Beebe-Wang J

Lee Y Y

Machida S

Prior C R

Raparia D

Wei J

English

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Beam properties in the SNS accumulator ring due to transverse phase space painting

BEAM PROPERTIES IN THE SNS ACCUMULATOR RING DUE TO TRANSVERSE PHASE SPACE PAINTING*  J. Beebe-Wang, Y. Y. Lee, D. Raparia, and J. Wei Brookhaven National Laboratory, Upton, NY 11973, USA C. R. Prior, Rutherford Appleton Laboratory, Chilton, Didcot Oxon OX11 0QX, UK S. Machida, KEK-Tanashi, Midori-cho, Tanashi, Tokyo, 188-8501, Japan Abstract       Beam properties resulting from transverse phase space painting for the injection of the Spallation Neutron Source (SNS) accumulator ring are summarized.   The focus is on the creation of closed orbit bumps that give suitable distributions at the spallation neutron target, at the same time minimizing the beam losses through tail/halo formation.  Related issues such as foil traversal rate and foil temperature/lifetime are also studied.  Finally, injection mismatch is investigated for large linac emittance to reduce the beam loss through scattering. 1 INTRODUCTION       Injection painting is a multi-turn injection process with a controlled phase space offset (6-D) between the centroid of the injected beam and the closed orbit in the ring to achieve a different particle distribution from the injected beam.  If the longitudinal beam manipulation is decoupled from transverse phase space painting, as is the case for the SNS accumulator ring injection [1], we can study the longitudinal painting separately [2].  In this paper we study beam properties due to transverse phase space painting [3], which will be implemented for the SNS accumulator ring injection.  The injection bumps will be optimized in order to:  (a)  Satisfy the target requirements  (Table 1); (b) Reduce beam losses due to space charge; (c) Reduce foil-hits, therefore reduce beam losses at       foil while maintaining an adequate foil lifetime.   Table 1  Beam requirements at the target. Beam horizontal dimension  200 mm Beam vertical dimension 70 mm Time-averaged beam current density over beam footprint < 0.143 A/m2 Beam power within target and outside nominal spot < 10 % Peak time-averaged beam current density over 1 cm2 ≤ 0.25 A/m2        The circulating beam properties are critically dependent on the choice of painting schemes and the optimization of injection orbit bumps. There are two basic painting schemes  correlated (Fig.1(a)) and anti-correlated painting (Fig. 1(b))  incorporated in the SNS accumulator ring design.            (a) (b) Fig. 1 Illustration of basic painting schemes in (x-y) space:  (a) correlated painting; (b) anti-correlated painting.   In both graphs, the small green ellipse represents the injected beam on the foil.  The closed orbit (red dots) moves in the direction indicated by the black arrows.  The beam shape and size from beginning to the end of injection are characterized progressively by the dot-dashed, short-dashed, long-dashed and solid lines.    2 ANALYTICAL EXPRESSION       Assume the linac beam with a Gaussian distribution (σ0x, σ0y) is continuously injected into the ring during interval [0, t].  At time t, the centroid of injected beam is at (XC(t), X′C(t), YC(t), Y′C(t)) and the closed orbit is at (XO(t), X′O(t), YO(t), Y′O(t)).  If painting in (x, x′) phase space is independent (y, y′), the (x, y) space distribution can be expressed as:   )1(),(),(),,( 10 11 dttyntxntyxntyx∫=with [4]   )2()())((1),( || 2/1222010/}|)(|2/)]({[20120121xxxxxxxtcatcaxx daxatcaIaetxn xxxxx∫ ∞+ +−−−=σπσσ _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________*Work performed under the auspices of the U. S. Department of Energy. 1465Proceedings of EPAC 2000, Vienna, Austriawhere I0(z) is the modified Bessel function of order zero, and cx(t) is the effective 2-D phase space offset between the two centers cx(t) ={∆X 2(t)+[βx ∆X′(t) + αx ∆X(t)] 2} 1/2 with ∆X= XC – XO(t), ∆X′= X′C – X′O(t).  In expression (1), ny(y, t1) can be obtained from Eq. (2) by replacing x by y.  In the derivation of Eq. (1), space charge and other non-linear effects are not included and the following assumptions have been made: • The painting in (x, x′) phase space is controlled independently from the (y, y′) painting. Therefore, the 4-D problem is reduced to 2-D. • The bumps change slowly compared to the betatron oscillation (for the SNS, < |dx/dt| >|bump = 40m/sec, and   < |dx/dt| >|beta= 1×106m/sec). These assumptions have been justified for the SNS injection.  (See reference [5] for details).        From this analytical expression we deduce:  • If cx(t)=cy(t)=0, there is a singularity in the local density at the center of the beam.  So, one should not have zero offset in 4-D phase space at any time. • Correlated painting will give a rectangular shaped beam distribution with high density along the diagonal line, and low density on the x- and y-axes. • If σx<<∆X(t), ax(t) and σy<<∆Y(t), ay(t), a careful choice of anti-correlated painting with offsets: )4()()(’,1)()3()()(’,)(2/12/1yyinjxxinjtYtYttBtYtXtXttAtXβαβα∆−=∆−=∆∆−=∆=∆ will give a 4-D KV-like transverse distribution at t=tinj:  )5(),,(),,(),,( 10 injinjinj tyxftyxftyxn +=  where f0(x,y) is the zeroth order solution of Eq (1): )6(.101),,(222222220>+≤+=ByAxforByAxforABttyxfinjinjπ  It is an elliptically shaped uniform distribution, which can also be obtained by projecting a 4-D KV-distribution to (x, y) space.  Defining  )8(,11,1)7(,11,1222222222222ByAxByByAxAx−−=−=−−=−=ζψζηξη  the first order term in Eq. (5) is given by [5]: where F is the elliptic integral of the first kind and Π is the elliptic integral of the third kind.  As long as f1(x,y,tinj)<<f0(x,y,tinj), a KV-like distribution is maintained.   3  COMPUTER SIMULATIONS       The investigations are performed by tracking 2x104 macro-particles through the ring lattice, in the presence of space charge, with the simulation code SIMPSONS [6].  All the physical quantities used in the simulations (Table 2) are chosen according to the specifications in the design [1].  The results of simulations at working point (5.82, 4.80) from correlated and anti-correlated painting are shown in Figs. 2 and 3 respectively.  In both figures, the simulation including space charge (red dots/lines) is compared to that without space charge (blue dots/lines) with identical physical and numerical parameters. The upper graphs show the distributions in (x, x′) and (y, y′) phase space. The lower two graphs show the distribution in (x, y) space and the distribution of 4-D phase space areas occupied by single particles.       Table 3 summarizes the beam properties due to correlated and anti-correlated painting.  The distribution from correlated painting may satisfy the target requirements, but it could be difficult to preserve the beam shape. The distribution from anti-correlated painting is immune to the transverse coupling, but there are excessive halo/tails.  In order to take advantage of both correlated and anti-correlated painting, an oscillating painting scheme was proposed at BNL [5]. However, it requires more aperture, and it is technically challenging for the power supplies.  Reference [7, 8] give more detailed studies on the effects of space charge forces and magnet errors in the SNS accumulator ring.  Table 2   Design parameters used in the simulations. Beam Kinetic Energy 1 GeV Beam Average Power 2.0 MW Protons per Pulse 2.08 × 1014 Pulse Repetition Rate 60 Hz Ring Circumference 220.88 m Proton Revolution Period 841 nsec Injected Pulse length 546 nsec Beam gap (injection) 295 nsec Number of Turns Injected 1225 Ring Fill Time 1.03 msec Horizontal tune νx 5.8 – 6.8 Vertical tuneνy 4.8 – 5.8 Un-nor. Emittance (99%) 160 πmm-mr )9()1,,0()1,,2(),0(),2()1,,0()1,,2(),0(),2(2),,(22222222222/51  Π−Π+−  Π−Π+−−=ξξπξηξξπησψψπψζψψπζσπBxFFBAxFFAABttyxfyxinjinjProceedings of EPAC 2000, Vienna, Austria1466Fig. 2 Particle distribution and emittance distribution resulting from an example of correlated painting.  Fig. 3 Particle distribution and emittance distribution resulting from an example of anti-correlated painting.   Table 3   Beam properties due to correlated and anti-correlated painting in the SNS accumulator ring. painting scenarios correlated anti-correlated Beam shape without SC Rectangular Oval Beam emittance evolution Small to large ~ constant Final emit. εx+εy(πmm-mr) 120+120 160 Est. foil-hitting rate  6.5 8.5 Est. max foil temp. (K)  1940 2070 Horizontal aperture (∆H ) 1:1 1:1 Vertical aperture (∆V ) 1:1 1:1.5 Susceptible to coupling  Yes No Capable for KV painting No Yes Paint over halo  Yes No Horizontal halo/tail Normal Normal Vertical halo/tail Normal Large Satisfy target requirements Likely Not likely Bump function candidates for optimization Square root; exp(-t/0.3ms); Combination Square root; exp(±t/0.6ms); Sinusoidal   4  INJECTION MISMATCH        Twiss function mismatch can be used as a tool to reduce the foil-hitting rate, thereby reducing the beam loss due to scattering in the foil.  A mismatched injection should satisfy two preferred conditions in order to stack the injected turns efficiently in phase space [9]:      )12(,’’OCOCmmiiXXXX−−−== βαβα and                          ( )13,3/1≥mimiεεββ where αi, βi and αm, βm are the values at the injection point of the Twiss functions in the transfer line and the ring respectively.  The foil hitting rate and maximum foil temperature for one matching condition and three different degrees of mismatch with correlated painting are shown in Fig. 4.  Similar results with slightly higher values are found for anti-correlated painting [9].  A lower foil-hitting rate is accompanied by a higher foil temperature due to a smaller beam size.  The mismatch for the SNS injection will be optimized to reduce the foil-hitting rate while maintaining an adequate foil lifetime.                  (a)        (b) Fig. 4 Foil-hitting properties due to injection mismatch for correlated painting. (a) foil-hitting rate vs. injected beam emittance εinj; (b) maximum foil temperature vs. εinj .      REFERENCES [1] Wei et al, “Low-Loss Design for the High-Intensity Accumulator Ring of the Spallation Neutron Source”, Accepted for publication in PRST-AB, 2000. [2]  J. Beebe-Wang, “Study of Longitudinal Injection/stacking in the SNS Accumulator Ring”, p.2843, Proc. of PAC99.  [3]  J. Beebe-Wang et al, “Transverse Phase Space Painting for    SNS Accumulator Ring Injection”,p.1743. Proc. of PAC99.  [4]  D. A. Edwards and M. J. Syphers, “An introduction to the Physics of High Energy Accelerators”, John Wiley & Sons, Inc., 1993. [5]  J. Beebe-Wang, “Oscillating Injection Painting and Related  Technical Issues”, BNL/SNS Tech Note #081, June 2000. [6]  S. Machida, “The Simpsons User’s Manual”, Dallas, 1992. [7]  J. Beebe-Wang et al, “Effects of Space Charge and Magnet Errors in the SNS Accumulator Ring”, these proceedings. [8]  A.V. Fedotov et al, “Halo and Space Charge Issues in the SNS Ring”, these proceedings. [9] J. Beebe-Wang and C. R. Prior, “Injection Mismatch for the SNS Accumulator Ring”, BNL/SNS Tech Note #080, June 2000. 0.5 1 1.5 2 2.5 3051015202530Foil Hits [hits/particle]Injection εRMS, Nor [πmm−mrad]correlated painting 120πmm−mrβi / βm= 1.00βi / βm= 0.64βi / βm= 0.36βi / βm= 0.220.5 1 1.5 2 2.5 3100015002000250030003500Maximum Foil Temperature [K]Injection εRMS, Nor [πmm−mrad]βi / βm= 1.0 βi / βm= 0.64βi / βm= 0.36βi / βm= 0.22temp. limit            −50 0 50−15−10−50510x   [mm]x,   [mrad]−50 0 50−15−10−50510y   [mm]y,    [mrad]−50 0 50−60−40−200204060x   [mm]y   [mm]0 100 200 300020406080100εT [mm−mr]Beam exceeding  εT  [%]corr. with SC   corr. no SC−50 0 50−15−10−50510x   [mm]x,   [mrad]−50 0 50−15−10−50510y   [mm]y,    [mrad]−50 0 50−60−40−200204060x   [mm]y   [mm]0 100 200 300 400020406080100εT [mm−mr]Beam exceeding  εT  [%]anti−corr. with SC   anti−corr. no SC1467Proceedings of EPAC 2000, Vienna, Austria

An introduction to the Physics of High Energy Accelerators”,

Beebe-Wang et al, “Transverse Phase Space Painting for SNS Accumulator Ring

Injection Mismatch for the SNS Accumulator Ring”,

Low-Loss Design for the High-Intensity Accumulator Ring of the Spallation Neutron Source”, Accepted for publication in PRST-AB,

Oscillating Injection Painting and Related

Study of Longitudinal Injection/stacking in the SNS Accumulator Ring”,

The Simpsons User’s Manual”,

Beam properties in the SNS accumulator ring due to transverse phase space painting

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ePubs: the open archive for STFC research publications

ePubs: the open archive for STFC research publications