Proceedings of IBIC2012, Tsukuba, Japan

MOPA45STUDY OF BEAM LENGTH MEASUREMENT BASED ON TM010 MODE
Renxian Yuan, Weimin Zhou, Luyang Yu, Yongbin Leng
SSRF, Shanghai, 201800 ChinaAbstract

INTRUDUCE
The measurement area and resolution of beam length
measurement in frequency domain is seriously limited bythe system SNR. So obtaining the system SNR up to100dB is the decisive factor of beam length measurementin frequency domain in FEL case. It is well known thatcavity BPM can achieve the position measurement
resolution up to ~10nm because the signal from TM011mode having a very high R/Q. The amplitude ratio ofTM010 mode and TM011 mode of the same cavity can bewritten as:

Kr( R / Q )0.5010

2 f110f 010

0.5( R / Q )110) J 0 ( Rc k 011 ) JJ01 (( rkrk010011 ) J1 ( Rc k 010 )˄1˅

Where f is the harmonic frequency of TM010 mode andTM011 mode, and J0 and J1 is the 0-order and 1-order
Bessel function respectively, r is the beam position fromthe cavity centre, Rc is the cavity’s radius, k is the wave
number of TM010 mode and TM011 mode. It is reported
that the cavity BPM’s resolution can achieve 0.05mwhen beam charge is 1nC [1][2]. It means that themeasurement system noise equals the output TM011 mode
signal with beam condition 0.05m@1nC. In the case, Kris up to 4×105. So the system SNR of TM010 mode can beinferred up to 112dB.
When the beam is a Gaussian distribution bunch, thesignal amplitude of TM010 mode can be written as:

V=S q  f 010 ZQL( QR )010 exp( 2S fc0102 V L )22

V1 =S q  f 010,1 Z
QL ,1( QR )010,1 exp(V2 =S q  f010,2 Z
QL ,2( QR )010,2 exp(22S 2 f 010,1V L2c02

22S 2 f010,2
V L2c02)

(3)

(4))

So the coupling of beam charge can be eliminated by
the outputs division. Then the beam length can be gettingas:

V L2c0222)
2S 2 ( f010,2 f 010,1fQ( R / Q)(ln(VV12 )  ln( f010,2 )  0.5ln( QL,1 ( R/Q)2 ))L,2010,1(5)1In the Eq.(5), the second and the third term is constantdecided by the two cavities, so the sum of the two terms
can be defined as ln(R1/R2 ), then:

VLc02222)
2S ( f 010,2  f 010,1

 ln( VV12RR21 )˄6˅And when the beam deviates the Gaussian distribution,
the rms beam length can get from a similar equation [3].
When the beam length is very shorter than c/f010, theresolution can be written as:'V L c02222)
2S ( f 010,2  f 010,1V SNRVL

˄7˅

Where SNRv is the signal-noise-ratio of the TM010 mode.
From the Eq.(7), it can be seen that the resolution of thebeam length measurement is seriously limited by the SNRof diagnostic system and beam length itself. Supposing
the SNR 112dB, f010,1 and f010,2 equal 3GHz and 8GHz
respectively, Fig.1 shows the relation between theresolution and beam length. It can be seen that theresolution can achieve 3.5m@1nC even the beam lengthis only 0.1ps.

2(2)

0

Where q is the beam charge, Z is output impedance, QL
is the quality factor, L is the beam length, (R/Q)010 is thenormalized shunt impedance of TM010 mode. So if used
two cavities which working as TM010 mode at different
frequency, the output signal can be written as:

Figure 1: Relation between the resolution and bunch length.

ISBN 978-3-95450-119-9
Longitudinal Diagnostics and Synchronization

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Beam length measurement in frequency domain is afamiliar method, and the resolution is seriously limited bythe system signal-noise-ratio (SNR) and the beam length
measured. Usually this method can only obtain theresolution about ~10ps with beam length ~30ps whenusing signal from button or stripline BPM. But in FELcase, the beam length is the ps or sub–ps order. The paper
discusses the probability of beam length measurement
based on the TM010 mode in FEL case. When adoptingHigh Order Mode(HOM) reject and system gain control,
the system SNR can arrive at 112dB and the resolution
can achieve 30fs with beam length ps or sub-ps order.

MOPA45

Proceedings of IBIC2012, Tsukuba, JapanSIMULATIONc 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Based on the theory analysis, some simulations aredone with MAFIA simulation code when considering
Shanghai SDUV FEL case. The working frequency of thecavity BPM of the SDUV FEL is designed at 4.7GHz, andthe TM010 mode’s frequency of the position cavity works
at 3.6GHz. Fig.2 and Fig.3 are the waveforms in time
domain and frequency domain from the reference cavity
with beam charge 1nC and beam length 10ps. Three cases
are simulated which the beam charge is 1nC and the beampositions are 0.25mm, 1.25mm and 5.3mm respectively.
Fig.4 is the output amplitudes of TM010 mode when beam
locates at different positions. It can be seen that the‘invariable’ TM010 mode signal changing when beam
position changing. The SNR is only about 40dB if thedeviations between the output amplitudes are seen as
diagnostic noise. Fig.5 is the simulation result of thebunch length measurement in frequency domain in thecase.

Figure 5: Beam length simulation result.
Because the amplitude difference is increasing when
position offset increasing, it can be supposed that someposition mode signals such as TM011 mode are coupling
into the TM010 mode’s output. The output structure has tobe improved for avoiding the coupling. Fig.6 and Fig.7
show the coupling improvement after the structure
improvement. Fig.8 and Fig.9 shows the result after thisimprovement. The SNR increases to 60dB and theresolution is about 0.3ps when beam length 10ps.

Figure 2: Output TM010 signal of reference cavity.
Figure 6: The coupling between the TM010 mode andTM011 mode.

Figure 3: Spectrum of reference cavity.

Figure 7: Improvement of modes coupling.

Figure 4: Amplitudes deviations when beam positionchanging.
Figure 8: Amplitudes difference after improvement.

ISBN 978-3-95450-119-92Longitudinal Diagnostics and Synchronization

Proceedings of IBIC2012, Tsukuba, Japan

Figure 9: Beam
improvement.

lengthsimulation

resultafter

MOPA45Figure 12: Amplitudes deviation after adjusting theJ0(rk) term.

From the equation 7, it can be seen that the resolution
is in verse proportion to the difference of the square ofworking frequencies. So the resolution will increase when
adding the difference. Fig.10 and Fig.11 is the result whenchanging the working frequencies to 4.7GHz and 5.8GHz
respectively. The resolution is less 0.3ps now.

Figure 10: Amplitudes
frequencies.

afterchanging

theworking

At last, the thermal noise should be considered. FromFig.2, the loaded shunt impedance is larger than 100Ohm
in the FWHM bandwidth. If considering bunch-by-bunch
beam length diagnostic, the bandwidth maybe is about
500MHz, the peak of the signal amplitude in thebandwidth is about 70V in this simulation case. The peakvoltage of the thermal noise in this bandwidth is only
about 0.12mV. It means that the system SNR will be up to134dB if only considering the thermal noise.

CONCLUTION
The beam length measurement in frequency domain
based on TM010 mode has a very high signal-noise-ratio.
So the anticipative resolution will be about to 10fs whenbeam length is only about to 100fs. A series simulation
based on Mafia had done and proved that the attainable
beam length resolution was up to the limit of thesimulation and accorded with anticipation.

REFERENCES
Figure 11: Result after frequencies changing.
From the Fig.8 and Fig.10, it can be seen that theabsolute deviation of output amplitudes is increasing inproportion to the working frequency. It means that there isa factor which in proportion to the frequency acting on
the TM010 mode’s output amplitudes. From the equation 1
and 2, it has to consider the effecting of (R/Q) which isdetermined by the term J0(rk010). Fig.12 and Fig.13 shown
the improved simulation result of Fig.10 and Fig.11 after
considering the effect of the term J0(rk010). The deviationof the output amplitude is decreasing to 0.1%, and thebeam length measurement resolution is changing better
than 100fs. Considering the minimum time step is about
200fs when simulation, the attainable and reasonable
resolution should be about 100fs in the simulation.

[1] H.Maesaka, S.Inoue et al., “Development of the RF cavity
BPM of XFEL/Spring-8” DIPAC09.
[2] Andrew Young et al., “LCLS resonant cavity beam
position monitors” TUPSM028, BIW10.
[3] Takao Ieiri et al., “Measurement of bunch length based onbeam spectrum in the KEKB” EPAC2000.

ISBN 978-3-95450-119-9Longitudinal Diagnostics and Synchronization

3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 13: Result after J0 (rk) term adjusting.