status of beam-beam simulations at cornell · outline of presentation • description of...

Status of Beam-BeamSimulations at Cornell

Jeremy UrbanMarch 19, 2004

Outline of Presentation

• Description of Simulations– ODYSSEUS Edwin Anderson & Joe Rogers– ODYSSEUS 2.0 Jeremy Urban & Joe Rogers– BEAMBEAM Dave Rubin

• Comparison of Results

• Conclusions

Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004

Strong-Strong & Weak-Strong

• Weak-Strong– the “strong” beam serves as the source for the electromagnetic

field that perturbs the other beam– the opposite beam is too “weak” to perturb the strong beam– strong beam is unperturbed, modeled

as fixed gaussian charge distribution

• Strong-Strong– both beams are sources of electromagnetic

fields that perturbs the opposing beam– both beams are strong ODYSSEUS

BEAMBEAM


ODYSSEUS: Overview

Optimized DYnamic Strong-Strong E-plus e-minUs Simulationby: Edwin Anderson & Joe Rogers

uses evolving distribution of macroparticles to model beamincluding longitudinal dynamics

Freedom of Calculation:– weak-strong or strong-strong– Gaussian model or Particle-in-Cell– calculation method adapts to maximize efficiency


ODYSSEUS: Tracking

Linear transport around ring

Input: energy, circumference, β∗, ξ∗,νx, νySR integrals, C-bar matrix, RF parameters

Features:– Radiation damping and excitation– Transverse coupling

Benefits:– quick execution– do not need BMAD lattice (current work with PEP-II)


ODYSSEUS: Interaction Point

The colliding beams are divided into slices longitudinally and the electromagnetic fields are calculated for each slice collision.

Beam stepped through IP as slices interact pair-wise.


ODYSSEUS: Slice Interactions

Longitudinal Tails are considered weak slicesBeam Core is divided into strong slices

Transverse Tails are handled with dynamic gaussian model


ODYSSEUS: Calculation Methods

Dynamic Gaussian Model

Soft-Gaussian: 1st & 2nd moments evolve

Field from Gaussian Charge Distribution:– complex error function solution (Bassetti & Erskine)– rational approximation (Talman & Okamoto)



Particle-in-Cell

typical grid size:

• Interpolate charge to grid point– typical method: 9 nearest grid points

• Use Green’s function for single charge in free space

rrrG ˆ

21 )(

oπε=rr



Particle-in-Cell

Find the electric field on the grid points:– Real Space: convolution– Fourier Space: multiplication

• Interpolate electric field to position of macroparticles in opposing beam– typically 9 nearest grid points

)(~)(~)(~)()()(

kkGkFrrGrFrrr

rrr

ρ

ρ

⋅=

∗=


ODYSSEUS 2.0: Overview

2nd version of ODYSSEUSby: Jeremy Urban & Joe Rogers

Limitations of Original Code:– linear transport around ring– no crossing angle collisions

Improvements in Version 2.0:– full capabilities of BMAD tracking– transverse Lorentz boost to allow crossing angle– Long Range Beam-Beam Interaction, from BMAD– corrections of errors in original code– update of code to Fortran 90


ODYSSEUS 2.0: BMAD Tracking

ring_pos: ring_struct used to track e+ forwardring_ele: ring_struct used to track e- backward

• symplectic tracking of all CESR elements

• radiation damping and excitation


ODYSSEUS 2.0: Crossing Angle

Crossing angle implemented as transverse Lorentz boost to frame where beams are colliding head-on. (Hirata)


ODYSSEUS 2.0: Check Boost


ODYSSEUS 2.0: Examples

Beam Halo Flip-Flop


BEAMBEAM: Overview

BEAMBEAMby: Dave Rubin

weak-strong model based on BMAD: LRBBI, non-linear transport, crossing angle, radiation

Beam-Beam Calculation:– BMAD beam-beam element– assumes Gaussian charge distribution– rational approximation of complex error function – strong beam sliced longitudinally to provide longitudinal dynamics


BEAMBEAM: Structure


Comparison of BB Codes

ODYSSEUS BEAMBEAMTracking Methods:

Linear Y YBMAD v 2.0 YPretzel/Crossing Angle v 2.0 Y

Simulation Methods:Weak-Strong Y YStrong-Strong Y N

Field Calculation Methods:Direct Force Y NGaussian Model SOFT HARDGreen’s Function Y N


Comparing BEAMBEAM to CESR

BEAMBEAM• l9a18a000_moverec.lat• energy = 5.289 GeV

Beam-Beam Tune Shift Luminosity


BEAMBEAM• 6wig_lum_20030915_v4.lat• energy = 1.88 GeV

Beam-Beam Tune Shift Luminosity



BEAMBEAM• 6wig_lum_20030915_v7.lat• energy = 1.88 GeV• horizontal tune: 0.52 - 0.54• vertical tune: 0.57 - 0.60

• Luminosity:– blue = – orange =


12291010 −−⋅ scm

1229102 −−⋅ scm


Comparing ODYSSEUS & BEAMBEAM

• 6wig_lum_20030915_v7.lat• energy = 1.88 GeV• horizontal tune: 0.533• vertical tune: 0.587

BEAMBEAM ODYSSEUS


Conclusions

• ODYSSEUS 2.0– still some question marks?– complete comparison checks– compare with other strong-strong 6-D codes (SLAC, KEK)– CESR-C: quick weak-strong scans followed by detailed

strong-strong scans– Future Work:

• increase speed• add interpolation between slices• modify Green’s function calculation on grid to allow more extreme

aspect ratios


Conclusions

• BEAMBEAM– looks good!– complete comparison checks– CESR-C: continue current scans and tune scans with

6 wiggler and 12 wiggler lattices


status of beam-beam simulations at cornell · outline of presentation • description of...

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