An analysis web page for our BBI compensation knob machine studies
is now available here:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/3may06/bbibeta/

Most remarkable is the confirmation by simulation of the empirical success in compensating the BBI at the IP using knobs designed for compensating the near-IP long-range BBI.

The text portion of the web page is appended to this message.

-- jim

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James Crittenden                   Tel. (607) 255-9424
Wilson Synchrotron Laboratory      Fax  (607) 255-8062
Cornell University
Ithaca, New York 14853-8001
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Machine studies were done for the BBI compensation knobs on 1/8/06, 3/20/06, 3/23/06, 4/3/06, 4/5/06 and 4/19/06. The calculations summarized below motivated those studies and characterize and quantify the expected performance improvement.

Most remarkable is the confirmation by simulation of the empirical success in compensating the BBI at the IP using knobs designed for compensating the near-IP long-range BBI. This result should prove instructive on means to build such compensation into the lattice design procedure.

We consider here two criteria for performance enhancement:

1) the distortion of e- horizontal beta function as a function of e+ current, indicated by the maximum value of beta in the ring

2) the narrowing of the dynamic aperture for electrons at a particular value of e+ bunch current. We use 4 mA/bunch in 8x3 and 3 mA/bunch in 8x4.


In this manner we address the effects on large-amplitude particles as well as on the core of the beam.

The plots are arranged in two columns, the column on the left showing
the distortions associated with the present operating mode in which the
effects of the BBI are mitigated by holding the tunes constant as the current
in the counter-rotating beam increases. The right-hand column shows the effects when the BBI compensation knobs are used, scaled with e+ current.

It should be noted that the global tune adjustment is calculated for the optical distortions associated with the particular parasitic crossing pattern for each electron bunch individually. During operation, the global tune adjustment is made averaged over all bunches. In consequence, the simulated correction is a best-case scenario which cannot be
carried out in practice, since tunes for individual bunches cannot be tuned. In contast, the BBI compensation knob coefficients were calculated for bunch 2 of train 1 only, then applied to all bunches of all trains as an approximation. Such an approximation is necessarily present in the operational implementation of this correction method. We will see that despite this unfair advantage given to the global tune adjustment method, the BBI compensation knobs show better results.

The first four plots show the calculations for an 8x3 configuration with
e+ current reaching a maximum of 4 mA/bunch, including only the parasitic crossings, i.e.  excluding the BBI at the south interaction point. One observes that the distortions are minor and the expected improvement from the BBI knobs consequently of little signficance. The beta distortions are about 2 m and the dynamic aperture shrinks by less than 1 sigma.

The second set of four plots shows the effects of the parasitic crossing in an 8x4 configuration up to a maximum e+ bunch current of 3 mA/bunch. For this same value of total current, the distortions induced by the BBI are marginally more severe, producing beta increases of up to 5 m, quite different from bunch to bunch. The dynamic aperture decreases from 12 to 7 or 8 sigma. The BBI compensation knobs,which were optimized for bunch 2 of train 1, are little better than the global tune adjustment alone, but do improve the dynamic aperture by 1-2 sigma.

The third and fourth sets of plots include the effect of the BBI at the IP in the 8x3 and 8x4 configurations. Here we describe briefly the empirical method we used
to compensate the BBI at the interaction point:

We do not yet have the software tools necessary to design compensation knobs for the IP, since we wish to optimize these on the basis of dynamic aperture (tracking) rather
than on beam functions. Compensating the IP BBI became necessary, however, when we began routinely injecting into collision.
So we used single-bunch collisions to deduce empirical values for the near-IP parasitic crossing knob coefficients to approximate a correction for the IP.
The horizontal and vertical-tune correction knobs were adjusted using the tune analyzer in 1x1 at a total current of about 4 mA.
We noted that the signs of the coefficients were as expected: opposite to those for the parasitic crossings horizontally and the same as those for the parasitic crossings vertically.

The four remaining beta function correction knobs were tuned on the basis of improving the beam lifetime while firing the east pulsed bump. Note that this method
tests only the aperture near 28E and 34E, while leaving the beams at the IP unperturbed. The simulation results below, in contrast, report on
the overall dynamic aperture.

The values deduced for these six knobs  were then superimposed on the correction for the nar-IP parasitic crossings, yielding encouraging operational increase in the current limits in the 8x3 and 8x4 configurations of about 15%.

The calculations shown below likewise superpose those empirically determined IP compensation knob values on those for the parasitic crossings, and the ring optics
simulation now includes the distortions from the IP BBI.
The locally compensating knobs now show distinct improvement over the global tune adjustment as a means of restoring design optics.

In both the 8x3 and 8x4 configurations, the beta blowup to the same value of total beam current is from 45 to 90 m with the tune adjustment and from 45 to 75 with the compensation knobs.

In the 8x3 configuration, the horizontal dynamic aperture narrows from 11 to less than 8 sigma with the tune adjustment, while the compensation knobs restore a dynamic aperture of 11 sigma for all bunches.

In the 8x4 configuration, the horizontal dynamic aperture narrows from 12 to less than 5 sigma with the tune adjustment, while the compensation knobs maintain a dynamic aperture of at least 8 sigma for all bunches.

One can conclude from these results that the BBI compensation knobs should provide an operational performance in 8x4 similar to that
of the present operational status in 8x3 using the global tune adjustment. The best performance, however, is likely to be achieved
by using the BBI compensation knobs in the 8x3 configuration.