In the recent polarized proton runs in the AGS, a 5% partial snake was used successfully to overcome the imperfection depolarizing resonances. Polarized proton beam was accelerated up to the required RHIC injection energy of 25 GeV. However, significant amount of polarization was lost at 0+{nu}{sub y}, 12+{nu}{sub y} and 36+{nu}{sub y}, which is believed to be partially due to the coupling resonances. To overcome the coupling resonance, an energy-jump was generated by rapidly changing the beam circumference using the powerful AGS rf system. It clearly demonstrates that the novel energy-jump method can successfully overcome coupling resonances and weak intrinsic resonances

Ahrens, L.

Alessi, J.G.

Huang, H.

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1997 Par t ic le  Accelerator Conf., Vancouver, B.C., Canada, f May 12-16, 1997. &&F- 970503 - -  i BNL- 63 8 83 Overcoming Weak Intrinsic Depolarizing Resonances with Energy-jump" H. Huang' , L. Ahrens', J.G. AIessi', M. Bai2e3, K.A. Brown', G. Bunce', P. Cameron', P. Ingrassia', A.E. Kponoul, K, Krueges, S.Y. Lee2, A.U. Luccio', Y.I. Makdisi', E Maria ' ,  M. Okamura5, L. Ratner', K. Reece', T. Roset', H. Sate*, H.M. Spinka3, N. Tsoupas', D.G. Underwood3, W. van Asselt', N.W. WilIiams', and A. Yokosawa3 ( I )  Brookhaven National Laborarory, Upton, M I  I I973, USA ( 2 )  Department of Physics, Indiana University, Bloomington, IN 47405, USA (3) Argonne National Laboratoq 9700 Cass Ave., Argonne, IL 60493, USA (4) KEK, 1-1 Oho, Tsukuba-shi, Ibaraki-ken, 305, Japan (5) RIKEN, Wako, Saitama, 351 -OI, Japan R ECEl VEQ ,)uw 2 5 @p 'I Abstract In the recent polarized proton runs in the AGS, a 5% par- tial snake was used success€ulIy to overcome the imper- fection depolarizing resonances. Polarized proton beam was accelerated up to the required RHIC injection energy of 25 GeV. However. significant amount of polarization was lost at O+vy, IZtv, and 36+v,, which is believed to be partially due to the coupling resonances. To overcome the coupling resonance, an energy-jump was generated by rapidly changing the beam circumference using the power- ful AGS rf system. It clearly demonstrates that the novel energy-jump method can successfully overcome coupling resonances and weak intrinsic resonances. 1 INTRODUCTION The spin vector of an orbiting particle in a synchrotron obeys the Thomas-BMT equation [I], where the dynam- ics of spin motion can be characterized by the spin tune v,, which is defined as the number of spin precessions per revolution about a stable spin direction. The acceleration of polarized beam will encounter depolarizing resonances whenever the spin precession frequency exactly matches the frequency with which the protons encounter depolar- izing horizontal magnetic fields. For an ideal accelerator, where orbiting particles experience only the vertical guide fieId, the spin tune is equal to G-1, where G = 1 .T928 is the anomalous G-factor of the proton, and y is the relativistic Lorena factor. The resonance condition for imperfection depolarizing resonances arises when v, = Gy = n, where n is an integer. The condition for inmnsic depolarizing res- onances arises when v, = G-/ = kP f vv, where k is an integer, vy is the vertical betatron tune, and P is the su- perperiodicity. For the Brookhaven Alternating Gradient Synchrotron (AGS), P = 12 and v, = 5.8. Traditionally, the imperfection depolarizing resonances are compensated with the tedious harmonic correction *Work performed under the auspices of the US. Dept of E n q y  method and the intrinsic depolarizing resonances are over- comed with tune-jump rnethod[Z]. The polarized proton runs of experiment E-880 at the AGS aim to demonstrate the feasibility of polarized proton acceleration using a 5% partial Siberian snake [3]. In the first run it was shown that a 5% snake is sufficient to avoid depolarization due to the imperfection resonances [4J. The results are shown in Fig. I as open circles and dashed lines. The pulsed tune- jump quadrupoles were not powered in this run. Although some depolarization at intrinsic resonances are expected, the level of the depolarization does not agree with a simple model calculation. A spin tracking study using SPINK [SI was then performed and it showed that there is an ex- resonance adjacent to the intrinsic resonance which causes further depolarization [6]. ?his additional resonance can be easily understood as a linear coupling effect. Since the solenoidal 3% partial snake introduces considerable linear coupling between the two transverse betanon motions, the vemcal betatron motion has also a component with the hor- izontal betatron frequency. As a consequence, the beam will see an additional resonance, the so-called coupling res- onance at G7 = 0 + vz, besides the intrinsic resonance at G r  = 0 + vg. In addition to the linear coupling effect, the synchrotron motion also causes some additional depolar- ization but to a smaller extent. The second run showed that it is possible to use the tune jump method in the presence of the partial snake. A new record high energy for accelerated polarized proton beam of 25 GeV was reached with about 12% beam polarization left. Again no polarization was lost due to the imperfection resonances and depolarization from most intrinsic resonances was avoided with the tune jump quadmpoles. However, as can be seen from Fig. I, signifi- cant amount of polarization was lost at Gr = Oi-v,,, 12+v, and 36 + vy. The first two of these three resonances were successfully crossed previously when the partial snake was not installed. It is believed that the losses are partially due to the coupling resonances. The tune jump method changes the vertical betatron tune within less than one revolution M -  m -  10 - GY F i p  1: Results of AGS 5% parrid snake t e s t  The mea- sured absolute value of the vertical polarization af C y  = n -k 3 up to Gy = 48.3. The open circks are the results without the tune-jump quadrupoles and the solid points are the results with the tune-jump quadrupoles. to effectively make the resonance crossing speed very fast However, the coupling resonance is still crossed at the nor- mal crossing speed and can cause polarization loss. The saength of the tune jump quadrupoles is not sufficient to jump the last resonance Gr = 36 + vy. Instead. we at- tempted to induce spin flip at this resonance but were only partially successful. A spin tracking shows that the amount of depolarization observed agrees with the effect of the strong coupling resonance at Gy = 36 + us. 2 OVERCOMING THE COUPLING RESONANCES As shown in the simulations, it is clear that the unexpected depolarization level after crossing the strong intrinsic reso- nances is due to the combined effect of the coupling res- onance and synchrotron oscillation. The coupling reso- nance Snengh can be decreased by separating the tune. However, separating the two tunes for more than 0.5 unit does not help, because the source of the coupling is local- ized at the snake solenoid. The ratio of the coupling res- onance strength to the inmnsic resonance strength with a 5% partial snake and 0.1 unit tune separation is about 0.06. With a larger tune separation of 0.3, the ratio goes down to 0.03. Also, since the coupling resonances are generally we&. the acceleration rate can be maximized to minimize the depolarization at the coupling resonance. With a 2 . 5 ~  mm-mnd polarized beam in the AGS, the Coupling reso- nances adjacent to the weak inmnsic resonances such as 24 - uy, 24 + vy and 48 - vy will have little effect with the regular acceleration rate a = 4.3 x lo-'. Bur the cou- pling resonances adjacent to the strong intrinsic resonances significant depolarization. 'This ratio makes it impossible to cross them at a singIe speed without losing polarization. Using a very slow crossing speed could fully flip spin af- ter the intrinsic resonance, but on the other hand, it also increases the depolarization from the coupling resonances. Even the uaditiond tune-jump quadrupole method is chd- lenged. The tune jump method changes the betrwon tunes in less than one orbit tum to effectively make the resonance crossing speed very fast. If the two tunes are separated, the coupling resonance is crossed by the beam at the n o d  crossing speed which causes depolarization. Moreover. the tune jump can increase the beam emittance and increase the strengths of subsequent coupling and intrinsic resonances. In short. the benefits of all these methods will be reduced or diminished without extra efforts to overcome the coupling resonances. To eliminate the coupIing resonances, one can think of compensating the linear coupling globally. Two sets of strong skew quadrupoles could compensate the linear cou- pling of the solenoidal partial snake globally. However, with a global decoupling, the orbit is fiat globally but not locally, which means that at certain locations, the coupling will be non-zero and may still cause some problem. One possible way is to eliminate only the coupling resonance closest to the intrinsic resonance instead of eliminating ev- eryone. Some further simulation is needed to test the idea. Practically, the skew quadrupoles in the AGS are not strong enough to compensate the coupling of the solenoidal snake. When the intrinsic resonances are crossed with coherent betatron oscillation excited with an AC dipole PI, slow ac- celeration rate or tune-jump, the coupling resonances can be crossed using a fast energy-jump at the resonance. This novel energy-jump method was used to cross the coupling resonance and the results are summarized in Fig. 2. In the experiment, an acceleration rate which was only 5% of the regular one was used to induce more spin ff ip at the inmn- sic resonance G-L = 0 -t vv = 8.8, while an energy-jump at about haIf of the regular acceleration rate was generated to cross the coupling resonance at Gr = 0 + vr = 8.6. The energy-jump was accomplished by rapidly changing the beam circumference by 88 mm using the powerful AGS rf system. Because of the large momentum spread of the beam indicated as a hashed band in the lower part of Fig. 2, not all the beam particles are crossing the resonance dur- ing the jump unless the jump timing is carefully adjusted. From the beam momentum dismbution, the ratio of the fi- nal to the initial polarization as a function of jump timing qUmp can be predicted and is shown as the solid line in the top half of Fig. 2. It shows good aggment with the data s u c h a ~ O + ~ y , 1 2 + ~ ~ , 3 6 - ~ ~  and36+vy w i l l c a ~ ~ e  c It c f d y  demonstrates that the novel enezy-jump method can successfully overcome couplins resonances and weak coupling resonances and the weak intrinsic resonances. intrinsic resonances. 4 REFERENCES li a7 ou 0.6 a3 Figure 2 Energy jump data and schematics. In the top half, solid points are the experiment data. the solid lhe is the predicted m e ,  where PI is the beam polarization measured aftercrossingbothGy = O+vz = 8.6 and Gr = 0 + vy = 8.8, and Pi is the beam polarization before the crossing. Bottom half shows the energy jump scheme. Grjump is the amount of change of Gr during the jump. The intrinsic resonance line Gy = 0 + vy = 8.8 is not shown. 3 OUTLOOK In the future, a novel scheme of overcoming saong inmn- sic resonances is going to be tested, which is to use an AC dipolem,(S]. Full spin flip can be achieved with a stronger artificial AC spin resonance excited by an AC dipore at a modulation tune v,. If we choose the AC spin resonance location KAC = rt f vm near the intrinsic spin resonance, the spin motion will be dominated by the AC dipole reso- nance and the spin neat the intrinsic resonance will adiabat- ically follow the spin closed orbit of the AC spin resonance. With the AC dipole, a new dominant resonance near the in- mnsic resonance is introduced, instead of enhancing the in- trinsic resonance and also the coupling resonance strength, as has been proposed earlier[9]. Spin uacking studies for the AGS ring have indicated that this scheme should work. The energy-jump method can then be used for the residual [I1 L.H. Thomas, Phil. Mag. 3, 1 (1927); V. Bargmann. L. PI F Z  K h i i  et al, Phys. Rev. D39.45 (1989). PI T. Roser, High Enew Spin Physics: 8th International Sym- posium Mimeapoiis in 1988, AIP Conference Rocetdigs. 187(1989) 1442. Michel V L  Teiegdi, Phys. Rev. Lea 2.435 ( 1959). I41 H. Huang. et d, Phys. Rev. Len. 73.2982 (1994). [51 A. Luccio. BNL Repon BNL-5248 I(  1995). [61 H. Huang, T. Row, k Luccio. These Proceedings. m M. Bai. et al, These Proceediigs. [SI M. BaL S.Y. Lee. H.Hmg, T. Roser, M. Syphers, "Over- coming the Intrinsic Spin Resonance Using Resonance Island C d  by RF Dipole". AGSRHIUSN No. 055. 191 T. Roser, Proceedings of the 10th International Symposium on High Energy Spin Physics, Nagoya, (1992) 429. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, m m -  mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 

Overcoming weak intrinsic depolarizing resonances with energy-jump

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Overcoming weak intrinsic depolarizing resonances with energy-jump

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