We investigate processes contributing to emittance growth in the Fermilab Recycler Ring. In addition to beam-gas multiple scattering, we also examine other external factors such as Main Injector ramping affecting the emittance growth

Brown, B C

Gattuso, C

Gounder, K

Hu, M

Johnson, D E

Marriner, J P

Mishra, S

Pruss, S M

Yang, M J

CERN Document Server

A Study of Emittance Growth in the Recycler Ring

Gounder, K.

Brown, B. C.

Gattuso, C.

Hu, M.

Johnson, D.

Marriner, J.

Pruss, S.

Yang, M.

UNT Digital Library

Fermilab FERMILAB-Conf-01/189-E  July 2001A STUDY OF EMITTANCE GROWTH IN THE RECYCLER RINGK. Gounder, B. C. Brown, C. Gattuso, M. Hu, D. Johnson,J. Marriner, S. Mishra, S. Pruss, M. Yang, FNAL, Batavia, IL 60510, USA.AbstractWe investigate processes contributing to emittancegrowth in the Fermilab Recycler Ring. In addition to beam-gas multiple scattering, we also examine other external fac-tors such as Main Injector ramping affecting the emittancegrowth.1 RECYCLER RINGThe Recycler Ring [1] located in the Main Injector tun-nel at Fermilab is designed to be a storage facility for an-tiprotons as a part of Run II luminosity upgrade program.The Recycler Ring (RR) is being commissioned using pro-tons. Beam emittance growth can be caused by many fac-tors such as injection mismatch, lattice properties, beamstructure, dynamic aperture, tunnel vibrations, power sup-ply noise, Main Injector ramping as well as beam-gas ef-fects. This study investigates the effect of beam-gas in-teractions and other external factors such as Main Injectorramping etc. on emittance growth in the Recycler Ring.The relevant RR parameters are listed in Table 1.Table 1: Recycler Ring ParamatersParamater ValueAcceptance (mm-mr) 40Average (m) 40.0Average beam pipe radius (in m)0.023Beam energy (GeV) 8.89Average beam 0.998Average beam 9.48Maximum energy loss (GeV) 0.0892 EFFECT OF BEAM-GAS SCATTERINGWe estimate the beam emittance growth due to multiplecoloumb scattering of the beam particles (protons) with theresidual gas atoms present in the beam pipe. The injectedbeam is assumed to be Gaussian:f(Z) =a222e (a2=22)Zwith Z = =a ranging from 0.0 to 1.0. With an initialbeam of 10  10 6 m-r,  = 11:53  10 3m-r. Here; a denote emittance and Recyler acceptance respectivelywhile a is the half aperture equal to the average radius ofthe beam pipe (0.023 m).The RR ultra high vacuum is maintained by a regulararray of ion and titanium sublimation pumps (TSP). Thepressure at a point inside the beam pipe varies significantlydepending on the distance from the pump locations. Thepressure profile has been computed for each component ofthe gas present in the beam pipe. The maximum and min-imum pressure for each gas are listed in Table 2. For lifetime estimations, we treat the ‘unknown’ component as Ni-trogen.Table 2: Vacuum Gas CompositionGas Content Min. Pres. Max. Pres.[%] [Torr] [Torr]H2 67.22 4.9E-11 1.2E-10H2O 21.13 1.8E-11 7.6E-11CO 3.36 1.7E-12 1.3E-11Ar 0.02 8.9E-12 1.1E-11CH4 0.85 2.4E-11 7.9E-11CO2 6.53 3.8E-12 2.9E-11Unknwon 0.89 4.5E-13 3.4E-12Total 100.00 1.1E-10 3.3E-10The mutiple coloumb scattering of beam particle causesemittance growth of the beam. As a result, protons are lostvia diffusion across the boundary of the allowed particledistribution in the beam pipe. Therefore, we should ap-proach this problem by solving the diffusion equation [4]for a particle distribution f:@f@=@@Z(Z@f@Z)subject to the boundary conditions:f(Z; 0) = f0(Z)f(1; ) = 0where Z ==a = emittance/acceptance, and = tR/a withR, the diffusion coefficient. The diffusion coefficient R isgiven in terms of scattering angle by:R = avgh _2iThe general solution of the above equation can be writtenas:f(Z; ) =XnCnJ0(npZ)e 2n=4with coefficientsCn:Cn =1J1(n)2Z10f0(Z)J0(npZ)dZwheren is nth root of the Bessel functionJ0(Z). Now wecan obtain the total beam particles as a function of time:N() =Z10f(Z; )dZ = 2XnCnnJ1(n)e 2n=4The life time due to multiple coloumb scattering can benow computed using the standard expression:mc =   N()dN()=dThe beam life time varies with time and normallyreaches an asymptotic value [5]:a =4a21R.To compute< _2 >, we use the small angle limit ofthe Rutherford scattering cross section, parametrization ofatomic and nuclear radii:< _2 >=8r2pc23XjnjZ2j In[38360(AjZj)1=3]with Aj denoting the atomic weight of jth gas component.Using Table 2 and the relevant Recycler parameters inTable 1, we obtain< _2 >= 4:23 10 12 rad=s for thecase of minimum gas pressure and1:25 10 11 rad=s forthe maximum pressure case.The emittance growth is obtained by:dNdt=2avg < _2 >.Now using the above estimates for< _2 >, we computethe emittance growth due to beam-gas multiple scatteringas8:0010 4 mm-mr/s for the minimum case and2:3710 3 mm-mr/s for the maximum case.3 THE EFFECT OF MAIN INJECTORRAMPINGThe Main Injector plays a pivotal role in the Fermilab ac-celerator complex for accelerating, decelerating and trans-ferring beams between the Booster, Antiproton Source, Ac-cumulator, Recycler Ring and the Tevatron. The RecyclerRing is located in the upper section of the Main Injec-tor tunnel and is separated by an average distance of onlyabout 2m. Therefore while the Main Injector is ramping,the stray fields may affect the beam in the Recycler Ringwhere shielding by-metal may not be adequate.To measure the effect of Main Injector ramping, we havemeasured the beam intensity and the emittance growth inhorizontal plane in the Recycler Ring as a function of timewhile the Main Injector is ramping and while not ramp-ing with identical Recycler setups. The relative emittanceFigure 1: The particle fraction a function of = tR=a dueto multiple coloumb scattering process. The beam particlesare lost via diffusion across the boundary of the allowedparticle distribution in the beam pipe.meaurement was done using Schottky detectors [6]. Thebeam intensity in the Recycler Ring with and with out theMain Injector ramping vs time is plotted in Figure 2. Thebeam intensity falls off more rapidly while the Main In-jector is ramping than compared to the case of no ramping.The beam life time obtained by fitting the beam intensity asa function of time is 6.13 hours while ramping and 10.29hours while not ramping.The relative horizontal beam emittance vs time is shownin Figure 3 for the cases of Main Injector ramping and notramping. The emittance growth rates are obtained by fittinga straight line to the data. The rate is 0.22 mm-mr/minutewhile ramping and is only 0.08 mm-mr/minute while notramping. The result is consistent with those obtained fromthe beam intensity measurements.4 OUTLOOKIn this study, we have considered two of the many pro-cesses contributing to the emittance growth in the RecyclerRing. Comparing the overall growth rate with that obtainedfrom multiple scattering of beam particles with residualgases in the beam pipe, we can conclude that Main Injec-tor ramping along with other factors are playing significantroles.5 REFERENCES[1] Gerry Jackson, “The Fermilab Recycler Ring Technical De-sign Report”, November 1996, Fermilab-TM-1991.[2] A. G. Ruggiero, Fermilab Pbar Note 54, November, 1979.Figure 2: The effect of Main Injector ramping on the Re-cycler beam. The life time is determined by fitting an ex-ponential form to the relevant beam profile. The Recyclerbeam pipe is being shielded from the stray fields caused bythe Main Injector ramping.[3] A. Wurlich in “CERN Accelerator School 1994”, CERN-94-01.[4] D. Edwards and M. Syphers, “An Introduction to Physics ofHigh Energy Accelerators”, John Wiley and Sons, 1993. .[5] For details, K. Gounder et. al, “Recycler Ring Beam LifeTime” in PAC2001 conference proceedings.[6] M. Hu et. al., “The Fermilab Recycler Diagnostics”, inPAC2001 conference proceedings.Figure 3: The Main Injector ramping more than doublesthe emittance growth in the Recycler Ring. The relativeemittance is measured using Schottky detectors.

A study of emittance growth in the recycler ring

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A study of emittance growth in the recycler ring

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