# Presentation: 120675

## Toward an Improved Model of the Fermilab Booster Synchrotron

- A. Drozhdin, J.-F. Ostiguy and W. Chou
- Beam Physics Department

- Introduction

- The Booster is the only machine in the FNAL complex that has not been extensively modified.
- Delivering protons to two important neutrino experiments, MiniBooNe (now on-line) and NUMI,
- represents a major operational challenge. In the NUMI era, the Booster  will have to deliver more
- protons than it has delivered in its 30 yrs lifetime ! One area of concern is beam losses, whose cumulative
- effects lead  to damage and/or activation of  tunnel components.   A well-designed collimation
- system can be used to mitigate losses by helping to control and confine them to specific areas.
- However, a detailed and validated model of the machine, including space-charge effects, is invaluable
- to understand loss mechanisms,  their relative importance and possible cures. To this end, a systematic
- Effort,involving the Beam Physics Department working in close collaboration with the Proton Source Department and the Computing Division has been organized. We describe some of the tools employed
- and present some experimental results.  Better understanding of the machine optics has already
- resulted in sizable improvements.

- Optics

- Space Charge

- A Coherent Picture for Losses during the first 3ms

- Performance Improvements

- An experiment was recently performed by the Proton Source Department.  The extraction chicane located at L13 was temporarily eliminated.  Beam losses were reduced by 50%, leading to a new milestone for MiniBooNE (5E16 protons per hour).

- Space charge has long been known to be associated with loss mechanisms. It causes beam size growth and induces energy dependent tune shift and tune spread which can trigger various
- types of nonlinear resonant behavior.  Simulation of space-charge effects is computationally intensive. A reasonable approximation in a synchrotron is to separately compute the transverse and longitudinal self-forces. To that effect, we have been using the code ORBIT. The code ESME is also used to study longitudinal dynamics. ORBIT predicts rapid emittance and beam size growth  during multi-turn injection. These results are not completely consistent with the predictions obtained with the 3D SYNERGIA/IMPACT which points to slower growth on a longer time scale.  The source of this disagreement is under study.

- A detailed lattice model of the Booster including the injection and extraction chicanes was constructed. The horizontal chicane is used for injection. The vertical extraction chicanes are used to steer the low energy beam away from septum magnets which are encroaching into the vertical aperture.  Because of additive edge focusing effects, the chicane bump magnets make the lattice functions deviate considerably from their design values. The most important  perturbation is caused by the vertical extraction chicanes (a.k.a doglegs) which induce a subtantial horizontal focusing perturbation.  Interestingly, since the chicanes are DC, the perturbations  rapidly disappear as the energy is ramped.

*Phase phase representation of 55 Linac micro-bunches coalesced into one Booster synchrotron bunch*. (*Courtesy  P. Lucas*)

- Chromaticity

- At high intensities, approximately 30% of the beam is lost in the first 3 ms.  Our current model provides a plausible and coherent explanation.
- _Longitudinal Loss_
- The measured Booster momentum acceptance is small, about 0.15-0.20% (see above)
- The injected linac beam momentum spread is comparable, about 0.13%
- When the RF is on, the beam is bunched and the momentum spread increases to 0.3%,     exceeding the acceptance and resulting in a loss.
- _Transverse Loss_
- The measured Booster aperture is small,  1.2in, corresponding to an acceptance   of 16 mm-mrad
- The perturbation caused by the bump magnets reduces the acceptance by 50%    to 8 mm-mrad
- The injected linac emittance is 7 mm-mrad
- During multi-turn injection, the space charge blows up the emittance and the beam is scraped     transversely, resulting in a loss. The situation is worsened by the injection orbit bumps     which  also reduce the acceptance_._

- The net pertubation caused by a chicane DC magnets scale approximately like
- 1/*f* = 2 / *L*
- Where *f* is the focal length due to edge focusing,  is the *total *bend angle and *L* is the magnet length.
_*Short Term – Possible Ways to Mitigate the Chicane Magnet Perturbations*_
-  Increase septum magnet height and reduce dogleg magnet strength
-  Use three-leg instead of four-leg chicanes
-  Build new, longer chicane magnets possibly using permanent magnets
-  Remote mechanical septum magnet height to accommodate different operation modes
_*Long Term – Eliminate both DC chicanes*_
-  Use pulsed magnets to move the beam out before extraction
-  Use special large aperture main bending magnet upstream of the septum magnets
_*Other Proposals Studied but Deemed not Feasible and/or Practical*_
_* *_Increase the spacing between magnets in the chicane to reduce the angle  (expensive, no available space)
-  Relocate the chicane from L13 to L5 or L11 (expensive, marginal improvement)
_* *_Use correction wedge magnets or tilt chicane magnets (transfer perturbation to other plane)
-  Use correction quads (cannot be used to correct geometric focusing)

*Measured Momentum Acceptance of the Booster.*

- Protons/hr when chicane at L13 is
- turned  OFF.

***Measured dispersion difference caused  by changing vertical chicane magnets excitation from 60% to 100%. ***
***(Courtesy  R.Tomlin, C. Ankenbrandt and M. Popovic)***

- The chromaticity settings of the Booster are determined by head-tail instability considerations.  Typically, negative/positive chromaticity is required below/above transition to ensure stability. Although the Booster has no beam pipe, the chromaticities vary significantly through the cycle, due to effects such as remanent magnetization and lattice pertubations induced by the chicanes. Recently,  two spare Booster magnets have been carefully re-measured. The sextupole contributions from the main magnets inferred from measured chromaticities and the lattice model are in excellent with magnetic measurements.

***Main Magnet sextupole inferred from various chromaticity measurements.  ***

***RMS beam size  for different  beam intensities (no of injected turns). ***

***Particle emittance distribution w/wo space charge. ***

- Acknowledgements

- This work is the result of a close collaboration. We gratefully acknowledge substantial technical discussions and contributions from the Proton Source and Operations Departments.***   ***

***Value from magnet measurement ******at injection current (t=0)***
***-0.04***

***Value from magnet measurement ******at injection current (t=0)***
***0.007***

***Performance after years of tuning !***

***Performance after a one day study  !***

***Booster beam  loss during the cycle (Courtesy R. Webber).***