- Email: [email protected]
II. Experiments on stochastic cooling at cern
D. Mbh! etal., Physics and technique of stochastic cooling
102
[1.61 H.R. Raemer, Statistical communication theory and application (Prentice-Hall, Englewood Cliffs, NJ., 1969) p. 36. [1.71 A.M. Rosie, Information and communication theory (Blackie, London, 1965) p. 56. [1.81 0. Buneman, Resistance as dissipation into many reactive circuits, J. Appi. Phys. 32 (1961) 1783. [1.91H.G. Hereward, The elementary theory of Landau damping, CERN 65-20 (1965). [1.10] R.B. Palmer, BNL, private communication (1975). [1.111 H.G. Hereward, Longitudinal cooling, transverse pick-up, unpublished (1975). [1.121 G. Carron and L. Thorndahl, Stochastic cooling of momentum spread by filter techniques, CERN-ISR-RF/78-12 (1978). [1.131 S. van der Meer, Precooling for the antiproton accumulator, CERN/PS/AA/78-26 (1978). [1.141 S. Ichimaru, Basic principles of plasma physics (Benjamin, Reading, Mass., 1973) ch. 10. [1.151 A. l-lofmann, Single-beam collective phenomena, in: Proc. mt. School of Particle Accelerators, Erice, 1976, CERN 77-13 (1977) p. 147. 11.161 Design study of a proton-antiproton colliding beam facility, CERN/PS/AA 78-3 (1978). [1.171 S. van der Meer, Stochastic stacking in the antiproton acclerator, CERN/PS/AA/78-22 (1978). [1.18] L. Thorndahl, Stochastic cooling of momentum spread and betatron oscillation for low-intensity stacks, CERN-ISR-RF/75-55 (1975). [1.19] H. Herr and D. MOhl, Bunched beam stochastic cooling, CERN-EP-Note/79-34.
II. EXPERIMENTS ON STOCHASTIC COOLING AT CERN G. Petrucci and L. Thorndahl
1. 1SR experiments Stochastic cooling of vertical betatron oscillations was initially proposed to reduce the effective height of coasting beams in tile ISR [11.1,11.2]. The first trials of this method of cooling, summarized hereafter, were undertaken over a period of several years during which the maximum intensity of beams stacked in the ISR rose from about 10 A to over 30 A. Since the cooling rate obtainable is inversely proportional to the circulating beam intensity, it became questionable whether it was worth while to install the four cooling systems initially foreseen for the two rings. Moreover, the operating conditions for physics runs in the ISR had been substantially improved (better vacuum and better beam control, leading to lower losses), so that in this respect also the gain expected from stochastic cooling appeared less attractive. In the meantime, the cooling and storage of low-intensity antiproton beams had gained much interest [11.3, 11.4] and thus appeared to be the most promising application of stochastic cooling. To collect a medium-intensity antiproton stack from many low-intensity beam bursts requires not only cooling in betatron phase space but also in momentum space. Therefore, the experiments in the ISR were continued and oriented towards this new goal: several systems for betatron cooling were tried out, as well as one for momentum cooling, as described below. 1.1. Betatron cooling 1.1.1. Directional loop coupler (0. 75 to 1.6 GHz) The first experimental evidence that betatron cooling did work was obtained in 1974 [11.5]. A cooling system was installed in ring 2 of the ISR: it consisted of a pair of 3 cm long loop pick-ups,
D. MOh! eta!., Physics and technique of stochastic cooling
103
connected to a differential transformer giving an output proportional to the vertical displacement of the centre of gravity of the beam sample [11.2]. The signal was amplified and transmitted to a vertical kicker (located about 120 m downstream from the pick-ups). The transmission path was 6 m shorter than the beampath: this was obtained by following with the coaxial cable the inner wall of the tunnel, while the beam swung around its wider, normal arc. In this way one could afford 18 ns for cable velocity lag, delays in electronics, etc., and the signal from a beam sample could still arrive in time for the kicker to act on the same sample. The total electronic gain was about 95 dB. The ioop detectors exhibited a sin (2~rlf/c)response (with 1 = loop length), as for classical directional couplers. During the experiment the adjustment of the electronics was done by maximizing the instantaneous decrease of the Schottky signals, due to the beam feedback action, as explained in part I (fig. 11.1). The long-term reduction in the height of the circulating, 0.91 A beam (N ~ 1.8 X 1 o’~protons) was monitored via the luminosity increase in three intersections, where the cooled beam collided with a normal beam circulating in the other ring (fig. 11.2). The average cooling rate [—(1/h)(dh/dt)] of the effective beam height h was about 2% per hour, or about a factor of 3.8 less than predicted by the simple theory [11.6] used at that time for the full correction case (g = 1): 1 r
=
—
1 dh hdt
—
(bandwidth) 2N
1.1.2. Loop coupler for low intensities (bandwidth 80 to 360 MHz) The coupler loops described in the preceding section had to be moved mechanically to approach the circulating beam and thereby increase the coupling. Furthermore, their frequency range permitted microwave propagation along the beam vacuum chamber. These two disadvantages could be overcome with fixed, lower-frequency pick-ups and kickers (fig. 11.3) at the expense of bandwidth (and therefore of cooling rate). The cooling rate obtained (71% per hour, see fig. 11.4) was nevertheless much higher than during the first tests, owing to the lower beam current (5 mA).
10
,
Frequency
(GHZ)
Fig. 11.1. Ratio of closed-loop to open-loop transverse signal versus frequency.
D. MOhl et al., Physics and technique of stochastic cooling
104
cooling 1.02
cooling
~
j
00
~
i.se
cooling
I
i 0
-
1.02
op
oO..f
I
v
~
~: fr/ o oS:~..f~0I
~i
0
0
0
~-f;~ r°~ I ~
I
o~2~
I
I
I
j
o~%;~
I
-—
I 0
too
I
I
—
ol~j~~oo~ 0
0.98 0
7
I 2
~°
1
I I
I
7.02
~
00
I
0.96
I
I
0
0.98
0
I
098
7.00
~
0..i;04
0
I 3
~
5
time
6
7
8
9
70
ii
72
¶3
(hod,)
Fig. 11.2. Relative effective height versus time, measured in three different interaction points. 335~
_______ ____
0.
co~pL~g ~oop A - k~ybHd
Fig. 11.3. Loop coupler pick-up.
Pick-up and kicker positions were chosen so that the particles complete almost one turn before the correction is applied. Thus, the electrical length of the loop is around 3 jis. This length is acceptable for the low-frequency band, since the spread in azimuthal path during one turn between particles of extreme momenta is shorter than one quarter wavelength. Tile closed-loop Schottky signals were strongly reduced with respect to the open-loop ones. This is expected if the cooling rate is limited by Schottky noise at current levels of tens of milliamperes. At smaller levels a limitation is given by the signal-to-amplifier noise ratio. The low-frequency system offers a lower performance than the system discussed next, based on the slot coupler, but it has the advantage of extreme simplicity. It will be used for vertical cooling of antiproton beams both in the ISR and in the low-density part of the stack in the Antiproton Accumulator (AA).
D. Moh1 et al., Physics and technique of stochastic cooling
105
Fig. 11.4. Vertical Schottky scans before and after 30 mm of cooling of a 5 mA beam. The initial cooling rate was 71% per hour.
1.1.3. Slot coupler Other improvements of the high-frequency loop couplers were found desirable. In fact, these couplers suffered from insufficient suppression of signals from beam current fluctuations (common mode), sensitivity to microwave modes (RF echoes) and, to some extent, restricted bandwidth. To overcome these problems a distributed pick-up was built [11.7],where the signal from the beam is coupled to a 1 m long transmission line via an array of 30 rectangular slots (fig. 11.5). The phase velocity in the transmission line is made equal to the particle velocity in the beam chamber. Each time a particle passes a slot it will induce a signal which adds linearly to the signals already induced through the previous slots, since particle and signal travel in synchronism. The signals induced by beam chamber wave-guide modes having VPh > c tend to average out. Thanks to the stringent dimensional tolerances, an excellent common-mode rejection was achieved. The coupling between beam and transmission line grows linearly with frequency: with small slot dimensions the structure can operate up to 4 GHz. This structure was thoroughly investigated theoretically: it serves also as a kicker, and it turned out that in common-mode operation it provided a wide-band sum pick-up or a momentum correction kicker. At the beginning the pick-up was designed for medium beam intensities, 0.2 to 2 X l0’~ protons in the ISR, aiming at the large bandwidth of 1 to 4 GHz. Owing to difficulties in obtaining gigahertz power amplifiers for two octaves, the cooling system was initially tested in the 1 to 2 GHz band. Recently, with the increasing interest in low-intensity antiproton beams, where the large bandwidth is no longer a necessity, the slot structure was reoptimized for the one-octave band by increasing the slot dimensions. In this case, the phase velocity in the transmission line would become too low to maintain the synchronism wave-particle for frequencies above 3GHz. The wider slots improve the signal-to-noise ratio by 10 dB and consequently give maximum cooling rates a factor of 10 faster at low intensities, as predicted by theory. Cooling rates [—(l/h)(dh/dt)] of up to 100% per hour were observed with aS mA circulating beam [11.81 (see fig. 11.6).
D. MO/il et al., Physics and technique of stochastic cooling
106
~HI El bt
L1i,f
TEM
-
slot centre:
I
line
—
bI
beam
TIi-ET1 w325 488
L n slots Fig. 11.5. Cross-sectional views of the coupling structure, schematic. PU and K are assumed to be identical. The field orientation corresponds 4fl1m~ly2Omm~n to push-pull mode 30. operation. Geometric dimensions: a 176 mm,y~= a/2, b 31 mm, c = 17mm, w = 16mm; slots: lx tern on signoI+
I
no~/h
041140
051110
Fig. 11.6. Decrease of the peak vertical Schottky signal amplitude of a cooled 5 mA beam at 26 GeV/c.
1.2. Momentum cooling Cooling of momentum spread is obtained when high-energy particles are decelerated and lowenergy ones accelerated towards a nominal momentum. 1.2.1. Stochastic deceleration Over many revolutions stochastic deceleration is obtainable with a feedback system where the pick-up signal from a particle is amplified and applied to an accelerating wide-band structure at the passage of the particle. Similarly the particle can accelerate via the chain when an inverting transformer is inserted. When the pick-up signal is position-independent the particle can either decelerate or accelerate and the distribution will diffuse, under the influence of amplifier and particle noise, as shown in fig. 11.7.
D. MOhI eta!., Physics and technique of stochastic cooling
107
Fig. 11.7. Longitudinal Schottky pictures of a narrow (1 mm wide) 4 ~iA proton beam under stochastic deceleration (a) to (c) and acceleration (d) to (f). 26 GeV/c at ISR central orbit; 200 Hz/cm; 5 MeV/cm; interval between photographs = ~. hour.
1.2.2. Experimental demonstration of .~p/pcooling If the pick-up signal is position-dependent and the feedback polarity is such that particles are accelerated or decelerated in the direction of decreasing sensitivity, an increase in density should be achieved [11.91. As a radial monitor two partial-aperture vertical pick-up loops were used in the sum mode by adding their signals via a hybrid transformer, see fig. 11.8. Inside this structure we distinguish between three regions. In region A, as indicated by the sensitivity curve, the pick-up works like a sum pick-up, since the signal caused at the passage of a particle is position-independent. Particles in this region were decelerated by a constant amount per turn towards region B where, owing to the decreasing pick-up sensitivity, accumulation took place. The peak density was increased by approximately 50% in 15 hours (see fig. 11.9). Particles in region C were hardly affected by the feedback action (steep flank to the right on photograph). Signals from particles in A and B, applied via the gap, are without effect on particles in C, since the revolution frequencies differ in the three regions. This method will be applied to cooling of the low-density tail of the stack in the AA.
D. MOhi et al., Physics and technique of stochastic cooling
108
~thed ___________________ _____________________
high rnomentQ’~
loop/” ~
\\
/
‘~
(
/
to hybrid transformer for addit~on
I
~r
A
TB,
shield I
______
~
t.4~wmomenta I’
tQi
C
r
—‘I I I
H~\
(c)
I B
C
I
Fig. 11.8. (a) Partial aperture pick-up (momentum cooling); (b) sensitivity curve of pick-up after hybrid transformer; (c) initial particle distribution in second experiment.
Fig. 11.9. (a) Initial longitudinal Schottky diagram; (b) the final diagram after 15 hours. 26 GeV/c at central orbit; 10 kHz/cm; 200 MeV/cm.
1.2.3. Momentum cooling in the gigahertz range During the theoretical investigation of the slot structure [11.7] it was found that it could also be used for acceleration or deceleration when the pick-up and the kicker were used in common mode instead of push-pull. Measured acceleration rates of 1 7 MeV/h were in good agreement with estimated values. Since the slot couplers offer the highest bandwidth capability, such structures have been selected for both momentum and betatron cooling of the high-density part of the stack in the AA, as described in ref. [11.10]. 2. Experiments in the ICE machine The main purpose of the ICE experiments was to study stochastic cooling techniques for application in the AA [11.71. Since the accumulation in the AA occurs in momentum space, the major experimental effort in ICE was oriented towards momentum cooling. A check of the general theory [11.11] was combined with the experimentation of the filter method [11.12] for fast momentum
D. M~ohlet a!., Physics and technique of stochastic cooling
109
cooling at low intensities, required to collect the nominal intensity in the AA [11.10]. Betatron cooling, having been studied in the ISR, was not investigated in detail and served mainly to overcome beam losses caused by multiple scattering on the residual gas.
2.1. The ICE storage ring ICE is a strong focusing machine with four magnetic sectors and four straight sections, where protons from the CPS or secondary particles from a conversion target are injected and cooled. The injection is done with a pulsed inflector and a fast full-aperture kicker. The magnets were built from the iron yoke and the coils of the dismantled g-2 ring (storage ring used to measure the magnetic moment of the muon). The pole pieces were modified to include the required gradient. Each quadrant consists of six defocusing and four focusing magnet blocks. All defocusing units are fitted with poleface windings for tuning and chromaticity correction (QH = 1.35, = 1.55). A completely new vacuum system was built, partly using existing spare parts from the ISR and the SPS. The working pressure is around 1 0~Ton (N2 equivalent). For stochastic cooling ICE was run at 1.73 and 2.1 GeV/c. 2.2. Momentum cooling 2.2.1. Hardware Each of the 16 sum pick-ups used for momentum cooling consists of a 6 cm long drift tube, short-circuited to earth at one end, surrounded by a ferrite frame in the middle and connected to a SO S2 output lead at the other end. The image current associated with the passage of a particle is coupled into the preamplifier. The ferrite choke allows adeqbate response in the frequency range 40—200 MHz (see fig. 11.11). The signals from the 16 pick-ups are combined in a summing network before being fed into the preamplifier. The general layout is given in fig. 11.12. For simplicity a filter consisting of one short-circuited line, two resistors, and an inductance was installed (see fig. 11.13). This filter has notches at nominal revolution harmonics w = nirc/l = no.,0 and poles at frequencies where the line capacitive reactance Z0 tg j(wl/c) cancels the lumped inductance wL: Z0 tgj ~l
—jwL.
If we substitute for frequencies near to the nth notch: (I.~
=
no)0
+ 1~W~
and linearize the tg function we obtain nLw0/Z0 ‘~n l/c+L/Z0 The nth pole is situated below the notch at a distance of ~w,7, increasing with the harmonic number (see fig. 11.14). Since the ICE momentum cooling system works approximately over two octaves (15 n ~ 60, 50—200 MHz) and the beam spectrum width is proportional to n, this linearly-increasing separation =
‘~
D. JI’fOhl et al., Physics and technique of stochastic cooling
110
r
5 5
/~ ~ ~/.
10 8
~ 7~6Om
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~
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/
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INJECTION LINE
2
INJECTION INFLECTOR
3
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MOMENTUM COOLING P(K-UP MOMENTUM COOLING RESONANT UNE
6
MOMENTUM COOLING CORP. GAPS
12
7 8
HORIZ. BETATRON COOLING PICK-UP HORIZ. BETt.TRON COOLING CORP. GAPS
12 6
9
VERT.
l°~l
S S4
BETATRON COOUNG PC1~-UPS
10
VERT. BETATRON COOUNG OORR. GAPS
11
RESERVED FOR ELECTRON COOLING
12
BEAM PROFILE
MONITORS
bJ~ 0401
Fig. 11.10. General floor layout.
between poles and notches appeared to be relevant. The ICE filter provides simultaneous acceleration and deceleration towards the nominal momentum. The lossy resonant line has a non-zero resistive impedance Z0 tanh a0l Zoctnl in the centre of the nth notch so that a complete signal suppression does not occur. The ICE filter has an output phase which lags below the notch and leads above. In the notch centre the phase is zero. At this frequency a perfect suppression can be obtained by adding after the filter a small fraction —Z0 anl of the inverted input signal. For good cancellation over many octaves, just like the loss parameter an, the additive correction must increase with the square root of frequency. The increase of 3 dB per octave is obtained by feeding the unfiltered signal simultaneously into a line with high losses and a line with low losses, both lines having the same electrical length. The difference signal at the end of the two lines offers the required frequency characteristics (see figs. II. 1 5 and II. 16).
-
D. Möhl eta!., Physics and technique of stochastic cooling
F
111
.~
Fig. 11.11. Single pick-up drift tube with shorted back plate, ferrite choke and coupling arms. (The signal is coupled out from one side only.)
Pick—up
~L._1~
Ga~
p1.g
II.tvorkf
~
Sp.ctr, Analyser
p
o—
~
-~
ticker. Cap.
~ ~
I
~‘~
Paver L
Splitt.i~
/‘.~
680Q
III Lius Filter (42 a)
J’Kz
Fig. 11.12. General layout of iSp/p cooling system.
600fL
LINE 42 m 600n.
Fig. 11.13. Diagram of ICE filter.
After the filter the signal is amplified by a I kW distributed power amplifier and fed onto 12 accelerating gaps, similar to the pick-up gaps. These correctors are in two groups of six, separated by half a horizontal betatron wavelength to cancel the betatron heating caused by momentum corrections. (The over-all characteristics are given in fig. 11.20.) 2.2.2. Experimental results in ICE First evidence of momentum cooling was obtained in December 1977 (see fig. 11.17). During the January 1978 shutdown six of the 12 I~p/pcorrectors were reversed to obtain cancel-
112
D. MOhI eta!., Physics and technique of stochastic cooling
Fig. 11.14. Phase (90°/cm)and amplitude (10 dB/cm) around the 17th and the 53d notches.
Dif. transformer Fig. 11.15. Loss compensating network.
lation of horizontal kicks caused by electric field components. After the start-up, higher cooling
factors and rates were quickly obtained. Two major improvements to the filter line followed: (a) reduction of reflections resulting in smaller frequency errors of the resonant notches, (b) passive compensation of filter line losses in the notches to increase the signal suppression. The e-folding time for the peak density was further lowered to 1 5 s (see fig. II. 18). Such high cooling rates were obtained with high electronic gains, also causing strong diffusion as can be seen from the theory, the cooling being proportional to the electronic gain, the diffusion to its square. Thus for low gains high density increase factors could be reached at the expense of the cooling rate (see fig. 11.19).
D. Möhl eta!., Physics and technique of stochastic cooling
113
Fig. 11.16. Filter characteristics without and with compensation. Centre frequency: 124 MHz; 34th harmonic; span: 0.48 MHz.
/
Fig. 11.17. First evidence of iSp/p cooling in ICE. Longitudinal Schottky scans at the 18th harmonic, taken at 1 mm intervals. The scans are the result of spectrum analysis of longitudinal statistical beam structure. The vertical axis is \/~7/7i7~ the horizontal is frequency.
Computer simulation of the cooling process at different intensities. Since the feedback system is the result of cascading many components such as pick-ups, signal combiners, amplifiers, filters, phase equalizers, wide-band gaps (and is also a function of the coherent beam response) the over-all gain characteristic G(w) becomes quite complicated (see fig. 11.20). Thus it is most conveniently expressed numerically and the Fokker—Planck equation can be integrated by computer for a given initial distribution. To check the theory with the experiment, G(w) of the system was recorded with a network analyser in 15 frequency points inside each of 45 harmonic bands (15
114
D. MOhI eta!., Physics and technique of stochastic cooling
Fig. 11.18. Fastest cooling in ICE. Conditions: 8 X 10~p, 10 s between scans, factor 4.75 in peak density in 30s, initial e-folding time is 15 s, ave~evalue 20 s. Centre frequency 60 MHz, 20 kHz/cm, total initial width iSp/p 3.5 X l0~. The vertical axis is proportional to \I~1.
Fig. 11.19. Slow cooling. Conditions: 60 mm, factor 28 in peak density, 2 X l0~protons.
Fig. 11.20. Over-all system phase (90°/cm)and gain (10 dB/cm) between 0 and 240 MHz.
D. Möhl eta!., Physics and technique of stochastic cooling
115
particle energies between +25 MeV and —25 MeV. The data were used in a computer program to calculate the evolution of initially flat distributions after 4 and 8 mm at different intensities N. The equivalent experiments were done with ICE (see figs. 11.2 1—11.23). There is good agreement for the increase in peak density and reduction of full width (see figs. 11.24—11.25). The ratio between open-loop and closed-loop signals was observed by looking at the Schottky signals of the 18th harmonic under both conditions for 1.27 X 1 O~particles after 8 mm. They were also computed for 8 mm for the two conditions (see figs. 11.26 and 11.27). The asymmetry is caused by the notch not coinciding with the density peak. Simultaneous stochastic cooling in all three planes became an urgent goal when in early 1978 a suspicion surfaced that momentum cooling could exclude horizontal cooling or vice versa. At that time only vertical and longitudinal cooling had been demonstrated, the horizontal pick-up and kicker being centred too far towards the inside of the machine acceptance. After modification the doubts were removed when a beam of 6 X lO~protons was cooled simultaneously in all three planes, and its loss rate decreased from typically 100% per hour to a residual value of around 2% per hour, a loss rate compatible with single Coulomb scattering (see figs. 11.28 to 11.30). Antiproton lifetime experiment. Shortly afterwards it was decided to establish a new experimental lower limit for the lifetime of antiprotons. The existing lower limit was 120 jis, far below the 24 h required to accumulate in the AA machine the nominal intensity of 6 X 1011 ~.A tungsten target was installed in the transfer tunnel and bursts of around 250 p were accepted in ICE. Particles could be detected destructively independently of their momentum spread. After momentum cooling to a
Fig. 11.21. (a) Observed density evolution after 4 and 8 mm. 7
x
101 protons. (b) Computed density evolution.
D. Möhl eta!., Physics and technique of stochastic cooling
116
i!!!!1!Y
~
Fig. 11.22. As fig. 11.21, but 5 X 10’ protons.
*
PEAK
10
DENSITY
measured with
INCREASE
beam
0.5
‘o calculated with + 1db
0.4
+
Fig. 11.23. As fig. 11.21, but 1.27 X 10~protons.
+
~ calculated
0
+
~0 o
5
.
40
:
J~E~4h
0.5
-
0.3 +
lxlO
Fig. 11.24. Peak density increase.
N
0.5
1x1O~
N
Fig. 11.25. Reduction of full width in iSp/p.
FWHH z.~p/p= iO~their Schottky signal from a resonant cavity, tuned to the 35th harmonic and having a Q of 5000, became visible with as few as 50 antiprotons [11.131. With cooling in all three planes antiprotons were kept circulating for 86 hours (see fig. 11.31) [11.141. Stochastic cooling of bunched beams was investigated in order to stack antiprotons in ICE [11.15]. Bunching was done with the first harmonic and bunch lengths ~ to ~ of the circumference, the
D. Möh! eta!., Physics and technique of stochastic cooling
117
CLOSED LOOP
/
/
I
Fig. 11.26. Observed signals for open loop (thin trace) and for closed loop (thick trace); 1.27 X 10’ protons.
p 0
OPEN LOOP
\\\\\~
I/I’
I
\
BINS I
10
20
30
I
40
50
60
70
Fig. 11.27. Computed signals for open loop (thin trace) and for closed loop (thick trace).
Fig. 11.28. Longitudinal Schottky scans before and after cooling in three planes for 30 mlii.
remainder being kept free for injection (kicker rise, flat top and fall). The maximum RF bucket height (hardware limit) was ~p/p = ±5 X 1 0~,whereas the injected particles had a ~p/p = ±3X 1 0~. With momentum cooling the beam progressively entered the bucket and accumulated in its centre until i~p/papproximately equalled the equilibrium value of ±2 X 1 0~,observed with low-intensity unbunched beams. The beam bunching was clearly visible both in the time domain (oscilloscope) and the frequency domain where the lines of the first three harmonics grew to a value proportional to N. (Schottky signals are ~ In addition, the full-aperture injection kicker, which could only kick in a limited particle-free interval of the RF period, did not cause beam loss. With stochastic cooling in all three planes the lifetime of the bunched beam was equal tolhat of equally intense unbunched beams. This technique permitted the ICE team to collect 14 000 p from many pulses, each containing only a few hundred particles [11.16].
118
D. Möhl et a!., Physics and technique of stochastic cooling
Fig. 11.29. Vertical and horizontal Schottky signals before and after 30 min of cooling. The r.m.s. betatron oscillation amplitude is ‘x Y and E ~xX.
Fig. 11.30. Horizontal beam profile before and after cooling, as seen by a monitor based on beam-induced ionization electrons from the residual gas.
a)
b)
Fig. 11.31. Longitudinal Schottky signal (a) at beginning, from
240
~ (b)
about 86 h later,
80 ~ are left.
D. Möh! et al., Physics and technique of stochastic cooling
119
Acknowledgements The ICE machine is the result of a collaboration between the EP, ISR, PS and SPS Divisions. The authors are grateful to C. Rubbia, W. Schnell and P. Strolin for discussions and encouragement.
References [11.1] [11.2] [11.3] [11.4]
S. van der Meer, Stochastic damping of betatron oscillations in the ISR, CERN/ISR-PO/72-31 (1972). W. Schnell, About the feasibility of stochastic damping in the ISR, CERN/ISR/RF/72-46 (1972). P. Strolin et al., Stochastic cooling of antiprotons for ISR physics, CERN EP Internal Report 76/05 (1976). C. Rubbia, CERN-NP/Note 77-1 (1977); D. Clime, P. McIntyre, F. Mills and C. Rubbia, Fermilab TM 689 (1976); C. Rubbia, P. McIntyre and D. Clime, Proc. Internat. Neutrino Conf., Aachen, 1976 (Braunschweig, Vieweg, 1977) p. 683. [11.5] P. Bramham et al., Stochastic cooling of a stored proton beam, Nucl. Instrum. Methods 125 (1975) 201. [11.6] H.G. Hereward, Cooling by Fourier components, unpublished (1974). [11.7] L. Faltin, Slot-type pick-up and kicker for stochastic beam cooling, Nucl. Instrum. Methods 148 (1978) 449. [11.81 H. Henke, private communication. [11.9] R.B. Palmer, private communication. [11.10] Design study of a proton-antiproton colliding-beam facility, CERN/PS/AA/78-3 (1978). [11.11] F. Sacherer, Stochastic cooling theory, CERN-ISR-TH/78-11 (1978). [11.12] G. Carron and L. Thorndahl, Stochastic cooling of momentum spread by filter techniques, CERN/ISR-RF/78-12 (1978). [11.13] W. Schnell, Measuring nanoamperes by Schottky scans, ISR Performance Report (private communication) (1978). [11.14] M. Bregman et al., Measurement of antiproton lifetime using the ICE Storage Ring, Phys. Lett. 78B (1978) 174. [11.15] H. Herr and D. Möhl, Stochastic cooling of bunched beams, presented at the Workshop on Cooling of High Energy Beams, Madison, USA, November 1978. [11.16] M. Bell et al., Antiproton lifetime measurement in the ICE storage ring using a counter technique, Phys. Lett. 86B (1979) 215.
102
[1.61 H.R. Raemer, Statistical communication theory and application (Prentice-Hall, Englewood Cliffs, NJ., 1969) p. 36. [1.71 A.M. Rosie, Information and communication theory (Blackie, London, 1965) p. 56. [1.81 0. Buneman, Resistance as dissipation into many reactive circuits, J. Appi. Phys. 32 (1961) 1783. [1.91H.G. Hereward, The elementary theory of Landau damping, CERN 65-20 (1965). [1.10] R.B. Palmer, BNL, private communication (1975). [1.111 H.G. Hereward, Longitudinal cooling, transverse pick-up, unpublished (1975). [1.121 G. Carron and L. Thorndahl, Stochastic cooling of momentum spread by filter techniques, CERN-ISR-RF/78-12 (1978). [1.131 S. van der Meer, Precooling for the antiproton accumulator, CERN/PS/AA/78-26 (1978). [1.141 S. Ichimaru, Basic principles of plasma physics (Benjamin, Reading, Mass., 1973) ch. 10. [1.151 A. l-lofmann, Single-beam collective phenomena, in: Proc. mt. School of Particle Accelerators, Erice, 1976, CERN 77-13 (1977) p. 147. 11.161 Design study of a proton-antiproton colliding beam facility, CERN/PS/AA 78-3 (1978). [1.171 S. van der Meer, Stochastic stacking in the antiproton acclerator, CERN/PS/AA/78-22 (1978). [1.18] L. Thorndahl, Stochastic cooling of momentum spread and betatron oscillation for low-intensity stacks, CERN-ISR-RF/75-55 (1975). [1.19] H. Herr and D. MOhl, Bunched beam stochastic cooling, CERN-EP-Note/79-34.
II. EXPERIMENTS ON STOCHASTIC COOLING AT CERN G. Petrucci and L. Thorndahl
1. 1SR experiments Stochastic cooling of vertical betatron oscillations was initially proposed to reduce the effective height of coasting beams in tile ISR [11.1,11.2]. The first trials of this method of cooling, summarized hereafter, were undertaken over a period of several years during which the maximum intensity of beams stacked in the ISR rose from about 10 A to over 30 A. Since the cooling rate obtainable is inversely proportional to the circulating beam intensity, it became questionable whether it was worth while to install the four cooling systems initially foreseen for the two rings. Moreover, the operating conditions for physics runs in the ISR had been substantially improved (better vacuum and better beam control, leading to lower losses), so that in this respect also the gain expected from stochastic cooling appeared less attractive. In the meantime, the cooling and storage of low-intensity antiproton beams had gained much interest [11.3, 11.4] and thus appeared to be the most promising application of stochastic cooling. To collect a medium-intensity antiproton stack from many low-intensity beam bursts requires not only cooling in betatron phase space but also in momentum space. Therefore, the experiments in the ISR were continued and oriented towards this new goal: several systems for betatron cooling were tried out, as well as one for momentum cooling, as described below. 1.1. Betatron cooling 1.1.1. Directional loop coupler (0. 75 to 1.6 GHz) The first experimental evidence that betatron cooling did work was obtained in 1974 [11.5]. A cooling system was installed in ring 2 of the ISR: it consisted of a pair of 3 cm long loop pick-ups,
D. MOh! eta!., Physics and technique of stochastic cooling
103
connected to a differential transformer giving an output proportional to the vertical displacement of the centre of gravity of the beam sample [11.2]. The signal was amplified and transmitted to a vertical kicker (located about 120 m downstream from the pick-ups). The transmission path was 6 m shorter than the beampath: this was obtained by following with the coaxial cable the inner wall of the tunnel, while the beam swung around its wider, normal arc. In this way one could afford 18 ns for cable velocity lag, delays in electronics, etc., and the signal from a beam sample could still arrive in time for the kicker to act on the same sample. The total electronic gain was about 95 dB. The ioop detectors exhibited a sin (2~rlf/c)response (with 1 = loop length), as for classical directional couplers. During the experiment the adjustment of the electronics was done by maximizing the instantaneous decrease of the Schottky signals, due to the beam feedback action, as explained in part I (fig. 11.1). The long-term reduction in the height of the circulating, 0.91 A beam (N ~ 1.8 X 1 o’~protons) was monitored via the luminosity increase in three intersections, where the cooled beam collided with a normal beam circulating in the other ring (fig. 11.2). The average cooling rate [—(1/h)(dh/dt)] of the effective beam height h was about 2% per hour, or about a factor of 3.8 less than predicted by the simple theory [11.6] used at that time for the full correction case (g = 1): 1 r
=
—
1 dh hdt
—
(bandwidth) 2N
1.1.2. Loop coupler for low intensities (bandwidth 80 to 360 MHz) The coupler loops described in the preceding section had to be moved mechanically to approach the circulating beam and thereby increase the coupling. Furthermore, their frequency range permitted microwave propagation along the beam vacuum chamber. These two disadvantages could be overcome with fixed, lower-frequency pick-ups and kickers (fig. 11.3) at the expense of bandwidth (and therefore of cooling rate). The cooling rate obtained (71% per hour, see fig. 11.4) was nevertheless much higher than during the first tests, owing to the lower beam current (5 mA).
10
,
Frequency
(GHZ)
Fig. 11.1. Ratio of closed-loop to open-loop transverse signal versus frequency.
D. MOhl et al., Physics and technique of stochastic cooling
104
cooling 1.02
cooling
~
j
00
~
i.se
cooling
I
i 0
-
1.02
op
oO..f
I
v
~
~: fr/ o oS:~..f~0I
~i
0
0
0
~-f;~ r°~ I ~
I
o~2~
I
I
I
j
o~%;~
I
-—
I 0
too
I
I
—
ol~j~~oo~ 0
0.98 0
7
I 2
~°
1
I I
I
7.02
~
00
I
0.96
I
I
0
0.98
0
I
098
7.00
~
0..i;04
0
I 3
~
5
time
6
7
8
9
70
ii
72
¶3
(hod,)
Fig. 11.2. Relative effective height versus time, measured in three different interaction points. 335~
_______ ____
0.
co~pL~g ~oop A - k~ybHd
Fig. 11.3. Loop coupler pick-up.
Pick-up and kicker positions were chosen so that the particles complete almost one turn before the correction is applied. Thus, the electrical length of the loop is around 3 jis. This length is acceptable for the low-frequency band, since the spread in azimuthal path during one turn between particles of extreme momenta is shorter than one quarter wavelength. Tile closed-loop Schottky signals were strongly reduced with respect to the open-loop ones. This is expected if the cooling rate is limited by Schottky noise at current levels of tens of milliamperes. At smaller levels a limitation is given by the signal-to-amplifier noise ratio. The low-frequency system offers a lower performance than the system discussed next, based on the slot coupler, but it has the advantage of extreme simplicity. It will be used for vertical cooling of antiproton beams both in the ISR and in the low-density part of the stack in the Antiproton Accumulator (AA).
D. Moh1 et al., Physics and technique of stochastic cooling
105
Fig. 11.4. Vertical Schottky scans before and after 30 mm of cooling of a 5 mA beam. The initial cooling rate was 71% per hour.
1.1.3. Slot coupler Other improvements of the high-frequency loop couplers were found desirable. In fact, these couplers suffered from insufficient suppression of signals from beam current fluctuations (common mode), sensitivity to microwave modes (RF echoes) and, to some extent, restricted bandwidth. To overcome these problems a distributed pick-up was built [11.7],where the signal from the beam is coupled to a 1 m long transmission line via an array of 30 rectangular slots (fig. 11.5). The phase velocity in the transmission line is made equal to the particle velocity in the beam chamber. Each time a particle passes a slot it will induce a signal which adds linearly to the signals already induced through the previous slots, since particle and signal travel in synchronism. The signals induced by beam chamber wave-guide modes having VPh > c tend to average out. Thanks to the stringent dimensional tolerances, an excellent common-mode rejection was achieved. The coupling between beam and transmission line grows linearly with frequency: with small slot dimensions the structure can operate up to 4 GHz. This structure was thoroughly investigated theoretically: it serves also as a kicker, and it turned out that in common-mode operation it provided a wide-band sum pick-up or a momentum correction kicker. At the beginning the pick-up was designed for medium beam intensities, 0.2 to 2 X l0’~ protons in the ISR, aiming at the large bandwidth of 1 to 4 GHz. Owing to difficulties in obtaining gigahertz power amplifiers for two octaves, the cooling system was initially tested in the 1 to 2 GHz band. Recently, with the increasing interest in low-intensity antiproton beams, where the large bandwidth is no longer a necessity, the slot structure was reoptimized for the one-octave band by increasing the slot dimensions. In this case, the phase velocity in the transmission line would become too low to maintain the synchronism wave-particle for frequencies above 3GHz. The wider slots improve the signal-to-noise ratio by 10 dB and consequently give maximum cooling rates a factor of 10 faster at low intensities, as predicted by theory. Cooling rates [—(l/h)(dh/dt)] of up to 100% per hour were observed with aS mA circulating beam [11.81 (see fig. 11.6).
D. MO/il et al., Physics and technique of stochastic cooling
106
~HI El bt
L1i,f
TEM
-
slot centre:
I
line
—
bI
beam
TIi-ET1 w325 488
L n slots Fig. 11.5. Cross-sectional views of the coupling structure, schematic. PU and K are assumed to be identical. The field orientation corresponds 4fl1m~ly2Omm~n to push-pull mode 30. operation. Geometric dimensions: a 176 mm,y~= a/2, b 31 mm, c = 17mm, w = 16mm; slots: lx tern on signoI+
I
no~/h
041140
051110
Fig. 11.6. Decrease of the peak vertical Schottky signal amplitude of a cooled 5 mA beam at 26 GeV/c.
1.2. Momentum cooling Cooling of momentum spread is obtained when high-energy particles are decelerated and lowenergy ones accelerated towards a nominal momentum. 1.2.1. Stochastic deceleration Over many revolutions stochastic deceleration is obtainable with a feedback system where the pick-up signal from a particle is amplified and applied to an accelerating wide-band structure at the passage of the particle. Similarly the particle can accelerate via the chain when an inverting transformer is inserted. When the pick-up signal is position-independent the particle can either decelerate or accelerate and the distribution will diffuse, under the influence of amplifier and particle noise, as shown in fig. 11.7.
D. MOhI eta!., Physics and technique of stochastic cooling
107
Fig. 11.7. Longitudinal Schottky pictures of a narrow (1 mm wide) 4 ~iA proton beam under stochastic deceleration (a) to (c) and acceleration (d) to (f). 26 GeV/c at ISR central orbit; 200 Hz/cm; 5 MeV/cm; interval between photographs = ~. hour.
1.2.2. Experimental demonstration of .~p/pcooling If the pick-up signal is position-dependent and the feedback polarity is such that particles are accelerated or decelerated in the direction of decreasing sensitivity, an increase in density should be achieved [11.91. As a radial monitor two partial-aperture vertical pick-up loops were used in the sum mode by adding their signals via a hybrid transformer, see fig. 11.8. Inside this structure we distinguish between three regions. In region A, as indicated by the sensitivity curve, the pick-up works like a sum pick-up, since the signal caused at the passage of a particle is position-independent. Particles in this region were decelerated by a constant amount per turn towards region B where, owing to the decreasing pick-up sensitivity, accumulation took place. The peak density was increased by approximately 50% in 15 hours (see fig. 11.9). Particles in region C were hardly affected by the feedback action (steep flank to the right on photograph). Signals from particles in A and B, applied via the gap, are without effect on particles in C, since the revolution frequencies differ in the three regions. This method will be applied to cooling of the low-density tail of the stack in the AA.
D. MOhi et al., Physics and technique of stochastic cooling
108
~thed ___________________ _____________________
high rnomentQ’~
loop/” ~
\\
/
‘~
(
/
to hybrid transformer for addit~on
I
~r
A
TB,
shield I
______
~
t.4~wmomenta I’
tQi
C
r
—‘I I I
H~\
(c)
I B
C
I
Fig. 11.8. (a) Partial aperture pick-up (momentum cooling); (b) sensitivity curve of pick-up after hybrid transformer; (c) initial particle distribution in second experiment.
Fig. 11.9. (a) Initial longitudinal Schottky diagram; (b) the final diagram after 15 hours. 26 GeV/c at central orbit; 10 kHz/cm; 200 MeV/cm.
1.2.3. Momentum cooling in the gigahertz range During the theoretical investigation of the slot structure [11.7] it was found that it could also be used for acceleration or deceleration when the pick-up and the kicker were used in common mode instead of push-pull. Measured acceleration rates of 1 7 MeV/h were in good agreement with estimated values. Since the slot couplers offer the highest bandwidth capability, such structures have been selected for both momentum and betatron cooling of the high-density part of the stack in the AA, as described in ref. [11.10]. 2. Experiments in the ICE machine The main purpose of the ICE experiments was to study stochastic cooling techniques for application in the AA [11.71. Since the accumulation in the AA occurs in momentum space, the major experimental effort in ICE was oriented towards momentum cooling. A check of the general theory [11.11] was combined with the experimentation of the filter method [11.12] for fast momentum
D. M~ohlet a!., Physics and technique of stochastic cooling
109
cooling at low intensities, required to collect the nominal intensity in the AA [11.10]. Betatron cooling, having been studied in the ISR, was not investigated in detail and served mainly to overcome beam losses caused by multiple scattering on the residual gas.
2.1. The ICE storage ring ICE is a strong focusing machine with four magnetic sectors and four straight sections, where protons from the CPS or secondary particles from a conversion target are injected and cooled. The injection is done with a pulsed inflector and a fast full-aperture kicker. The magnets were built from the iron yoke and the coils of the dismantled g-2 ring (storage ring used to measure the magnetic moment of the muon). The pole pieces were modified to include the required gradient. Each quadrant consists of six defocusing and four focusing magnet blocks. All defocusing units are fitted with poleface windings for tuning and chromaticity correction (QH = 1.35, = 1.55). A completely new vacuum system was built, partly using existing spare parts from the ISR and the SPS. The working pressure is around 1 0~Ton (N2 equivalent). For stochastic cooling ICE was run at 1.73 and 2.1 GeV/c. 2.2. Momentum cooling 2.2.1. Hardware Each of the 16 sum pick-ups used for momentum cooling consists of a 6 cm long drift tube, short-circuited to earth at one end, surrounded by a ferrite frame in the middle and connected to a SO S2 output lead at the other end. The image current associated with the passage of a particle is coupled into the preamplifier. The ferrite choke allows adeqbate response in the frequency range 40—200 MHz (see fig. 11.11). The signals from the 16 pick-ups are combined in a summing network before being fed into the preamplifier. The general layout is given in fig. 11.12. For simplicity a filter consisting of one short-circuited line, two resistors, and an inductance was installed (see fig. 11.13). This filter has notches at nominal revolution harmonics w = nirc/l = no.,0 and poles at frequencies where the line capacitive reactance Z0 tg j(wl/c) cancels the lumped inductance wL: Z0 tgj ~l
—jwL.
If we substitute for frequencies near to the nth notch: (I.~
=
no)0
+ 1~W~
and linearize the tg function we obtain nLw0/Z0 ‘~n l/c+L/Z0 The nth pole is situated below the notch at a distance of ~w,7, increasing with the harmonic number (see fig. 11.14). Since the ICE momentum cooling system works approximately over two octaves (15 n ~ 60, 50—200 MHz) and the beam spectrum width is proportional to n, this linearly-increasing separation =
‘~
D. JI’fOhl et al., Physics and technique of stochastic cooling
110
r
5 5
/~ ~ ~/.
10 8
~ 7~6Om
Lr2O~
I
ICE
lfr~-~
~
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SS 2~
—
~
015
RING
/
/
~
z
~
~F:iO8
> f~
1
INJECTION LINE
2
INJECTION INFLECTOR
3
INJECTION FAST KKKER
4 5
MOMENTUM COOLING P(K-UP MOMENTUM COOLING RESONANT UNE
6
MOMENTUM COOLING CORP. GAPS
12
7 8
HORIZ. BETATRON COOLING PICK-UP HORIZ. BETt.TRON COOLING CORP. GAPS
12 6
9
VERT.
l°~l
S S4
BETATRON COOUNG PC1~-UPS
10
VERT. BETATRON COOUNG OORR. GAPS
11
RESERVED FOR ELECTRON COOLING
12
BEAM PROFILE
MONITORS
bJ~ 0401
Fig. 11.10. General floor layout.
between poles and notches appeared to be relevant. The ICE filter provides simultaneous acceleration and deceleration towards the nominal momentum. The lossy resonant line has a non-zero resistive impedance Z0 tanh a0l Zoctnl in the centre of the nth notch so that a complete signal suppression does not occur. The ICE filter has an output phase which lags below the notch and leads above. In the notch centre the phase is zero. At this frequency a perfect suppression can be obtained by adding after the filter a small fraction —Z0 anl of the inverted input signal. For good cancellation over many octaves, just like the loss parameter an, the additive correction must increase with the square root of frequency. The increase of 3 dB per octave is obtained by feeding the unfiltered signal simultaneously into a line with high losses and a line with low losses, both lines having the same electrical length. The difference signal at the end of the two lines offers the required frequency characteristics (see figs. II. 1 5 and II. 16).
-
D. Möhl eta!., Physics and technique of stochastic cooling
F
111
.~
Fig. 11.11. Single pick-up drift tube with shorted back plate, ferrite choke and coupling arms. (The signal is coupled out from one side only.)
Pick—up
~L._1~
Ga~
p1.g
II.tvorkf
~
Sp.ctr, Analyser
p
o—
~
-~
ticker. Cap.
~ ~
I
~‘~
Paver L
Splitt.i~
/‘.~
680Q
III Lius Filter (42 a)
J’Kz
Fig. 11.12. General layout of iSp/p cooling system.
600fL
LINE 42 m 600n.
Fig. 11.13. Diagram of ICE filter.
After the filter the signal is amplified by a I kW distributed power amplifier and fed onto 12 accelerating gaps, similar to the pick-up gaps. These correctors are in two groups of six, separated by half a horizontal betatron wavelength to cancel the betatron heating caused by momentum corrections. (The over-all characteristics are given in fig. 11.20.) 2.2.2. Experimental results in ICE First evidence of momentum cooling was obtained in December 1977 (see fig. 11.17). During the January 1978 shutdown six of the 12 I~p/pcorrectors were reversed to obtain cancel-
112
D. MOhI eta!., Physics and technique of stochastic cooling
Fig. 11.14. Phase (90°/cm)and amplitude (10 dB/cm) around the 17th and the 53d notches.
Dif. transformer Fig. 11.15. Loss compensating network.
lation of horizontal kicks caused by electric field components. After the start-up, higher cooling
factors and rates were quickly obtained. Two major improvements to the filter line followed: (a) reduction of reflections resulting in smaller frequency errors of the resonant notches, (b) passive compensation of filter line losses in the notches to increase the signal suppression. The e-folding time for the peak density was further lowered to 1 5 s (see fig. II. 18). Such high cooling rates were obtained with high electronic gains, also causing strong diffusion as can be seen from the theory, the cooling being proportional to the electronic gain, the diffusion to its square. Thus for low gains high density increase factors could be reached at the expense of the cooling rate (see fig. 11.19).
D. Möhl eta!., Physics and technique of stochastic cooling
113
Fig. 11.16. Filter characteristics without and with compensation. Centre frequency: 124 MHz; 34th harmonic; span: 0.48 MHz.
/
Fig. 11.17. First evidence of iSp/p cooling in ICE. Longitudinal Schottky scans at the 18th harmonic, taken at 1 mm intervals. The scans are the result of spectrum analysis of longitudinal statistical beam structure. The vertical axis is \/~7/7i7~ the horizontal is frequency.
Computer simulation of the cooling process at different intensities. Since the feedback system is the result of cascading many components such as pick-ups, signal combiners, amplifiers, filters, phase equalizers, wide-band gaps (and is also a function of the coherent beam response) the over-all gain characteristic G(w) becomes quite complicated (see fig. 11.20). Thus it is most conveniently expressed numerically and the Fokker—Planck equation can be integrated by computer for a given initial distribution. To check the theory with the experiment, G(w) of the system was recorded with a network analyser in 15 frequency points inside each of 45 harmonic bands (15
114
D. MOhI eta!., Physics and technique of stochastic cooling
Fig. 11.18. Fastest cooling in ICE. Conditions: 8 X 10~p, 10 s between scans, factor 4.75 in peak density in 30s, initial e-folding time is 15 s, ave~evalue 20 s. Centre frequency 60 MHz, 20 kHz/cm, total initial width iSp/p 3.5 X l0~. The vertical axis is proportional to \I~1.
Fig. 11.19. Slow cooling. Conditions: 60 mm, factor 28 in peak density, 2 X l0~protons.
Fig. 11.20. Over-all system phase (90°/cm)and gain (10 dB/cm) between 0 and 240 MHz.
D. Möhl eta!., Physics and technique of stochastic cooling
115
particle energies between +25 MeV and —25 MeV. The data were used in a computer program to calculate the evolution of initially flat distributions after 4 and 8 mm at different intensities N. The equivalent experiments were done with ICE (see figs. 11.2 1—11.23). There is good agreement for the increase in peak density and reduction of full width (see figs. 11.24—11.25). The ratio between open-loop and closed-loop signals was observed by looking at the Schottky signals of the 18th harmonic under both conditions for 1.27 X 1 O~particles after 8 mm. They were also computed for 8 mm for the two conditions (see figs. 11.26 and 11.27). The asymmetry is caused by the notch not coinciding with the density peak. Simultaneous stochastic cooling in all three planes became an urgent goal when in early 1978 a suspicion surfaced that momentum cooling could exclude horizontal cooling or vice versa. At that time only vertical and longitudinal cooling had been demonstrated, the horizontal pick-up and kicker being centred too far towards the inside of the machine acceptance. After modification the doubts were removed when a beam of 6 X lO~protons was cooled simultaneously in all three planes, and its loss rate decreased from typically 100% per hour to a residual value of around 2% per hour, a loss rate compatible with single Coulomb scattering (see figs. 11.28 to 11.30). Antiproton lifetime experiment. Shortly afterwards it was decided to establish a new experimental lower limit for the lifetime of antiprotons. The existing lower limit was 120 jis, far below the 24 h required to accumulate in the AA machine the nominal intensity of 6 X 1011 ~.A tungsten target was installed in the transfer tunnel and bursts of around 250 p were accepted in ICE. Particles could be detected destructively independently of their momentum spread. After momentum cooling to a
Fig. 11.21. (a) Observed density evolution after 4 and 8 mm. 7
x
101 protons. (b) Computed density evolution.
D. Möhl eta!., Physics and technique of stochastic cooling
116
i!!!!1!Y
~
Fig. 11.22. As fig. 11.21, but 5 X 10’ protons.
*
PEAK
10
DENSITY
measured with
INCREASE
beam
0.5
‘o calculated with + 1db
0.4
+
Fig. 11.23. As fig. 11.21, but 1.27 X 10~protons.
+
~ calculated
0
+
~0 o
5
.
40
:
J~E~4h
0.5
-
0.3 +
lxlO
Fig. 11.24. Peak density increase.
N
0.5
1x1O~
N
Fig. 11.25. Reduction of full width in iSp/p.
FWHH z.~p/p= iO~their Schottky signal from a resonant cavity, tuned to the 35th harmonic and having a Q of 5000, became visible with as few as 50 antiprotons [11.131. With cooling in all three planes antiprotons were kept circulating for 86 hours (see fig. 11.31) [11.141. Stochastic cooling of bunched beams was investigated in order to stack antiprotons in ICE [11.15]. Bunching was done with the first harmonic and bunch lengths ~ to ~ of the circumference, the
D. Möh! eta!., Physics and technique of stochastic cooling
117
CLOSED LOOP
/
/
I
Fig. 11.26. Observed signals for open loop (thin trace) and for closed loop (thick trace); 1.27 X 10’ protons.
p 0
OPEN LOOP
\\\\\~
I/I’
I
\
BINS I
10
20
30
I
40
50
60
70
Fig. 11.27. Computed signals for open loop (thin trace) and for closed loop (thick trace).
Fig. 11.28. Longitudinal Schottky scans before and after cooling in three planes for 30 mlii.
remainder being kept free for injection (kicker rise, flat top and fall). The maximum RF bucket height (hardware limit) was ~p/p = ±5 X 1 0~,whereas the injected particles had a ~p/p = ±3X 1 0~. With momentum cooling the beam progressively entered the bucket and accumulated in its centre until i~p/papproximately equalled the equilibrium value of ±2 X 1 0~,observed with low-intensity unbunched beams. The beam bunching was clearly visible both in the time domain (oscilloscope) and the frequency domain where the lines of the first three harmonics grew to a value proportional to N. (Schottky signals are ~ In addition, the full-aperture injection kicker, which could only kick in a limited particle-free interval of the RF period, did not cause beam loss. With stochastic cooling in all three planes the lifetime of the bunched beam was equal tolhat of equally intense unbunched beams. This technique permitted the ICE team to collect 14 000 p from many pulses, each containing only a few hundred particles [11.16].
118
D. Möhl et a!., Physics and technique of stochastic cooling
Fig. 11.29. Vertical and horizontal Schottky signals before and after 30 min of cooling. The r.m.s. betatron oscillation amplitude is ‘x Y and E ~xX.
Fig. 11.30. Horizontal beam profile before and after cooling, as seen by a monitor based on beam-induced ionization electrons from the residual gas.
a)
b)
Fig. 11.31. Longitudinal Schottky signal (a) at beginning, from
240
~ (b)
about 86 h later,
80 ~ are left.
D. Möh! et al., Physics and technique of stochastic cooling
119
Acknowledgements The ICE machine is the result of a collaboration between the EP, ISR, PS and SPS Divisions. The authors are grateful to C. Rubbia, W. Schnell and P. Strolin for discussions and encouragement.
References [11.1] [11.2] [11.3] [11.4]
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