Reversible electron beam heating for suppression of microbunching instabilities at free-electron lasers

1.5 MB·English

by  Christopher Behrens

Reversible electron beam heating for suppression of microbunching instabilities at
free-electron lasers
Christopher Behrens1, Zhirong Huang2, and Dao Xiang2
1 Deutsches Elektronen-Synchrotron DESY, Notkestr.85, 22607 Hamburg, Germany
2 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
(Dated: January 18, 2012)
The presence of microbunching instabilities due to the compression of high-brightness electron
beams at existing and future X-ray free-electron lasers (FELs) results in restrictions on the at-
tainablelasingperformanceandrendersbeamimagingwithopticaltransitionradiationimpossible.
The instability can be suppressed by introducing additional energy spread, i.e., “heating” the elec-
tron beam, as demonstrated by the successful operation of the laser heater system at the Linac
2 Coherent Light Source. The increased energy spread is typically tolerable for self-amplified spon-
1 taneous emission FELs but limits the effectiveness of advanced FEL schemes such as seeding. In
0 thispaper,wepresentareversibleelectronbeamheatingsystembasedontwotransversedeflecting
2 radio-frequency structures (TDSs) up and downstream of a magnetic bunch compressor chicane.
The additional energy spread is introduced in the first TDS, which suppresses the microbunching
n
instability,andtheniseliminatedinthesecondTDS.Weshowthefeasibilityofthemicrobunching
a
gainsuppressionbasedoncalculationsandsimulationsincludingtheeffectsofcoherentsynchrotron
J
radiation. Acceptable electron beam and radio-frequency jitter are identified, and inherent options
7
fordiagnosticsandon-linemonitoringoftheelectronbeam’slongitudinalphasespacearediscussed.
1

PACSnumbers: 29.27.-a,41.60.Cr,41.85.Ct
]
h
p
- I. INTRODUCTION flecting rf structures (TDSs) are routinely used for high-
c
resolutiontemporalelectronbeamdiagnosticsatpresent
c
a X-ray FELs (e.g., Refs. [14–17]) and are proposed to use
X-rayfree-electronlasers(FELs)provideanoutstand-
. for novel beam manipulation methods (e.g., Refs. [18–
s ing tool for studying matter at ultrafast time and
c 23]). Recently, a TDS was used to increase the slice en-
atomic length scales [1], and have become a reality
i ergyspreadinanecho-enabledharmonicgenerationFEL
s with the operation of the Free-Electron Laser in Ham-
y experiment[24,25]. Inthispaper,wepresentareversible
burg (FLASH) [2], the Linac Coherent Light Source
h electronbeamheatingsystemthatusestwoTDSslocated
(LCLS) [3], and the SPring-8 Angstrom Compact Free
p upanddownstreamofamagneticbunchcompressorchi-
[ Electron Laser (SACLA) [4]. The required high trans-
cane. The additional slice energyspread is introduced in

verse and longitudinal brightness of the X-ray FEL driv-
2 thefirstTDS,whichsuppressesthemicrobunchinginsta-
ing electron bunches may encounter various degrada-
v bility, and then is eliminated in the second TDS.
tion effects due to collective effects like coherent syn-
2 The method of reversible beam heating is shown in
2 chrotron radiation (CSR) or microbunching instabilities
Sec.IIbymeansoflinearbeamopticsandacorrespond-
1 (e.g., Refs. [5–7]), and need to be preserved and con-
ing matrix formalism. In Sec. III, we show the feasibil-
4 trolled. In order to suppress a microbunching instability
ity of this scheme to preserve both the transverse and
. associated with longitudinal bunch compression that de-
1
longitudinalbrightnessoftheelectronbeam,anddiscuss
1 teriorates the FEL performance, the LCLS uses a laser
theimpactofcoherentsynchrotronradiation. SectionIV
1 heater system to irreversibly increase the uncorrelated
coversthegainsuppressionofmicrobunchinginstabilities
1 energy spread within the electron bunches, i.e., the slice
v: energy spread, to a level tolerable for operation of a self- byanalyticalcalculationsandnumericalsimulations,and
inSec.Vwediscusstheimpactofbeamandrfjitter,and
i amplifiedspontaneousemissionFEL[8,9]. ForfutureX-
X show inherent options for diagnosis and on-line monitor-
ray FELs that plan to use external quantum lasers (seed
ing of the electron beam’s longitudinal phase space. The
r lasers) to seed the FEL process in order to achieve bet-
a results and conclusions are summarized in Sec. VI.
ter temporal coherence and synchronization for pump-
probe experiments, a smaller slice energy spread is re-
quired to leave room for the additional energy modula-
tion imprinted by the seed laser. Thus, the amount of II. METHOD
tolerable beam heating is more restrictive and the longi-
tudinal phase space control becomes more critical (e.g.,
In this and the following sections, we consider a linear
Refs.[10,11]). Thesamestrictrequirementonsmallslice
accelerator (linac) employing a single bunch compressor
energyspreadsisvalidforopticalklystronenhancedself-
for a soft X-ray FEL, such as the proposed linac config-
amplified spontaneous emission free-electron lasers [12].
uration for the Next Generation Light Source (NGLS)
Originally designed for high-energy particle separa- at LBNL [26]. The choice of a single magnetic bunch
tion by radio-frequency (rf) fields [13], transverse de- compressor simplifies our consideration and analysis, al-
2
FIG. 1: Layout of a reversible electron beam heater system including two transverse deflecting rf structures located up and
downstream of a magnetic bunch compressor (BC) chicane, and longitudinal phase space diagnostics using screens and syn-
chrotron radiation monitors (SRM). Parameters related to the reversible beam heater system are denoted in curly brackets.
though the concept is also applicable for typical bunch where K = eωV /(cE) is the vertical kick strength,
y y
compressor arrangements with multiple stages. We note V is the peak deflection voltage in the TDS, c is the
y
that a single bunch compressor arrangement has also speed of light in vacuum, E is the electron energy, and
beenconsideredfortheFERMI@ElettraFELinorderto y is the mean vertical position over the structure length
minimize the impact of microbunching instabilities [27]. L along the beamline relative to the central axis inside
The generic layout of the reversible electron beam the finite TDS. Here, z is the internal bunch length co-
heatersystemisdepictedinFig.1. Itconsistsoflinacsec- ordinate of the electron relative to the zero-crossing rf
tionsprovidingandacceleratinghigh-brightnesselectron phase. Both the additional transverse kicks and relative
beams, a magnetic bunch compressor chicane in order to energy deviations are induced by the TDS operation it-
achievesufficientpeakcurrentstodrivetheFELprocess, self and generate correlations within an electron bunch.
and two transverse deflecting rf structures located up In fact, near the zero-crossing rf phase (see Eq. (2)),
anddownstreamofthebunchcompressor. Anadditional the induced transverse kick correlates linearly with the
higher-harmonic rf linearizer system (Linearizer), like at internal bunch length coordinate (z = ct) and enables
theLCLSorFLASH[28],canbeusedtoachieveuniform high-resolutiontemporaldiagnostics(e.g.,Refs.[14–16]),
bunchcompressionbymeansoflongitudinalphasespace whereas the induced relative energy deviation correlates
linearization upstream of the bunch compressor. The with the vertical offset inside the TDS and results in an
whole system can be supplemented by dedicated longi- induced relative energy spread ∆σ = K σ . Here, the
δ y y
tudinal phase space diagnostics (see Sec. V), and except symbol σ denotes the root mean square (r.m.s.) value,
forthetwoTDSs,thelayoutiscommonlyusedforbunch and σ is the vertical r.m.s. beam size. This additional
y
compression at present and future X-ray FELs. energy spread (cf. laser heater [8, 9]), in combination
The principle of the reversible electron beam heater with the momentum compaction R of a bunch com-
56
relies on the physics of TDSs arising from the Panofsky- pressor chicane, is able to smear microbunch structures,
Wenzeltheorem[29,30],whichstatesthatthetransverse and correspondingly suppresses the associated instabil-
momentum gain ∆p(cid:126) of a relativistic electron imprinted ity as is shown in Sec. IV. The effect of induced energy
⊥
byaTDSisrelatedtothetransversegradientofthelon- spread (“beam heating”) is generated by off-axis longi-
gitudinal electric field inside the TDS, and yields tudinal electric fields, related to the principle of a TDS
⊥ z
∇ E
e (cid:90) L bythePanofsky-Wenzeltheorem,andhasbeenobserved
∆p(cid:126) = i dz˜, (1) experimentally at FLASH [33] and the LCLS [34]. The
⊥ ⊥ z
− ω ∇ E
0 inducedenergyspreadisuncorrelatedinthelongitudinal
where ω/(2π) is the operating rf frequency, e is the ele- phase space (z,δ), but shows correlations in the phase
mentary charge, L is the structure length, and z˜ is the space(y,δ),whichisthereasonthatitcanbeeliminated
longitudinal position inside the structure (not to be con- (“beamcooling”)withasecondTDSinareversiblemode
fused with the beamline coordinate, which is given by s as is shown in the following by two different approaches.
in the following). Operating a TDS with vertical deflec-
tion, i.e., in y-direction, near the zero-crossing rf phase
ψ =ω/cz, electrons experience transverse kicks [14]
A. Linear beam optics
eωV
∆y(cid:48) = yz =K z (2)
y
cE
The transverse betatron motion of an electron passing
and relative energy deviations (δ =∆E/E) [31, 32]
through a TDS with vertical deflection (in y) is given by
1 (cid:90) L
∆δ =K y(s)ds=K y, (3)
yL 0 y y(s)=y0(s)+Sy(s,s0)z (4)
3
with the vertical shear function (e.g., Refs. [14, 15, 32]) lengthsbecome(omittingtheargumentiny(s)andS(s))
Sy(s,s0)=R34Ky =(cid:113)βy(s)βy(s0)sin(∆φy(s,s0))eωcEVy , ∆δ =K1y1CEE12 +K2(y2+S1z1) (10)
(5)
with the mean vertical offsets y and (y +S z ) in-
where R is the angular-to-spatial element of the ver- 1 2 1 1
34 side the TDSs. For constant vertical offsets inside the
tical beam transfer matrix from the TDS at s to any
0 TDSs or short structure lengths, the mean vertical off-
position s, β is the vertical beta function, ∆φ is the
y y sets can be replaced by the actual offsets, i.e., y y
verticalphaseadvancebetweens ands,andy describes 1 → 1
0 0 and (y +S z ) (y +S z ). The latter describes the
the vertical beam offset independent of any TDS shear- 2 1 1 → 2 1 1
offsetinthesecondTDSandinvolvesthespatialchirpin-
ing effect. Referring to the layout depicted in Fig. 1 and
ducedbythefirstTDSwithS sin(∆φ (s ,s )),which
taking bunch compression into account, the induced ver- 1 ∼ y 2 1
vanishes in the case of spatial chirp cancelation given by
ticalbeamoffset(∆y =y y )downstreamofthesecond
− 0 Eq. (8). In order to cancel the relative energy spread
TDS becomes (omitting the subscript y in S )
y induced by the combined TDS operation, it follows
∆y(s)=S (s,s )z +S (s,s )z E
1 1 1 2 2 2 K y C 1 +K y =0. (11)
1 1 2 2
=(CS1(s,s1)+S2(s,s2))z2 (6) E2
The general transverse beam transport optics with the
with the bunch compression factor C = z /z and the
1 2 vertical phase advance condition in Eq. (8) gives y =
2
shear functions S (s,s ) of the corresponding TDSs. (cid:112)
1,2 1,2 y β (s )/β (s ), and taking β (s ) β (s )E /E
Here, S1(s,s1)z1 describes the vertical beam offset in- ±(see1 prioyr E2q. (y7))1into account yiyelds2 ex→actlyy t2he s1am2e
duced by the first TDS located at s that is independent
1 condition as in Eq. (9). Simultaneous spatial chirp and
of the second TDS. In order to cancel the spatial chirp
energyspreadcancelationinthesecondTDSisthebasic
induced by the combined TDS operation, the beam off-
principleforreversibleelectronbeamheatingandenables
set ∆y in Eq. (6) must vanish for any z . Hence, using
2 local increase of slice energy spread. The additional en-
Eq.(5)forS inEq.(6)andtakingaccelerationfromE
1,2 1 ergy spread in the bunch compressor, which is added in
to E in Linac2 into account by making the replacement
2 quadrature by the first TDS, can be controlled by the
β (s)β (s ) β (s)β (s )E /E [14], we get
y y 1 → y y 1 1 2 kick strength K1 and the vertical beam size σy(s1).
(cid:113) (cid:112) Inthefollowing, acomplementaryapproachtodiscuss
C βy(s1)sin(∆φy(s,s1)) E1K1 the reversible beam heating system is shown. It uses the
(cid:113) (cid:112) matrix formalism for beam transport and provides an
+ β (s )sin(∆φ (s,s )) E K =0, (7)
y 2 y 2 2 2 analytical way to show microbunching gain suppression
and to discuss the impact of beam and rf jitter.
where K are the vertical kick strengths of the corre-
1,2
sponding TDSs, and ∆φ (s,s ) describes the vertical
y 1,2
phase advances between s1,2 and s, respectively. As a B. Matrix formalism
consequence, the phase advance between both TDSs is
∆φ (s ,s ) = ∆φ (s,s ) ∆φ (s,s ). A general solu-
y 2 1 y 1 y 2 We adopt the beam transport matrix notation of a
−
tion, valid for any position s downstream of the second 6x6 matrix for (x,x(cid:48),y,y(cid:48),z,δ) but leaves (x,x(cid:48)) out for
TDS, is only possible for a phase advance difference of simplicity, i.e., (y,y(cid:48),z,δ) is used in the following. The
4x4 beam transport matrix for a vertical deflecting TDS
∆φ (s ,s )=n π (8)
y 2 1 · in thin-lens approximation reads (e.g., Refs. [19, 31, 33])
with n being integer, and the kick strength 1 0 0 0
(cid:115) (cid:114) Rthin =0 1 K 0. (12)
βy(s1) E1 T 0 0 1 0
K = C K , (9)
2 ± β (s ) E 1 K 0 0 1
y 2 2
As discussed above, the main components of the given
wherethesigndependsontheactualphaseadvance,i.e.,
reversible heater system shown in Fig. 1 consist of TDS1
∆φ (s ,s )=π+n 2π for (+) and ∆φ (s ,s )=n 2π
fory( 2). 1The diffe·rent sign of K cany t2ech1nically·be with the kick strength K1, a bunch compressor with the
achie−ved by changing the rf phase in the TDS by 180◦ momentum compaction factor R56, and TDS2 with the
kick strength K . Including the momentum compaction
which results in a zero-crossing rf phase with opposite 2
factor R and acceleration in Linac2 (E E ), the
slope and deflection. Besides cancelation of the induced 56 1 → 2
4x4 beam matrix between the two TDSs is given by
spatialchirps,theinducedenergyspreadofthefirstTDS
 
needs to be eliminated in the second structure in order R33 R34 0 0
tinoghEavqe. (a3)fuslilmyirlaervetrosiEblqe.e(l6e)c,trtohne rbeelaamtiveheeanteerrg.yAdpepvliya-- RC =R043 R044 01 R056 . (13)
tion downstream of the second TDS for finite structure 0 0 0 E1
E2
4
In order to allow the energy change in the first TDS of the reversible heater system, the beam is slightly cou-
to be compensated for in the second TDS, we require plediny(cid:48) δ andy z ,whichresultsinasmallgrowth
0 0
− −
the point-to-point imaging from TDS1 to TDS2 (i.e., of the projected emittance given by
R = 0), which corresponds to an equivalent vertical
34
β γ K2R2
phase advance of ∆φy(s2,s1) = n π with n being inte- (cid:15)2 =(cid:15)2 +(cid:15) (cid:15) y0 z0 1 56 , (17)
ger (see Eq. (8)). Then we get the· magnification factor y,z y0,z0 y0 z0 (1+hR56)2
(cid:112)
R = β (s )/β (s ) and R =1/R .
3T3he±linearyac2celeryato1r section44with hig3h3er-harmonic rf where (cid:15)y0,z0 is the initial vertical (longitudinal) emit-
tance, and β and γ are the initial Twiss parameters.
linearizer (Linac1 and Linearizer) upstream of the first y0 z0
Asisshowninthefollowingsection, thisprojectedemit-
TDS introduces an appropriate energy chirp h for uni-
tance growth is typically negligible.
form bunch compression. Without loss of generality, we
neglect acceleration between the two TDSs, i.e., we do
not consider Linac2 anymore. Including Linac2 would
(cid:112) III. REVERSIBLE HEATING AND
simply result in a correction term E1/E2 (cf. Eqs. (9) EMITTANCE PRESERVATION
and (15) below) but would leave the physics unchanged.
Then the entire 4x4 beam transport matrix from the be-
We demonstrate the feasibility of the reversible beam
ginning of TDS1 to the end of TDS2 becomes
heater system by numerical simulations using the par-
  ticle tracking code elegant [35], and the simulations in
R 0 0 0
33 the following include 5 105 particles. Table I summa-
R43+K1K2R56 R133 RK313 +K2(1+hR56) K2R56 . rizes the main paramet×ers used in the simulations, and
 K1R56 0 1+hR56 R56  the adopted accelerator optics model, including the po-
K +R K 0 0 1
1 33 2 1+hR56 sitions of the TDSs, is shown in Fig. 2. The magnetic
(14) bunchcompressorchicaneisassumedtobendinthehor-
Cancelation of the induced spatial chirp (∆y(cid:48) z0, cf. izontalplane,andtheTDSsareorientedperpendicularly
∼
Eq. (2)) requires R45 =0 (6x6-matrix notation), i.e., with vertical deflection. In the previous section, we in-
cludedLinac2forageneralderivationofthemethod,but
K1/R33+K2(1+hR56)=0, (15) in practice, due to wakefield concerns, we recommend
putting TDS2 right after the bunch compressor. In or-
where R45 describes the coupling between y(cid:48) and z0. We der to show numerical examples based on this approach,
note that the coupling between δ and y0 (i.e., R63 ele- Linac2 is not considered anymore throughout the rest of
ment)isnonzeroinEq.(14)becausethebunchisenergy- thispaper. ExceptfortheTDSs,theparametersaresim-
chirped after compression (δ z y0), which can be ilar to the magnetic bunch compressor system discussed
∼ ∼
removed by Linac3 downstream of TDS2. For uniform for the Next Generation Light Source at LBNL [26, 36].
bunch compression with C−1 = (1+hR56), no acceler- The initial longitudinal electron bunch profile is as-
tahtiaotnRin33L=inac2(cid:112), iβ.ey.(,s2E)2/β=y(Es11),,aEnqd.t(a1k5i)ngisinidtoenatciccaoluntot ssulimceeednteorgbyesflparte-atdopofwith1kaepVea(rk.mcu.sr.r)e.nTtohfe∼in4it0iaAl lainndeaar
Eq. (9). Thus±, both formalisms yield the same result. and quadratic chirp is∼set for a uniform compression fac-
SincethekickstrengthofthefirstTDSisveryweak,it tor C of about 13acrossthe entire bunchlength. This is
canbeimplementedbymeansofashortrfstructureand
the thin-lens approximation is still valid. However, the
kick strength of the second TDS is usually stronger, and
TABLEI:Parametersoftheelectronbeam,ofthebunchcom-
the effect of the finite structure length should be taken pressorsystem,andofthetransversedeflectingrfstructures.
into account. The symplectic beam transport matrix of
a finite TDS with the length L is given in Ref. [19] by Parameter Symbol Value Unit
2
Beam energy at TDS1/2 E 350 MeV
 1 L2 K2L2/2 0 Lorentz factor at TDS1/2 γ 685
Rthick = 0 1 K2 0. (16) Initial transverse emittance γ(cid:15)x,y 0.6 µm
T  0 0 1 0
Initial slice energy spread σ ∼1 keV
K K L /2 K2L /6 1 E
2 2 2 2 2 Momentum compaction factor R −138 mm
56
Compression factor C ∼13
Inthiscase,werequirethepoint-to-pointimagingisfrom
Final bunch current I ∼520 A
the first TDS to the middle of the second TDS in order f
tohaveacompletecancellation. Theoverallmatrixfrom TDS1/2 rf frequency ω/2π 3.9 GHz
TDS1 to the end of TDS2, when Eq. (15) is fulfilled, be- Voltage of TDS1 V1 0.415 MV
comesmorecomplicated. Afewcorrectiontermscontain- Voltage of TDS2 (without CSR) V 5.440 MV
2
ing the length L2 of TDS2 appear, which however does Length of TDS1 L1 0.1 m
not change the working principle of the reversible beam
Length of TDS2 L 0.5 m
2
heatersystem. Itshouldbepointedoutthatdownstream
5
300 )
d
ra3 m)0.6 Dx 1 Horizontalemittance 20
) ( ( φy Verticalemittance
nctions(m200 seadvance2 dispersion0.4 ββTxyDS ε(µm)N 0.8 Coreenergyspread 1168 Eσ(keV)
u a
f100 h al
Beta calp1 zont0.2 0.6 14
rti ori 5.2 5.3 5.4 5.5 5.6 5.7
e H
0 V0 0 V2(MV)
0 10 20 30
(a)Projectedemittancesandcoreenergyspread.
Position (m)
10
FIG. 2: Relevant accelerator optics (Twiss parameters) and
positionsofthetransversedeflectingrfstructuresusedtonu- 8 Upstream of TDS1
merically demonstrate the reversible beam heater system. Downstream of TDS1
V) Upstream of TDS2, scaled by 1/C
e 6
k Downstream of TDS2, scaled by 1/C
(
possibleevenwithbunchcompressornonlinearitiesbyus- E
σ 4
ingahigher-harmonicrflinearizerupstreamofthebunch
compressor [28] and needed to achieve uniform cancela-
2
tion of the induced energy spread downstream of TDS2.
Figure 3 shows the principle of the reversible beam
0
heater system by means of simulation of the longitudi- −1.5 −1 −0.5 0 0.5 1 1.5
nal phase space at different positions along the beam- z/σz
line. The impact of CSR is not taken into account (cf. (b)Sliceenergyspread.
next subsection for CSR effects). The initial slice en-
ergy spread is heated up to 10keV (r.m.s.) in the first FIG.4: SimulationswithoutCSReffectsontheimpactofthe
∼
TDS, increased by the compression factor in the bunch reversibleheatersystemonprojectedemittances,coreenergy
compressorto 130keV(r.m.s.),andfinallycooleddown spread, and slice energy spread : (a) Projected emittances
∼ (normalized) and core energy spread, and (b) slice energy
spread for V at minimum emittance (see Fig. 4(a)). The
2
longitudinal coordinate is normalized to the bunch length.
1 1
) 20 0.8 ) 20 0.8
V V
e 0.6 e 0.6
k 0 k 0
E( 0.4 E( 0.4 to ∼13keV (r.m.s.) by the second TDS (see Figs. 3(a)-
∆ 20 0.2 ∆ 20 0.2 3(d)). The plot in Fig. 4(b) shows that the heating in-
− −
0 0 duced by the first TDS is perfectly reversible, and the
4 2 0 2 4 4 2 0 2 4
− − − − final slice energy spread is simply the initial slice energy
z/c(ps) z/c(ps)
spread scaled with the compression factor, which would
(a)UpstreamofTDS1. (b)DownstreamofTDS1.
be exactly the same like in the case without using the
400 1 400 1 reversible beam heater system. Figure 4(a) shows the
0.8 0.8 heater system impact on both the projected emittance
V) 200 V) 200
e 0.6 e 0.6 (horizontalandvertical)andthecoreenergyspread,i.e.,
E(k 0 0.4 E(k 0 0.4 the slice energy spread in the center of the bunch, for
∆−200 0.2 ∆−200 0.2 different voltages in the second TDS. The minimum of
400 400
− 0 − 0 theverticalemittanceisrelatedtothecancelationofthe
0.4 0.2 0 0.2 0.4 0.4 0.2 0 0.2 0.4
− − z/c(ps) − − z/c(ps) spatialchirpandenergyspreadinducedbythefirstTDS.
(c)UpstreamofTDS2. (d)DownstreamofTDS2. The horizontal emittance is not affected at all, and the
small projected emittance growth (6 %) in the vertical
FIG. 3: Simulation of the longitudinal phase space after re- plane at the minimum is due to residual coupling gener-
moving the correlated energy chirp: (a) upstream of the first ated by the system that is described by Eq. (17). Never-
TDS, (b) directly downstream of the first TDS, (c) directly theless,asshowninSec.IIIA,eveninthecasewithCSR
downstreamofthebunchcompressorandupstreamofthesec- effects, the horizontal slice emittance stays unaffected at
ond TDS, and (d) downstream of the second TDS. The axes all and the vertical slice emittance exhibits only devia-
scales change from (b) to (c) when bunch compression takes tions in the bunch head (z/c < 0) and tail (z/c > 0).
place. The bunch head is on the left, i.e., where z/c<0.
6
A. Impact of coherent synchrotron radiation a 4-dimensional (4-D) distribution function F(y,y(cid:48),z,δ),
the bunching factor b(k) is given by
Thepreviousresultsundergosmallmodificationswhen
(cid:90)
includingCSReffects,whichisshowninFig.5. Thevolt- b(k)= dydy(cid:48)dzdδe−ikzF(y,y(cid:48),z,δ)
ageofthesecondTDSforminimumprojectedemittance
(cid:90)
in the vertical is shifted by about 0.2MV to lower val-
= dy dy(cid:48)dz dδ e−ikK1R56y0−ik(1+hR56)z0
ues which is due the additional energy chirp induced by 0 0 0 u
CSR. In comparison to the case without any CSR effects e−ikR56(δu+δm(z0))F (y ,y(cid:48),z ,δ ), (19)
(cf. Fig.4),theprojectedemittanceintheverticalplane 0 0 0 0 u
is slightly increased and the slice energy spread is not
where F (y ,y(cid:48),z ,δ ) is the initial 4-D distribution.
perfectly canceled in the head and tail. The slice energy 0 0 0 0 u
If the induced energy modulation is small such that
spread in the core part of the bunch is also slightly in-
kR δ 1, we can expand the exponent of Eq. (19)
creased to 17.5keV (r.m.s.) (instead of 13.5keV (r.m.s.) | 56 m| (cid:28)
up to the first order in δ to obtain
in the absence of CSR). The projected emittance in the m
horizontalisabout1.7largerwhichisindependentofthe (cid:90)
reversible beam heater operation. This horizontal emit- b(k) b (k ) ikR dz δ (z )e−ik0z0
0 0 56 0 m 0
≈ −
tance growth can further be reduced by minimizing the
(cid:90)
horizontal beta function in the last dipole of the chicane dy dδ e−ikK1R56y0−ikR56δuU(y )V(δ ), (20)
0 u 0 u
where the bunch length becomes the shortest. This op- ×
timization is independent of the relevant motion in the
vertical and does not affect the results of the reversible where k = Ck0, C = 1/(1+hR56), U(y0) describes the
heater system. Albeit the fact that the projected emit- transverse profile, and V(δu) is the initial energy distri-
tances are increased, the horizontal slice emittance stays
unaffected and the vertical slice emittance exhibits only
deviations in the head and tail due to CSR effects as
1 20
is shown in Fig. 6. Thus, the core emittances are well
preserved. We note that vertically streaked bunches in
the bunch compressor chicane may change the impact of m) 18 Eσ
CSReffectsbutrequirea3-dimensional“point-to-point” µ (
tracking which is not available neither in elegant nor in ε(N 0.8 16 keV)
CSRtrack [37], and is beyond the scope of this paper.
Horizontalemittance
Verticalemittance 14
0.6 Coreenergyspread
IV. MICROBUNCHING GAIN SUPPRESSION
5 5.1 5.2 5.3 5.4 5.5
V2(MV)
The principle of the microbunching gain suppression (a)Projectedemittancesandcoreenergyspread.
with the reversible beam heater system is shown by an
analytical treatment following Ref. [9] and by using the
10
beam transport matrix in Eq. (14). Then we show the
feasibilityofthereversibleheatersystemtosuppressmi- Upstream of TDS1
8
crobunching instabilities by means of particle tracking Downstream of TDS1
simulations with initial density and energy modulations. V) Upstream of TDS2, scaled by 1/C
e 6
k Downstream of TDS2, scaled by 1/C
(
E
σ 4
A. Analytical calculations
2
Usingthevectornotation(y ,y(cid:48),z ,δ )forparticlesin
0 0 0 0
thefirstlinacupstreamofthefirstTDS,thelongitudinal 0
−1.5 −1 −0.5 0 0.5 1 1.5
position downstream of the second TDS is given by
z/σ
z
z =K R y +(1+hR )z +R δ . (18) (b)Sliceenergyspread.
1 56 0 56 0 56 0
Supposethatδ0 =δu+δm,whereδuistheuncorrelated FIG. 5: Simulation on the impact of the reversible beam
relative energy deviation, and δ (z ) is the relative en- heater system on projected emittances, core energy spread,
m 0
ergymodulationaccumulatedbeforeandinthefirstlinac and slice energy spread: (a) Projected emittances (normal-
(Linac1). Following Ref. [9], the initial energy modula- ized) and core energy spread, and (b) slice energy spread for
tion at the wavenumber k is converted into additional V2 at minimum emittance (see Fig. 5(a)). CSR effects are
0
includedbymeansofthe1-dimensionalmodelinelegant[35].
density modulation at a compressed wavenumber k. For
7
0.7
750
Horizontal: UpstreamofTDS1
Horizontal: DownstreamofTDS2
500
Vertical: UpstreamofTDS1
)
) 0.65 Vertical: DownstreamofTDS2 V
m e
k
µ ( 250
( E
εN ∆
0
0.6
250
−1.5 −1 −0.5 0 0.5 1 1.5 − 0.4 0.2 0 0.2 0.4
− −
z/σ z/c(ps)
z
(a)DownstreamofTDS2: Heatersystemoff.
FIG.6: Simulationofthenormalizedsliceemittanceforboth
the vertical and horizontal upstream of the first and down- 750
stream of the second TDS. CSR effects are included.
500
bution. For both Gaussian profiles (U and V), we have V)
e
k
b(k)=b (k ) ikR δ (k )exp(cid:2) (k2R2 K2σ2 /2)(cid:3) E( 250
0 0 − 56 m 0 − 56 1 y1 ∆
exp(cid:2) (k2R2 σ2 /2)(cid:3) . (21)
× − 56 δu 0
Here, we denote the Fourier transform of δ (z ) as
m 0
δ (k ), which is the accumulated energy modulation at
m 0 250
the wavenumber k in the first linac due to longitudinal − 0.4 0.2 0 0.2 0.4
0 − −
z/c(ps)
space charge and other collective effects. The initial en-
ergy spread is given by σ , and σ is the vertical beam (b)DownstreamofTDS2: Heatersystemon.
δu y1
sizeinthefirstTDS.WeseethatK σ actslikeeffective
1 y1
energy spread for microbunching gain suppression. FIG.7: Simulationonsuppressionofmicrobunchinginstabili-
tiesduetoaninitialdensitymodulation,i.e.,simulatingCSR-
driven microbunching. The entire longitudinal phase space,
after removing the correlated energy chirp, is shown.
B. Numerical simulations
Suppression of microbunching instabilities is demon-
strated by using both a pure initial density modulation
is that the microbunches at the compressed wavelength
with 5% peak amplitude and 100µm modulation wave-
aresmearedduetoR K σ (cf. Eq.(21)),andaccord-
length (λ ), and a pure initial energy modulation with 56 1 y1
m ingly,themodulationsappearascorrelationsinthephase
3keV peak amplitude and λ = 50µm. Whereas the
m spaces (y,z) and (y(cid:48),δ). The same effect of microbunch-
case with initial energy modulation is immediately con-
ing suppression is given for initial energy modulations
sistent with the previous analytical treatment and de-
as shown in Fig. 8. The effect of the microbunching
scribesthelongitudinalspacechargedrivenmicrobunch-
instability appears even stronger compared to the sim-
ing instability [7], the initial density modulations need
ulations case with initial density modulations, but the
to be converted into energy modulations by longitu-
performance of the reversible heater system is the same
dinal CSR-impedance which expresses the consistency
with a smooth residual longitudinal phase space when
and describes the CSR-driven microbunching instabil-
thereversiblebeamheaterisswitchedon(seeFig.8(b)).
ity [6]. The simulations were performed using the code
elegant with 1 106 particles. Figure 7 shows the lon- Figures7and8areobtainedforamagneticbunchcom-
×
gitudinal phase space downstream of the second TDS, pressor system as shown in Fig. 1. The electron bunch
after removing the correlated energy chirp (linear and will be further accelerated and transported throughout
quadraticchirp),forboththereversiblebeamheatersys- therestoftheacceleratortoreachthefinalbeamenergy
tem switched off (Fig. 7(a)) and on (Fig. 7(b)). In the and peak current in order to drive an X-ray FEL (not
case without reversible beam heater, energy and density studiedinthispaper). Amicrobunchedelectronbeamas
modulations at the compressed modulation wavelength illustratedinFigs.7(a)and8(a),i.e.,whenthereversible
λ /C appear, i.e., CSR-driven microbunching becomes beamheatersystemisswitchedoff,willaccumulateaddi-
m
visible. When switching the reversible beam heater on, tionalenergyanddensitymodulations,whichwouldlead
the microbunching instability disappears and the result- to unacceptable longitudinal phase space properties for
inglongitudinalphasespaceremainssmooth. Thereason an X-ray FEL such as a large slice energy spread.
8
from jitter of the individual peak deflection voltages V
200 1
and V of the TDSs, and lead to growth of the projected
2
vertical emittance as is shown in Fig. 5(a), where the
voltage of the second TDS is varied. Even in the case of
)
V a large TDS voltage jitter of 1%, the vertical projected
e
k 0 emittance growth is less than 2% (see Fig. 5(a)). In the
(
E case of acceleration between the first and second TDS,
∆
also energy jitter, which is similar or smaller than TDS
voltage jitter, due to this intermediate acceleration leads
to deviation of the condition in Eq. (15). The choice
200
− of superconducting accelerator technology even provide
0.3 0.2 0.1 0 0.1 0.2 0.3 much better rf stability [38, 39]. Pure arrival time jit-
− − −
z/c(ps) ter upstream of the first TDS has no impact as long as
(a)DownstreamofTDS2: Heatersystemoff. the condition in Eq. (15), which describes the coupling
between y(cid:48) and t = z/c, is fulfilled. In the case that
Eq. (15) is not exactly fulfilled, e.g., due to TDS volt-
200
age jitter which is on the percent-level, the impact of
typical arrival time jitter well below 100fs, like at the
LCLS [3] or FLASH [39], is negligible. The most criti-
)
V caljittersourcesarisefromenergyjitterupstreamofthe
e
k 0 bunchcompressorchicaneandfromrfphasejitterinthe
(
E TDSs. The momentum compaction factor translates en-
∆
ergy jitter into arrival time jitter, which leads to vertical
kicks in the second TDS. The same effect of additional
verticalkicksisgeneratedbyrfphasejitterintheTDSs.
200
− In order to have small impact of vertical kicks on the re-
0.3 0.2 0.1 0 0.1 0.2 0.3 mainingbeamtransport,wedemand∆σy(cid:48) σy(cid:48) directly
− − − (cid:28)
z/c(ps) downstreamofthesecondTDSwiththeinducedvertical
(b)DownstreamofTDS2: Heatersystemon. r.m.s. kick ∆σy(cid:48) and the intrinsic beam divergence σy(cid:48).
The relevant total vertical r.m.s. kick is given by
FIG. 8: Simulation on suppression of microbunching insta- (cid:115)
bilities due to an initial energy modulation, i.e., simulating (cid:16) σE(cid:17)2 (cid:16) c (cid:17)2 (cid:18)K1 c (cid:19)2
longitudinalspacechargedrivenmicrobunching. Forthesake ∆σy(cid:48) = K2R56 E + K2ωσϕ2 + R ωσϕ1
33
of clarity, only the core of the longitudinal phase space, after
(cid:115)
removing the correlated energy chirp, is shown. (cid:16) σ (cid:17)2 (cid:16) c(cid:17)2(cid:18) 1 (cid:19)
= K R E + K σ2 + σ2
2 56 E 2ω ϕ2 C2 ϕ1
(cid:114)
V. PRACTICAL CONSIDERATIONS (cid:16)K R σE(cid:17)2+(cid:16)K c(cid:17)2σ2 (22)
≈ 2 56 E 2ω ϕ2
The previous sections covered the principle of re-
withtheenergyjitterσ /E upstreamofthebunchcom-
E
versible electron beam heating and microbunching gain
pressor, the rf phase jitter σ of the TDSs, the magni-
suppression by means of analytical calculations and nu- ϕ1,2
fication factor R from the first to the second TDS (see
33
merical simulations. In real accelerators, we also have
Eq.(13)),andusingEq.(15)withthecompressionfactor
to deal with imperfections, jitter and drifts of various C = (1+hR )−1. We see that the vertical r.m.s. kick
56
parameters, and accordingly supplementary studies with due to rf phase jitter in the first TDS scales with C−2
respecttosensitivityonjittersourcesandtoleranceshave
andcanbeneglectedcomparedtotheverticalr.m.s.kick
to be performed. In the following, we discuss the impact
induced by the second TDS when we assume the same
of beam and rf jitter on the reversible beam heater sys-
amount of rf phase jitter in both TDSs. The condition
tem, and also point out the inherent possibility of longi- (cid:112)
tudinal phase space diagnostics and on-line monitoring. for trajectory stability ∆σy(cid:48) (cid:28)σy2(cid:48) = (cid:15)y2/βy2 with the
intrinsic(uncorrelated)r.m.s.beamdivergenceσy(cid:48) down-
2
stream of the bunch compressor at TDS2, where (cid:15) is
y2
the geometrical emittance, can be restated as
A. Jitter and tolerances
(cid:114)
(cid:16)R σE(cid:17)2+(cid:16)cσ (cid:17)2 (cid:15)y2 = √(cid:15)y2(cid:15)y1 .
The impact of beam and rf jitter on the reversible 56 E ω ϕ2 (cid:28) K2(cid:112)βy2(cid:15)y2 C∆σδ1
beam heater method can effectively be discussed using (23)
the Eqs. (2) and (14) with the condition in Eq. (15). Here, ∆σ is the additional relative energy spread in-
δ1
Deviations from the conditions in Eq. (15) can appear ducedbythefirstTDSforsuppressionofmicrobunching
9
instabilities, and (cid:15) denotes the geometrical emittance evenfullynoninvasivemeasurementsutilizingincoherent
y1
upstream of the bunch compressor at TDS1. synchrotron radiation, emitted in the bunch compressor
Fortheexampleparametersdiscussedthroughoutthis bendingmagnets,arepossible(see,e.g.,Ref.[41]). When
paper (see also Table I), i.e., C = 13, γ(cid:15) = 0.6µm, usingafastgatedcamera,theimplicationwillbethepos-
y1
γ(cid:15) = 0.72µm (see Fig. 5(a)), and ∆σ E 10keV sibilityofon-linemonitoringthelongitudinalphasespace
y2 δ1 ≈
with E = 350MeV (γ = 685), the stability condition of individual bunches in multi-bunch accelerators.
in Eq. (23) yields pure relative energy jitter (neglecting
rf phase jitter) of σ /E 1.9 10−5 or pure rf phase
E
jitter (neglecting energy ji(cid:28)tter) of· σ 0.012◦. A com-
ϕ2 (cid:28) VI. SUMMARY AND CONCLUSIONS
bination of both will obviously tighten the acceptable
jitter. This level of rf stability is difficult to achieve in
Our studies show that the reversible beam heater sys-
normal conducting linacs with single bunch operation,
tem proposed here can suppress microbunching insta-
but might be achieved with superconducting accelerator
bilities and preserve the high beam brightness at the
technologylikeatFLASHorasplannedforNGLS,where
same time. Due to CSR effects, some vertical emittance
manybunchescanbeacceleratedinalongrfpulse,i.e.,in
degradation in the head and tail region of the bunch
abunchtrain. Currently,severalrffeedforwardandfeed-
occurs, but the core emittances are well preserved. In
backcontrolsareabletostabilizethebunchesatFLASH
thenumericaldemonstrationsusingthecodeelegant,the
toσ /E =3.010−5andσ =0.007◦at150MeV[38,40],
andEfurtherim·provementsϕtowardsσ /E 1.0 10−5 are first TDS generates about 10keV (r.m.s.) slice energy
E ≤ · spread, which is similar to the laser heater but with a
planned using a fast normal conducting cavity upstream
more Gaussian energy distribution (cf. laser heater).
ofthebunchcompressors[38,39]. Withperfectscalingof
The bunch compression process increases the slice en-
rf jitter from several independent rf power stations that
ergy spread to 130keV (r.m.s.), which is then reversed
adds uncorrelated, we would expect an improvement of ∼
(cid:112) to 17keV (r.m.s.) after the second TDS in the pres-
150MeV/350MeV 0.66 compared to the results at ∼
≈ ence of CSR effects. Without CSR effects, the slice
FLASH with 150MeV and assuming the beam energy of
energy spread is reversed to 13keV (r.m.s.), which
350MeV in the bunch compressor of the NGLS design. ∼
demonstrates perfect cancelation. The simulations also
Continuous-wave rf operation, as planned for the NGLS
show that initial bunching in energy and density in the
design [26], and a proper choice of rf working points for
beam can be smeared out during the process in the re-
FEL operation might improve the stability further.
versiblebeamheatersystem,i.e.,microbunchinginstabil-
ities can be suppressed. The resulting smooth beam can
then propagate through the remaining accelerator with-
B. Integrated longitudinal phase space diagnostics
out further generation of much additional energy spread
and is advantageous for any kind of laser seeding ma-
A practical spin-off of the reversible beam heater sys-
nipulations and experiments. For example, this scheme
tem is the availability of longitudinal phase space diag-
significantly loosen the required laser power for short-
nostics. Theverticalbetatronmotionofelectronspassing
wavelength HHG seeding [10] and may strongly impact
through a TDS is described by Eq. (4), which enables a
the design of future seeded FELs. In addition, the re-
mapping from time (longitudinal coordinate) to the ver-
versible beam heater system exhibits integrated options
tical [14–16], and finally a possibility to obtain temporal
for diagnosis and on-line monitoring of the longitudinal
bunchinformationbymeansoftransversebeamdiagnos-
phase space applicable for multi-bunch machines, which
tics. In a similar manner, the relative energy deviation
is also the preferred type of accelerator for the reversible
is mapped to the horizontal in the presence of horizontal
heater system due to large sensitivities on energy and rf
momentumdispersion,likeinamagneticbunchcompres-
jitter. Linear accelerators based on superconducting rf
sorchicane(see,e.g.,Refs.[15,16]). Thecombinedoper-
technology might be able to match the strict tolerances
ationmakessingle-shotmeasurementsofthelongitudinal
inordertokeepverticalkickssmallandtoachieveasuf-
phasespacepossible,andinthecaseofthegenericlayout
ficienttrajectorystabilityinthedownstreamundulators.
of a reversible electron beam heater system as depicted
inFig.1,longitudinalphasespacemeasurementsbecome
feasible using the first TDS and observation screens in
Acknowledgments
the dispersive section of the bunch compressor chicane.
In order to get information of the bunch length after the
bunch compression, the second TDS can be used with WewouldliketothankP.Emma,Ch.Gerth,A.Lump-
downstream observation screens (not shown in Fig. 1). kin, H. Schlarb, and J. Thangaraj for useful discussions
In addition to invasive longitudinal phase space mea- and suggestions. This work was supported by Depart-
surements of a single bunch using observation screens, ment of Energy Contract No. DE-AC02-76SF00515.
10
[1] S. Jamison, Nature Photonics 4, 589 - 591 (2010). [23] D.XiangandA.Chao,Phys.Rev.STAccel.Beams14,
[2] W. Ackermann et al., Nature Photonics 1, 336 - 342 114001 (2011).
(2007). [24] D. Xiang et al., Phys. Rev. Lett. 105, 114801 (2010).
[3] P. Emma et al., Nature Photonics 4, 641 - 647 (2010). [25] D. Xiang et al., Phys. Rev. Lett. 108, 024802 (2012).
[4] D. Pile, Nature Photonics 5, 456 - 457 (2011). [26] J. Corlett et al., Proceedings of the 24th Particle Accel-
[5] E.L.Saldin,E.A.Schneidmiller,andM.V.Yurkov,Nucl. erator Conference, New York, USA, 2011, TUOCS5.
Instrum. Methods Phys. Res., Sect. A 398, 373 (1997). [27] M. Venturini and A. Zholents, Nucl. Instrum. Methods
[6] M. Borland et al., Nucl. Instrum. Methods Phys. Res., Phys. Res., Sect. A 593, 53 (2008).
Sect. A 483, 268 (2002). [28] H. Edwards, C. Behrens, and E. Harms, Proceedings
[7] E.L.Saldin,E.A.Schneidmiller,andM.V.Yurkov,Nucl. ofthe25thInternationalLinearAcceleratorConference,
Instrum. Methods Phys. Res., Sect. A 528, 355 (2004). Tsukuba, Japan, 2010, MO304.
[8] Z.Huang,M.Borland,P.Emma,J.Wu,C.Limborg,G. [29] W.PanofskyandW.Wenzel,Rev.Sci.Instrum.27,967
Stupakov,andJ.Welch,Phys.Rev.STAccel.Beams7, (1956).
074401 (2004). [30] M.J.Browman,Proceedingsofthe15thParticleAcceler-
[9] Z.Huanget al.,Phys.Rev.STAccel.Beams13,020703 ator Conference, Washington, D.C., USA, 1993, p. 800.
(2010). [31] S. Korepanov, M. Krasilnikov, F. Stephan, D. Alesini,
[10] D.J.Dunninget al.,Proceedingsofthe1stInternational and L. Ficcadenti, Proceedings of the 8th European
Particle Accelerator Conference, Kyoto, Japan, 2010, WorkshoponBeamDiagnosticsandInstrumentationfor
TUPE049. Particle Accelerators, Venice, Italy, 2007, TUPB32.
[11] M. Cornacchia, S. Di Mitri, G. Penco, and A. Zholents, [32] C.BehrensandCh.Gerth,Proceedingsofthe9thEuro-
Phys. Rev. ST Accel. Beams 9, 120701 (2006). pean Workshop on Beam Diagnostics and Instrumenta-
[12] Y.Ding,P.Emma,Z.Huang,andV.Kumar,Phys.Rev. tion for Particle Accelerators, Basel, Switzerland, 2009,
ST Accel. Beams 9, 070702 (2006). TUPB44.
[13] O. Altenmueller, R. Larsen, and G. Loew, Rev. Sci. In- [33] C.BehrensandCh.Gerth,Proceedingsofthe10thEuro-
strum. 35, 438 (1964). pean Workshop on Beam Diagnostics and Instrumenta-
[14] P.Emma,J.Frisch,andP.Krejcik,TechnicalReportNo. tionforParticleAccelerators,Hamburg,Germany,2011,
LCLS-TN-00-12, 2000. TUPD31.
[15] M. Ro¨hrs, Ch. Gerth, H. Schlarb, B. Schmidt, and [34] P. Emma (private communication).
P. Schmu¨ser, Phys. Rev. ST Accel. Beams 12, 050704 [35] M. Borland, ANL/APS Report No. LS-287, 2000.
(2009). [36] M.Venturiniet al.,Proceedingsofthe24thParticleAc-
[16] D. Filippetto et al., Phys. Rev. ST Accel. Beams 14, celerator Conference, New York, USA, 2011, THP180.
092804 (2011). [37] M.DohlusandT.Limberg,Proceedingsofthe26thInter-
[17] Y. Ding, C. Behrens, P. Emma, J. Frisch, Z. Huang, H. national Free Electron Laser Conference, Trieste, Italy,
Loos, P. Krejcik, and M-H. Wang, Phys. Rev. ST Accel. 2004, MOCOS05.
Beams 14, 120701 (2011). [38] H. Schlarb (private communication).
[18] A. Zholents, P. Heimann, M. Zolotorev, and J. Byrd, [39] C. Schmidt et al., Proceedings of the 33rd International
Nucl. Instrum. Methods Phys. Res., Sect. A 425, 385 Free Electron Laser Conference, Shanghai, China, 2011,
(1999). THPA26.
[19] M. Cornacchia and P. Emma, Phys. Rev. ST Accel. [40] S. Pfeiffer et al., LLRF-2011 workshop, Hamburg, Ger-
Beams 5, 084001 (2002). many, 2011, “Feedback Strategies for longitudinal Beam
[20] P.Emma,Z.Huang,K.-J.Kim,andP.Piot,Phys.Rev. Stabilization”.
ST Accel. Beams 9, 100702 (2006). [41] Ch. Gerth, Proceedings of the 8th European Workshop
[21] D. Xiang and Y. Ding, Phys. Rev. ST Accel. Beams 13, on Beam Diagnostics and Instrumentation for Particle
094001 (2010). Accelerators, Venice, Italy, 2007, TUPC03.
[22] P. Piot, Y.-E Sun, J.G. Power, and M. Rihaoui1, Phys.
Rev. ST Accel. Beams 14, 022801 (2011).