# Presentation: 878654

## Beambeam3D and IMPACT: Development and Applications

Ji Qiang
Lawrence Berkeley National Laboratory

**Ji Qiang**
**Lawrence Berkeley National Laboratory**

## BeamBeam3D

## BeamBeam3D

- Comprehensive parallel PIC code for modeling colliding beams (weak-strong, strong-strong, head-on, crossing angle, long-range)
- Recent enhancements
- Integrated Green function
- Non-uniform grid Green function
- Energy variation during collisions
- Multi-bunch and multi-collision
- Applied to Tevatron, LHC, PEP-II, KEK-B, and RHIC

## A Schematic Plot of the Geometry 

- 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 

_*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 for long range beam-beam forces*_*:*
- - Ref: J. Qiang, M. Furman, R. Ryne, **PRST-AB**, vol. 5, 104402 (2002).

## Ey

_*Integrated Green function Algorithm for large aspect ratio*__:_
- - Ref: K. Ohmi, Phys. Rev. E, vol. 62, 7287 (2000). J. Qiang, M. Furman, R. Ryne, J. Comp. Phys., 2004 (in press).

- x (sigma)

- Ey

## Green Function Solution of Poisson’s Equation

**On Non-Uniform Grid**

## Non-Uniform Grid vs. Standard Uniform Grid

- Errors of Er vs. r

- Er vs. r

- Non-uniform grid

- Uniform grid

- (Gaussian density distribution with aspect ratio 1 and 128x128 grid)

## Green Function Solution of Poisson’s Equation 

- Standard shifted uniform grid method
- (2N)2log (2N)
- Low aspect ratio
- Long range beam-beam
- Lower accuracy than the non-uniform grid method
- Integrated shifted uniform grid method
- (2N)2log (2N)
- Large aspect ratio
- Long range beam-beam
- Costly in calculation of the effective Green function
- Non-uniform grid method
- 2N2log (2N)
- Low aspect ratio

## Parallel Implementation Issues:Performance Counts!

**Example: Scaling of BeamBeam3D**

| # of processors | executiontime (sec) |
| --- | --- |
| 128 | 1612 |
| 256 | 858 |
| 512 | 477 |
| 1024 | 303 |
| 2048 | 212 |

- Strong-strong beam-beam will be crucial to LHC Optimization

- Scaling using weak-strong option

- Performance of different parallelization
- techniques in strong-strong case

## Benefit to HEP and NP Programs

- Beambeam3D has been applied to:
- LHC
- RHIC
- Tevatron
- PEP-II
- Effort has involved collaboration with many people:
- LBNL: M. Furman, R. Ryne, W. Turner
- FNAL: T. Sen, M. Xiao, P. Spentzouris, J. Amundson
- BNL: W. Fischer
- SLAC: Y. Cai
- KEK: K. Ohmi

## Beam Sweeping Detector for LHC

- stationary, accidentally
- displaced beam

- rotating, deliberately
- displaced beam

## Simulated LHC Luminosity Signal and 

**Emittance Growth after One Million Turns**

- LHC beam-beam
- simulation
- x1=x2= y1=y2=0.31,
- 0=–0.0034

- parallel PIC code
- 128x128 grid
- 10**6 particles/bunch
- 1 kick
- 16 processors
- 1 bunch/beam

- Emittance growth vs. Number of Macroparticles

##  Power Spectrum of Horizontal Centroid Motion of Three Bunches

** ****Power Spectrum of Horizontal Centroid Motion of Three Bunches**
**  ****in RHIC (Self Consistent Strong-Strong Simulation)**

- mode

- mode

- Collaboration w/ Wolfram Fischer, BNL

## Power Spectrum under Different Tunes

**Power Spectrum under Different Tunes**

- Horizontal tune of beam 2: 0.21

- Horizontal tune of beam 2: 0.20

## Parameter Studies of Anti-Proton Lifetime 

**Parameter Studies of Anti-Proton Lifetime **
**           ****of Tevatron at Injection Energy**

- Antiproton Lifetime vs. Beam-Beam Separation

- Antiproton Lifetime vs. Antiproton Emittance

## Parameter Studies of Anti-Proton Lifetime 

**Parameter Studies of Anti-Proton Lifetime **
**           ****of Tevatron at Injection Energy**

- Antiproton Lifetime vs. Proton Intensity

- Antiproton Lifetime vs. Vertical Chromaticity

-           simulations
-                raw data

## Beam-Beam Studies of PEP-II

**Collaborative study/comparison of beam-beam codes (J. Qiang/LBNL, Y. Cai/SLAC, K. Ohmi/KEK)**
**Predicted luminosity sensitive to # of slices used in simulation **

- 20 slices
- 1 slice

## IMPACT

## IMPACT (Integrated-Map and Particle Accelerator Tracking) code

- A code suite (linac design code, 3D rms envelope code, 2 parallel PIC tracking codes)
- Recent enhancements
- IMPACT-T: time-based (instead of z-based) version
- Cathode emission model
- Images from cathode
- Poisson solver for high aspect ratio situations
- Energy binning for large energy spread
- Multi-charge state capability
- These enhancements benefit projects
- Modeling rf photoinjectors
- Modeling beams w/ large energy spread, as for electron bunches emerging from plasma-based accelerators
- Multi-charge state for RIA

## Poisson Solvers

**Integrated 3D Green function**
**Shifted 3D Green function**
**High aspect ratio Poisson solvers based on Hermite-Gaussian expansion**

- Potential of a beam in a toroidal conducting pipe

## Impact User-Map

## Benefit of IMPACT to HEP and NP Programs

- _FNAL booster modeling_ reuses portions of IMPACT
**Collaboration with LANL, ANL, MSU**
- Simulation of the _RIA driver linac_
**Studies of space-charge effects, resonances, and equipartitioning in rings**
- Simulation and analysis of CERN PS experiment
**Collaboration w/ P. Piot (FNAL)**
- Modeling photocathode for _linear collider_

**Benefit of IMPACT to HEP and NP Programs**

## Combining IMPACT and MXYZPLTK for FNAL Booster modeling

**Booster simulation results and experimental results. P. Spentzouris and J. Amundson, FNAL.**

## Beam Dynamics Modeling of RIA Linac Driver

- Kinetic Energy vs. Distance

- RMS Phase Width vs. Distance

## Physics Study and Code Benchmarking of CERN PS experment using IMPACT-Z

**Study of emittance exchange near a 4th order coupling resonance during tune scan (collab. w/ Ingo Hofmann)**
**Experimental measurements and 3D simulation with IMPACT show that exchange overshoot is reduced with slower ramping**
**this is a 3D effect involving synch. motion;**
**  **_**2D simulation does not predict this**_

- 240 turn ramp
- 480 turn ramp
- 960 turn ramp
- 1920 turn ramp

**emittance**

**turn #**

## Several customers are using IMPACT-T for photoinjector studies, and others have expressed interest
Using:
LUX
ALS streak camera
LCLS
Cornell ERL
Fermilab RF photoinjector 
Expressed interest:
ANL advanced accelerator project
BNL electron cooling project
JLab

**Using:**
**LUX**
**ALS streak camera**
**LCLS**
**Cornell ERL**
**Fermilab RF photoinjector **
**Expressed interest:**
**ANL advanced accelerator project**
**BNL electron cooling project**
**JLab**

**Photoinjector Modeling **

## RF photoinjector simulation using 3D IMPACT-T

**Parallel simulation w/ IMPACT-T using 1M particles is more than 2x faster than PARMELA using 100K particles**
**Good agreement for test case (azimuthal symmetry)**

**In general, 3D problems require more particles & mesh points than 2D**
**Parallel processing makes it possible to perform 3D simulations, and perform parametric studies, with reasonable turnaround time**

## Modeling Collisional Effects

- Finite difference curves are underneath Langevin results

- In collaboration w/ J. Wei (BNL), have performed comparisons of the Langevin approach with a finite difference model
- Langevin results and FD results are in excellent agreement, but Langevin does not have instability problem present in FD method

## Summary

- Our new capabilities are benefiting national and international programs
- The codes we have developed or helped develop have been applied to many important problems. Examples:
- Beam-beam effects at Tevatron, LHC, PEP-II, and RHIC
- Dynamics of beams w/ large energy spread from plasma accelerators
- RF photocathode simulation
- Beam losses at FNAL booster
- Understanding beam halo formation, emittance growth, and equipartitioning in high intensity beams

## Publications (Jan 2002 - Present)Refereed Journals

- J. Qiang, R. D. Ryne, I,. Hofmann, “Space-charge driven emittance growth in a 3D mismatched anisotropic beam,” Phys. Rev. Lett. 92, 174801 (2004).
- J. Qiang, M. Furman, and R. Ryne, “A Parallel Particle-In-Cell Model for Beam-Beam Interactions in High Energy Ring Colliders,” J. Comp. Phys. (in press)
- J. Qiang, R. Gluckstern, "Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe", Comp. Phys. Comm. 160, 120 (2004).
- K. Ohmi, M. Tawada, Y. Cai, S. Kamada, K. Oide, J. Qiang, “Study of the beam-beam limit in e+e- circular colliders, “ Phys. Rev. Lett. 92, 214801 (2004).
- J. Qiang, "Halo formation due to beam-beam interactions of beams optically mismatched at injection", PRST-AB, vol 7, 031001 (2004).
- T. P. Wangler, C. K. Allen, K. C. D. Chan, P. L. Colestock, K. R. Crandall, R. W. Garnett, J. D. Gilpatrick, W. Lysenko, J. Qiang, J. D. Schneider, M. E. Shulze, R. L. Sheffield, H. V. Smith, “Beam-halo in mismatched proton beams,” Nucl. Instr. Meth. Phys. Res. A 519, 425 (2004).
- I. Hofmann, G. Franchetti, O. Boine-Frankenheim, J. Qiang, and R. D. Ryne, "Space Charge Resonances in Two and Three Dimensional Anisotropic Beams," PRST-AB, vol 6, 024202 (February 2003).

## Publications (Jan 2002 - Present) Refereed Journals (cont.)

- J. Qiang and R. W. Garnett, "Smooth Approximation with Acceleration in an Alternating Phase Focusing  Superconducting Linac," Nucl. Instr. Meth. Phys. Res. A 496, 33 (2003).
- J. Qiang, P. L. Colestock, D. Gilpatrick, H. V. Smith, T. P. Wangler, and M. E. Schulze,  "Macroparticle Simulation Studies of a Proton Beam Halo Experiment," PRST-AB, vol 5, 124201 (2002).
- C. K. Allen, K. C. D. Chan, P. L. Colestock, K. R. Crandall, R. W. Garnett, J. D. Gilpatrick, W. Lysenko, J. Qiang, J. D. Schneider, M. E. Shulze, R. L. Sheffield, H. V. Smith, and T. P. Wangler, "Beam-Halo Measurements in High-Current Proton Beams," Physics Review Letters 89 (21) (November 2002).
- J. Qiang, M. Furman, and R. Ryne, "Strong-Strong Beam-Beam Simulation Using a Green Function Approach," PRST-AB, vol 5, 104402 (October 2002).
- J. Qiang, R. Ryne, and R. Garnett, "Systematic Comparison of Position and Time Dependent Macroparticle Simulations in Beam Dynamics Studies," PRST-AB, vol 5, 064201 (June 2002).