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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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)
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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.
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS: Slice Interactions
Longitudinal Tails are considered weak slicesBeam Core is divided into strong slices
Transverse Tails are handled with dynamic gaussian model
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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)
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS: Calculation Methods
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS: Calculation Methods
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS: Calculation Methods
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
⋅=
∗=
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS 2.0: Crossing Angle
Crossing angle implemented as transverse Lorentz boost to frame where beams are colliding head-on. (Hirata)
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS 2.0: Check Boost
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
ODYSSEUS 2.0: Examples
Beam Halo Flip-Flop
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
BEAMBEAM: Structure
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
Comparing BEAMBEAM to CESR
BEAMBEAM• l9a18a000_moverec.lat• energy = 5.289 GeV
Beam-Beam Tune Shift Luminosity
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
BEAMBEAM• 6wig_lum_20030915_v4.lat• energy = 1.88 GeV
Beam-Beam Tune Shift Luminosity
Comparing BEAMBEAM to CESR
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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 =
Comparing BEAMBEAM to CESR
12291010 −−⋅ scm
1229102 −−⋅ scm
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
Comparing ODYSSEUS & BEAMBEAM
• 6wig_lum_20030915_v7.lat• energy = 1.88 GeV• horizontal tune: 0.533• vertical tune: 0.587
BEAMBEAM ODYSSEUS
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
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
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004
Conclusions
• BEAMBEAM– looks good!– complete comparison checks– CESR-C: continue current scans and tune scans with
6 wiggler and 12 wiggler lattices
Jeremy Urban Cornell University Brown Bag Seminar March 19, 2004