# Modification of Antiproton Source Transfer Lines and their Optics Correction

##### Valeri Lebedev

April 12, 2001

### Motivation

Currently we experience multiple problems with the antiproton source
transfer lines. This document presents a proposal for correction of the
problems. That should yield better stability and reproducibility of the
optics, an increase of the antiproton production and a decrease of
emittance dilution in the course of beam transfers. The document also
outlines the optics tuning procedure and requirements for optics
measurements.

### 1. Modifications of AP1 transfer line (Transport of the 120 GeV beam from Main injector to the antiproton production target)

**1.1. Line status and requirements**

Currently, we can focus the beam on the antiproton production target to
the rms beam sizes ~x~ 130 m, ~y~ 220 m and the vertical beam size
growing with increase of beam energy spread. The optimum beam size is in
the range of 100-150 m; and it is desirable to decrease the vertical
beam size but it is more crucial to prevent any significant beam size
increase or beam scraping with increase of the beam energy spread.

The aim of the transfer line optics changes is to build the optics with
the achromatic beam transport and effective regulation of rms beam sizes
at the target in the range of 100-150 m. For the normalized 95% beam
emittance of 20 mm mrad and the base line 95% momentum spread of
2.410^-4^ it requires the beta-function at the target to be in the range
of 38 - 86 cm and residual dispersion to be below 20 cm. It is expected
that with the slip stacking the energy spread will grow in three times
which will require a better dispersion correction.

**1.2. Optics**

The beta-functions and dispersions of the proposed optics are presented
in Figure 1. As one can see the beam transport in horizontal plane is
achromatic (the horizontal dispersion and its derivative are equal to
zero at the target). Unfortunately, it is impossible to achieve
achromatic beam transport for vertical plane without changes of beam
line magnets, i.e. adding new or moving existing magnets. It originates
from improper locations of two groups of major vertical benders, F11AH -
F11BH and 17LAM1 -- 4. Instead of required cancellation their effects
are added up due to inappropriate vertical betatron phase advance
between them. To archive dispersion cancellation one would need to
increase the phase advance from about to about 2. It is impossible to do
with small number of quads between these groups. Therefore we adopted a
choice where only vertical dispersion is nullified on the target. The
base line design presented in Figure 1 has beta-function on the target
equal to 68 cm. That corresponds to rms beam size of 130 m for both
horizontal and vertical plane. For the base line optics we adopted that
the vertical dispersion is equal to 10 cm at the target. The dispersion
is sufficiently small so that the synchrotron beam size, *~Dy~* =
*D~y~p*/*p* = 24 m, for *p*/*p*=2.410^-4^ is 5 times smaller than the
betatron size and contributes only 4% into the vertical beam size. This
is a compromise between minimum dispersion at the target and in the
final focus quads. Figure 2 depicts the beta-functions and dispersion
for the case when vertical dispersion is nullified on the target. As one
can see this increases the vertical dispersion in two times for the
final focus quadrupoles and also significantly increases the
beta-functions in Q201 and Q202 quads.

![](media/image1.wmf){width="6.498611111111111in"
height="2.9451388888888888in"}

Figure 1. The beta-functions and dispersions for the base line optics
from the main injector extraction to the target; *~x~*^\*^ = *~y~*^\*^ =
68 cm, *D~y~*^\*^ = 10 cm, *D~x~*^\*^ = 0.

![](media/image2.wmf){width="6.498611111111111in"
height="2.892361111111111in"}

Figure 2. The beta-functions and dispersions for the case of zero
vertical dispersion on the target from the main injector extraction to
the target; *~x~*^\*^ = *~y~*^\*^ = 68 cm, *D~y~*^\*^ = *D~x~*^\*^ = 0.

The maximum of beta-function in the final focus quads is equal to 500 m.
That is about two times smaller than for currently used optics. This
decrease is achieved due to reconnection of quadrupoles to power
supplies. Figure 3 presents a comparison of optimized behavior of
beta-functions for the current and proposed powering of quads.
Currently, the final focus quadrupoles are connected in pairs so that
two nearby 3 m quads represent a single 6 m quadrupole. That yields that
the quads are powered to less than half of their maximum allowed
strength, which unnecessary amplifies maximum beta-functions. Proposed
reconnection of quadrupoles uses quads at their maximum strength, which
yields better stability of the final focus optics due to smaller
beta-functions, and reduced effects of residual magnetic field and
ripple of power

![](media/image3.wmf){width="3.198611111111111in"
height="2.0208333333333335in"}
![](media/image4.wmf){width="3.198611111111111in"
height="2.015972222222222in"}

Figure 3. The comparison of optimized beta-functions near the final
focus for new (left) and current (right) powering of AP1 line quads;
*~x~*^\*^ = *~y~*^\*^ = 68 cm, longitudinal coordinate is inversed and
starts at the target.

supplies. Table 1 presents comparison of focusing strength of optimized
optics for current and new powering scheme of quads.

If necessary the beta-functions and beam sizes at the target can be
decreased. Figure 4 presents the beta-functions and dispersions for the
case of the rms beam sizes equal to 80 m. In this case both betatron and
synchrotron beam sizes grow in the final focus quads and a use of such
scheme requires clearing current aperture limitations at the end of AP1
line.

Better matching of the proposed optics in comparison with currently used
optics allowed us to get smaller beam sizes through the entire beam line
and therefore even in a few places with tight aperture of only 36 mm
there is sufficiently large room for orbit correction. Figure 5 shows
the beam sizes through the line for the base line optics presented in
Figure 1 and decreased spot size optics presented in Figure 4. Table 2
presents aperture limitations for AP1 line.

![](media/image5.wmf){width="6.493055555555555in"
height="1.8152777777777778in"}

Figure 4. The beta-functions and dispersions for the case of decreased
spot size on the target from the main injector extraction to the target;
*~x~*^\*^ = *~y~*^\*^ = 26 cm, *D~y~*^\*^ = *D~x~*^\*^ = 0. *~x~* =*~x~*
= 80 m.

**Table 2. Aperture limitations for AP**1 line

  ------------ ---------- ------------ --------------- ------------- ------------------
  **Magnet**   **Serial   **Length**   **Horizontal    **Vertical    **Comments**
               \#**                    aperture**      aperture**    

                          meters       millimeters     millimeters   

  **AP1**                                                            

  F17B3                   6.096        73              \>100         B-3 dipole

  CMAG1        C102       3.011        37              76            

  CMAG2        C103       3.011        37              76            

  PHT0         2          0.506        95              48            

  PB1          MH203-6    3.048        80              35            EPB

  PB2          MH203-23   3.048        80              35            EPB

  PBR1         MH203-2    3.048        37              50            EPB, rolled 41
                                                                     degrees

  PBR2         MH203-8    3.048        37              50            EPB, rolled 41
                                                                     degrees

  PQ1          3Q120-07   3.048        73              73            QQK

  PVT1A        SY-trim    0.506        48              95            

  PVT1         SY-trim    0.890        48              95            

  PQ2          3Q120-10   3.048        73              73            QQK

  PBR3                    3.048        47              47            EPB, rolled 45
                                                                     degrees

  PB3                     3.048        80              35            EPB

  PB4                     3.048        80              35            EPB

  PB5                     3.048        80              35            EPB

  PQ3          3Q120-5    3.048        73              73            QQQ

  PQ4          3Q120-1    3.048        73              73            QQQ

  PQ5A         3Q120-2    3.048        73              73            QQQ

  PQ5B         3Q120-3    3.048        73              73            QQQ

  PHT5         SY-trim    0.890        85              **35**        

  PBV1         MH201-8    3.048        **35**          80            EPB

  PBV2         MH203-5    3.048        **35**          80            EPB

  PQ6A         3Q120-13   3.048        73              73            QQK

  PQ6B         3Q120-1    3.048        73              73            QQK

  PQ7A         3Q120-9    3.048        73              73            QQK

  PQ7B         3Q120-5    3.048        73              73            QQK

  PHT7         SY-trim    0.890        85              **35**        

  PQ8A         3Q120-6    3.048        73              73            QQK

  PQ8B         3Q120-4    3.048        73              73            QQK

  PVT8         SY-trim    0.890        **35**          85            

  PQ9A         3Q120-2    3.048        73              73            QQK

  PQ9B         3Q120-11   3.048        73              73            QQK
  ------------ ---------- ------------ --------------- ------------- ------------------

**1.3. Powering of quadrupoles**

Proposed optics does not require any change in powering quads of P1 and
P2 lines. All optics adjustments are achieved by changing currents of
existing supplies. Table 1 presents comparison of focusing strength of
optimized optics for current and new powering scheme of quads.

power supplies. But new optics requires reconnection of quads for AP1
line. All AP1 quads are of the same 3Q120 type with 3 inch aperture and
120 inch length. Table 3 presents required gradients and currents for
all quads of 120 GeV beam transport. Quads of AP1 line shown for
proposed new powering. It requires seven instead of currently used nine
500 A power supplies. Five quads Q204, Q2051, Q2052, Q2061 and Q2062
have zero gradients and are not necessary for optics adjustments. Quads
Q204, Q2061 and Q2062 have to be demagnetized and disconnected from
power supplies. Quads Q2051 and Q2052 will be used for 8 GeV antiproton
transport discussed below. They can be dismounted later when new optics
arrangement will prove that the beam transport is reliable and does not
require further improvements.

![](media/image6.wmf){width="6.4944444444444445in"
height="1.9493055555555556in"}

![](media/image7.wmf){width="6.490277777777778in"
height="1.9270833333333333in"}

Figure 5. The beam envelopes from the main injector extraction to the
target for the base line optics of Figure 1 (top) and decreased beam
size optics of Figure 4 (bottom) for the 95% normalized emittance of 20
mm mrad and the 95% energy spread of 610^-4^.

**1.5. Optics tuning procedure**

###  

### Table 3. Gradients and currents of quadrupoles for 120 GeV operation

+------+----+----+----+------------------+-----+-------+-----+------+
| P    | P  | S  | S  | Quad name        | Q   | L\    | Ape | G\   |
| ower | ow | hu | hu |                  | uad | [cm\] | rtu | [kG/ |
| su   | er | nt | nt |                  | t   |       | re, | cm\] |
| pply | su | na | c  |                  | ype |       |     |      |
| name | pp | me | ur |                  |     |       | 2*  |      |
|      | ly |    | re |                  |     |       | a*, |      |
|      | c  |    | nt |                  |     |       | \[c |      |
|      | ur |    | \  |                  |     |       | m\] |      |
|      | re |    | [A |                  |     |       |     |      |
|      | nt |    | \] |                  |     |       |     |      |
|      | \  |    |    |                  |     |       |     |      |
|      | [A |    |    |                  |     |       |     |      |
|      | \] |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
|      |    |    |    | Q522             |     | 2     |     | 1.6  |
|      |    |    |    |                  |     | 13.36 |     | 4076 |
+------+----+----+----+------------------+-----+-------+-----+------+
| ##   |    |    |    |                  |     |       |     |      |
| #### |    |    |    |                  |     |       |     |      |
|  P1  |    |    |    |                  |     |       |     |      |
| Line |    |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 2  |    |    | Q701             |     | 304.8 |     | -1.  |
| Q701 | 59 |    |    |                  |     |       |     | 3041 |
|      | .9 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 1  |    |    | Q702             |     | 304.8 |     | 0.98 |
| Q702 | 94 |    |    |                  |     |       |     | 6002 |
|      | .9 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 25 |    |    | Q703, Q705,      |     | 2     |     | -1.4 |
| Q703 | 93 |    |    | Q707, Q709       |     | 13.36 |     | 8547 |
+------+----+----+----+------------------+-----+-------+-----+------+
|      |    |    |    | Q704, Q706, Q708 |     | 2     |     | 1.4  |
|      |    |    |    |                  |     | 13.36 |     | 8547 |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 1  |    |    | Q710             |     | 304.8 |     | 0.96 |
| Q710 | 93 |    |    |                  |     |       |     | 2833 |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 1  |    |    | Q711             |     | 304.8 |     | -0.8 |
| Q711 | 69 |    |    |                  |     |       |     | 4891 |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 1  |    |    | Q712A            |     | 304.8 |     | 0.84 |
| Q712 | 62 |    |    |                  |     |       |     | 2468 |
+------+----+----+----+------------------+-----+-------+-----+------+
|      |    |    |    | Q712B            |     | 152.4 |     | 0.83 |
|      |    |    |    |                  |     |       |     | 7106 |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 2  |    |    | Q713A            |     | 304.8 |     | -1.2 |
| Q713 | 52 |    |    |                  |     |       |     | 7656 |
+------+----+----+----+------------------+-----+-------+-----+------+
|      |    |    |    | Q713B            |     | 152.4 |     | -1.2 |
|      |    |    |    |                  |     |       |     | 6843 |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 2  |    |    | Q714             |     | 304.8 |     | 1.1  |
| Q714 | 36 |    |    |                  |     |       |     | 6987 |
+------+----+----+----+------------------+-----+-------+-----+------+
| **P2 |    |    |    |                  |     |       |     |      |
| Li   |    |    |    |                  |     |       |     |      |
| ne** |    |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| IQ   | 3  |    |    | QF11A            |     | 152.4 |     | -1.7 |
| F11A | 65 |    |    |                  |     |       |     | 4096 |
|      | .2 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| IQ   | 2  |    |    | QF11B            |     | 304.8 |     | 1.1  |
| F11B | 37 |    |    |                  |     |       |     | 7051 |
|      | .6 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 16 |    |    | QF12, QF14, QF16 |     | 2     |     | -0.9 |
| QF12 | 55 |    |    |                  |     | 13.36 |     | 4907 |
|      | .9 |    |    | QF13, QF15, QF17 |     |       |     |      |
|      |    |    |    |                  |     | 2     |     | 0.94 |
|      |    |    |    |                  |     | 13.36 |     | 9072 |
+------+----+----+----+------------------+-----+-------+-----+------+
| ###  |    |    |    |                  |     |       |     |      |
| ###  |    |    |    |                  |     |       |     |      |
| AP1  |    |    |    |                  |     |       |     |      |
| line |    |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 1  |    |    | Q201             | 3Q  | 304.8 | 7   | -0.7 |
| Q201 | 62 |    |    |                  | 120 |       | .62 | 4732 |
|      | .4 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 2  |    |    | Q202             | 3Q  | 304.8 | 7   | 1.0  |
| Q202 | 17 |    |    |                  | 120 |       | .62 | 0094 |
|      | .5 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 2  |    |    | Q203             | 3Q  | 304.8 | 7   | -1.2 |
| Q203 | 81 |    |    |                  | 120 |       | .62 | 9605 |
|      | .6 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| IQ   | 3  |    |    | Q2071            | 3Q  | 304.8 | 7   | 1.4  |
| 2071 | 08 |    |    |                  | 120 |       | .62 | 1872 |
|      | .3 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| IQ   | 4  |    |    | Q2072            | 3Q  | 304.8 | 7   | -1.8 |
| 2072 | 09 |    |    |                  | 120 |       | .62 | 8189 |
|      | .0 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 4  |    |    | Q1081, Q1092     | 3Q  | 304.8 | 7   | 2.2  |
| Q208 | 78 |    |    |                  | 120 |       | .62 |      |
|      | .1 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+
| I    | 3  |    |    | Q1082, Q1091     | 3Q  | 304.8 | 7   | -    |
| Q209 | 65 |    |    |                  | 120 |       | .62 | 1.68 |
|      | .1 |    |    |                  |     |       |     |      |
+------+----+----+----+------------------+-----+-------+-----+------+

### 2. Modifications of AP3 - P1 transfer line (Transport of the 8 GeV antiproton beam from Accumulator to Main injector)

**2.1. Line status and requirements**

Currently, the line for transfer antiprotons from the Accumulator to the
Main injector has two problems. First, the amplitude of beta-function in
many quads is too large making the line oversensitive to quadrupole and
dipole errors. Second, the vertical dispersion is not matched to the
main injector causing the emittance dilution in the process of beam
transfers. The aim of the transfer line optics changes is to build the
optics with matched dispersions and beta-functions in both vertical and
horizontal planes. The maximum beta-functions and beam overfocusing
should be minimized.

**2.2. Optics**

The beta-functions and dispersions of the proposed optics are presented
in Figure 6 and the beam envelopes in Figure 7. The dispersions and
beta-functions for both vertical and horizontal planes are matched to
the rings. The horizontal dispersion is nullified in part of AP1 line.
This feature is useful for optics tuning and measurements. The vertical
dispersion leakage from

![](media/image8.wmf){width="6.493055555555555in"
height="1.9055555555555554in"}

Figure 6. The beta-functions and dispersions for antiproton transport
from the accumulator to the main injector.

![](media/image9.wmf){width="6.493055555555555in"
height="1.9055555555555554in"}

Figure 7. The beam envelopes for antiproton transport from the
accumulator to the main injector for the 95% normalized emittance of 20
mm mrad and the 95% energy spread of 2.510^-4^.

### Table 4. Gradients and currents of quadrupoles for 8 GeV antiproton transport

+------+------+------+------+---------+------+------+------+------+
| P    | P    | S    | S    | Quad    | Quad | L\[  | A    | G\   |
| ower | ower | hunt | hunt | name    |      | cm\] | pert | [kG/ |
| su   | su   | name | cur  |         | Type |      | ure, | cm\] |
| pply | pply |      | rent |         |      |      |      |      |
| name | cur  |      |      |         |      |      | 2    |      |
|      | rent |      | \    |         |      |      | *a*, |      |
|      |      |      | [A\] |         |      |      | \[   |      |
|      | \    |      |      |         |      |      | cm\] |      |
|      | [A\] |      |      |         |      |      |      |      |
+------+------+------+------+---------+------+------+------+------+
| ###  |      |      |      |         |      |      |      |      |
| ###  |      |      |      |         |      |      |      |      |
| AP3  |      |      |      |         |      |      |      |      |
| line |      |      |      |         |      |      |      |      |
+------+------+------+------+---------+------+------+------+------+
| I    | 104  |      |      | Q901    | SQC  | 70.1 |      | -0.4 |
| Q901 |      |      |      |         |      |      |      | 3142 |
+------+------+------+------+---------+------+------+------+------+
| I    | 80   |      |      | Q902    | SQD  | 82.8 |      | 0.33 |
| Q902 |      |      |      |         |      |      |      | 1517 |
+------+------+------+------+---------+------+------+------+------+
| I    | 2    |      |      | Q903A   | SQD  | 82.8 |      | -0.8 |
| Q903 | 01.4 |      |      |         |      |      |      | 3213 |
|      |      |      |      | Q903B,  | SQD  | 82.8 |      |      |
|      |      |      |      | Q906    |      |      |      | 0.83 |
|      |      |      |      |         |      |      |      | 2134 |
+------+------+------+------+---------+------+------+------+------+
|      |      |      |      | Q904    | SQB  | 6    |      | 0    |
|      |      |      |      |         |      | 4.01 |      |      |
+------+------+------+------+---------+------+------+------+------+
| I    | 2    |      |      | Q905    | SQC  | 70.1 |      | -1.0 |
| Q905 | 52.2 |      |      |         |      |      |      | 3996 |
+------+------+------+------+---------+------+------+------+------+
| I    | 36.1 |      |      | Q907    | SQE  | 13   |      | -0.1 |
| Q907 |      |      |      |         |      | 1.17 |      | 5329 |
+------+------+------+------+---------+------+------+------+------+
| I    | 1    |      |      | Q908,   | SQA  | 4    |      | 0.7  |
| Q908 | 79.1 |      |      | Q912    |      | 5.72 |      | 4504 |
+------+------+------+------+---------+------+------+------+------+
| I    | 1    |      |      | Q909,   | SQA  | 4    |      | -0.4 |
| Q909 | 14.7 |      |      | Q913    |      | 5.72 |      | 7679 |
|      |      |      |      |         | SQC  |      |      |      |
|      |      |      |      | Q916    |      | 70.1 |      | -0.4 |
|      |      |      |      |         | SQA  |      |      | 7577 |
|      |      |      |      | Q918    |      | 4    |      |      |
|      |      |      |      |         |      | 5.72 |      | -0.4 |
|      |      |      |      |         |      |      |      | 7679 |
+------+------+------+------+---------+------+------+------+------+
| I    | 1    |      |      | Q910    | SQA  | 4    |      | 0.5  |
| Q910 | 26.1 |      |      |         |      | 5.72 |      | 2422 |
|      |      |      |      | Q927    | SQC  |      |      |      |
|      |      |      |      |         |      | 70.1 |      | 0.52 |
|      |      |      |      |         |      |      |      | 3138 |
+------+------+------+------+---------+------+------+------+------+
| I    | 89.5 |      |      | Q911,   | SQA  | 4    |      | -0.3 |
| Q911 |      |      |      | Q920    |      | 5.72 |      | 7232 |
+------+------+------+------+---------+------+------+------+------+
|      |      |      |      | Q914    | SQA  | 4    |      | 0    |
|      |      |      |      |         |      | 5.72 |      |      |
+------+------+------+------+---------+------+------+------+------+
| I    | 1    |      |      | Q915    | SQC  | 70.1 |      | 0.64 |
| Q915 | 54.7 |      |      |         |      |      |      | 2237 |
+------+------+------+------+---------+------+------+------+------+
| I    | 2    |      |      | Q917    | SQA  | 4    |      | 1.0  |
| Q917 | 44.1 |      |      |         |      | 5.72 |      | 1184 |
+------+------+------+------+---------+------+------+------+------+
| I    | 70.5 |      |      | Q919    | SQB  | 6    |      | 0.29 |
| Q919 |      |      |      |         |      | 4.01 |      | 3867 |
|      |      |      |      | Q921    | SQA  |      |      |      |
|      |      |      |      |         |      | 4    |      | 0.2  |
|      |      |      |      |         |      | 5.72 |      | 9404 |
+------+------+------+------+---------+------+------+------+------+
| I    | 59   |      |      | Q922    | SQA  | 4    |      | -0.2 |
| Q922 |      |      |      |         |      | 5.72 |      | 4691 |
|      |      |      |      | Q926    | SQB  |      |      |      |
|      |      |      |      |         |      | 6    |      | -0.2 |
|      |      |      |      | Q928    | SQD  | 4.01 |      | 4676 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      |         |      | 82.8 |      | -0.2 |
|      |      |      |      |         |      |      |      | 4582 |
+------+------+------+------+---------+------+------+------+------+
| I    | 98   |      |      | Q923,   | SQA  | 4    |      | 0.40 |
| Q923 |      |      |      | Q925    |      | 5.72 |      | 7484 |
+------+------+------+------+---------+------+------+------+------+
| I    | 165  |      |      | Q924    | SQA  | 4    |      | -0.6 |
| Q924 |      |      |      |         |      | 5.72 |      | 8636 |
+------+------+------+------+---------+------+------+------+------+
| *    |      |      |      |         |      |      |      |      |
| *AP1 |      |      |      |         |      |      |      |      |
| li   |      |      |      |         |      |      |      |      |
| ne** |      |      |      |         |      |      |      |      |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 18.7 |      |      | Q2072   | 3    | 3    |      | -0.0 |
| 2072 |      |      |      |         | Q120 | 04.8 |      | 9311 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 21.4 |      |      | Q2071   | 3    | 3    |      | 0.10 |
| 2071 |      |      |      |         | Q120 | 04.8 |      | 5616 |
+------+------+------+------+---------+------+------+------+------+
|      |      |      |      | Q2062,  | 3    | 3    |      | 0    |
|      |      |      |      | Q2061   | Q120 | 04.8 |      |      |
+------+------+------+------+---------+------+------+------+------+
| I    | 21.7 |      |      | Q2052   | 3    | 3    |      | -0.1 |
| Q205 |      |      |      |         | Q120 | 04.8 |      | 0701 |
|      |      |      |      | Q2051   |      |      |      |      |
|      |      |      |      |         | 3    | 3    |      | 0.10 |
|      |      |      |      |         | Q120 | 04.8 |      | 7006 |
+------+------+------+------+---------+------+------+------+------+
|      |      |      |      | Q204    | 3    | 3    |      | 0    |
|      |      |      |      |         | Q120 | 04.8 |      |      |
+------+------+------+------+---------+------+------+------+------+
| I    | 5.12 |      |      | Q203    | 3    | 3    |      | -0.0 |
| Q203 |      |      |      |         | Q120 | 04.8 |      | 3025 |
+------+------+------+------+---------+------+------+------+------+
| I    | 9.6  |      |      | Q202    | 3    | 3    |      | 0.05 |
| Q202 |      |      |      |         | Q120 | 04.8 |      | 0979 |
+------+------+------+------+---------+------+------+------+------+
| I    | 7.21 |      |      | Q201    | 3    | 3    |      | -0.0 |
| Q201 |      |      |      |         | Q120 | 04.8 |      | 3992 |
+------+------+------+------+---------+------+------+------+------+
| **P2 |      |      |      |         |      |      |      |      |
| li   |      |      |      |         |      |      |      |      |
| ne** |      |      |      |         |      |      |      |      |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 111  |      |      | QF17    |      | 21   |      | 0.06 |
| F12K |      |      |      |         |      | 3.36 |      | 3616 |
|      |      |      |      | QF16    |      |      |      |      |
|      |      |      |      |         |      | 21   |      | -0.0 |
|      |      |      |      | QF15    |      | 3.36 |      | 6362 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      | QF14    |      | 21   |      | 0.06 |
|      |      |      |      |         |      | 3.36 |      | 3616 |
|      |      |      |      | QF13    |      |      |      |      |
|      |      |      |      |         |      | 21   |      | -0.0 |
|      |      |      |      | QF12    |      | 3.36 |      | 6362 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      |         |      | 21   |      | 0.06 |
|      |      |      |      |         |      | 3.36 |      | 3616 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      |         |      | 21   |      | -0.0 |
|      |      |      |      |         |      | 3.36 |      | 6362 |
+------+------+------+------+---------+------+------+------+------+
| IQF  | 1    |      |      | QF11B   |      | 3    |      | 0.08 |
| 11BK | 7.01 |      |      |         |      | 04.8 |      | 3825 |
+------+------+------+------+---------+------+------+------+------+
| IQF  | 2    |      |      | QF11A   |      | 1    |      | -0.1 |
| 11AK | 5.68 |      |      |         |      | 52.4 |      | 2241 |
+------+------+------+------+---------+------+------+------+------+
| **P1 |      |      |      |         |      |      |      |      |
| li   |      |      |      |         |      |      |      |      |
| ne** |      |      |      |         |      |      |      |      |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q714    |      | 3    |      | 0.09 |
| 714K | 8.47 |      |      |         |      | 04.8 |      | 1577 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q713B   |      | 1    |      | -0.0 |
| 713K | 7.58 |      |      |         |      | 52.4 |      | 8849 |
|      |      |      |      | Q713A   |      |      |      |      |
|      |      |      |      |         |      | 3    |      | -0.0 |
|      |      |      |      |         |      | 04.8 |      | 8906 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q712B   |      | 1    |      | 0.06 |
| 712K | 3.11 |      |      |         |      | 52.4 |      | 7741 |
|      |      |      |      | Q712A   |      |      |      |      |
|      |      |      |      |         |      | 3    |      | 0.06 |
|      |      |      |      |         |      | 04.8 |      | 8175 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q711    |      | 3    |      | -0.0 |
| 711K | 4.93 |      |      |         |      | 04.8 |      | 7503 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q710    |      | 3    |      | 0.0  |
| 710K | 4.51 |      |      |         |      | 04.8 |      | 7239 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 18   |      |      | Q709,   |      | 21   |      | -0.1 |
| 703K | 7.55 |      |      | Q707    |      | 3.36 |      | 0745 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      | Q708,   |      | 21   |      | 0.10 |
|      |      |      |      | Q706    |      | 3.36 |      | 7445 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      | Q705,   |      | 21   |      | -0.1 |
|      |      |      |      | Q703    |      | 3.36 |      | 0745 |
|      |      |      |      |         |      |      |      |      |
|      |      |      |      | Q704    |      | 21   |      | 0.10 |
|      |      |      |      |         |      | 3.36 |      | 7445 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q702    |      | 3    |      | 0.06 |
| 702K | 3.46 |      |      |         |      | 04.8 |      | 8074 |
+------+------+------+------+---------+------+------+------+------+
| IQ   | 1    |      |      | Q701    |      | 3    |      | -0.0 |
| 701K | 9.63 |      |      |         |      | 04.8 |      | 9851 |
+------+------+------+------+---------+------+------+------+------+

vertical bends located at the beginning of AP1 line is used for
cancellation of the vertical dispersion excited in P2 line so that the
vertical dispersion and its derivative would be equal to zero at the
line end.

**2.3. Powering of quadrupoles**

Table 3 presents parameters of quadrupoles for new optics. It does not
require any change in powering quads of P1 and P2 lines but involves
reconnection of quadrupoles in AP1 and AP3 lines. New arrangement
requires the same number of quadrupole power supplies for AP3 line and 6
versus current 7 power supplies for AP1 line. Quad arrangements in AP1
line for 8 GeV antiproton transport is consistent with 120 GeV proton
transport to the target.

The same as for proton transport five quads of AP1 line (Q204, Q2061 and
Q2062) have zero gradients and are not necessary for optics adjustments.
Additionally, two quadrupoles of AP3 line (Q904 and Q914) are not
required. All these quadrupoles have to be demagnetized and disconnected
from power supplies. They can be dismounted later when new optics
arrangement will prove that the beam transport is reliable and does not
require further improvements.

**2.3. Optics tuning procedure**

### 3. Field maps of quadrupoles

We have sufficiently good magnetic measurement data for SQ type
quadrupoles. Figure 8 presents data and their fit for SQA, SQB, SQC, SQD
and SQE quadrupoles. As one can see short quads are saturated faster
than the long ones. The measured data can be fitted well with fourth
order polynomials. Three sets of polynomial coefficients are used to fit
five quad families. Lengths of SQB and SQC, and SQD and SQE are close
and the same polynomials can be used for each pair. For rising
hysteresis curve the polynomials can be written in the following form:

$$\begin{array}{r}
\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} = 0\text{.}4 + 0\text{.}\text{182}I + 4\text{.}5 \cdot \text{10}^{- 5}I^{2} - 1 \cdot \text{10}^{- 8}I^{3} - 3\text{.}1 \cdot \text{10}^{- \text{10}}I^{4} \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} = \frac{\text{63}\text{.}\text{34}}{\text{45}\text{.}\text{27}}\left( 0\text{.}4 + 0\text{.}\text{182}I + 4\text{.}5 \cdot \text{10}^{- 5}I^{2} - 1 \cdot \text{10}^{- 8}I^{3} - 2\text{.}\text{87} \cdot \text{10}^{- \text{10}}I^{4} \right) \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQC}} = \frac{\text{69}\text{.}\text{25}}{\text{45}\text{.}\text{27}}\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQD}} = \frac{\text{81}\text{.}\text{67}}{\text{45}\text{.}\text{27}}\left( 0\text{.}4 + 0\text{.}\text{182}I + 4\text{.}5 \cdot \text{10}^{- 5}I^{2} - 5 \cdot \text{10}^{- 8}I^{3} - 1\text{.}7 \cdot \text{10}^{- \text{10}}I^{4} \right) \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQE}} = \frac{\text{129}\text{.}\text{55}}{\text{45}\text{.}\text{27}}\left( \int_{}^{}\text{BdL} \right)_{\text{SQD}}
\end{array}$$

For descending hysteresis curve they are

$$\begin{array}{r}
\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} = 0\text{.}4 + 0\text{.}\text{1955}I - 8\text{.}9 \cdot \text{10}^{- 5}I^{2} + 5\text{.}\text{57} \cdot \text{10}^{- 7}I^{3} - 1\text{.}1 \cdot \text{10}^{- 9}I^{4} \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} = \frac{\text{63}\text{.}\text{34}}{\text{45}\text{.}\text{27}}\left( 0\text{.}4 + 0\text{.}\text{1975}I - \text{10}\text{.}9 \cdot \text{10}^{- 5}I^{2} + 5\text{.}9 \cdot \text{10}^{- 7}I^{3} - 1\text{.}\text{065} \cdot \text{10}^{- 9}I^{4} \right) \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQC}} = \frac{\text{69}\text{.}\text{25}}{\text{45}\text{.}\text{27}}\left( \int_{}^{}\text{BdL} \right)_{\text{SQA}} \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQD}} = \frac{\text{81}\text{.}\text{67}}{\text{45}\text{.}\text{27}}\left( 0\text{.}4 + 0\text{.}\text{1975}I - \text{10}\text{.}9 \cdot \text{10}^{- 5}I^{2} + 5\text{.}9 \cdot \text{10}^{- 7}I^{3} - 1\text{.}\text{043} \cdot \text{10}^{- 9}I^{4} \right) \\
\left( \int_{}^{}\text{BdL} \right)_{\text{SQE}} = \frac{\text{129}\text{.}\text{55}}{\text{45}\text{.}\text{27}}\left( \int_{}^{}\text{BdL} \right)_{\text{SQD}}
\end{array}$$

Here the quadrupole current is in amps and the integrated gradient is in
kG. As one can see polynomials fit data with accuracy better than data
accuracy and an error estimate of the fit related to maximum strength at
400 A is about 310^-3^.

![](media/image10.wmf)

Figure 8. Measured dependence of effective quad gradient
$\left( \frac{\int_{}^{}\text{GdL}}{L_{\text{eff}}} \right)$ on
quadrupole current and their polynomial fits for SQ series of
quadrupoles: SQA - red , *L~eff~*=45.27 cm; SQB - blue +, *L~eff~*=63.34
cm, SQC - magenta , *L~eff~*=69.25 cm; SQD - green , *L~eff~*=81.67 cm,
SQE -brown , *L~eff~*=129.55 cm. For better resolution the linear
dependence with *k*=4.197 G/cm/A has been subtracted from the data.

###