.0021

- Momentum spread                            0.111e-3

- Beam-Beam Parameter                    0.0034

## IP1

- IP5

- A

- B

- C

- D

- E

- F

- 1

- 2

- 3

- 4

- 5

- 6

- A Schematic Plot of LHC Collision Scheme

## One Turn Transfer Map

- M = Ma M1 Mb M2 Mc M3 Md M4 Me M5 Mf M6

- M = M6-1 Mf M6 Ma M1 Mb M1-1 M1 M2 M3
-        M3-1 Mc M3 Md M4 Me M4-1 M4 M5 M6

- Here, Ma and Md are the transfer maps from head-on
- beam-beam collisions; Mb,c,e,f are maps from long-range
- beam-beam collisions; M1-6 are maps between collision points.

- Linear half ring transfer matrix with phase advanced:
- 90 degree phase advance between long-range collision points and IPs
- 15 parasitic collisions lumped at each long-range collision point with 9.5  separation

## Horizontal and Vertical RMS Emittance Evolution

-  (with/without Long Range Beam-Beam Effects)
-                       (0 crossing angle)

- with long range

- without long range

- X vs. Turn

- Y vs. Turn

## Definition of 99.999% Emittance 

- For each particle i, calculate emittance

- 99.999% emittance is defined as the emittance
- which contains 99.999% particles

## Horizontal and Vertical 99.999% Emittance Evolution

-     (with/without Long Range Beam-Beam Effects)
-                          (0 crossing angle)

- X vs. Turn

- Y vs. Turn

## X

- Phase Space Plots of a Test Particle at (6,0)

- Px

- Y

- Py

## Px

- X

- Y

- Py

- Phase Space Plots of a Test Particle at (0,6)

## Px

- X

- Y

- Py

- Phase Space Plots of a Test Particle at (5,0)

## Px

- X

- Y

- Py

- Phase Space Plots of a Test Particle at (0,5)

## Horizontal and Vertical RMS Emittance Evolution

-              (with 300 micron crossing angle)

- X vs. Turn

- Y vs. Turn

- Long range + headon

-  headon only

- Long range + head

- Long range only

## Horizontal and Vertical 99.999% Emittance Evolution

-              (with 300 micron crossing angle)

- X vs. Turn

- Y vs. Turn

## Tentative Summary

**Simulation shows that for scan case 2 at RHIC, blue beam 1 has a larger emittance growth than the yellow beam 2; for scan case 4, both beams have similar growth**
**Simulation shows that blue beam in scan case 2 has a larger emittance growth than the beams in scan case 4**
**These simulations seem to be in qualitative agreement with the experiment observation**
**Simulation shows strong nonlinear long-range effects at LHC **

## Future Work

**Include dynamic effects in the simulation of RHIC long-range effects**
**Include wire compensation at RHIC**
**Include density variation in the simulation of LHC long-range effects**
**Include beam size anisotropy in the simulation of LHC long-range effects**
**Include beam mismatch in the simulation of LHC long-range effects**
**Include dynamic effects in the simulation of LHC long-range effects**
**Study pacman bunch effects at LHC**
**Include wire compensation at LHC**
**Receptive to comments **