ESS RFQ Error Study v1.3 - Lu

Microsoft Word - ESS_RFQ_Error_Study_v1.3.docxDocument No v1.3
European Spallation Source ESS AB Visiting address: ESS, Tunavägen 24
P.O. Box 176 SE-221 00 Lund
SWEDEN
www.esss.se
ESS RFQ Error Study
Name Affiliation Authors E. Sargsyan ESS Reviewers H. Danared, M. Eshraqi, A. Ponton ESS Approver
Distribution: <<add names>>
Document No v1.3
1.0 New Document 2013-09-06
1.1 Document reviewed 2013-09-23
1.3 Input beam mismatch tolerance corrected 2014-04-14
TABLE OF CONTENT
1. Introduction ...................................................................................................... 4
3. Sensitivity study ............................................................................................... 6
3.3 Vane voltage .......................................................................................................... 8
4. Error study ....................................................................................................... 9
4.1 Single error .......................................................................................................... 10
4.1.3 Vane displacement ............................................................................................. 13
4.1.4 Vane tilt ............................................................................................................ 15
4.1.5 Section displacement .......................................................................................... 17
4.1.6 Section tilt ......................................................................................................... 18
4.2 Combined errors ................................................................................................... 22
5. Tolerance specifications .................................................................................. 24
Document No v1.3
Document No v1.3
1. INTRODUCTION
The ESS RFQ has been redesigned to improve its RF stability [1]. The length of the RFQ has been increased from 4 m to 4.5 m and the output beam energy has been increased from 3 MeV to 3.62 MeV, improving the beam dynamics in the downstream MEBT and DTL.
To ensure an acceptable output beam quality, the performance of the RFQ has to be evaluated in presence of different sources of errors. Those errors include but are not limited to the RFQ machining, alignment and voltage errors, missteering and mismatch of the input beam. The effects of those errors on the beam quality can be rather large. For some of those errors tolerances can be specified only by running a large number of statistical simulations.
The purpose of this document is to define tolerances on the considered errors from beam dynamics point of view. The tolerances from the RF point of view may be different.
2. NOMINAL BEAM DYNAMICS
The nominal beam dynamics assumes the design parameters of the RFQ [1] with no errors. The assumed input beam parameters and the resulting output beam parameters are summarized in Tables 1 and 2 respectively. The output beam phase-space projections are plotted in Figure 1.
Table 1: RFQ input beam parameters
Parameter Value Unit
Number of particles 100000 -
Beam energy 0.075 MeV
Beam current 70 mA
Twiss parameter ! 1.02 -
Twiss parameter ! 1.02 -
Document No v1.3
Parameter Value Unit
RMS longitudinal emittance !" 0.131 π.deg.MeV
RMS longitudinal emittance !!! 0.33 π.mm.mrad
Twiss parameter ! -0.064 -
Twiss parameter ! -0.291 -
Twiss parameter ! 0.555
Document No v1.3
6(25)
Figure 1: RFQ output beam projections (red ellipses contain 99% of the particles)
With the assumed input beam current, emittance and distribution the transmission of the accelerated particles is >98% and there is less than 1% transverse RMS emittance growth. At such a low beam energy and high beam current the beam dynamics in the RFQ is space charge dominated.
3. SENSITIVITY STUDY
The nominal beam dynamics presented in Section 3 is based on certain assumptions concerning the input beam parameters, which are an educated guess based on a previous experience and needs to be verified by measurements, when the systems are available. Meanwhile, to ensure an acceptable performance of the RFQ for input beam parameters differing from those assumed above, a sensitivity study has been performed.
3.1 Input beam emittance
The sensitivity of the RFQ output beam emittances and beam transmission to the input beam RMS emittance is presented in Figures 2-4. The input beam current is fixed at 70 mA. Dashed lines in the plots represent design values.
The transverse emittance growth decreases with increasing input beam emittance due to decreasing space charge forces. Starting from input beam normalized RMS emittance value of about 0.27 π.mm.mrad the beam size becomes rather large and the combination of weaker space charge forces and increasing beam losses reduce the RMS emittance growth to negative values. The longitudinal RMS emittance is increasing rather linearly with the increasing input transverse RMS emittance. For an input transverse normalized RMS emittance of 0.31 π.mm.mrad the beam transmission is reduced by less than 0.5% with respect to its design value.
Figure 2: Transverse emittance growth vs. input transverse RMS emittance
Figure 3: Output longitudinal RMS emittance vs. input transverse RMS emittance
!10$ !5$ 0$ 5$
10$ 15$ 20$ 25$ 30$ 35$ 40$ 45$ 50$ 55$ 60$ 65$ 70$ 75$ 80$ 85$ 90$
0.09$ 0.11$ 0.13$ 0.15$ 0.17$ 0.19$ 0.21$ 0.23$ 0.25$ 0.27$ 0.29$ 0.31$ 0.33$ 0.35$ 0.37$ 0.39$
Tr an
ce (g ro w th ([%
](
0.09$
0.10$
0.11$
0.12$
0.13$
0.14$
0.15$
0.16$
0.09$ 0.11$ 0.13$ 0.15$ 0.17$ 0.19$ 0.21$ 0.23$ 0.25$ 0.27$ 0.29$ 0.31$ 0.33$ 0.35$ 0.37$ 0.39$
O u tp u t% lo n gi tu d in al %R M S% em
i2 an
eV ]%
I=70%mA,%3%sigma%Gaussian%distribuEon%
Description ESS RFQ Error Study
Document No v1.3
Figure 4: Accelerated beam transmission vs. input transverse RMS emittance
3.2 Input beam current
The sensitivity of the RFQ output beam emittances and beam transmission to the input beam current is presented in Figures 5-7. Here the input beam transverse normalized emittance is fixed at 0.25 π.mm.mrad. Dashed lines in the plots represent the nominal case.
For input beam currents of 5-100 mA the transverse RMS emittance variation is a few per cents, however the 99% transverse emittance grows linearly with the increasing input beam current. The beam transmission at 100 mA input beam current is reduced by only 5%. The output longitudinal RMS emittance is optimum at about 40 mA input beam current. Its maximum value is 17% higher than at the nominal input beam current of 70 mA, which results in 8% higher beam phase spread.
Figure 5: Transverse emittance growth vs. input beam current
Figure 6: Output longitudinal RMS emittance vs. input beam current
96.0%
96.5%
97.0%
97.5%
98.0%
98.5%
0.09% 0.11% 0.13% 0.15% 0.17% 0.19% 0.21% 0.23% 0.25% 0.27% 0.29% 0.31% 0.33% 0.35% 0.37% 0.39%
A cc el er at ed
)[% ])
!5#
0#
5#
10#
15#
20#
25#
0# 10# 20# 30# 40# 50# 60# 70# 80# 90# 100#
T ra n sv e rs e (e m i+ a n ce (g ro w th ([ % ](
Input(beam(current([mA](
3(sigma(Gaussian(input(beam,(RMS(emi+ance(0.25(π.mm.mrad(
0.120%
0.125%
0.130%
0.135%
0.140%
0.145%
0.150%
0.155%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
O u tp u t% lo n gi tu d in al %R M S% em
i2 an
eV ]%
Document No v1.3
3.3 Vane voltage
The beam transmission and the output RMS emittances as a function of the vane voltage are presented in Figures 8-9. Dashed lines in the plots represent the nominal case.
Below approximately 85% of the nominal voltage no particles are accelerated to an acceptable energy of 3.5 MeV, nonetheless particles with lower energies and down to the input beam energy of 0.075 MeV can still make through the RFQ. The lower acceptable energy limit of 3.5 MeV is defined by the downstream DTL energy acceptance of 3.6 MeV ± 0.2 MeV and considering the energy spread of the beam of 0.1 MeV. Longitudinal tails start appearing already at 98% of the nominal voltage. For the vane voltages above the nominal the beam transmission slightly increases and plateaus.
The transverse and longitudinal output RMS emittances in Figure 9 are only plotted for the accelerated beam. For vane voltages above the nominal value the transverse RMS emittance increases, whereas the longitudinal one decreases as compared to their respective nominal values. Both transverse and longitudinal RMS emittances increase rapidly for vane voltages below 94% and 96% of the nominal value respectively. This is due to weaker focusing forces in both planes. The largest emittance growth with respect to its nominal values is about 13% for the transverse plane and about 96% for the longitudinal one.
93#
94#
95#
96#
97#
98#
99#
100#
0# 10# 20# 30# 40# 50# 60# 70# 80# 90# 100#
A cc e le ra te d )b e a m )t ra n sm
is si o n )[ % ])
Document No v1.3
9(25)
Figure 8: Beam transmission vs. vane voltage Figure 9: Output RMS emittances vs. vane voltage
4. ERROR STUDY
Different errors in fabrication, assembly, alignment and operation settings of the RFQ will result in a degraded RFQ performance and degraded beam quality. Error studies have been performed to define the tolerances on errors and to ensure acceptable RFQ performance in the presence of imperfections. The effects of the errors are evaluated solely from the beam dynamics point of view.
Thirteen different sources of errors are considered in this study, which represent RFQ machining and alignment errors, vane voltage error, input beam centre displacement and angle errors and input beam mismatch. A single error is considered first and its effect on the beam quality is evaluated. Then the combination of all errors is considered to ensure an overall acceptable performance of the RFQ. For each single error series of 500 statistical simulations were carried out with uniform distribution of the error within defined range, except for the voltage error, where the distribution is assumed to be Gaussian. In the case of the combined errors, 1000 statistical simulations were carried out. Several values for the maximum error have been considered for each error type. The simulations are done using TraceWin and Toutatis codes [2].
The criteria for evaluating the beam quality are its transmission, emittance growth, output beam centre displacement and angle as well as the output beam energy variation. For each single error we define an acceptable limit for the additional emittance growth of <2% and additional beam losses of <1% for the 99th percentile of all the statistical runs. Assuming the considered errors and their effects are not strongly correlated, with the defined limits the overall effect of the combination of those errors is expected to be around 7% additional emittance growth.
NB. All results of the error study are given with respect to the nominal output beam, i.e. they only represent the additional effect on a beam parameter on top of the nominal one (e.g. they do not contain the nominal beam losses or emittance growth).
0"
10"
20"
30"
40"
50"
60"
70"
80"
90"
100"
0" 0.1" 0.2" 0.3" 0.4" 0.5" 0.6" 0.7" 0.8" 0.9" 1" 1.1"
B ea m %t ra n sm
is si o n %[ % ]%
3%sigma%Gaussian%input%beam,%RMS%emi=ance%0.25%π.mm.mrad%
total" accelerated"
0.84$ 0.88$ 0.92$ 0.96$ 1.00$ 1.04$ 1.08$ 1.12$
O u tp u t% lo n gi tu d in a l%R
M S% e m i2 a n ce %[ π .d e g. M e V ]%
O u tp u t% tr a n sv e rs e %n o rm
a li ze d %R M S% e m i2 a n ce %[ π .m
m .m
ra d ]%
Voltage%factor%
transv.$norm.$rms$emi7.$ long.$rms$emi7.$
Document No v1.3
4.1 Single error
The following single errors (TraceWin notation is used) are considered in this study:
• Longitudinal vane profile error dR [mm] • Transverse curvature of the vane d [mm] • Parallel displacement of the vane (see Fig. 10) DEpa [mm] • Perpendicular displacement of the vane (see Fig. 10) DEpe [mm] • Parallel tilt of the vane with respect to its centre (see Fig. 11) TEpa [mm] • Perpendicular (to Fig. 11 plane) tilt of the vane with respect to its centre TEpe [mm] • Horizontal displacement of the section (block of four vanes) DSHori [mm] • Vertical displacement of the section (block of four vanes) DSVerti [mm] • Horizontal tilt of the section (block of four vanes) TSHori [mm] • Vertical tilt of the section (block of four vanes) TSVerti [mm] • Vane voltage jitter error E [%] • Input beam Twiss parameter [-] and [mm/mrad] mismatch • Input beam centre displacement dx, dy [mm] and angle dxp, dxy [mrad]
NB. The ESS RFQ consists of five roughly equal sections; therefore the vane tilt errors TEpa and TEpe are considered over the length of the section and may be different from section to section.
Figure 10: Vane displacement errors (exaggerated for the effect)
Figure 11: Parallel vane tilt error (exaggerated for the effect)
DEpa
DEpe
TEpa
Document No v1.3
4.1.1 Longitudinal vane profile
The effects of longitudinal vane profile (machining) errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 12-14. Beam parameters are rather sensitive to this error. An acceptable value for this error is ±0.02 mm. For that error max beam losses are 0.23%; max output beam centre displacement is ±0.1 mm; max output beam centre angle is ±0.05 mrad; max output beam energy variation is -8.5 keV.
Figure 12: Transverse RMS emittance growth vs. longitudinal vane profile error
Figure 13: Longitudinal RMS emittance growth vs. longitudinal vane profile error
Figure 14: Beam losses vs. longitudinal vane profile error
0"
1"
2"
3"
4"
5"
6"
7"
Tr an
i. an
Longitudinal(vane(profile(error([µm](
10" 20" 30" 40" 50" 60" 70"
Lo n gi tu d in al +R M S+ em
i1 an
mean"
99th"percen4le"
maximum"
limit"
0"
0.1"
0.2"
0.3"
0.4"
0.5"
0.6"
0.7"
0.8"
0.9"
B ea m %lo ss es %[ % ]%
Longitudinal%vane%profile%error%[µm]%
mean"
99th"percen6le"
maximum"
Document No v1.3
4.1.2 Transverse vane curvature
The effects of transverse vane curvature errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 15-17. An acceptable value for this error is ±0.02 mm. For that error max beam losses are 0.2%; the effect on the output beam centre displacement and angle is negligible; max output beam energy variation is -6.6 keV.
Figure 15: Transverse RMS emittance growth vs. vane transverse curvature error
Figure 16: Longitudinal RMS emittance growth vs. vane transverse curvature error
Figure 17: Beam losses vs. vane transverse curvature error
0"
0.5"
1"
1.5"
2"
2.5"
3"
Tr an
i. an
Vane(transverse(curvature(error([µm](
0% 10% 20% 30% 40%
i1 an
mean%
Vane%transverse%curvature%error%[µm]%
mean"
99th"percen3le"
maximum"
Document No v1.3
4.1.3 Vane displacement
Small symmetric displacements of opposite vanes have no significant effect. They change slightly the quadrupole strength and can be compensated by slightly increasing the vane voltage. Non- symmetric displacements, however, generate odd-order multipoles and may have rather strong effects.
The effects of parallel vane displacement errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 18-20. An acceptable value for this error is ±0.03. For that error max beam losses are 0.3%; max output beam centre displacement is ±0.12 mm; max output beam centre angle is ±0.04 mrad; max output beam energy variation is -7.9 keV.
Figure 18: Transverse RMS emittance growth vs. parallel vane displacement error
Figure 19: Longitudinal RMS emittance growth vs. parallel vane displacement error
Figure 20: Beam losses vs. parallel vane displacement error
0"
0.5"
1"
1.5"
2"
2.5"
3"
3.5"
4"
4.5"
Tr an
i. an
Parallel(vane(displacement(error([µm](
10" 20" 30" 40" 50" 60" 70"
i1 an
mean"
99th"percen5le"
maximum"
limit"
0"
0.1"
0.2"
0.3"
0.4"
0.5"
0.6"
Parallel%vane%displacement%error%[µm]%
mean"
99th"percen5le"
maximum"
Document No v1.3
14(25)
The effects of perpendicular vane displacement errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 21-23. An acceptable value for this error is ±0.07 mm. For that error max beam losses are 0.2%; max output beam centre displacement is ±0.08 mm; max output beam centre angle is ±0.17 mrad; max output beam energy variation is - 6.6 keV.
Figure 21: Transverse RMS emittance growth vs. perpendicular vane displacement error
Figure 22: Longitudinal RMS emittance growth vs. perpendicular vane displacement error
Figure 23: Beam losses vs. perpendicular vane displacement error
0"
1"
2"
3"
4"
5"
6"
20" 30" 40" 50" 60" 70" 80" 90" 100" 110" 120" 130"
Tr an
i. an
Perpendicular(vane(displacement(error([µm](
mean"
99th"percen5le"
maximum"
limit"
0"
0.5"
1"
1.5"
2"
2.5"
3"
20" 30" 40" 50" 60" 70" 80" 90" 100" 110" 120" 130"
i1 an
mean"
99th"percen6le"
maximum"
limit"
0"
0.05"
0.1"
0.15"
0.2"
0.25"
0.3"
0.35"
0.4"
20" 30" 40" 50" 60" 70" 80" 90" 100" 110" 120" 130"
Perpendicular%vane%displacement%error%[µm]%
mean"
99th"percen6le"
maximum"
Document No v1.3
4.1.4 Vane tilt
The effects of parallel vane tilt errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 24-26. An acceptable value for this error is ±0.03 mm over the section length (TraceWin definition, see Fig. 11), which corresponds to an angle of ±0.07 mrad. For that error max beam losses are 0.25%; max output beam centre displacement is ±0.09 mm; max output beam centre angle is ±0.05 mrad; max output beam energy variation is -8.4 keV.
Figure 24: Transverse RMS emittance growth vs. parallel vane tilt error
Figure 25: Longitudinal RMS emittance growth vs. parallel vane tilt error
Figure 26: Beam losses vs. parallel vane tilt error
0"
0.5"
1"
1.5"
2"
2.5"
3"
3.5"
4"
4.5"
5"
Tr an
i. an
Parallel(vane(:lt(error([µm](
20" 40" 60" 80" 100"
i1 an
mean"
99th"percen5le"
maximum"
limit"
0"
0.1"
0.2"
0.3"
0.4"
0.5"
0.6"
B e a m %lo ss e s% [%
]%
mean"
99th"percen5le"
maximum"
Document No v1.3
16(25)
The effects of perpendicular vane tilt errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 27-29. An acceptable value for this error is ±0.06 mm over section length (TraceWin definition), which corresponds to an angle of ±0.13 mrad. For that error max beam losses are 0.16%; max output beam centre displacement is ±0.2 mm; max output beam centre angle is ±0.05 mrad; max output beam energy variation is -6.7 keV. From the point of view of emittance growth and beam losses even ±0.07 mm of perpendicular vane tilt error would be acceptable, however the beam centre displacement would be ±0.3 mm, which is too high for a single source of error.
Figure 27: Transverse RMS emittance growth vs. perpendicular vane tilt error
Figure 28: Longitudinal RMS emittance growth vs. perpendicular vane tilt error
Figure 29: Beam losses vs. perpendicular vane tilt error
0"
0.5"
1"
1.5"
2"
2.5"
3"
3.5"
Tr an
i. an
Perpendicular(vane(=lt(error([µm](
20" 30" 40" 50" 60" 70" 80" 90" 100"
i1 an
mean"
99th"percen6le"
maximum"
limit"
0"
0.02"
0.04"
0.06"
0.08"
0.1"
0.12"
0.14"
0.16"
0.18"
0.2"
Perpendicular%vane%5lt%error%[µm]%
mean"
99th"percen6le"
maximum"
Document No v1.3
4.1.5 Section displacement
The effects of vertical section displacement errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 30-32. The effect is the same for the horizontal section displacement. An acceptable value for this error is ±0.03 mm. For that error max beam losses are 0.16%; max output beam centre displacement is ±0.2 mm; max output beam centre angle is ±0.04 mrad; max output beam energy variation is -6.7 keV.
Figure 30: Transverse RMS emittance growth vs. section displacement (H or V) error
Figure 31: Longitudinal RMS emittance growth vs. section displacement (H or V) error
Figure 32: Beam losses vs. section displacement (H or V) error
0"
0.5"
1"
1.5"
2"
2.5"
3"
3.5"
4"
Tr an
i. an
Sec8on(displacement(error([µm](
10" 20" 30" 40" 50"
i1 an
Sec9on+displacement+error+[µm]+
Sec.on%displacement%error%[µm]%
Document No v1.3
4.1.6 Section tilt
The effects of vertical section tilt errors on transverse and longitudinal RMS emittances and beam losses are presented in Figures 33-35. The effects are the same for the horizontal section tilt. An acceptable value for this error is ±0.04 mm (TraceWin definition), which corresponds to an angle of ±0.09 mrad. For that error max beam losses are 0.18%; max output beam centre displacement is ±0.17 mm; max output beam centre angle is ±0.11 mrad; max output beam energy variation is - 6.7 keV.
Figure 33: Transverse RMS emittance growth vs. section tilt (H or V) error
Figure 34: Longitudinal RMS emittance growth vs. section tilt (H or V) error
Figure 35: Beam losses vs. section tilt (H or V) error
0"
0.5"
1"
1.5"
2"
2.5"
3"
3.5"
4"
Tr an
i. an
Sec8on(8lt(error([µm](
20" 30" 40" 50" 60" 70"
i1 an
Sec9on+9lt+error+[µm]+
Sec.on%.lt%error%[µm]%
Document No v1.3
4.1.7 Vane voltage jitter
To the contrary of all the errors considered in this document, the voltage error jitter is a dynamic error, which varies in time and cannot be corrected. Therefore, the tolerable effects of this error should be much smaller then those from static errors. Assuming an initial RFQ input beam position error of 0.2 mm and 2 mrad, we define an acceptable limit of ±0.05 mm and ±0.2 mrad for the output beam centre displacement and angle variation due to the voltage jitter. We also define as an acceptable limit <1% additional emittance growth with respect to the nominal output beam and <0.2% variation in the beam transmission. Since we are looking at very small effects here, one million macro-particles were used in the simulations. The effects of the voltage jitter on the output beam centre position, transverse and longitudinal RMS emittances and beam losses are presented in Figures 36-38. The data is rather noisy in some cases; therefore it has been fitted with a linear or polynomial curve. Based on the above criteria, a maximum acceptable limit of ±0.5% is defined for the voltage jitter. The output beam energy variation is negligible for that error.
Figure 36: Output beam centre position variation vs. vane voltage jitter
Figure 37: Output beam RMS emittance variation vs. vane voltage jitter
Figure 38: Beam transmission variation vs. vane voltage jitter
!0.18&
!0.16&
!0.14&
!0.12&
!0.10&
!0.08&
!0.06&
!0.04&
!0.02&
0.00&
0.02&
0.04&
0.06&
0.08&
!0.7& !0.6& !0.5& !0.4& !0.3& !0.2& !0.1& 0& 0.1& 0.2& 0.3& 0.4& 0.5& 0.6& 0.7&
O u tp u t% b ea m %c en
tr e% va ri a/
o n %
Voltage%error%[%]%
Simula3on&data&(dXc,&mm)& Simula3on&data&(dX'c,&mrad)& Linear&fit&(dXc,&mm)& 2nd&order&poly.&fit&(dX'c,&mrad)&
!1.2%
!1.0%
!0.8%
!0.6%
!0.4%
!0.2%
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
!0.7% !0.6% !0.5% !0.4% !0.3% !0.2% !0.1% 0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7%
O u tp u t% b ea m %e m i+ an
ce %d iff er en
ce %[ % ]%
Voltage%error%[%]%
Simula3on%%data%(XX'%plane)% Simula3on%%data%(YY'%plane)% Simula3on%%data%(ZZ'%plane)% Linear%fit%(ZZ'%plane)% Linear%fit%(YY'%plane)% Linear%fit%(XX'%plane)%
!0.08%
!0.06%
!0.04%
!0.02%
0.00%
0.02%
0.04%
0.06%
0.08%
0.10%
!0.7% !0.6% !0.5% !0.4% !0.3% !0.2% !0.1% 0% 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7%
Be am
%d iff er en
Document No v1.3
4.1.8 Input beam position
The effects of the input beam centre displacement and angle in the horizontal plane are considered together. Their effects on transverse RMS emittances and beam transmission are presented in Figures 39-41. The effects are the same for the errors in the vertical plane. The combined effects of beam position errors in both planes are more complex since they are correlated. Several combinations of the input beam centre displacement and angle were considered. The retained combination of input beam centre position is a displacement of ±0.2 mm and an angle of ±2 mrad, for which the results are summarized in Tables 3.
Figure 39: XX’ RMS emittance growth vs. input beam centre horizontal displacement and angle
Figure 40: YY’ RMS emittance growth vs. input beam centre horizontal displacement and angle
Figure 41: Beam transmission vs. input beam
centre horizontal displacement and angle
Document No v1.3
21(25)
Table 3: Effects of the RFQ input beam displacement ±0.2 mm and angle ±2 mrad
Parameter Mean 99th perc. Max. Unit
Beam losses 0.11 0.25 0.28 %
Transverse RMS emittance growth 0.83 1.78 1.98 %
Longitudinal RMS emittance growth 0.48 1.64 1.96 %
Output beam center displacement 0 ±0.06 ±0.07 mm
Output beam center angle 0 ±0.05 ±0.06 mrad
4.1.9 Input beam mismatch
The effects of the input beam Twiss parameter ! and ! variation (mismatch) in the horizontal plane are considered together. Their effect on transverse RMS emittances and beam transmission are presented in Figures 42-44. The effect is the same for the variation of Twiss parameters in the vertical plane. The combined effect of those errors in both planes is more complex and makes it difficult to define an acceptable range. Different combinations of Twiss parameter variation ranges have been considered. The acceptable variation range for the input beam Twiss parameters is 0.8<<1.2 and 0.1<<0.12 mm/mrad, which results in ~20% mismatch in and ~10% mismatch in . The results are summarized in Table 4. They have no effect on the output beam centre displacement and angle.
Figure 42: XX’ RMS emittance growth vs. input beam Twiss parameter ! and !
Figure 43: YY’ RMS emittance growth vs. input beam Twiss parameter ! and !
Document No v1.3
22(25)
Figure 44: Beam transmission vs. input beam Twiss parameter ! and !
Table 4: Effects of the RFQ input beam mismatch 0.8<<1.2 and 0.1<<0.12 mm/mrad
Beam losses 0.19 0.59 0.67 %
4.2 Combined errors
Series of 1000 statistical simulation were carried out with the combination of errors discussed above. In order to be compatible and consistent with vane and section displacement errors, corresponding tilt errors were reduced despite the fact that higher values are found to be acceptable as single errors.
The applied errors are summarized in Table 5. All errors are uniformly distributed within the defined range. The vane voltage jitter is not considered in the combined errors study. The results are acceptable from the beam dynamics point of view and are summarized in Tables 6 and 7.
Document No v1.3
Error Max. value Unit
Longitudinal profile of the vane (dR) ±0.02 mm
Transverse curvature of the vane (d) ±0.02 mm
Parallel displacement of the vane (DEpa) ±0.03 mm
Perpendicular displacement of the vane (DEpe) ±0.03 mm
Parallel tilt of the vane (TEpa) over section length ±0.03 mm
Perpendicular tilt of the vane (TEpe) over section length ±0.03 mm
Displacement of the section (DSHori, DSVerti) ±0.03 mm
Tilts of the section (TSHori, TSVerti) ±0.03 mm
Vane voltage jitter (E)* ±0 %
Input beam centre displacement (Δx! ,Δ!) ±0.2 mm
Input beam centre angle (Δx′! ,Δ′!) ±2 mrad
Input beam Twiss parameter !, ! range 0.8 – 1.2 -
Input beam Twiss parameter !, ! range 0.1 – 0.12 mm/mrad
* The vane voltage error considered in Section 4.1.7 is a dynamic error and cannot be corrected. It is not considered in the combined errors study.
Table 6: Effects of the RFQ machining and alignment errors
Beam losses 0.15 0.35 0.49 %
Output beam centre displacement 0 ±0.31 ±0.43 mm
Output beam centre angle 0 ±0.14 ±0.19 mrad
Output beam energy variation -6.1 -8.8 -9.5 keV
Document No v1.3
Beam losses 0.36 0.84 1.04 %
Output beam centre displacement 0 ±0.32 ±0.40 mm
Output beam centre angle 0 ±0.15 ±0.20 mrad
Output beam energy variation -5.9 -8.7 -9.7 keV
Output transverse beam Twiss parameter variation - - ±9 %
Output longitudinal beam Twiss parameter variation - - ±13 %
5. TOLERANCE SPECIFICATIONS
The ESS RFQ tolerances are specified in Table 8 and are based on the beam dynamics considerations. This does not define tolerances required for RF field and frequency stability. In case of differences, the tighter specifications apply. Tolerances on vane and section tilts are specified tighter then those suggested by the beam dynamics results for a single error since they have to be compatible and consistent with displacement errors, which are more sensitive and therefore tighter.
Table 8: RFQ error tolerances
Machining errors Tolerance (max) Unit
Longitudinal profile of the vane (dR) ±0.02 mm
Transverse curvature of the vane (d) ±0.02 mm
Alignment and voltage errors
Parallel and perpendicular vane displacement (DEpa, DEpe) ±0.03 mm
Parallel and perpendicular vane tilt (TEpa, TEpe) over 1 m ±0.03 mm
Section displacement (DSHori, DSVerti) ±0.03 mm
Section tilt (TSHori, TSVerti) ±0.03 mm
Vane voltage jitter (E) ±0.5 %
Input beam errors
Document No v1.3
[1] A. Ponton, Note on the ESS RFQ design update

Documents

ESS RFQ Error Study v1.3 - Lu