Nuclear Instruments and Methods in Physics Research A293 (1990) 301-304North-Holland

DETERMINATION OF REAM POSITION A

ANGLE TO MINIMIZE BEAM LOSSIN THE LOS ALAMOS PROTON STORAGE ICING

Mary BURNSMP-6, MS-H852, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM 87545, USA

A beam of negatively charged hydrogen ions passes through a stripper magnet to produce a neutral hydrogen beam before it isinjected into the proton storage ring at the Los Alamos Meson Physics Facility. Inside the ring the injected beam passes through acarbon foil which strips off the remaining electrons to produce a proton beam . It is desirable to position the foil where it willminimize beam losses due to multiple Coulomb scattering in the ring . Beam loss is also decreased if the position and angle of theinjected beam are chosen so that the phase ellipse of the injected beam has the best match with the phase ellipse of the ring beam . Toachieve these two objectives, the position and angle of the injected beam must be determined at the foil. This is done by describingthe beam path in the ring, and interpolating at the foil. A number of beam-position monitors placed at intervals around the ringprovide data on the position of the beam at these points. A multiple-regression algorithm uses the data from the beam-positionmonitors to estimate the position and angle of the injected beam at the foil, along with correlation coefficients and confidence limits.

1 . Introduction

The Proton Storage Ring (PSR) is a pulse compres-sor which provides high-intensity pulses of protons tothe Los Alamos Neutron Scattering Center (LANSCE)

for neutron production. The PSR was designed to de-liver an average current of 100 wA to the LANSCEneutron-production target with losses in the storage ring

of 0.1-0.3 WA [1]. High beam 1 )sses during injectionand storage of the beam in the ring are preventing thePSR from reaching its design goal of 100 pA.

Losses during the injection process are partly due tothe optical mismatch of the H° be to the proton-storage-ring acceptance and can be minimized by steer-ing the injected beam to correct this, as shown in fig. Ia.Significant beam loss also occurs while the beam iscirculating in the ring and is due to scattering when theclosed-orbit (or circulating) beam makes multipletraverses of the injection stripper foil, which is locatedinside the ring . To minimize these losses, the foil needs

to be positioned away from the centroid of the closed-orbit beam and the injected beam steered into the foil(fig . lb) . Thus, to decrease losses, accurate estimates of

the injected beam's position and angle at the foil are

necessary .

ition monitors

The proton storage ring consists of ten cells, as

shown in fig . 2, each containing a focussing quadrupole

* Work supported by the U.S . Department of Energy .

0168-9002,/90/$03 .50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

magnet, a bending magnet and a defocussing quadru-pole. There are two beam-position monitors (BPMs) ineach of nine cells, and one in the tenth.

The calculation of the beam centroid, and of itsangle at the stripper foil, uses measurements obtainedfrom the BPMs which are described below. Each BPM

Badly-matched Well-snatchedPhase Ellipses

Phase Ellipses

301

v

Injection foil

Fig . 1 . (a) Matching the phase ellipses of the injected bears and

the storage ring decreases beam losses . (b) The injection foil is

positioned off-center to decrease the probability of the closed-orbit beam passing through it.

IX. FEEDBACK

302

I N"CT10Nl l lv

EXTRACTIONKICKERS

consists of two pairs of electrodes. The log ratio of theamplitudes of the voltage on a pair of electrodes is ameasure of the beam position, in the plane passingthrough both electrodes (horizontal or vertical) . Thesignals from the BPMs are multiplexed to two Intel8085s, one for the horizontal plane and one for thevertical plane [2] . All components except the 201 MHzcomponent are filtered out before the signals reach theprocessors. The processed signals are digitized andbuffered in a CAMAC FIFO module . The CAMACbuffer is read by subroutines which pass the data to aBPM applications program running on the MicroVAX3, which controls the operation of the proton storagering. The program corrects the data for any electricaloffset in each BPM and converts it to a beam positionin cm relative to the center of the beam pipe .

3 . Determination of beam position and angle at the foil

In beam dynamics it is often useful to describe thebeam by its horizontal or vertical phase-space ellipse .The vertical or Y- Y' beam ellipse can be expressed asYY2 + 2aYY' + py' 2 = E/,ir,

M. Burns /Determination ofbeam position and angle to minimize beam loss

STRIPPERMAGNET

where a, ß and Y are the Twiss parameters, E is theemittance, Y is the position off the injected beam and Y'its angle in the vertical plane .

The following equation is a parameterization of thebeam ellipse in the vertical plane as a function of thedistance s around the storage ring from the foil posi-

STRIPPERFOIL

Fig. 2. The proton storage ring at LAMPF.

tion . This allows the calculations to be made for differ-ent foil locations in the ring. A similar equation is usedto calculate beam position X and angle X' in thehorizontal plane . The Pquation can be written simply asY(s) = YA(s) + Y'B(s),

(1)where

A(s) =

ß(s)/lß(0) [cos 4(s) + a(0) sin ~(s)],

B(s) =

(3(s)ß(0) sin ~(s),and where ip is the phase advance of the beam .

A(s) and B(s) are calculated using the beam-trans-port code DIMAD, for the horizontal and vertical planesand for two different foil-actuator positions. The valuesare stored in a file which the BPM program can access .The BPM code obtains the beam-position data fromeach of the 19 beam-position monitors in the ring, inboth planes . If no reading is obtained for either planefor a particular beam-position monitor, the correspond-ing equation is not used in the calculation .

Since the position and angle of the injected beamwith respect to the closed orbit are the quantities ofinterest, the BPMs are first read with the circulatingbeam to obtain the closed-orbit positions . The BPMsare then read again during the first turn of the injectedbeam . The closed-orbit positions are subtracted fromthe first-turn positions at all the BPMs, to obtain thepositions of the injected beam with respect to the closedorbi

Multiple linear regression [3] was used to determinethe beam position and angle at the strinner foi]_ ; as it is

t .

a good estimator and facilitates the calculation of thecorrelation coefficients . Horizontal and vertical planeswere treated independently .

Eq. (1) can be written as

Y=YA i +Y'Bi ,

i=1 . . . n,

(2)

where Y, A; and B; are discrete values correspondingto Y(s i ), A(si ) and B(si ), respectively . (s, ; i = 1 . . . n )is the set of discrete distances of the BPMs around thering . In this case, n =19 . Adding all n equations anddividing by n gives the mean-value equation

Y.= YAT11 + Y'B111 .

(2) gives

(Y - Y,) = Y(Ai - Am) + Y'(Bi - Bm)+

For convenience, eq. (4) is rewritten as

A=

al b la 2

b2

a,, b,,

Y1Y2

V=

:

,

andU=ly ~-

P

I Yn

D

-1 .00

-2 .00L

0

2.00

RBI. Burns / Determination ofbeamposition and angle to minimize beam loss

Lw~

M Var . " 0 .25

V Ver.- 9 .04

Subtracting eq. (3) from each of the n equations in eq.

i=1 . . . n .(4)

Yi =Yai +Y'bi ,

i=1 . . . n .

(5)

Define the n X 2, n x 1 and 2 x 1 matrices A, U and Vas follows:

R R R

4 5 52 1 2

A*U=V .

Y8® -0.41+-8 .934 a

Then eq . (5) can be written in matrix form as

Then Y and Y' can be found by the minimum-norm,least-squares estimator [4J as

U = (ATA)_ t

* ATV,

where AT is the transpose of A. The correlation coeffi-cient R is found from

R2 =1: {(YAj +Y'Bi ) 2 } /y,

(Yi),

where E( ) indicates summation over i from 1 to n . Toestimate the dispersion parameters, first calculate theGaussian multipliers Cll , C12, C21 and C22 , where C =(ATA) -1 , D = det(ATA) and

CI, = E {b,2)/D,C12 = C21 = - 1:(aibi)ID ,C22=Y{a?}/D .

The deviation mean square S2 is given by[1:( 2)- yj:

n-2

The standard error of Y is given by S x

Cll , and thestandard error of

Y'

is S X

C22 . The confidencelimits for Y and Y' can be found from these.

6 6 7 8 8 9 91 2 2 1 2 1 2

TUUGMORTJTPLOTY0® -®.®t+,-8 .8®9 a RE " 0 .7814,X0 " 0.32+i°0 .016 ® RE " ® .99t

303

X®® 1 .30+/-0 .863 0

Fie . 3 . The BI'M program interface displaying the plots of the vertical- and horizontal-position data for each BI'M .

IX . FEEDBACK

304

4. Results

M. Burns / Determination ofbeam position andangle to minimize beam loss

The BPM program for the PSR is run on a Micro-VAX3 with the user interface on a Lexidata 3400. Thehorizontal and vertical beam positions and the beamintensity can be displayed in a plot as shown in fig. 3 .The program calculates the injected-beam position (Xand Y) in millimeters, and the injected beam angles X'and Y' in milliradians . The results are written acrossthe bottom of the displays shown in fig. 3. The 686confidence levels for each of the values, and the correla-tion coefficient for each plane, are also displayed.

This method of accurately determining the positionand angle of the injected beam made it possible toposition the injected beam with respect to the closedorbit, so as to obtain optimum injection steering for aparticular position of the stripper foil. The probabilityof the closed-orbit beam multiply traversing the foil wasreduced, and thus beam scattering was reduced. Theaverage intensity delivered to the Neutron ScatteringCenter was increased from 35 to 50 pA in 1989, and thepeak intensity was raised to 64 pA.

Acknowledgements

The author is grateful to her colleagues in MP-5 andMP-6 at LAMPF for helpful discussions . Special thanksare due to Viola Martinez for help in production of themanuscript .

References

[1] R.J . Macek, Status of the PSR, Internal LAMPF Report(Los Alamos National Laboratory, 1989).

[2] E.F. Higgins and F.D . Wells, Proc. 1981 IEEE ParticleAccelerator Conf., Washington, DC, IEEE Trans. Nucl.Sci . NS-28 (1981) 2308 .

[3] G.W. Snedecor and W.G. Cochran, Statistical methods(Iowa State University Press, Iowa, 1976).

[4] B. Noble, in : Generalized Inverses and Applications : Pro-ceedings of an Advanced Seminar, Mathematics ResearchCenter, Univ. of Wisconsin at Madison, Oct. 8-10, 1973,ed . M . Zuhair Nashed (Academic Press, New York, 1976)p . 245 .