# Presentation: 808726

## Beam-Beam Effects and Optics at the Tevatron

_*Alexander Valishev*_* *
*Y.Alexahin, V.Lebedev, D.Shatilov*
*Fermilab, Batavia IL*

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Contents

- Purpose and Means of Simulation
- Beam-Beam Algorithm
- Random Noise
- Machine Optics – Nonlinearities, Coupling, etc.
- Chromaticity of Tunes and Beta-Functions
- Technology
- Optics Measurement at Tevatron
- Accelerator Model
- Beam-Beam Program
- Results
- Effect of Long Range Collisions and Optics Distortion
- Scallops
- Chromaticity
- 28 cm Beta*
- New Bunch Train Scheme

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Purpose and Means of Simulation

- The goal:
-       Simulation of beam-beam effects with realistic machine optics including Long Range collisions, beta-functions, helix, coupling and chromaticity
- The problems we want to address*:
-       Beam-beam effects in Tevatron at LowBeta.
- Scallops
- Antiproton beam life time
- Proton beam life time

- * V. Shiltsev, Beam-Beam Phenomena in Tevatron, Beams-doc-1064

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Beam-Beam  Program LIFETRAC*

- Weak-Strong (incoherent) with Gaussian strong beam profile. Strong beam is unchanged during simulation.
- 3-Dimensional, Beam-Beam kick is computed using interpolated formulae
- Macro particle weak beam (~10,000 particles)
- Parallel computation

- * D.Shatilov, Part. Accel. **52**, 65 1996

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Diffusion (Random Noise )

-       An important question for simulation of hadron beams is the diffusion rate (IBS, RF Noise, etc.).
- With present computer capabilities 24 hrs of simulation correspond to ~80 s of beam time in Tevatron.
- We would like to simulate first 10 hours of the store, when beam-beam effects dominate
- Hence, we use the diffusion rate which is ~1000 times stronger than real, and 2e6 turns ~ 10 hrs of beam time.
- Noise is introduced as a short kick at each turn
- Can account for coupling between degrees of freedom
- This approach needed verification ->

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Diffusion                              2

- Analysis by Y. Alexahin

- Naïve expectation:

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Diffusion                              3

- Analysis by Y. Alexahin

*L*/*L*0

- Fit using 3 data points on the right:

- Expected:

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Machine Optics

- Does not include nonlinearities (but the code has this capability) – linear transformations between IPs (both main and parasitic)
- Full account of betatron coupling via coupled beta-functions*
- Longitudinal motion with sinusoidal RF (wavelength for Tev is 564.5 cm with bunch length ~55cm)

- * V.Lebedev, S.Bogacz, http://tnweb.jlab.org/tn/2000/00-022.pdf

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Machine Chromaticity

- Tune chromaticity – variation of the betatron phase advance with particle’s momentum. However, this excludes important
- Chromaticity of beta-functions which is modeled as an additional drift in Final Focus

- For Tevatron         is ~ 0.1-0.2 at the RF bucket

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Computation Cycle 

- Optics measurement at Tevatron – differential orbits
- Fitting computer model of accelerator to the measured data
- Extraction of optics data relevant to beam-beam simulation
- Creation of input file for beam-beam program
- Tracking
- Post processing – data plotting and analysis

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Optics Measurement at Tevatron

- Excite orbit in Tevatron (P163 application by V.Lebedev) using
- 4 dipole correctors (2 horizontal and 2 vertical)
- Revolution frequency change
- and record difference between the excited and reference orbits. Hence, the term *differential orbits*
- Record helix
- Vary selected quadrupoles and record corresponding betatron tune shifts

- Proton Collision Helix

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Accelerator Model                 1

-      Fit the computed differential orbits to experimental data adjusting strengths of individual quadrupoles and skew-quadrupoles in the model

- X corr. #1

- Y corr. #1

- VFKNOB

## Accelerator Model                     2

-      As the result, the computer model gives lattice functions and sources quadrupole ans skew-quadrupole errors around the ring.

- Ring beta-functions

|   | dQx meas | dQx model | Error (%) |   | dQy meas | dQy model | Error (%) |
| --- | --- | --- | --- | --- | --- | --- | --- |
| C:B0Q2H | 0.0114 | 0.01285 | -11.3 |  | 0.0111 | 0.01017 | 9.2 |
| C:B0Q3H | 0.0123 | 0.01512 | -18.6 |  | 0.0127 | 0.01144 | 11.0 |
| C:B0QT2H | 0.0081 | 0.00929 | -12.8 |  | -0.0153 | -0.01574 | -2.8 |
| C:B0QT3H | 0.0075 | 0.00852 | -12.0 |  | -0.002 | -0.00233 | -14.1 |
| C:D0Q2H | 0.0117 | 0.01228 | -4.7 |  | 0.0109 | 0.01103 | -1.2 |
| C:D0Q3H | 0.0128 | 0.01375 | -6.9 |  | 0.0129 | 0.01272 | 1.5 |
| C:D0QT2H | 0.0085 | 0.00883 | -3.7 |  | -0.016 | -0.01726 | -7.3 |
| C:D0QT3H | 0.0078 | 0.00806 | -3.3 |  | -0.0025 | -0.00267 | -6.5 |

- Measured and calculated tune shifts from variation of selected quadrupoles.

## LIFETRAC Input

- Start from accelerator model in the OptiM* code
- Select the bunch to be studied and extract optics parameters relevant to this bunch
- Add simulation parameters like noise, beam-beam parameter, etc.

- * _[http://www-bdnew.fnal.gov/pbar/organizationalchart/lebedev/OptiM/optim.htm](http://www-bdnew.fnal.gov/pbar/organizationalchart/lebedev/OptiM/optim.htm)_

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## LIFETRAC Output

- 2D distributions and histograms at each time step
- Emittances
- Luminosity
- Lost particles –  turn where they died and initial coordinates

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Effect LR Collisions - Design Optics

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Effect of Distortions & LR Collisions -Design Optics vs. ‘January/27’

## Effect of Distortions - Design Optics vs. ‘January/27’ and ‘June/24’

## Scallops

- Initial vertical emittance
- of pbar bunches (#3554)

- Relative change of vertical
- emittance after 15 min.

- Vertical emittance
- after 15 min

## Scallops – Naïve Explanation of First 15 minutes

- Assume the beam-beam blow-up is equal for all bunches except 12th, which has smaller horizontal tune – far from 1/5 resonance
- The bunches are scraped with the same scraper, i.e. differently due to variation in initial emittance

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Scallops – Naïve Explanation

- #3414

- #3421

## Scallops – Naïve Explanation

- #3444

- #3446

- Wrong!

## Store #3554 Step by Step

- t=46 sec  dN=0.14%

- t=107 sec  dN=0.26%

## Store #3554 Step by Step

- t=900 sec  dN=2.2%

- Result:
- Scallops develop quickly,
- half of the blow up occurs during
- first 2 minutes of the store

## Simulation of Scallops

- Effect is tune-dependent!

## Tevatron Working Point

- Y. Alexahin

## Tevatron Working Point     2

## Effect of Betatron Tune Chromaticity

- June 24 Optics

## Beta* = 28cm

## New Bunch Train Pattern

- Long Range collisions give a strong contribution to beam-beam effects. With 3 x 12 bunches the nearest parasitic collision points dominate.
- Increase separation? Increasing the bunch spacing - 3 x 11 bunches with separation of 23 buckets instead of 21. Number of LR collisions 70 -> 64. The length of abort gap is conserved. Such filling pattern can be made with the use of Recycler.

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## New Bunch Train Pattern   2

- June 24 Optics

## What’s Next?

- Get experimental data (emittances, intensities, tunes) and compare to simulation
- Improve the model – coupling, diffusion rate, orbit
- Proton life time

## Summary

- A model of the Tevatron was built which allows to simulate beam-beam effects with various (realistic) optics parameters
- The simulation results are in qualitative agreement with experimental observations
- Some understanding of Scallops was achieved, although the simulation does not reproduce all details
- Several ideas of improvement of the Tevatron performance were tested, including:
- Decreasing the betatron tune chromaticity (10% int. luminosity)
- Smaller (28cm) beta function at the IPs (10% peak and int. luminosity)
- Implementing the new bunch separation scheme (25% peak luminosity)
- Change of the betatron tune working point
- Future efforts will be concentrated on analysis of experimental data and improvement of the model.

- Accelerator Physics Seminar, Fermilab

- 9/30/2004

## Backup                       1

## Backup                      2