May SLAC-PUB-6209 1993 (A)
Beam Based Alignment of the SLC Final Focus Sextupoles*
P. Emma, J. Irwin, N. Phinney, P. Raimondi, N. Toge, N.J. Walker, V. Ziemann Stanford Linear Accelerator Center Stanford, California 94309 offsets with respectto the final focus orbit are calculated. Alignment correctionis implementedby closedorbit bumps with horizontal and vertical dipole correctormagnetswithin the tinal focus. A desirable quality of the technique that the is measurement tolerancesare consistent with the alignment goals - if there are no measurablewaist, dispersion, or coupling changesin the IP beam given significant sextupole strength changes, the necessary then alignmentis achieved. For SLC, there are just two power suppliesfor the four sextupoles tinal focus. The two X-sextupoles(horizontal per chromaticitycorrection)are in serieson one supply,while the Y-sextupoles in serieson a secondsupply. Fortunately, are due to the -I transform betweenpairs, this is ideal - the waist, dispersion, and coupling changesat the IP can be independentlyseparated symmetric and anti-symmetric into componentsof sextupole pair misalignment in X and Y. Figure 1 illustrates the eight different observable misalignment components. The individual sextupole I. MOTIVATION misalignments simply linear combinationsof theseeight are The motivation for achieving good static [l] sextupole components. alignmentis actually two-fold in the SLC final focus. Tuning time is minimized by orthogonalizing chromaticity control with respectto IP beam waist adjustments ` dispersion Cp* ), control, and coupling correction. Furthermore, to space due requirements, the SLC final focus chromatic correction xdisp sections employ ` nested' horizontalandverticalsextupole pairs - four per final focus [2]. The linear optics between two the sextupole pairsaredesigned providea -I transformto cancel to y-waist 4Y-a geometricand chromaticdispersionaberrations. Misaligned sextupoles within the nestedsystemgenerate skew andnormal x-disp quadrupole fields which distort the-I transfcmn so generate and 45-a +c3 higher order optical aberrations which arc not all correctable. Therefore,it is critical to achieve static alignment of these skew d@.@-++ sextupoles to within -200 l.tm for present SLC beam parameters. -/&+-,o,+y&p II. THE ALIGNMENT METHOD The scxtupolepairs are placedrr.Qin phasefrom the IP at points of largehorizontal dispersion. Therefore,a horizontal & .-b' -~~~skew --*0' sextupole offset will introducea normal quadrupole field and generatehorizontal IP dispersion and both horizontal and ,y-disp -~~~O$.-o.,@ vertical waist shifts. A vertical offset will introducea skew \' quadrupole field and generatevertical IP dispersion and coupling. The SLC final focus design provides orthogonal A X-orbit @ X-sextupole correctionfor eachof theseeffects. By measuring amount the , h \ - - Y-orbit of IP waist, dispersion,and coupling changeas a function of IY-scxtupole eachsextupolestrength,the horizontal and vertical sextupole ABSTRACT The strongdemagnification inherentin final focus systems requires local cancellation of the resulting chromaticity. Strong sextupole pairs separatedby a -I transform are positionedx12 in betatron phaseaway from the Interaction Point (IP) in order to cancelchromaticaberrations primarily dueto the final quadrupoles. Sextupole alignmentis critical in order to provide orthogonaltuning of the chromaticityand, in the caseof the SLC, to limit the third andhigherorderoptical aberrations generated from misalignedand ` nested' horizontal and vertical sextupole pairs. Reported here is a novel techniquefor aligning the beam centroid to the sextupole centers,which usesmeasurements the critically dependent of parameter the beam size at the IP. Results for the SLC final focus sextupoles presented, are wherea resolutionof ~50 pm is achieved.
x-waist
0
*
Work supported by Department of Energy contract DE-AC0376SF00515
1. The eight measured sextuple misalignment combinations RT plane) and the dominant generated optical effect observed at the IP (waist shift, dispersion, and coupling or ` skew' ).
Presented the ParticleAccelerator at Conference (PAC ` Washington,DC, 93). May 17-20.1993
In order to illustrate the connectionbetweenmisalignment remove the y-waist dependence on Y-sextupole strength components generated and optical effects suppose sextupole (shown is an extremecaseof 1 mm to test bump closure). the is misaligned (~0, yo) with respect to the beam centroid. The 150 sextupole kick angles, (Ax' Ay' of a particle with centroid , ), position deviation (x + ~6, y ) in one sextupole of strength k = 3.94 mm2 Ak then become
dx' (x,Y,rl,s,x,,Y,)=~dk((x+x,+~~~*-(Y+Y,)*~ ,
100
Ay' (x,y,~,~,xo,~o)=Ak(x+x,+~~6)(~+~0)
.
(1)
Here 6 is the fractional energy deviation (=SEI&) and q is the nominal horizontal dispersion at each sextupole per pair. Note, the final focus dispersionmust first be correctedto fairly loosetolerances before the alignmentprocedure begins. Each optical effect is labeled below in (2) and (3) after summing the two kicks due to misalignments of one sextupolepair and using the -Z transform betweensextupoles. These kicks become positions at the IP through the R 12 and R34 transfermatrix elementsfrom relevant sextupoleto IP. Ax;(x, y, v, 8, ~01,Y,,&- W-x, 2Akxq6 + AWG,~ + -G,Z I+
AkwVxol x02)
50 67 3 -w b
0 200 150 100 50 k= 1.97m-2
-Y, %& qcv Y,,) = (2) (x-chromaticity)
(x-waist)
-
A~~(YoI+ YOZ I+ ANif1 - &) - (Y& - y;2 )I
AY;(x,Y,v, (dew) ~,xol,~ol)-A~;(-x,-~,~~~,x02~~02)=
(x-dispersion) (x-steering)
2AkyqS+ AWx,, + x,x I+ AkwVyol- ~02) + AWYOI + ~02) +
AmolYol - Xo*Yo*)
0 (3) -3 -2 -1 0 1 2 3 C@romaticity) IP x-waist position [cm] (y-waist) Fig 2. Two x-waist scans (IP beam size vs. waist position) done at (y-dispersion) different X-sextupole strengths, k, reveal a horizontal symmetric
(skew) (y-steering) component of sextupole misalignment of 354 f 21 pm.
With measurements waist, dispersion,and skew changes of at the IP as a function of sextupolepair strength changes,the symmetric, (x01+x02) and (yol+y&, and the asymmetric, (x01-x02) and (yol-~02). misalignment components are calculated per pair. For example, the horizontal symmetric misalignment of the X-sextupole pair is calculated by measuring the x-waist shift, Aw,, per strength change, Ak, using the large R12 (3.3 m) from thesesextupolesto IP. Aw x0, +x,,)=A 2R;,Ak Figure 2 shows two ` waist-scans' done at different Xsextupole strength settings. The waist positions have shifted with respect to each other by Aw, = 1.49 rt 0.09 cm for a sextupole strength change of Ak = 1.97 m-2 and indicate the symmetric horizontal misalignment is 354 f 21 pm. HI. ALIGNMENT CORRFCTION After measurement a specific misalignment component, of an orbit bump is introduced with dipole corrector magnets which removesonly that component. Figure 3 shows a large horizontal symmetric bump introduced at the Y-sextupolesto
l3
B k4
X-sextupoles 1 II I,, , 1 I I
v
-lI
e- I
North Final Focus
IP
SouthFinal Focus
Fig 3. A horizontal symmetric e- orbit bump introduced with dipole correctors to remove y-waist dependence on Y-sextupole strength (shown is an extreme case of 1 mm to test bump closure).
There are sufficient dipole correctors in the final focus to orthogonally correct all eight misalignment componentsper side (North e- and South e+). A second iteration is always performed to verify the sign and magnitude of correction. With large corrections(>400 pm), a secondsmaller correction is usually necessary align to nearmeasurement to precision.
With the sextupoles detuned, uncorrected chromaticity causes the minima of these scans to increase. A practical approachis to run the two scanson either side of the nominal sextupole setting. This optimizes the waist measurement precisionby reducingthe chromaticincrease. To further optimize measurementprecision, the IP beam size measurements made at low beam current (O.5x1O1o) are with the existing 4 pm diameter Carbon filament wires near the IP [3]. The measurementis corrected for the large wire diameterand clean, reproducibleresults for the single beamof interesthave beenachieveddown to 1.3 l.tm beam sizes [4]. When the alignment is complete and all corrections have been verified, two linear combinations of the two sextupole pair strengths are scannedto minimize the IP beam size per plane. The linear combinations are intended to orthogonally control horizontal and vertical IP chromaticity [5]. With the sextupoles aligned, these scans will now reliably minimize chromaticity and achieve the optimal IP beam sizes. Figure 4 shows a vertical chromatic&y scandone after alignmentwhich achievesa 1.55 l.trn vertical IP e- beam size.
IV. CONCLUSIONS This sextupole alignment technique has been used succes...