LINAC4 to PBS transfer line reference optics – update May 2014
Alessandra Lombardi for the beam dynamics team
Introduction
The 160 MeV beam from LINAC4 will be transported through a new section of transfer line , 70 m in
length composed of 17 quadrupoles, 5 bending magnets (3 horizontal and 2 vertical) and debuncher
/rebuncher cavity before joining the present LINAC2 to PSB transfer line at the position of LT.
BHZ20. After BHZ20 the existing line is composed of 2 bending magnets, 18 quadrupoles , a septum
and a distributor for injection in the 4 rings of the PSB. The purpose of this note is to document the
optics to match the 160 MeV linac4 beam on the PSB injection stripping foil. All the calculations are
done for a nominal beam (65 mA, ex=ey=0.3 mm mrad rms normalised).
There are presently 6 possible matching set to inject in the PSB (injMatchingQuality by C. Carli) , they
are summarised in the following table.
Table 1 . Matched condition on the PSB stripping foil
A penalty function was defined to quantify the quality of the matching :
A penalty function below 10% is considered acceptable.
Case 1 : dispersion zero.
The cases where the dispersion is nullified are somehow simpler as the matching of the dispersion
and the matching of the beta function is completely decoupled. In particular the dispersion and its
derivative are matched to zero after BHZ30 and then they stay zero until the foil. The quadrupoles of
the BI line are used to obtain the big/medium/small beta function.
The quadrupole settings necessary for the three cases are reported in table 2. The Rms beam size in
both planes is shown in Fig 1,2,3 and the full information on all optics parameters is stored in file
disp_zero.xls . Please note that the rms quantities include the effect of the dispersion. The penalty
function for all three cases is below 5%.
Table 2 – Quadrupole setting for big/medium/small beta and disp=0
L4T.MQD.0110
L4T.MQF.0210
L4T.MQD.0310
L4T.MQF.0410
L4T.MQF.0510
Lenght(m)
T/m
T/m
T/m
0.105
7.5151
7.5151
7.5151
0.105
-7.82351
-7.82351 -7.82351
0.3
2.72079
2.72079
2.72079
0.3
-4.76669
-4.76669 -4.76669
0.3
-4
-4
-4
L4T.MQD.0610
0.3
2.33333
2.33333
2.33333
L4T.MQF.0710
0.3
-1.92969
-1.92969 -1.92969
L4T.MQD.0810
0.3
0.92647
0.92647
0.92647
L4T.MQF.0910
0.3
-0.85037
-0.85037 -0.85037
L4T.MQD.1010
0.3
0.352
0.352
0.352
L4T.MQD.1110
0.3
2.33221
2.33221
2.33221
L4T.MQF.1210
0.3
-2.34466
-2.34466 -2.34466
L4T.MQD.1310
0.3
5.25
5.25
5.25
L4T.MQF.1410
0.3
-3.38333
-3.38
-3.38
L4T.MQD.1510
0.3
5.25
5.25
5.25
L4T.MQD.1610
0.3
4.47953
4.47953
4.47953
L4T.MQF.1710
0.3
-2.91959
-2.91959 -2.91959
QFN50
0.255
-1.1909
-1.1909
-1.1909
QDN55
0.255
1.3859
1.3859
1.3859
QFN60
0.255
-1.82279
-1.82279 -1.82279
QDN65
0.255
1.15105
1.15105
1.15105
QFW70
0.467 0.401532
0.401532 0.401532
QDN75
0.255
-1.46635
-1.46635 -1.46635
QFN10
0.255
1.0816
1.0816
1.0816
QDN20
0.255
-0.40911
-0.40911 -0.40911
QFW30
0.461
-1.40927
-1.40927 -1.40927
QDW40
0.461
1.65575
1.65575
1.65575
QFW50
0.461
-1.33639
-1.33639 -1.33639
QDW60
0.461
1.06024
1.06024
1.06024
BI.QN10
0.462
-1.04465
-1.28068 -1.04465
BI.QN20
0.462
1.01876
1.22486
1.01876
BI.QN30
0.462
-0.96627
-0.82535 -1.02548
BI-QN40
0.462 0.972508
0.914672
0.99931
BI-QN50
0.466
-1.84028
2.138508
-1.6121
BI-QN60
0.466 2.015537
2.359182 1.781536
The only quadrupoles that need to be changed are the one highlighted in red. In this way the
trajectories for the 4 rings don’t need to be re-corrected at each matching, see the separation
scheme at the last chapter.
1.00E-02
8.00E-03
6.00E-03
4.00E-03
2.00E-03
x RMS [m]
y RMS [m]
0.00E+00
0.00E+00
2.00E+01
4.00E+01
6.00E+01
8.00E+01
1.00E+02
1.20E+02
1.40E+02
1.60E+02
1.80E+02
Figure 1 : top trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ big beta “ case.
1.00E-02
8.00E-03
6.00E-03
4.00E-03
2.00E-03
x RMS [m]
y RMS [m]
0.00E+00
0.00E+00
2.00E+01
4.00E+01
6.00E+01
8.00E+01
1.00E+02
1.20E+02
1.40E+02
1.60E+02
1.80E+02
Figure 2 : top trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ medium beta “ case
1.00E-02
8.00E-03
6.00E-03
4.00E-03
2.00E-03
x RMS [m]
y RMS [m]
0.00E+00
0.00E+00
2.00E+01
4.00E+01
6.00E+01
8.00E+01
1.00E+02
1.20E+02
1.40E+02
1.60E+02
1.80E+02
Figure 3 : top trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ small beta “ case
Tunability
The three cases presented above are the nominal ones for dispersion zero. By varying the last
quadrupoles within 10% a series of other twiss parameters can be found, as shown in Figure 4. All
cases present dispersion less than 1.5 cm and no losses.
(X,X' ) Alpha , (X,X')Beta[m/rad]
20
18
16
14
12
10
8
6
4
2
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Figure 4 : values of alphax and betax achievable by tuning (within 10% ) the last 4 quadrupoles
before the foil. The red dots represent the three nominal cases for D=0. All cases have full
transmission and dispersion limited to1.5 cm.
(Y,Y' ) Alpha , (Y,Y')Beta[m/rad]
20
18
16
14
12
10
8
6
4
2
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Figure 5 : values of alphay and betay achievable by tuning (within 10% ) the last 6 quadrupoles
before the foil. The red dots represent the three nominal cases for D=0. All cases have full
transmission and dipersion limited to1.5 cm
Case 2 : dispersion matched to -1.4m .
This case is intrinsically more difficult as the matching of the dispersion and of the beta function is
coupled. Nevertheless a suitable set of quadruole setting has been found for the big and medium
beta case. For the small beta case, with the current quadrupole polarity, the penalty function cannot
be lower than 15% without generating some losses. If this case turns out to be the nominal one, a
readjustment of the polarity of the lines will be necessary.
The quadrupole settings necessary for the three cases are reported in table 4. The Rms beam size in
both planes is shown in Fig 5,6,7 and the full information on all optics parameters is stored in file
disp_14
Length
(mm)
L4T.MQD.0110
L4T.MQF.0210
L4T.MQD.0310
L4T.MQF.0410
L4T.MQF.0510
L4T.MQD.0610
L4T.MQF.0710
L4T.MQD.0810
L4T.MQF.0910
L4T.MQD.1010
L4T.MQD.1110
L4T.MQF.1210
L4T.MQD.1310
L4T.MQF.1410
L4T.MQD.1510
L4T.MQD.1610
L4T.MQF.1710
QFN50
QDN55
QFN60
QDN65
QFW70
QDN75
QFN10
QDN20
QFW30
QDW40
QFW50
105
105
300
300
300
300
300
300
300
300
300
300
300
300
300
300
300
255
255
255
255
467
255
255
255
461
461
461
T/m
T/m
T/m
7.5151
7.5151
7.5151
-7.82351 -7.82351 -7.82351
2.72079 2.72079 2.72079
-4.76669 -4.76669 -4.76669
-4
-4
-4
2.33333 2.33333 2.33333
-1.92969 -1.92969 -1.92969
0.92647 0.92647 0.92647
-0.85037 -0.85037 -0.85037
0.352
0.352
0.352
2.33221 2.33221 2.33221
-2.34466 -2.34466 -2.34466
5.25
5.25
5.25
-3.38
-3.38
-3.38
5.25
5.25
5.25
4.47953 4.47953 4.47953
-2.91959 -2.91959 -2.91959
-1.21153
-1.1909
-1.1909
1.657855
1.3859
1.3859
-1.57211 -1.48306 -1.48306
0.935826 1.077851 1.077851
0.508536 0.383437 0.383437
-1.56731 -1.40174 -1.40174
1.0816
1.0816
1.0816
-0.40911 -0.40911 -0.40911
-1.40927 -1.40927 -1.40927
1.65575 1.65575 1.65575
-1.33639 -1.33639 -1.33639
QDW60
BI.QN10
BI.QN20
BI.QN30
BI-QN40
BI-QN50
BI-QN60
461 1.06024 1.06024 1.06024
462 -1.14711 -1.04465 -0.95114
462 1.096658 1.01876 1.060401
462 -1.02548 -1.04099 -1.04099
462 0.99931 1.070225 1.070225
466 -1.53973 -1.95651 -1.98625
466 1.573803 2.209061 2.235629
1.00E-02
x RMS [m]
8.00E-03
y RMS [m]
6.00E-03
4.00E-03
2.00E-03
0.00E+00
0.00E+00 2.00E+01 4.00E+01 6.00E+01 8.00E+01 1.00E+02 1.20E+02 1.40E+02 1.60E+02 1.80E+02
Figure 5 : Top: trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ big beta “ case.
1.00E-02
x RMS [m]
8.00E-03
y RMS [m]
6.00E-03
4.00E-03
2.00E-03
0.00E+00
0.00E+00 2.00E+01 4.00E+01 6.00E+01 8.00E+01 1.00E+02 1.20E+02 1.40E+02 1.60E+02 1.80E+02
Figure 6 : Top trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ medium beta “ case.
1.00E-02
x RMS [m]
8.00E-03
y RMS [m]
6.00E-03
4.00E-03
2.00E-03
0.00E+00
0
20
40
60
80
100
120
140
160
180
200
Figure 7 : top trace3d x and y total beam size, bottom PATH rms x and y beam size vs length (z=0 is
the PIMS output) for the “ small beta “ case.
Tunability
The three cases presented above are just three possible conditions. By varying the last quadrupoles
within 10% a series of other matched condition can be found, as shown in Figure 4. All cases have a
dispersion between -1.2 and -1.8 m and no losses.
(X,X')Alpha and Beta[m/rad]
2.00E+01
1.80E+01
1.60E+01
1.40E+01
1.20E+01
1.00E+01
8.00E+00
6.00E+00
4.00E+00
2.00E+00
-3.00E+00
-2.00E+00
0.00E+00
-1.00E+00
0.00E+00
1.00E+00
2.00E+00
3.00E+00
Figure 9 : Values of alphax and betax achievable by tuning (within 10% ) the last 4 quadrupoles
before the foil. The red dots represent the three nominal cases for D=1.4. All cases have full
transmission and dispersion limited between1.2 and 1.8 m .
(Y,Y') Alpha and Beta[m/rad]
2.50E+01
2.00E+01
1.50E+01
1.00E+01
5.00E+00
-2.00E+00
-1.50E+00
-1.00E+00
-5.00E-01
0.00E+00
0.00E+00
5.00E-01
1.00E+00
Figure 10 : Values of alphay and betay achievable by tuning (within 10% ) the last 4 quadrupoles
before the foil. The red dots represent the three nominal cases for D=1.4. All cases have full
transmission and dispersion limited between 1.2 and 1.8 m.
Vertical dispersion in the injection area
The pulse from the linac is divided amongst the 4 independent booster rings by the combined action
of a system of steerers (DVT30 and DVT40) a distributor (DIS) and a Septum (SMV) according to the
sketch of Fig. 11
Figure 11 : Schematic of the PSB injection line with the DIS and SMV vertical separation schemes.
As a result the vertical dispersion will be different for the 4 rings. The dispersion for ring 3 and ring 1
is plotted in the following. At injection the vertical dispersion for the two rings differ by 20 cm.
vertical dispersion [m] in PSB injection area.
1
vertical dispersion [m]
0.8
0.6
0.4
ring 3
0.2
ring 1
0
0
5
10
15
20
25
30
-0.2
-0.4
distance from DVT30 [m]
Figure 12: Vertical dispersion in the PSB injection area.
Conclusions
The layout of the transfer line is flexible enough to accommodate varying alphas and betas
parameters at the PSB injection, as well as matching the horizontal dispersion to values between 0
and 2 meters. The vertical dispersion introduced by the separation schemes is limited to 0.8 m in the
injection line.