A Pinger Magnet System For Tune Measurements in the IPNS Rapid Cycling

Synchrotron (RCS)

J. C. Dooling, L. Donley, F. R. Brumwell, G. E. McMichael, S. Wang Argonne National Laboratory

9700 S. Cass Ave., Argonne IL, 60439

Abstract. Pinger magnets for measuring horizontal and vertical tunes in the IPNS RCS have been constructed and installed. Reference horizontal tune data was collected using the extraction kicker magnets in December 2005. More recent data collected at the end of February 2006 with the dedicated pinger magnets confirms December measurements and provided simultaneous vertical tune information. Chromaticity variation with sextupole field strength is examined in an effort to optimize tune profiles.

Keywords: tune, chromaticity, ferrite pinger magnet. PACS: 29.27.Fh, 41.75.-i

INTRODUCTION A low-power, dual pulsed-magnet system has been constructed and installed in the

IPNS RCS to facilitate tune profile and chromaticity measurements. The RCS, operating at 30 Hz, accelerates protons from 50 MeV to 450 MeV in approximately 14 ms. The RF frequency in the h=1 machine varies from 2.21 MHz at injection to 5.14 MHz at extraction. The bare tunes are 2.18 and 2.32 in the horizontal and vertical planes, respectively.

EXPERIMENTAL DESCRIPTION

Pinger Hardware The pinger magnets are fabricated from ferrite blocks arranged in a "C"

configuration. In both vertical and horizontal magnets, the clear aperture is 10.8 cm (4.25") H by 5.4 cm (2.125") V. Copper Faraday shields are used around the ferrite to confine the magnetic field to the region of the pinger magnet and help maintain field uniformity near the edge of the “C.” The V- and H-magnets are shown in Figure 1. Measuring resonant the frequency with parallel capacitances of C/2, C, and 2C (C= 0.01 μF), the inductance of the H-magnet is found to be 0.4 μH. Based on geometry, the inductance of vertical pinger magnet is estimated to be 0.2 μH. Presently, the

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Figure 1: V- (left) and H-pinger magnets pinger magnets are energized using a single E2V 1725 thyratron switch tube; four of these tubes are used for fast-extraction of beam from the RCS. Typical kicker PFN bias is in the range of 45-50 kV; however the pinger bias is limited to 10 kV. In the future, the pinger tube may be replaced with a solid-state switch. A 10-Ω termination load is mounted to an electrode feedthrough flange on the RCS vacuum vessel in the L4 straight section, the location of the pinger magnets. The terminating resistor stack acts as a 3-way socket which can be rotated to allow for 3 modes of operation: H-plane only, V-plane only, and simultaneous H- and V-plane pinger operation. After initial testing using the differing configurations, it was found that energizing H and V magnets together provided good S/N in both planes. Simultaneously pulsing both pinger magnets is now the normal method of operation. Five 50-Ω, HV coaxial cables are run in parallel to approximately match the impedance of the magnets and resistive load. The cables extend 8.0 m from the kicker tank on top of RCS shielding directly above the pinger magnets through a penetration to the terminating load. In Figure 2a, the installation of the pinger magnets can be seen through an outboard 25.4 cm (10 in) port. Upstream is to the left and the location of the vertical pinger magnet. The 10-Ω load socket positioned for V-only operation is shown in Fig. 2b. Initial estimates of the required pinger strength were established from known extraction kicker parameters. The kicker magnet current rises to 4-kA in 100 ns over a total magnet length 0.86 m deflecting the 450-MeV proton beam 23.5 mrad. From magnetic rigidity, ρB=p/q, the bend angle through the pinger is expressed as,

eff

o

qBlm c

θ =βγ

(1)

The effective length, leff, is determined by measuring the longitudinal field profile with a pick-up coil. The profile through the center of the H-magnet is presented in Figure 3a. The data, recorded on the RCS Kicker Test Stand, yields an leff=13 cm. The peak

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Figure 2: Left: Partial view of the pinger magnet installation, upstream is left; right: terminating load. current in the coil is 400 A and the peak voltage across the coil is approximately 3.5 kV. Transversely, the field varies by ± 1.5 percent across approximately 6 cm of the horizontal aperture, as shown in Figure 3b. A pinger deflection angle of 0.5 mrad was initially suggested [1] as a reasonable amplitude for bumping the beam orbit. To achieve a 0.5 mrad kick of 450 MeV protons from a 13 cm length pinger, a field of 123 Gauss is required. In fact, we find that a substantially smaller bump is adequate for observing the sidebands and measuring the tune when employing a spectrum analyzer and operating the RCS at 30Hz.

Figure 3: H-pinger a) longitudinal and b) transverse field profiles

Prior to installation of the pinger magnets, the means of imparting a small angular deflection to the beam involved using two of the four extraction kicker magnets. In the early days of the machine, an RF “knockout” frequency was applied to shake the beam, but the approach was abandoned because of poor response. In the "kicker-as-pinger" (KAP) mode, beam is not extracted from the machine; this makes real-time

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measurements impossible, couples weakly into the vertical plane, requires significant set-up time and contributes to activation of synchrotron hardware. In spite of these drawbacks, KAP data provides valuable H-tune measurements. The KAP method exhibits good isolation between the transverse planes. Figure 4 shows spectra of difference signals from both horizontal and vertical pie electrodes located in the short straight section 5 (S5) of the RCS. The data are recorded simultaneously 10 ms after injection and show at least 30 dB of isolation between the transverse planes for the first three harmonics. Also visible in the “V” spectrum is a small oscillation the pinger generates in the vertical plane indicating the vertical tune. Pie electrodes behave as short striplines where the longitudinal length of the line is much less than the length of the beam bunch; therefore each segment of the pie electrode generates a signal proportional to di/dt.

Figure 4: KAP difference signal in H and V planes; kicker moves the beam horizontally.

Data Analysis

Data from the pie electrodes are typically digitized using fast 8-bit oscilloscopes; in the present arrangement, a TDS7254 Tektronix unit is used. To prevent aliasing, the pie data is sampled at a rate of 1.25x109 samples per second (1.25 GS/s). The pie diagnostic provides data in pairs: inside/outside and top/bottom. The single-ended data is recorded on four channels of the TDS7254. When only horizontal data is

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available, adjacent horizontal pie pairs in S5 and S6 are obtained. Record lengths of 0.5 MS (400 µs) or 1.0 MS (800 µs) on each channel are acquired. A pre-trigger setting of 10 percent is used to observe beam motion prior to the pinger pulse. A sampling period of 60 μs (75 kS) is chosen to provide good frequency resolution in the FFT; in this case, the resolution frequency bin width, Δf=16.67 kHz. Linear interpolation is used to over-sample the time data and generate a 2N set; therefore, with 75 kS sets, N>16 and typically, N=17. To reduce the required CPU time with this large set, averaging is employed. In most of the spectral data presented here, 5 adjacent points are averaged reducing the data set to 15 kS. In this case, N=14, substantially reducing the time required to generate a spectrum. Sample size reduction is important in the spectrum optimization procedure where multiple spectra are generated. Averaging reduces the time required to generate an optimized spectrum; however, during the last 4 ms (10 ms to extraction) of the acceleration cycle, substantial high frequency components above 125 MHz are present in the beam. As a result, aliasing may occur in the spectra of time-averaged data. This is especially true shortly after phase modulation (PM) is initiated approximately 9.5 ms after injection. Aliasing can be avoided if, after using averaging to find the optimized window index, one then returns to the full 75 kS case to generate the final spectrum.

FFT Optimization

Prior to identifying the side-band peak associated with the betatron tune, the frequency of the bunch must be accurately determined. As indicated above, the bunch revolution frequency changes by more than an octave during acceleration. The maximum change in the revolution frequency occurs at 6.1 ms after injection. The FFT optimization algorithm seeks the narrowest line width at the fundamental bunch revolution frequency. In the case of a static FFT, where the sample window is fixed, the width of the frequency bins are fixed as well. As the beam accelerates, a bin which initially contains the fundamental harmonic will experience a drop in amplitude until the adjoining bin on the high-frequency side contains an equal amount of energy. At this point, the two bins indicate an amplitude 6 dB below the actual peak. Also, when the fundamental harmonic is shared in this way, the spectrum will appear smeared out. It is important that the fundamental frequency be located as close as possible to the center of a bin; this is the same as requiring that an integer number of bins define the position of the fundamental frequency.

The algorithm first estimates the frequency of the fundamental bunch using a polynomial fit of bunch revolution frequency versus time in the acceleration cycle. An initial FFT is generated from the data window following the one in which the pinger occurs; this avoids noise components associated with the pinger trigger. The first spectrum is used to identify the bin with the peak amplitude; this is assumed to be the fundamental frequency. The polynomial fit of bunch revolution frequency versus time from injection allows discrimination against possible higher amplitude components which may appear at the second or third beam harmonics. With the fundamental frequency bin identified, the amplitudes in the adjoining bins are compared. If the lower frequency bin is higher in amplitude than the adjoining high-side bin, the actual frequency is lower than the initial result; in this case, the sample

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window is made larger. If the opposite case is true, then the data window must be reduced. The algorithm tests the following inequality:

( ) ( )N 1, j N 1, j N 1, j 1 N 1, j 1f f f f

N , j N , j 1f f

F F F F

F F

− + − − + −

−< (2)

where Fi,j is the complex spectral amplitude from the FFT for bin i and window sample width Nwin(j). Nf represents the bin of peak amplitude which is constrained to be the fundamental bunch revolution frequency. After the initial FFT is calculated (j=0), the value of Nwin is decremented by 1, incrementally increasing the bin size. The new sample set is again interpolated to obtain 2N points, and a new FFT (j=1) is generated. The inequality in Eq. 2 is now evaluated. If the inequality is true, the value of Nwin is decremented again by 1 and the process continues with a new Nwin (j=2). The algorithm proceeds to reduce the value of Nwin until the inequality becomes false; at this point, an optimized spectrum has been found. If at the j=1 step Eq. (2) is false, then the j=1 spectrum is replaced by that for Nwin+1 from the initial sample size (j=0), incrementally reducing the resolution frequency width. For a time-sample window containing 15,000 points and covering a period of 60 µs, a one-sample change represents a frequency shift per bin of Δf/Nwin=1.1 Hz. By adjusting Nwin until the amplitudes of both adjoining bins are minimized relative to the center bin, the fundamental beam frequency can be accurately determined.

TUNE MEASUREMENTS

Installation of the pinger magnets in February 2006 was driven by the need to diagnose, understand, and mitigate an instability which limits the time-average RCS beam current to 16 μA or 3.3x1012 ppp (2.2x10E12 ppp without phase modulation[2]). With the pinger magnets in place, tune data can be obtained at full intensity whenever required. A third RF station has recently been added to the RCS increasing the available accelerating voltage by 50 percent or providing second harmonic RF (SHRF) to flatten the current profile by extending the bucket. The application of SHRF could lead to an increase in the current limit of the RCS; however, before such an increase can be realized, it is necessary to understand the nature of the instability. For example, is the instability driven by peak current or total charge in the bunch? Before this and other instability questions can be answered, basic tune profiles and chromaticity of the RCS beam needed to be measured. A systematic tune measurement had not been performed in the RCS since the early 1980’s. In anticipation of having the pinger magnets available, a number of machine research periods have been set aside to measure the tune and chromaticity of the RCS, first with the kicker magnet (KAP mode) then by pinger operation as mentioned above. Typical machine research periods occur once per week and last 6 hours. In addition to these normal study times, we have added extended machine research (XMR) periods, where over a period of three consecutive days, an entire 8-hour shift is dedicated to machine

286

studies. Five such XMR sessions have been built into the FY2006 IPNS operating schedule, three of which have been completed by the time of this writing.

In the first XMR session, tune data was collected in KAP mode only. In this mode, horizontal tune lines are dominant; therefore, only data in this plane is analyzed. Rather than look at the vertical S5 electrode data as is typically the case, beam signals were collected on adjacent horizontal Pie electrodes in the S5 and S6 straight sections. When bringing the pinger magnets on-line in February, tune measurements at selected times in the cycle were obtained to compare with KAP measurements as shown in Figure 5a; in addition, we had our first look at simultaneous vertical tune values as presented in Figure 5b. All data in Fig. 5 were obtained at the reference orbit. With

Figure 5: a) KAP and Pinger magnet H-tune measurements compared with Dec. ’05 KAP data, b) vertical. The time for triggering pulsed quadrupoles A and B are indicated by the arrows.

the pinger magnets in place, preliminary tests have been conducted at full beam intensity (3.5-3.7x1012 ppp) to study the effects of space charge on the tune. Specifically, an instability is known to grow in the vertical plane near the end of the acceleration cycle. The space-charge tune shift between low intensity (0.5x1012 ppp) and full intensity versus time in the acceleration cycle is plotted in Figure 6. A 3rd order polynomial fit suggests the tune shift to be approximately -0.025 early in the cycle for a space-charge increment of 3x1012 protons. The space-charge tune shift is well within acceptable limits; however, the overall trend of the vertical tune to drop near 0.25 by the end of the cycle is more troublesome. Strong oscillations result near f=(n±1/4)f0 where n is an integer and f0 is the revolution frequency late in the acceleration cycle. The nature of this oscillation is presently under investigation.

To study the chromaticity, the beam is parked at several positions across the horizontal aperture of the machine by finely adjusting the RF frequency at a given time which in turn modifies the beam momentum. At low intensity, the beam is moved from its reference position either inside or outside until losses are observed. Beam position is determined from the frequency increment as follows: in a synchrotron, the time interval for a charge to travel the ring circumference, C, is expressed as,

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Figure 6: Space-charge tune depression in the vertical plane with 3rd order polynomial fits.

Cv

τ = (3)

and differentially,

2 o

o

Dd dC dv 1 dC v R p

dpp

⎛ ⎞τ= − = −⎜ ⎟⎜ ⎟τ γ⎝

= η

p

⎠ (4)

The revolution frequency fo = 1/τ and dτ = -df/fo2, so the momentum can be

determined from the frequency shift as follows[3],

o o

dp 1 dfp f

= −η

(5)

In a straight-section (where the pie-electrodes are located), horizontal position is a function of momentum through the local value of dispersion, D(s). The displacement of the beam due to an energy or momentum shift is expressed as,

D Do o

dp pdx (s) D(s) or x (s) D(s)p p

Δ= Δ ≈ (6)

therefore, the displacement of the beam from its reference position can be expressed in terms of the frequency shift,

Do

D(s) fx (s)fΔ

Δ = −η

(7)

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For the chromaticity, the radial tune profile is fit with a polynomial of order 2 which includes the octupole component. Defining x=xD-xo+xβ, then,

D D

o

xdx d(x x ) dx d

pD(s)p

ββ

∂= + = +

∂νΔ

≈

ν (8)

Assuming the amplitude-dependent tune shift is small, dx≈dxD. (x) f (x) and d f (x)dx′ν = ν = (9) The chromaticity is defined as the change in tune with change of momentum,

d (x)(x,s)dp xp D(s)(x)D(s)

′ν νξ = =

⎛ ⎞ ⎛ ⎞Δ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠′≈ ν

dx

)

(10)

With the tune modeled as a second order polynomial, (11) 2

o 1 2(x) b b x b xν = + + then, (12) 1 2(x) b 2b x′ν = + and the chromaticity can be expressed as, (13) ( 1 2(x,s) D(s) b 2b xξ = + For a linear tune profile, the chromaticity is simply D(s)b1. Tune profiles also vary with time according to pinger data. In Figure 7, horizontal and vertical tune profiles are compared for 1 and 7 ms after injection. Significantly, the horizontal tune starts off having positive chromaticity with a profile that is mainly linear and evolves to negative chromaticity (at the reference orbit) with substantial second-order chromaticity or octupole component. On the other hand, the vertical chromaticity remains generally constant and negative.

Reference orbit chromaticity, ξ(0), is plotted versus time in Figure 8. The initial positive horizontal chromaticity becomes less so with time; after 9 ms, ξx(0) is generally negative except briefly around 12 ms. Vertical reference orbit chromaticity,

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Figure 7: Horizontal and vertical tune profiles 1 and 7 ms after injection.

ξy(0), is for the most part negative, though it approaches zero near 9 ms. The data presented in Fig. 8 is sparser in the vertical plane since the initial tune study was done is in KAP mode which looks only at the horizontal plane. Recent tune data is also compared with that obtained during the last systematic measurement. Notably, the chromaticity early in the acceleration cycle appears to have changed sign in the intervening years from negative to positive. The tune profile obtained approximately 2.5 ms after injection during the past study is compared with recent data at 2 ms in Figure 9.

Figure 8: Recent H- and V-chromaticity measurements

Starting in the second XMR session at the end of February 2006, sextupole currents studies began. Adjustments of the H-plane sextupole (sextupole pair “A”) currents were made to measure its influence on chromaticity. In Figure 10, the variation in sextupole A current is presented. Though it was desired to modify the current specifically at 12 ms, the response time of the magnet is slowed by its inductance and currents at other times varied as well. The greatest change in current actually occurred near 11 ms as Figure 10 indicates. Figure 11 shows the variation in tune slope and resultant chromaticity change for the three current profiles at 11 ms. Further work is

290

being conducted to characterize the effects of similar current variations in the V-plane sextupoles (sextupole pair “B”).

Figure 9: Recent and past tune profiles and chromaticity at 2 and 2.5ms

Figure 10: Variation of sextupole A current for tune-tilt characterization.

Figure 11: H- and V- tune tilt measurement data at 11 ms for the current variations given in Figure 10.

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DISCUSSION

As mentioned above, if the current limit in the RCS is to be increased, it is important to understand the nature of the instability that prevents operation of the accelerator above 16 μA. The proper use of sextupole magnets helped to increase the current limit during the initial years of operation[4] by controlling the growth of a head-tail instability. The instability appeared when the horizontal chromaticity changed from negative to positive late in the acceleration period. This description is very similar to what is presently observed in recent tune data, with the exception that now we also appear to have positive chromaticity early in the cycle as well. Theory[5,6,7] states that chromaticity should remain slightly negative, but otherwise close to zero to prevent head-tail effects below transition. The recent measurements also show significant second order chromaticity or octupole component which will contribute to Landau damping. At present we do not have a means of controlling the octupole term.

ACKNOWLEDGMENTS

This work is made possible by the dedicated staff of the IPNS Accelerator Operations Group and is supported by the U.S. Dept. of Energy under contract no. W-31-109-ENG-38.

REFERENCE

1. A. V. Rauchas, et al., IEEE Trans. Nuc. Sci., 28(3), 2338 (1981). 2. C. Potts, et al., IEEE Trans. Nuc. Sci., 32(5), 3107(1985). 3. S. Y. Lee, Accelerator Physics, World Scientific, Singapore, 1999, p. 121. 4. Y. Cho and A. V. Rauchas, IEEE Trans. Nuc. Sci., 28(3), 2585 (1981). 5. F. J. Sacherer, Proc. IX Int’l. Conf. on High Energy Accelerators, May 2-7, 1974, SLAC CONF 740522. 6. D. A. Edwards and M. J. Syphers, An Introduction to the Physics of High Energy Accelerators, Wiley, New York, 1993, p. 203. 7. A. W. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, New York, 1993, p. 197.

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