TOLERANCE STUDY ON RF AMPLITUDE AND PHASE OF
MAIN SUPERCONDUCTING CAVITIES AND INJECTION TIMINGFOR THE COMPACT ERL
N. Nakamura, ISSP, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8581 Chiba, Japan
M. Shimada, T. Miyajima, Y. Kobayashi, S. Sakanaka.
High Energy Accelerator Research Organization(KEK), Tsukuba, 305-0801 Ibaraki, Japan
R. Hajima, Japan Atomic Energy Agency(JAEA), Tokai, 319-1195 Ibaraki, Japan
Abstract
Tolerance study on RF amplitude and phase of mainsuperconducting(SC) cavities and injection timing wasperformed for the compact ERL. As a result, it was foundthat errors of the RF amplitude and phase should becontrolled down to the level of 0.01 % and 0.01° in rms,
respectively, in order to satisfy requirements for thearrival time and the bunch length in bunch compression
mode. In high current and low emittance modes, thesecontrol errors can be relaxed to the level of 0.1 % and0.1° for early operation, though the RF amplitude error
should be reduced to the level of 0.01 % in future toimprove the momentum variation. The injection timing
error is allowed up to at least 200 fs in all the operation
modes.

INTRODUCTIONIn ERL-based light sources, higher accuracy is
expected to be required for RF control and timing,
because the beam has shorter bunch length and smaller
momentum (energy) spread compared with that of theexisting ring-based synchrotron radiation(SR) sources.
We have studied effects of RF amplitude and phasevariations of main superconducting(SC) cavities andeffects of timing jitter of beam injection from an injector
with simulation in order to know requirements for the RFcontrol and the injection timing.
Figure 1 shows layout of the compact ERL[1] used forthis study. The compact ERL has two TBA(Triple BendAchromat) arc sections and eight main SC cavities incryomodules. Basic parameters for three operation modes
are listed in Table 1. It is assumed in this simulation study
that the bunched beam has a six-dimensional Gaussian
distribution just after the merger as the initial conditions
and all errors of the injector except injection timing jitterare not considered. In this paper, we present simulation
results for the three operation modes and discuss
individual tolerances for RF amplitude and phase errors
and injection timing error.
Chicane system
1st TBA arc

Extractor
Beam dump

2nd TBA arc

Main SC cavity cryomodules

MergerInjector

Figure 1: Layout of a 1-loop compact ERL.

Table 1: Basic Parameters of the Compact ERL for Three
Operation Modes (HC: High Current Mode, LE: Low
Emittance Mode, BC: Bunch Compression Mode)
Parameter
RF frequency[GHz]Injection energy[MeV]
Number of main SC cavities
Effective cavity length[m]Accelerating field[MV/m]
Repetition rate [GHz]Average beam current[mA]
Bunch charge[pC]
Emittance1)[mm·mrad]
Bunch length[ps]1)
Normalized emittance

HC

1.3
10077
12

LE
1.3
58
115
1.3
10
7.7
0.1
2BC 0.001
 77
< 0.1

BUNCH COMPRESSION MODE
Beam Parameters and Optics
In this mode, bunch charge of 77 pC, initial rms
normalized emittance of 1 mm mrad, initial rms bunch
length of 1 ps, and initial rms momentum spread of 210-3
are assumed. The beam is accelerated off-crest by theeight main SC cavities with the accelerating field of 15MV/m and compressed by the 1st TBA arc section withnon-zero R56. Since the RF phase of the main SC cavities
RF is set at about 15 degrees, the beam energy after theacceleration is about 121 MeV. The R56 value of the 1stTBA arc section is set at 0.131 m and the fields of thesextupole magnets in the 1st TBA arc section are
optimized to minimize the bunch length at the exit of the
1st TBA arc section[1]. When momentum of an electron isdeviated from the reference momentum p by p, thearrival time of the electron is changed by

T R56 pv p(1)Here v is the electron velocity.

Effects of RF Amplitude Error
Variations of the arrival time and the bunch length at
the exit of the 1st TBA arc section due to RF amplitude
error of the main SC cavities are obtained with asimulation code “elegant”[2]. Figure 2 shows the changeof 2D electron distribution of the bunch on arrival timemomentum plane for the RF amplitude error of -0.5 % to

0.5 % in 0.1 % step. The bunch arrival time is clearly
increased with the RF amplitude. Furthermore, as the RF
amplitude error becomes large, the bunch is inclined
toward the right or left side on the plane and as a result
the bunch length is increased. Figure 3 shows the arrival
time and bunch length variations due to the RF amplitude
error. The arrival time variation is almost linear and 410
fs for the RF amplitude error of 0.1 %. This is consistent
with the time variation calculated from p/pV/V=0.001,
R56=0.131 m and Eq. (1). The bunch length variation isparabolic around the reference RF amplitude and muchsmaller than the arrival time variation. The bunch lengthis about 55 fs without the error. In order to keep theeffective bunch length including the arrival time variation
within 60 fs and 100 fs, the RF amplitude error should beless than 0.005 % and 0.02 % in rms, respectively.

decreasing the RF phase. The bunch length is increased as
the RF phase error becomes large. Figure 5 shows thearrival time and bunch length variations due to the RFphase error. The arrival time variation is almost linear and200 fs for the RF amplitude error of 0.1°. This is also
consistent with the time variation calculated fromp/pRFtanRF=0.00047, R56=0.131 m and Eq. (1).
The bunch length variation is negligibly smaller than thearrival time variation. The RF phase error should be
suppressed to 0.01° and 0.04° in rms to keep the effective
bunch length within 60 fs and 100 fs.

Figure 4: Change of 2D electron distribution of the bunchon the arrival time-momentum plane for the RF phaseerror of -0.5° to 0.5° in 0.1° step..

125

0100

-1000

75-2000

50
t-3000-0.5 -0.4 -0.3 -0.2 -0.1

025
0.1 0.2 0.3 0.4 0.5

RF amplitude error V/V [%]Figure 3: Variations of the arrival time and the bunch
length due to the RF amplitude error.

Effects of RF Phase Error
Like the RF amplitude error, the RF phase error causes
variations of the arrival time and the bunch length. The
simulated change of 2D electron distribution of the bunch
for the RF phase error of -0.5° to 0.5° in 0.1° step isshown in Fig. 4. The arrival time is increased withT [fs]

150

T500

125

0100-500

75-1000

50t [fs]

1000

Arrival time variation

Tt [fs]Arrival time variation

150

Bunch length

T [fs]

2000

1000

Bunch length

Figure 2: Change of 2D electron distribution of the bunchon the arrival time-momentum plane for the RF amplitude
error of -0.5 % to 0.5 % in 0.1 % step.

t-1500-0.5 -0.4 -0.3 -0.2 -0.1

025
0.1 0.2 0.3 0.4 0.5

RF phase error

RF [deg]

Figure 5: Variations of the arrival time and the bunch
length due to the RF phase error.

Effects of Injection Timing Error
Effects of Injection timing error were obtained from theeffects of the RF phase error. The arrival time variation
due to the injection timing error is the sum of the injection
timing error tinj and the arrival time variation due to theRF phase error RFftinj, where f is the accelerating
frequency. On the other hand, the bunch length variation
is equal to that due to the RF phase error. The arrival timeand bunch length variations due to the injection timing
error are shown in Fig. 6. The arrival time variation isonly less than 10 fs for the injection error of 200 fs. Thisis because the injection timing error is almost cancelledby the arrival time variation due to the RF phase error
caused by the injection timing error. The bunch lengthvariation is less than 5 fs for the injection error of 200 fs.
Possible injection timing error due to the gun ripple andRF amplitude and phase errors of injection cavities wasalready evaluated with simulation to be less than 200 fs,
though it was usually coupled with the other beam
parameters[3]. Here only the injection timing is changed.

T

0-20

100-4080-6060t-80-100-1200-800-400

040040800

Error
Arrival time
Bunch length
Momentum
Momentum spreadHor. emittanceVert. emittance V/V-0.1/0.1 %-25/1.3 fs<1%-0.1/0.1 %
<1%
<1%
<1%

 RF
-0.1/0.1 °-0.11/0.16 fs<1%< 0.0002 %-4.7/7.1 %<1%<1%

 tinj-200/200 fs-200/200 fs<1%< 0.0002 %-4.4/6.6 %
<1%
<1%

 V/V
-0.1/0.1 %-24/2.4 fs<1%-0.1/0.1 %
<1%
<1%
<1%

 RF
-0.1/0.1 °-0.02/0.08 fs<1%< 0.0002 %<2%<1%<1% tinj
-200/200 fs-200/200 fs<1%< 0.0002 %
<2%
<1%
<1%

(b) LE mode

120t [fs]Arrival time variation

140

Bunch length

T [fs]

20

Table 2: Variations of Parameters due to RF Amplitudeand Phase Errors and Injection Timing Error.
(a) HC mode

20
1200

Injection timing error tinj [fs]Figure 6: Variations of the arrival time and the bunch
length due to the injection timing error.

HIGH CURRENT AND LOW EMITTANCE
MODES
Bunch charge of 77 and 7.7 pC and initial normalized
emittance of 1 and 0.1 mm mrad are assumed in HC(highcurrent) and LE(low emittance) modes, respectively. In
both modes, initial bunch length of 2 ps, and initialmomentum spread of 210-3 are assumed. The beam isaccelerated on-crest by the eight SC cavities with theaccelerating field of 15 MV/m and the beam energy after
the acceleration is about 125 MeV. The R56 value of the 1stTBA arc section is set at 0 m and the sextupole magnets
in the 1st TBA arc section are turned off.
Table 2 summarizes the variations of momentum,momentum spread, horizontal and vertical normalized
emittances as well as the arrival time and bunch length at
the exit of the 1st TBA arc due to RF amplitude error in
HC and LE modes, together with those in BC mode forcomparison. The arrival time variations for all the errors
in HC and LE modes are negligibly small for the bunch
length of 2 ps. Variations of the other beam parameters in
HC and LE modes are also not serious for the compact
ERL. However the RF amplitude error should be finallyreduced by one order of magnitude, because themomentum variation due to the RF amplitude error of±1 % is much larger than the momentum spread without
the error (1.7  10-4 for HC mode and 2.0  10-4 for LEmode) at the exit of the 1st arc section. In BC mode, all
the momentum variations in Table 2c are smaller than themomentum spread of 2.6  10-3 at the 1st arc exit.

Error
Arrival time
Bunch length
Momentum
Momentum spreadHor. emittanceVert. emittance(c) BC mode
Error

 V/V RF tinj
-0.1/0.1 %-0.1/0.1 °-200/200 fs
Arrival time-417/408 fs 204/-208 fs-9.7/6.0 fs
Bunch length
9.9/6.3 %3.8/6.7 %3.6/6.3 %Momentum-0.09/0.09 % -0.05/0.04 % -0.04/0.04 %Momentum spread
<1%
<2%
<2%
Hor. emittance-2.3/5.5 %2.7/-1.1 %2.5/-1.0 %Vert. emittance
4.5/-1.6 %-1.3/2.1 %-1.2/2.0 %SUMMARY
From the tolerance study, in bunch compression mode,
required stability of the RF amplitude and phase of themain SC cavities should be the level of 0.01% and 0.01°
to avoid significant increase of the effective bunch lengthincluding the arrival time variation. In high current andlow emittance modes, stability of 0.1 % and 0.1° isenough for early operation of the compact ERL, thoughstability of the RF amplitude should be improved to thelevel of 0.01 % for making the most of the small
momentum spread in future. The injection timing error of
200 fs is enough for preserving the beam quality in all theoperation modes. Similar error analysis can be applied to
the 2-loop compact ERL[4].

ACKNOWLDGEMENTS
We would like to thank Dr. M. Borland(APS) for his
help with our simulations.

REFERENCES[1] T. Shiraga et al., PAC09, Vancouver, 2009.
[2] M. Borland, Phys. Rev. ST-AB 4, 070701 (2001).
[3] T. Miyajima et al., ERL09, Ithaca, 2009.
[4] M. Shimada et al., in these proceedings.