THE CREATION OF SMALL INTERACTION DIAMONDS IN THE CERN INTERSECTING STORAGE RINGS (ISR)

The original ISR design included the possibility of superposing equilibrium orbits in four of the eight intersection regions by means of supplementary quadrupoles. This scheme has two advantages. Firstly, the beam density is increased so improving the ratio of beam-beam to beam-gas counts and secondly, the size of the interaction diamond is greatly reduced. The closed orbit modulation was measured and the effects of this scheme on the betatron frequencies was studied. Since the scheme is applied with the stacks already circulating, dynamic computer control of the correcting elements is required to maintain the correct tuning in the ISR. In total, 31 power supplies are progressively changed. Since the machine is strongly perturbed by this scheme, nearly all aspects of operation are affected. This particularity applies to the excitation of localized bumps in the closed orbits. Fully satisfactory operation for physics experiments has been achieved with beams of typically 6 A, a luminosity of 1.4 x 103' crn-*~-~ and a diamond size corresponding to a single injected pulse.


Introduction
The use of a harmonic gradient perturbation for the superposition of equilibrium orbits of particles of different momenta in storage rings was described by K.M. Terwilligerl.
By this means, very small interaction diamonds can be formed and, as a consequence of the higher beam current densities achieved, the ratio of beam-beam to beam-gas counts is improved.For the ISR, the reduction in beam-gas counts is considered to be of less importance than the simple reduction in beam size, since pressures in the intersection regions are often below lo-l1 mmHg.Some advantages and disadvantages of the small size of the interaction diamond are: a) The source of an event can be estimated more accurately which is important for small angle scattering experiments.All the equilibrium orbits pass through the diamond with the zero angle, as well as zero position, with respect to the central orbit.
Spectrometer arms with a small angular acceptance see more of the diamond.

All momentum resolution
with radial position is lost.
The orbit perturbations reduce the maximum current for any given aperture.

General Description of the ISR Superposition Scheme
The original ISR design included 24 supplementary quadrupoles, which are powered in three groups: TF, TDl and TD2, where F and D signify that the quadrupoles are horizontally focusing or defocusing, respectively.The magnet layout for one octant is shown in Figure 1.The quadrupole groups TDl and TD2 are distributed so as to preferentially excite an 8th order gradient harmonic.This is sufficient, in fact, to reduce the momentum compaction function (up) to zero at eight regularly spaced points around the machine.Here the beam width is reduced and depends only on the amplitude of the betatron oscillations.
The shift in the horizontal and vertical machine tunes (QH, Qv), due to the additional gradient is then compensated by the TF quadrupoles which are placed at the zero points in a fortunately, the outer and inner arcs in the I R are is .Unnot equivalent (see Figure 1) and the intersection regions do not correspond to an 8th order harmonic.For this reason, only four intersections (the even numbered) can benefit from the reduced beam width.The unfavoured intersections are positioned such that the beam characteristics are only marginally changed.
The exact quadrupole excitations and the detailed effects of the scheme are calculated with a computer progrsm2.The program minimizes the ap and its radial derivative  The momentum compaction function through one superperiod for normal operation and for the superposition of equilibrium orbits FIGURE 2 at zero.At the remaining four null points, ap and a' are reduced to nearly zero.Figure 2 shows ap throug R one superperiod both with and without the supplementary quadrupoles excited.Table 1 lists the principal parameters for the two cases.The luminosity is largely unaffected, since it is independent of beam width and the increases in SV are very small.In the superposition scheme, the fluctuations in ap have maxima twice as ,large as those in the normal machine.Thus, the beam will be a series of tightly waisted bulges.Unfortunate ly, this increase in "fi limits the maximum current that can be stacked compare to that of the normal machine.However, there is still space for at least 10 A in the ISR with the scheme applied, but at present, other factors are limiting the current.The maximum achieved to date is 7.2 A during machine development time.The values in Table 1 show that the odd numbered intersections in fact lose very little.
One problem, however, which is not directly evident, is the vulnerability of the odd numbered intersections to background noise.This arises from the adjacent up maximum being only 20 m upstream of the intersection and any beam halo or tail is preferentially swept against the chamber walls at these points.
By scraping the beam edges, this problem can usually be solved.Figure 3 shows the first orbit measurements made to verify that ap was azimuthally modulated by an 8th order harmonic and that it was zero in the even numbered intersections.The four quadrants are not exactly the same owing to the basic closed orbit distortion which was 5.8 mm peak-to-peak.
The beam position monitors are too widely spaced to check all the characteristics shown in the computed curve in Figure 2.
It has been tacitly assumed, so far, that the supplementary quadrupoles are sufficient by themselves.In practice, the simple application of the quadrupoles causes small but unacceptable changes in QB and QV with accompanying increases in the Q-spreads across the chamber.These effects are s ummarized in the stability diagram shown in Figure 4.The lines 1 and 2 are called "working lines" and represent the Q-values for the equilibrium orbits with momenta differing from the central orbit in the range 2 1.5 %.This is approximately the largest momentum spread which can be accepted in the ISR for the superposition scheme.Line 1 is the working line known as FATA which is used as a base for all calculations.
Line 2 shows that the simple application of the superposition scheme shifts the stack across the 5th order resonances.
Before this problem had been fully evaluated, a physics run was made under precisely these conditions.The bad background observed can now be attributed to these resonances in the stack.
As has been mentioned, the TF quadrupoles are used to compensate the Q-changes caused by the TDl and TD2 quadrupoles.
Since both QH and QV have to be adjusted, this compensation is not perfect.
One possibility is to create an extra degree of freedom by independently powering some of the TF quadrupoles.
The alternative chosen in the ISR is to use the poleface windings to apply a correction.
The increase in Q-spread in the working line comes from a different source.The sextupolar component seen by the beam is partly created by individual sextupoles and partly by the poleface windings.The latter are mounted on all the magnet units and their average effect is unchanged by this scheme but the former are localized and their effect depends on the local perturbations in the machine parameters.This involves the smooth progressive powering of the quadrupoles and 28 correcting elements in each ring.The transformation is performed on-line in a few minutes by the ISR control computer ARGUS.For beam currents of a few hundred mA, the power supplies can be changed rapidly without beam loss, but for higher currents, the rate of change becomes a critical parameter.Table 2 compares the beam losses from similar 6 A stacks for different application times up to 400 s, which is now used operationally in the ISR.These beam losses are accompanied by a blow-up of the betatron oscillations.This is negligible at low beam intensities and rises to an 8 % increase in vertical beam size at 6 A for an application speed of 400 s. 6.5 These effects have been fully evaluated and the corrections calculated.
The agreement between theory and measurement can be seen in Figure 4 where the solid lines represent theoretical calculations and the broken lines measurements.

Dynamic Application of the Superposition Scheme
The standard ISR injection or'oit is at an average position of 42 + 2 mm inside the central orbit.With the superposition scheme applied, this orbit passes outside the vacuum chamber at ap maxima, thus making it irnpcssiblr to inject directly onto the stnndard working ~.Injection can be moved closer to the central orbit but this complicates the setting up of the machine.For these reasons, an alternative approach was sought after.
Working lines in the l&-Q, stability diagram for the useful stacking region ;t hns been found possible to apply this scheme, lcclltding the working line corrections with sextupoles FILGURE 1 Although the working line is unchanged, the locw parameters are different from those of the normaI machine.Of the two closed orbit correction progrsms3, the least squares method can be used without modification, since it locates the field errors and corrects them directly.
The harmonic method applies a distributed correction which is susceptible to parameter changes.
In the case of closed orbit bumps, which are used for luminosity measurements and for positioning the interaction diamond, it was necessary to make new calculations.
The measurement of these bumps is rather complicated.
A single pulse is accelerated to the required radial position and kept trapped by the radio frequency system in order to maintain the bunched structure.This is necessary for the functioning of the beam position monitors.
Once the superposition scheme is applied, the trapped pulse can be used almost indefinitely for the various orbit measurements.
At the null points in up, the beam's potential well is approximately four times deeper than for a normal beam of the same current.
Under most conditions, the existing clearing electrode system can still remove the trapped electrons.
An exceptional case, for which some difficulties have been experienced, is the use of a titanium cloud for luminosity measurements.

Operational Results
The superposition scheme was first used for physics experimentation in June 1972.Its performance has steadily improved and it is regularly scheduled at all energies.
Figure 5 compares the transverseand longitudinal dimensions of the interaction diamond as seen in the normal and the superposition modes.Each pair of curves is normalized to the same total number of events.At the half height of the beam-beam count distribution, the superposition scheme reduces the diamond width to 8.5 mm, which corresponds closely to the width expected for a single pulse.This is independent of the initial beam width.Typically the scheme can be operated with 6 A in each beam with beam decay rates of 1 in 105 per minute and a luminosity of 1.4 x 1030 cma2s-1.It is hoped to increase these currents to 10 A. Other possibilities, which have not yet been explored, are the partial application of the scheme to increase the currents while accepting a larger diamond size and the inverse scheme in which cp maxima are used to increase the diamond size so giving a very large momentum resolution across the beams.
FIGURE 1 , the beams become unstable and are li-.able to be lost suddenly while the power supplies are changing.This probably indicates that there is insufficient Q-spread in the working line or at some time during the transformation.Using modified working lines during machine development time, a current of 7.2 A has .been reached.. . .

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and poleface windings, to beams which are already circulating under normal conditions.