The MAMI C accelerator

Eur. Phys. J. Special Topics 198, 19–47 (2011)c© EDP Sciences, Springer-Verlag 2011DOI: 10.1140/epjst/e2011-01481-4

THE EUROPEANPHYSICAL JOURNALSPECIAL TOPICS

Review

The MAMI C accelerator

The beauty of normal conducting multi-turn recirculators

M. Dehn1,a, K. Aulenbacher1, R. Heine1, H.-J. Kreidel1, U. Ludwig-Mertin1,and A. Jankowiak2

1 Johannes Gutenberg-Universitat, Institut fur Kernphysik, Johann-Joachim-Becher-Weg45, 55099 Mainz, Germany

2 Helmholtz-Zentrum Berlin fur Materialien und Energie GmbH, ElektronenspeicherringBESSY II, Albert-Einstein-Str. 15, 12489 Berlin, Germany

Received 08 July 2011 / Received in final form 21 July 2011

Published online 23 September 2011

Abstract. The demand for CW electron beam energies of more than1GeV led to the decision of constructing a worldwide unique acceler-ator – the Harmonic Double-Sided Microtron (HDSM). This machinenearly doubles the beam energy of the Mainz Microtron cascade fromup to 855MeV to now 1.6GeV to extend the experimental capabilitiesfor nuclear and particle physics experiments to higher excitation ener-gies. For the recent decade the construction and commissioning of theHDSM at the Institut fur Kernphysik has been the major task of theaccelerator department.

1 Historical overview

Since the first microtron accelerator producing 4.6MeV electrons according to anidea of V.I. Veksler [1,2] had been constructed in 1947 at the National ResearchCouncil of Canada [3], several endeavours have been made to extend this principleof electron acceleration for gaining higher energies. The first step was the race trackmicrotron (RTM), suggested in 1945 by J.S. Schwinger and first proposed in [4] and[5]. The first RTM was also constructed and operated in Canada at the Universityof Western Ontario in 1961, delivering 4–12MeV [6]. One big problem in an RTM,the vertical defocusing of the fringe field at the dipole edges, was solved in 1967 byH. Babic and M. Sedlacek [7] by introducing a thin field region with reverse polarityin front of the two dipole magnets. This stimulated many proposals for RTMs oper-ating in the energy range 5–200 MeV at various sites. However, in most of the casesthe concept was discarded in favour of other solutions. In the beginning of the 1970’sat the University of Illinois the first RTM using a superconducting linac with 19MeVoutput energy was constructed [8]. With an improved design some years later up to67MeV were reached and the accelerator was operated for several years for nuclearphysics experiments [9].

a e-mail: [email protected]

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http://dx.doi.org/10.1140/epjst/e2011-01481-4

20 The European Physical Journal Special Topics

At that time the Institute of Nuclear Physics of the University of Mainz (IKPH)operated a pulsed linac for electrons with a maximum of 300MeV (later 400MeV)output energy and a duty cycle of 1:5000 [10]. This machine consisted of eight 4m longacceleration sections fed by eight 17.5MW pulsed klystrons and had been purchased asa turn-key-system from CSF/France and the German company Gutehoffnungshutte(GHH). Though the accelerator was operated successfully, it turned out that oneneeds experienced accelerator physicists to make optimal use of such an investment.Realising this, H. Herminghaus formed a group of accelerator physicists who wereable to achieve significant improvements in the performance and the operating of thislinac [11,12]. It further turned out that it is very important to have excellent me-chanical and electrical workshops to develop and construct necessary modifications.As since 1975 a strong demand raised to construct CW electron accelerators to

perform coincidence experiments in nuclear physics [13], many ideas for new acceler-ators were discussed at the IKPH. Superconducting linacs were not reputed reliableenough at that time and linac/stretcher ring combinations were limited in CW cur-rent. In 1976 Herminghaus et al. published a proposal for a normal conducting 3-stageRTM-cascade delivering an electron beam of more than 800MeV at 100μA current[14]. Advantages of such a solution are the very good beam emittance, the excellentenergy definition and the modular approach by constructing, learning and testingstage by stage. However, there were some challenges: The high power rf system hasto be robust and stable and the two dipole magnets of the last stage turn out tobe really large and heavy. Correction dipoles (steerers) are foreseen at the returnpaths to compensate for slight deflection errors. To keep the requirements for thesesteerers within reasonable limits and to provide a proper longitudinal motion with-out phase jumps, the dipoles must be homogeneous to 10−4 over the whole pole facearea that is covered by the recirculated beam orbits, which amounts to several squaremetres in the third stage. The klystrons drive CW standing wave rf linac sectionswith about 30 kW power each. To ensure the use of conventional production com-ponents like ready-made industrial heating klystrons, the standard microwave ovenS-band frequency of 2.45GHz was chosen. In 1979 the first microtron stage, deliv-ering 14MeV, was set into operation. The second stage was commissioned in 1983delivering 180MeV [15]. As injector a van de Graaff accelerator was used, which wasthe reason for several problems concerning reliability and beam stability. Neverthe-less this construction very successfully delivered beam of up to 65μA for nuclearphysics experiments from 1983 to 1987 [16]. This stage of construction was called“MAMI A”.MAMI A provided convincing evidence that a third RTM-stage would open up

a new era of photo-nuclear experiments [17]. This perspective enabled the funding ofthe third stage and for new buildings to house the accelerator cascade. In 1982 theconstruction of the third stage and of a 3.5MeV CW injector linac as a replacementfor the van de Graaff together with the development of a 100 keV polarised electronsource started [18,19]. The third stage was successfully set into operation in 1990[20]. All design values were reached or surpassed. The standard energy was chosen tobe 855MeV which allows accelerating 100μA of beam current, limited only by theavailable rf power. An increase of the energy to 883MeV could be easily achieved,which was important for several near threshold experiments [21]. This microtron cas-cade (“MAMI B”, orange marked area in Fig. 1) turned out to be an extraordinarilyreliable accelerator running for more than 6000 hours per year for experiments in nu-clear physics [22]. Still today, roughly half of the experiments are carried out in theenergy range achievable with the first three microtron stages, and the third stage ofMAMI is still the world’s largest RTM. Recently an output energy of 909MeV wasachieved within the scope of the energy upgrade project for MAMI C (→ section 4.2)[23].

Many-Body Structure of Strongly Interacting Systems 21

Fig. 1. Floor plan of the institute.

Using parts of the MAMI-design some institutes proposed and constructedRTMs, in some cases as injector for their accelerators, e.g. NBS-Los Alamos [24,25];Moscow State University [26]; University of Sao Paulo [27]; MAX-lab, Lund [28,29];Scanditronix AB, Uppsala [30].

1.1 Achieving higher energies

The RTM-type accelerators proved to be suitable for output energies of up to 1GeV.When trying to design RTMs for even higher energies two fundamental problems arise.The first one is that the homogeneous magnetic dipole field must be established overan area of several square metres which is only reasonably achievable by using largeiron yokes. Due to the saturation of ferromagnetic materials this limits the magneticfield to about 1.5T which is almost reached in the third MAMI stage (1.29T). Toscale an RTM to higher energies therefore means to enlarge the linear dimensions ofits magnets by almost the same scale, yielding a dependence of the magnet volume orweight with the 3rd power of output energy. Doubling the energy of the third MAMIRTM would therefore result in an unrealistic huge weight of more than 3000 t perdipole. The second problem arises from the relative small energy gain per turn: Thebeam has to recirculate many times through the machine. In each turn it loses energystochastically due to synchrotron radiation which may lead to emittance growth inthe longitudinal and also in the horizontal plane. As the energy loss per turn growswith the 3rd power of the beam energy, it can be shown that energies significantlyabove 1GeV are actually not reachable. A possible solution may be to acceleratein a way that the path-length growth is a multiple instead of one rf wavelength, ase.g. done at the NBS microtron (n = 2) [24], but this leads to smaller longitudinal


Fig. 2. Scheme of RTM, DSM and Hexatron (from left to right).

acceptance and enforces the use of a superconducting linac to achieve the necessaryenergy gain.Some design studies with the intention to modify the RTM-principle in a way to

solve these problems lead to the so-called polytrons [31]. Instead of using only twodeflection dipoles, four, six or more dipoles can be used (Fig. 2). This reduces thepath-lengths in the dipoles where the synchrotron radiation is emitted and allows moreflexible shaping of the transversal beam properties. Furthermore their required sizecan be reduced significantly. A design with 6 dipoles, called Hexatron, was proposedby T.K. Khoe [32,33] in 1982, which was a competition project to the SoutheasternUniversities Research Association (SURA) design (pulse stretcher ring) for a 4GeVelectron accelerator. Both concepts were discarded in favour of a recirculating super-conducting linac (CEBAF). Polytrons have been suggested for output energies up to15GeV [31].In 1979 K.H. Kaiser, another member of IKPH’s accelerator team, published a pro-

posal for a polytron with 4 deflection dipoles [34], a Double Sided Microtron (DSM,also called bicyclotron), and 1999, together with S. Ratschow, he published a de-tailed design to nearly double the output energy of the existing microtron cascade byadding a DSM as fourth stage [35,36]. In 1999 the CRC443 (“Many Body Structureof Strongly Interacting Systems”) was established. In its framework the constructionof the proposed accelerator stage with an output energy of 1.5GeV at 100μA electronbeam current to perform nuclear physics experiments at higher energies was recom-mended. The constraints imposed by funding limitations and other restrictions wererather severe: It had to fit into existing buildings of the institute, it should preservethe excellent beam quality, it should be a very reliable machine and the constructionwork should only minimally disturb the ongoing physics program. Therefore the de-sign relied on the institute’s expertise of 25 years experience in normal conductingrf systems and linacs and the accelerator stage was designed in a way to fit into twojoined experimental halls. To achieve enough energy gain per turn with reasonablerf power, the rf frequency of the DSM was doubled to 4.9GHz, thus working on thefirst harmonic of the input beam bunch repetition rate (→ section 2.1).The main design challenge for the DSM was the compensation of the vertically

strongly defocusing 45◦ dipole entries and exits. For that, the dipole fields are shapedwith a special nonlinear field gradient, which in consequence causes the synchronousrf phase to move to more negative values during the acceleration. On the first glancethis seems to be harmless, because the longitudinal stable region of a DSM is muchlarger than of an RTM; but it turns out that there may be an instable region inbetween (for further details read section 2.3). However, K.H. Kaiser found that thisproblem can be avoided if only one of both linacs is driven at the first harmonicbut the other at the fundamental frequency. This scheme was then named HarmonicDouble Sided Microtron (HDSM) [37]. The HDSM at MAMI has been successfullyset into operation in December 2006. Since February 2007 it delivers beam for nuclearphysics experiments [22] (Fig. 3).


Fig. 3. A sketch of the HDSM of the MAMI accelerator facility.

2 The fundamental principles of Microtron-Like Accelerators

2.1 Longitudinal optic

The first fundamental equations when constructing an RTM are the static and thedynamic coherence conditions, which demand that the revolution time in the firstorbit and also its increment for each turn is an integer number of rf periods. Whilethe first can be met merely by choosing adequate distances, the latter defines afixed relation between a few fundamental parameters of the microtron. This dynamiccoherence condition is a result of geometric considerations and reads as

Δs = 2πΔTRTMeβcB

= nλ, (1)

which means that the increase of path length Δs in each turn, given by the energygain per turn ΔTRTM and the magnetic field B in the dipoles, must be a multiple ofthe rf wavelength λ. For relativistic particles at β ≈ 1 a fixed ratio between energygain and field is obtained. For a DSM, resp. a Hexatron, this equation becomes forone unit cell of the lattice (DSM: 1/2 turn, Hexatron:

1/3 turn)

nλ = (π − 2)ΔTDSMeβcB

(2)

nλ = 2[π3− sin

(π3

)] ΔTHEXeβcB

. (3)

Solving these equations to ΔT yields the energy gain per turn which must be providedby the linacs. Comparing DSM and RTM we get

ΔTDSMΔTRTM

=2π

π − 2 ≈ 5.5. (4)

This emphasises: assuming the same magnetic field and the same rf wavelength aDSM must obtain more than 5 times higher energy gain per turn than an RTM. Eventhough a DSM has two linacs, each of them must provide slightly more than twice ofthe gain of an equivalent RTM. Since the technically and economically reasonable rf


power level per unit length is set by the parameters of the RTM, this calls either fordoubling the length of the linacs or for reducing the rf wavelength to one half of itsvalue in the RTM.Further conditions concern the longitudinal beam focusing. To obtain phase

focusing the synchronous phase ϕS of the electron bunches must be on the risingslope of the rf wave, thus ϕS must be negative. For a periodic accelerator it can beeasily shown that a stable acceleration of bunches is only possible if the absolute valueof the trace of the one-turn transfer matrix M is smaller than 2:

|Tr(M)| < 2. (5)

For an RTM this stability criterion yields:

|1 + nπ tan(ϕS)| < 1 (6)

which defines the interval of the stable longitudinal region to

− arctan(2

nπ

)< ϕS < 0 (7)

yielding approx. [−32.5◦, 0◦] if n = 1 is chosen. Obviously the stable region shrinksdramatically, if the change of path length per turn n (in units of wavelengths) is setto 2 (or any higher integer number) to enable an increased energy gain per turn. Ina DSM the stability criterion modifies to

∣∣∣1 + nπ2tan(ϕS)

∣∣∣ < 1 (8)

resulting in a significantly larger stability region [−51.8◦, 0◦]. Unfortunately, the exactsymmetry between the two linacs in a DSM is not possible in reality, e.g. a finite phaseerror between the linacs will always remain. This causes a half integer resonance, or’stop band’, to become effective at ϕS = −32.48◦ (see Fig. 6). In the DSM, this regionwould indeed be passed due to the phase migration caused by the inhomogeneous mag-netic fields. To counteract this potential showstopper, a unique longitudinal focusingscheme was invented by K.H. Kaiser, which returns to the fundamental frequency (ofthe RTM) in one of the linacs.

2.2 Transversal optic

The transversal focusing in microtrons is typically achieved by quadrupole-doubletson the acceleration line(s). Due to the increasing energy their focal strengths de-crease with the turn number in a quadratic manner, which in turn leads to a growingbeta-function. Fortunately the shrinking geometric emittance due to pseudo-dampingcounterbalances this, so that the amplitude of a betatron oscillation remains nearlyconstant over all turns. Nevertheless, the transversal focusing should stay well insidethe stable region for all turns and detailed acceptance considerations show that theratio of output to input energy cannot be arbitrarily high. For an RTM it can beroughly estimated by “Herminghaus’ rule”:

Tout

Tin≤ 10. (9)

For this reason a microtron accelerator must be split into several stages for achievingmore energy gain.


-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

60% Bmax

B =1.539Tmax

B[T

]y

z [m]

pole edge

defo

cusin

g

focu

sing

Fig. 4. Magnetic field value against penetration depth in an HDSM dipole.

An additional challenge in higher order polytrons is the stronger vertical defo-cusing of the beam by the dipole entries and exits through rotated pole faces. Tocompensate for this there have been several concepts in the past, summarised in [38].These include reverse field stripes, pole face modifications and quadrupoles on theenergy dispersive beam pipes (“harps”). The latter has been investigated in moredetail by Ratschow [36], who found, that the possible coupling of longitudinal andhorizontal phase space would not only badly complicate the optics but also reduce thephase space acceptance. Furthermore, it would be a technical challenge, because theretypically will not be enough separation distance between the harp-pipes to installadequate focusing magnets. The investigations concerning the DSM for MAMI (sepa-ration distance approx. 42mm) resulted in very tough requirements for the mechanicaland electrical manufacturing tolerances of the quadrupoles to avoid sextupole errorswhich would induce serious phase-space distortions. Therefore this focusing schemewas discarded. Another solution could be a sawtooth-like dipole pole face [31], butdue to the expected problems with fringe field effects of such a scheme, this never hasbeen investigated in-depth.For the DSM at MAMI a different method to compensate for the vertical defo-

cusing was chosen by introducing special-shaped nonlinear field gradients into theoriginally homogeneous dipole fields [37]. Though this turned out as an ideal solutionin transverse optics it has important consequences to the longitudinal beam dynam-ics, because of the phase migration induced in the higher turns where the beam ispropagating in a lower field. Since this phase shift jeopardises longitudinal stabilityby passing a half integer resonance, this led to the design with two rf frequencies,named HDSM.

2.3 The HDSM at MAMI

Due to the spatial constraints the design output energy of the HDSM, as fourth stageof the MAMI accelerator facility, was limited to 1.5GeV. This stage uses the wholearea of two connected former experimental halls in the building of the institute. Tohalve length of the linacs, the rf frequency is doubled from 2.45GHz to 4.9GHz. Bythis means the coherence condition can be fulfilled with only half of the energy gainper turn, but only every second rf bucket is filled with an electron bunch by the in-jected beam bunched with 2.45GHz. Within 43 turns the input energy of 0.855GeVis boosted to 1.5GeV.The principle of compensating the defocusing effects of the rotated dipole edges

in the HDSM is to establish a focusing field gradient inside the magnet. To achievethis, the magnetic field must decrease with the increasing penetration depth ofthe beam into the magnet (Fig. 4). The field profile was calculated by numerical


-20

-15

-10

-5

0

5

10

15

20

E [MeV]

horizontal

vertical

D, D

]m[

hv

800 1000 1200 1400 1600

Fig. 5. Horizontal and vertical drift-lengths of a deflecting 180◦ system of the HDSM.

-32.48°

S[°]-60 -50 -40 -30 -20 -10 0

Stopband

ytiliba

T)

long

itudi

nal

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Fig. 6. Trace of the longitudinal transfer matrix versus synchronous phase: green – RTM,black – ideal DSM, red – DSM with ±5◦ phase error.

integration using the tracking code PTRACE [39] with the boundary condition thatthe defocusing term in the dipole matrix cancels to zero for all electrons between0.855 and 1.5GeV, i.e. the matrix is a drift-matrix in this energy range. The field hasits highest value Bmax of 1.54T near the entrance edge of the dipole and decreases by39% for the full penetration depth of the last orbit. The absence of a gradient on linesparallel to the front pole edge, through which the beam enters and exits the dipole,leads to the fact, that the horizontal beam optic can also be regarded as a drift spacebut with negative length. The lengths of the energy dependent horizontal and verticaldrifts in a pair of magnets deflecting 180◦ are shown in Fig. 5. For symmetry reasonssuch a system is achromatic. By this construction the resulting transversal optics canbe kept almost as simple as in an RTM.However, the average magnetic field B acting on the beam is not constant any

more but is a function of the energy T . By reason of the field gradient it decreasesfrom one turn to the next. On the other hand the dynamic coherence condition(Eq. (2)) requires the energy gain per turn ΔT to follow in the same way. There-fore ΔT (T ) decreases with rising energy and involves a migration of the synchronousphase ϕS(T ) during the acceleration process towards more negative values. But thisis not discouraging taking into account the rather large longitudinal acceptance of


phase [°]-45 -40 -35 -30 -25 -20 -15 -10 -5 0 5

40 30

20

10

3 2 1possiblestopband

1/3 1/4 1/51/6

0.75

0.80

0.85

0.90

0.95

1.00

1.05

turn

S

Fig. 7. Migration of the synchronous phase on the rf wave.

a DSM. The trouble comes out, if one assumes symmetry disturbances in the longi-tudinal optics, e.g. phase errors between the two linacs. Then a region of instability(half-integer stop-band) opens around −32.48◦ which blows up the longitudinal phasespace. With a phase displacement of e.g. ±5◦ between the linacs in opposite direc-tions, the region of instability covers about 8◦ in the phase angle ϕS (compare Fig. 6).In Fig. 7 the migration of the synchronous phase on the rf wave during accelerationis shown for this case; obviously it enters the instable region at about turn number30. To prevent this, the arising of a too strong longitudinal focusing must be avoided;the strength is proportional to the slope of the rf wave.The charming idea to accomplish this, originated by realising that only in one of

both linacs all buckets are filled while in the other one only every second rf bucketis used. This opens the possibility to drive the latter linac with the fundamental of2.45GHz instead of 4.9GHz. When the synchronous phase now migrates on thesetwo rf waves, the change in focusing strength is considerably smaller than before, dueto the flatter slope of the fundamental. By this means many more recirculations arepossible before crossing the instability. Within the intended 43 turns the synchronousphase can be maintained in safe distance from the stop-band. A particle trackingsimulation shown in Fig. 8 demonstrates the severe deterioration of the longitudinalphase space in the 43-turn DSM and the quite stable phase space dimensions of theHDSM with an even larger displacement of the linac phases.

3 Construction and commissioning of the HDSM

3.1 Overview

The newly constructed HDSM uses the whole area of two former experimental halls(see Fig. 10) with one 180◦ bending system in each hall while both linacs, injectionand extraction extend through two new openings in the wall between the halls.The beam enters the hall through a beam transfer line (BTL) through the wall

close to HDSM dipole 3. The midplane level of the accelerators in all MAMI stagesis set to 1.8m which offers sufficient mechanical stability. Since the ground level inthe MAMI C halls is lower it is possible to inject the beam through a hole in the


Fig. 8. Particle tracking of the longitudinal phase-space with a phase displacement of 3◦

(DSM) resp. 5◦ (HDSM, relative to 4.9GHz) between the linacs. Red dots: after 43 turns.

Fig. 9. Photograph of the 180◦ bending system with HDSM dipole 3 and 4 in the back-ground. The injection beam line extends towards the lower left corner after it crossed theextraction beam line right in front of dipole 3. In the middle the matching section is installed.

upper part of the magnet yoke of HDSM dipole 3 (Fig. 9). The height difference isthen compensated by a parallel shift, which is foreseen in the injection as well as inthe extraction. To improve the longitudinal matching and to provide injection energytuning, two 4.9GHz accelerating structures have been installed into the injection line.The following BTL guides the beam towards the gap of HDSM dipole 1, where twosmall magnets in front and behind the HDSM dipole steer the beam to the firstdispersion beam line.The extraction beam line following the acceleration process resembles the injection

procedure in opposite direction: the beam is brought back to the original MAMI Bbeam transport system which has been upgraded for 1.5GeV operation in 2001 [40].


dipole 1

dipole 3

dipole 2

dipole 4

synchrotron lightmonitor

synchrotron lightmonitor

linac 1(4.90 Ghz) linac 2

(2.45 Ghz)

quadrupoledoublets

rf monitors

855 MeV1508 MeV

controls,electronics,

power-supplies

el.

5 m

Fig. 10. Scaled scheme of the HDSM (for a better visibility the accelerator sections aredisplayed in double width and in the recirculation system only every sixth path is shown).A magnified detail drawing of the corrector magnet system at the recirculation lines is shownat dipole 4.

3.2 RF system

The rf system of the HDSM is based on the very reliable biperiodic on-axis coupled2.45GHz structures [41] used for years at all microtrons of MAMI B. Small modifi-cations to improve stability of amplitude and phase have been applied. The 4.9GHzstructures however are a completely new in-house design, based on the scaled 2.45GHz


Fig. 11. The 2.45GHz and the 4.9GHz accelerating sections, equipped with vacuum win-dows, tuning plungers and diagnostic probes.

structures, but had to be optimised to a larger beam aperture (10mm instead 7mmscaled) and for relaxed mechanical tolerances [42]. Figure 11 shows both types ofindustrially manufactured sections. Each linac has to provide an accelerating voltageof up to 10MV at gradients of about 1MV/m. The 2.45GHz linac with its 5 sectionsand 5 klystrons (TH2174, 50 kW CW, Thales) resembles the one of RTM3 whereasthe 4.9GHz linac was constructed using 4 pairs of the shorter sections fed by oneklystron (TH2166, 50 kW CW, Thales) per pair. Another unit in the injection beamline is operated as matching section at lower gradients.Many high power components, like klystrons, phase shifters and alike, had to

be developed for the 4.9GHz frequency range. The linac, including all componentsfrom low level RF (LLRF, some W) to high power (≈ 40 kW), proved to operatevery reliably concerning phase and amplitude stability. Two independently workingLLRF feedback loops for each klystron acting on fast attenuators and phase shiftersstabilise the amplitudes to some 10−4 and the phase deviation between klystron andaccelerating section is limited to some 0.1◦.

3.3 Bending magnet systems

During the acceleration process in the HDSM the electron beam is mainly guidedby the four 90◦ bending magnets. Their relative magnetic field precision ΔB/B hasto be better than 10−4 while being operated at Bmax = 1.54T. Otherwise deflectionerrors of more than 1mrad as well as turn to turn phase jumps, caused by path lengthfluctuations in the order of a few tenths of a millimetre, would arise. However, therather large gap of the magnets, 85mm minimum to fit in the vacuum chamber andthe correction coils, reduces the strength of localised higher order magnetic multipolescausing chromatic aberrations.The ideal field profile introduced in sections 2.2 and 2.3 was emulated with the

magnet simulation tool TOSCA [43] to obtain the pole profile. Nevertheless, the finishof the pole surface at the manufacturer site requires piecewise flat profiles becauseof the milling process. Resulting small deviations were iteratively optimised usingTOSCA for the magnetic field and PTRACE for the beam dynamics to match theoriginal magnetic properties at best [44]. As the weight of the magnets together withtheir magnetic fields lead to strong forces acting on the yoke, the deflection under loadhad to be considered and was modelled using IDEAS [45]. Finally the French companySFARSteel produced the four magnets, each magnet consisting of two parts (Fig. 12).Water cooled coils were designed together with the magnet engineer SIGMAPHI.The specifications prohibited braze points within the coils and postulated a very


Fig. 12. HDSM dipole 4 during assembly.

small temperature rise to prevent long term temperature drifts during operation atapproximately 80 kW electrical power per magnet.In spite of the large dimensions of the magnets (7m×2.8m×4m, 260 t each) the

field maps1 of the assembled magnets deviated by less than 1.5mT from the designprofile, which would expectedly cause only slight changes to the beam dynamics.The reference profiles for both pairs of dipoles have been adjusted to the actuallymeasured gradients. For each magnet two individually powered pairs of symmetricsurface correction coils have been built from the field maps to correct for the remainingdeviations of less than 0.5mT in the central regions. Towards the corners of themagnet TOSCA predicted larger field deficiencies of up to 15mT which could becorrected using iron shims. Together with a small correction dipole magnet on eachend of the linac axes the remaining displacement and deflection errors would beglobally reduced to less than 1mrad. Section 4.2 and Fig. 16 through 19 present someresults of the magnetic field quality for different settings. For the first time at MAMIadditional steering coils (“in-gap steerers”, green areas within the dipole magnets inFig. 10) at the point of maximum penetration into the dipole were installed to eitherchange the path length of 5–6 adjacent turns (if used symmetrically within one 180◦bending system) or to adjust the deflection of the corresponding HDSM dipole. Thisturned out to be very important for the successful energy upgrade towards 1.6GeV.The vacuum chamber should provide a vertical opening of 15mm for lossless beam

transport. To resist the atmospheric pressure the flat chamber of approximately 14m2

had to be equipped with four supporting bars crossing also the beam trajectories.Altogether 172 openings within each magnet had to be located with sub-millimetreprecision to not limit the aperture.

3.4 Beam diagnostics

The HDSM is equipped with different non invasive monitoring systems to providebeam positions, phases and intensities using rf resonators (Fig. 10, red dashed circles)[46]. A detailed description of these rf monitors will follow in section 3.4.1.Additionally synchrotron radiation monitors at dipoles 2 and 4 image the light

emitted by all recirculations simultaneously as the beams travel towards the linac(Fig. 13). Equipped with a panning zoom camera it is possible to observe each beamspot at maximum resolution of the optical system. This system was used to study thecharacteristics of the transverse beam emittance starting from injection energy up tofull energy [47].

1 The field maps were measured by an automated system using Hall probes.


Fig. 13. Image taken from the synchrotron radiation of HDSM dipole 4. First turn is onthe right side, on the left side full energy is reached, neither betatron oscillation nor betabeat is obvious. Horizontal resolution is 640 pixel.

During routine operation a DC transformer on the 4.9GHz linac measures thebeam current with an intrinsic resolution of 0.2μA. Since the beam passes the trans-former up to 43 times, the current it measures reads 43 times higher than the beamcurrent. That improves the resolution of the beam current measurement to < 10 nA.During routine operation with beam currents of 10μA or more there is very goodagreement with the readings of the DC transformer of the RTM3 which measures thecurrent at 90 recirculations.The beam transport lines are equipped with luminescent screens. TV cameras

image the beam spot to monitors in the control room for visual inspection by theoperator. For the first time at MAMI such screens (with a hole in the centre) havealso been installed on the linac straights. This allows to (destructively) observe anyturn while the beam is accelerated with minimal distortions up to that point.Beam losses are detected with 10 ionisation chambers installed at critical areas

around the accelerator. This system has already been used extensively at MAMI Band proved that good beam quality comes along with low background radiation due tobeam losses. Under favourable conditions the system may detect beam losses as low as10 pA whereas less than 1 nA may be considered as typical sensitivity. Finally beamlosses above a preset threshold level automatically interrupt operation to preventdamage to the machine.

3.4.1 RF cavity monitors at MAMI

The primary diagnostic tools to measure beam position, phase and intensity for therecirculated beams of a microtron are rf cavity monitors which have been employedfor years in the RTM cascade [46,48]. The installation of the monitors for the HDSMis illustrated in Fig. 10. Automatic routines rely on the information acquired by thesemonitors in order to align each recirculated beam to the linac straight (→ section4.4) [49].At MAMI two different types of these monitors are involved: TM010-resonators

to measure the phase and intensity (PIMO) and TM110-resonators to measure thetransversal position (XYMO), both with high and low quality factors.The very sensitive high-Q monitors with a moderate signal bandwidth of up to

100 kHz are installed within the beam transfer lines providing CW signals duringnuclear physics experiments. These monitors are used to continuously track the beamposition or they are used for the energy stabilisation system (→ section 4.3). Thelow-Q monitors serve in the microtrons to separate the consecutive signals of therecirculated turns (the time Δt for one recirculation ranges from 15 ns to 200 ns forRTM1 to HDSM).For all types the rf signal is demodulated with a double balanced mixer to yield

a voltage proportional to the extracted signal power with respect to a local oscillator(LO). That LO in turn is locked to the MAMI master oscillator via phase shifters.For the hitherto existing RTMs the use of these monitors was very convenient.

Due to the nearly constant phase during the acceleration process the phase of the LO(which is locked directly to the phase of the rf wave of the linac) can be optimised to


Fig. 14. Comparison of a routinely performed phase measurement (black, hollow) and acalibration measurement (red, solid) of the phase signals of the 4.9GHz linac (upper plot)and the 2.45GHz linac (lower plot). The grey crosses mark the phase information duringthe calibration measurement using the same analysis as during routine measurements toillustrate the scattering due to inaccuracies of the measurement.

best sensitivity measuring phase deviations and beam positions for all turns simulta-neously. But the phase migration of the HDSM with respect to the accelerating waveof up to 45◦ for the 4.9GHz wave causes the LO to be correct only for a few turns andfor all other turns the detected pulse heights are reduced by a factor cos(φbeam−φLO).That required a redesign of the monitor signal analysis software in order to providecorrect phase and position information again. Most of all the phase measurementdepends on time-consuming calibration measurements, so this procedure cannot beperformed if different machine configurations are to be compared within a reasonablemeasurement time. However, the precision of relative phase measurements based onthe calibration measurements usually is better than 1◦ while the acquisition time isnegligible (→ Fig. 14, compare the red solid plot with the white hollow plot) [48,50].Yet the injection phases have to be determined to complete the phase measurement.

3.4.2 Determining RF phase and voltage

The phase of the first turn relative to the accelerating wave can be measured usingthe longitudinal dispersion of the 180◦ deflection system, which leads to phase vari-ations in the following phase monitor if the energy changes [50]. If the energy gainis varied by a change of the phase of the accelerating wave, the point of maximumenergy gain corresponds to an injection phase of φmax = 0

◦. Thus, the phase dif-ference between the original phase and φmax is the injection phase. The results forboth linacs are incorporated to the standard phase measurement procedure and areroutinely rechecked for deviations due to temperature drifts within the rf distributionor different rf amplitudes after each start of the machine.Systematic tests with different rf amplitudes revealed only slight correlations of

the linac phases and their amplitudes. Obviously these effects are almost completelyeliminated by the analogue rf phase- and amplitude stabilisation loops.With the precise knowledge of the longitudinal dispersion computed from the mea-

sured field maps it is also possible to estimate the rf voltage Uacc. of the correspondinglinac. However, the finite aperture of the bending system limits the precision because


Fig. 15. Different methods to measure the rf voltage of both linacs. For the 2.45GHz linacthey show good agreement while the 4.9GHz linac measurements are much more spread.The green curves were obtained from from phase space scans (→ section 5).

the energy acceptance of an individual dispersion beam line of the bending system isabout ±1MeV. As the linacs are operated at approximately 9-10MV and the accord-ing energy variation, when the phase is driven from 0◦ to 360◦, is much larger thanthe aperture for a single dispersion line tolerates.To enlarge the effective measuring range, the first two dispersion beam lines which

are separated approximately by 16MeV can be used. This was done with a specialconfiguration running decreased magnetic fields in HDSM dipole 3 and 4. At thattime the accelerated beam was guided through the second and the decelerated beamthrough the first dispersion beam line2. The resulting rf amplitudes of the 4.9GHzlinac for routinely performed measurements are illustrated in Fig. 15 (right plot, solidred curves). They agree with the special measurements within their respective errors.Another method to compute Uacc. uses the shunt impedance RS and the dissipated

power PRF within a section with ncav. accelerating cavities:

Uacc. =√PRF · ncav./2 · λRF ·RS. (10)

From low-power rf measurements RS of the accelerating structures have been deter-mined with network analysers. PRF can be measured either directly with calibratedpower metres attached to the waveguide of the section, alternatively the cooling waterflow and its temperature rise can be considered. Both methods show good agreementfor the 2.45GHz linac while the measurements of PRF for the 4.9GHz linac are sep-arated by approximately 10%. Information about the relative phases between the upto 8 linac sections is inaccessible with this method but beam tests revealed no signifi-cant errors of the relative phases. This can be seen in Fig. 15, where the calorimetricmeasurement and the measurement using the dispersion method match well for bothlinacs.

3.5 Operational experiences

The MAMI facility is a very reliable and stable machine usually serving around theclock operation in a two weeks cycle followed by one day of maintenance. Thus MAMIhas been delivering an average beam time of 6162 h per year during the last ten

2 This method is only applicable for the 4.9GHz linac, the field of HDSM dipole 1 and 2cannot be varied because the beam has to pass through them before it reaches the 2.45GHzlinac.


Table 1. MAMI C operational statistics of the years 2007–2010.

2007 2008 2009 2010

Beam time [h] 7171 6967 6014 5889

E ≥ 1.5GeV [%] 45.6 60.2 71.9 35.9

Polarised beam [%] 41.3 35.5 55.3 60.8

Down time [%] 5.9 2.7 3.2 2.6

years, with an all-time record of 7171 h in 2007. On average 84% of the beam time isdedicated to user operations (i.e. beam on target), the remaining beam time is usedfor setup and optimisation of the machine. The setup procedure of the facility takesabout two hours, which is dominated by the time the eddy currents need to settle inthe large bending magnets of RTM3 and HDSM. The machine is very stable, whichappears in the fact that it usually can be run for 24 h without any intervention by theoperator, with an all-time record of 76 h. Down time due to machine failure is onlyabout 3% of the overall beam time (for details see Table 1) [23,51,52].In 2010 the portion of operations with HDSM of the overall beam time decreased

to roughly 36%. This is due to the fact that a major reconstruction of the beamtransfer line inside the 3-spectrometer hall took place. So one of the two main userscould not apply for beam time. It is expected that in 2011 this group will catch uptheir accumulated needs in high energy operations.Since 1991 till end of 2010 MAMI has accumulated 116719 h of operation. Hereby

the demands posed by the experimentalists groups towards the machine are widelyspread: currents from 10 pA up to 100μA and energies between 180MeV and 1.6GeVhave to be delivered by MAMI.The commissioning of the fourth microtron stage HDSM was started in December

2006 and in February 2007 the machine was dedicated to user operation. The firstbeam was completely led through the machine in only one shift. The design current of100μA at 1.5GeV, i.e. 150 kW of beam power, was achieved in October 2007 for thefirst time. The beam dynamics have extensively been investigated since the beginningof operations, special topics are reported in section 5. Soon an increase of the endenergy of MAMI C took place (section 4.2). The energy raise was conducted in twophases. The first one took place in December 2008 when 1558MeV with a beamcurrent of 30 μA were achieved [52], the final phase was carried out in September2009 in which 20 μA could be accelerated [23]. Further in March 2009 the setup tostabilise the output energy of the HDSM was set into operation. A short account onthis feature can be found in section 4.3.

4 Consolidation of MAMI C

4.1 Variable energy extraction

One of the great advantages of a microtron is the possibility to deliver a set of discreteoutput energies up to its end energy without changing the machine setup. In thecase of an RTM it is only necessary to apply a defined kick to the beam, so itsnew trajectory follows the extraction beam transfer line (BTL) instead of the linac.Thus a movable dipole magnet is installed at the dispersive beam-pipe representingthe desired energy. At the RTM3 this technique is well-proven [53], the change ofextraction energy can be easily done by the operators within 2 hours.


Fig. 16. Field map of HDSM dipole 02 at 1.5T without correction coils.

Fig. 17. Field map of HDSM dipole 02 at 1.5T with correction coils.

At the HDSM a similar extraction dipole is installed [52]. As the output energycan be up to a factor of two larger than at the RTM3, the magnet has to providehigher field strength. This results in a larger, heavier magnet that cannot be handledby a person without lifting tools anymore. The HDSM variable extraction magnetis realised as a C-shape magnet that can be separated at the yoke. Fixed transportmechanisms support the operators with their task. Up to now only HDSM energiesbetween 872MeV and 1322MeV can be provided, because placing the extractionmagnet for higher energy would demand a reconstruction of the steerer magnet setupof those dispersive beam-pipes. The experiments have not yet demanded for thosemissing energies.

4.2 Increased output energy

The maximum output energy Emax of a microtron is determined by the magnetic fieldB and the maximum bending radius Rmax, which is fixed by the dimensions of thevacuum chamber. Therefore increasing Emax can only be realised by an increase ofB, while maintaining Rmax (→ section 2.1). Under this conditions it is evident thatthe injection energy has to be scaled by the same factor as the output energy. So anincrease of the end energy of a microtron cascade means upscaling every single stage.The MAMI C facility has, as mentioned before in section 3, a design energy of

1.5GeV, so all components were specified for this energy including some margin.Especially the HDSM main magnets were optimised by their correction coils to thatdesign value, which corresponds to a magnetic flux Bmax of 1.54T (→ section 3.3 andFig. 16 and Fig. 17).

After those correction coils were mounted, also field maps at 1.64T, which corre-sponds to a beam energy of 1.6GeV (Table 2), were measured to obtain informationon the behaviour of those correctors at higher fields. It turned out that especially atthe edges of the magnets the field deviation at 1.64T was about four times largerthan at 1.54T (compare Fig. 17 and Fig. 19).


Table 2. Overview of the maximum output energy Emax of each stage for the three endenergies Eend of MAMI C with corresponding magnetic flux BNMR and the bending radiusat maximum output energy Rmax. (At the HDSM BNMR is only 90% of the max. real gapfield!).

Eend : 1.5 GeV 1.56 GeV 1.6 GeV 1.5 GeV 1.56 GeV 1.6 GeVStage Emax Emax Emax BNMR BNMR BNMR Rmax

[MeV] [MeV] [MeV] [T] [T] [T] [m]

ILAC 3.97 4.10 4.22 – – – –

RTM1 14.86 15.35 15.81 0.102 0.106 0.109 0.484

RTM2 180 185.9 191.46 0.555 0.573 0.59 1.082

RTM3 855.1 883.11 909.54 1.284 1.326 1.366 2.221

HDSM 1508 1557.4 1604 1.383 1.428 1.471 3.638

Fig. 18. Field map of HDSM dipole 02 at 1.6T without correction coils.

Fig. 19. Field map of HDSM dipole 02 at 1.6T with correction coils for 1.5T.

Those field errors (→ Fig. 19) may introduce some higher order magnetic multi-poles, but more than this, they introduce transverse kicks leading to disturbed beampaths. This could be crucial, because the beam always enters and exits the 180◦deflection system at those edge positions and so this disturbance is present in allturns. The high energy beam paths also transit edge regions inside the deflectionsystem, the beam is here exposed to the disturbances twice as often than at lowand medium energies. As fabricating new correction coils is a large enterprise andinstalling them into the magnets would cause a major shut-down of the machine, itwas decided to conduct some tests to verify whether a new set of correction coils ismandatory for an energy upgrade.


Fig. 20. A comparison of the steerer strength in the HDSM at return paths 1–42 at thethree different energies taken from two exemplary setups each. To distinguish between thetwo setups the second graph is marked with a “(2)” in the legend. The displayed steerersare the first horizontal ones on the dispersive beam-pipe following the 4.9GHz linac. Thethick red line denotes the thermal limit of the steerer coils, which is at 2mrad.

4.2.1 Beam tests

The energy upgrade then was realised in a two step process. The first step was tojust increase the energy of MAMI C based on an existing MAMI B 883MeV setup[16], so only the HDSM energy had to be scaled up by 3.3% to 1558MeV. From theoutcome of this first test, one could judge the feasibility of an energy upgrade to> 1600MeV which also requires scaling up all three RTM to values which were neverrealised before.The main goal of the first beam test was to find out whether the field decay at

the magnet edges could be compensated by the use of the steerer magnets inside the180◦ deflection system. Each of the dispersive beam paths has two sets of horizontaland vertical steerer magnets, one at the beginning and another one at its end. Alsoit was intended to scale the current of the outer correction coil windings more thanthe rest to catch the edge decay.The 1558MeV test was straight forward successful [52]. The particle beam was

led through the machine within a few hours and after this the further beam timewas dedicated to user experiments at that particular energy. Analyses of optimisedmachine3 setups, which are depicted in Fig. 20, revealed that the excitations of thereturn path horizontal steerers were not significantly above the usual fluctuation ofsuccessive setups saved at the standard energy. Figure 21 shows that the horizontalsteerers on the linac axes near the main magnets also contribute to the compensationof the introduced orbit distortion. It also turned out that it was not necessary tooverexcite the outer correction coil windings, they worked perfectly at the nominalscale. As expected, no effect in the vertical beam plane was found. The maximum ac-celerated current at 1.56GeV was 30μA. With all those positive results the prognosisto reach 1.6GeV was quite sure.Prior to the full energy upgrade a careful investigation on possible hardware lim-

itations was carried out: the specifications of the hardware were compared to theirnominal value at 1604MeV. Some components turned out to be critically close totheir technical limits, but only the 240 kW power supply of the main field of the twoRTM3 bending magnets in combination with saturation effects in the magnets, is able

3 An optimised machine means that no betatron oscillations are detectable.


Fig. 21. A bar plot of the horizontal steerer excitations on both linac axes at the threeenergies taken from the same setups as in Fig. 20.

to hinder the energy upgrade. Replacement or upgrade of this power supply would bea major investment. Field tests showed that the power supply was able to build up thenecessary field. Furthermore long-term field testing verified that this field strengthcould be maintained over a longer period of time. The tests clearly showed that thepower supply is able to compensate the non-constant resistance due to the heating ofthe magnet coils. Further the main and reverse fields of all RTMs were adjusted tonominal values using Hall probes.Although starting from scratch only with a calculated machine setup, setting

MAMI C at 1.6GeV into operation was successfully finished within only three shifts[23]. Threading the beam through the microtron cascade turned out to be a littlemore tricky than experienced at 1.56GeV. This is partially due to the growing influ-ence of the field errors but also because of the fact that it was not possible to rely ona well established RTM cascade setup.Analysing the first 1.6GeV HDSM steerer settings one could see that the steerers

were, as expected, substantially stronger excited than at lower energies. Especiallyfor the high energy dispersive beam paths the thermal limit was exceeded (Fig. 20).This was due to the mentioned transversal kick introduced by the missing field atthe magnet edges. By switching on the in-gap steerers, foreseen in the HDSM mainmagnet pole faces by design (→ section 3.3), this lag of bending force could be com-pensated. In Fig. 20 the effect of the in-gap steerers can be seen, the loading of thesteerers at the high energy dispersive beam paths is decreased from up to 2mrad toless than 0.8mrad. The maximum accelerated current at 1.6GeV was 20μA.

4.3 Energy stabilisation

For parity violating experiments excellent beam stability is required to measure verysmall helicity correlated asymmetries of about 10−6 or smaller. Except for the energystabilisation the existing systems to stabilise the beam current and the beam posi-tion on the target could be used from the beginning, since they are installed directlyupstream of the experiments.The relative change of the energy can be detected measuring the time of flight

through a bending magnet. In case of the RTM3 this method was successfully in-troduced using one RTM3 dipole as spectrometer and measuring the relative phasechange between a phase monitor on the entrance and one on the exit of the magnet


Fig. 22. Sketch of the energy stabilisation system of the HDSM.

[54]. With very small-sized resonators at 9.8GHz4 phase deviations of 0.1◦ correspondto an energy variation of approximately 1 keV. If the acceleration voltage is adjustedto provide an adequate longitudinal tune, the output energy can be varied in a con-trolled fashion within some 10 keV by applying small injection phase variations ofabout 1◦.To stabilise the output energy of the HDSM a similar system was installed. The

relative change of the beam energy is measured with two 4.9GHz phase monitorswhich detect changes of the relative time of flight through the last 90◦ bending mag-net towards the extraction beam line (Fig. 22). From simulations with PTRACE andTOSCA the effects on the measured phase deviation Δφ due to energy deviations Δpand angle fluctuations Δx′ follows:

Δφ[◦] = −0.013◦ ·Δp[keV]− 0.037◦ ·Δx′[μrad]. (11)

Again, to steer the output energy with the injection phase, the acceleration processhas to turn phase variations at injection to energy variations at extraction energy.Nevertheless, it is much more difficult than with the RTM3 to find such suitablelongitudinal settings by adjusting the rf settings of both linacs while simultaneouslyrunning the accelerator at 20μA (or 30 kW beam power). Therefore an automaticalgorithm monitors the correlation between injection phase and output energy whilean appropriate area of 2◦ (4.9GHz) by 1◦ (2.45GHz) is scanned for maximum corre-lation while at the same time the beam losses must remain under control. While themachine runs for the nuclear physics experiments, the phase change is continuouslymeasured and used to compute the correction of the injection phase at a frequency of1 kHz. Figure 23 demonstrates the difference between a normal (stabilisation off) andan experimental (stabilisation on) running of the HDSM. It shows from the long termexperience that the stability of the longitudinally acting components of the HDSMis very good and the energy can be stabilised to better than 10 keV (i.e. some 10−6)during a typically one or two week long experiment.

4.4 Automatic beam threading

The adjustment of the transversal beam optics is not critical. Using the design focalstrengths for the quadrupoles in the linac straights, only some empirical correctionswere necessary to get a sufficient beam focusing and a good matching. The former

4 The diameter of the resonator must be smaller than 4 cm to fit in between the beamdispersion lines of the RTM3.


Fig. 23. Comparison between normal operation (stabilisation OFF, upper) and stabilisedoperation (lower).

can be controlled via the betatron-oscillations monitored with the low-Q rf resonators(XYMOs, see section 3.4.1), the latter via the synchrotron radiation spots of all turns,viewed with a tv-camera in dipole 2 or dipole 4 (→ section 3.4). Threading of thebeam through all turns of the accelerator is achieved by adjusting the two horizontaland vertical steerers in the dispersion line of each half-turn in a way that the beamposition deviations in the XYMOs in the following linac straight become zero.However, the steerer setting is not perfectly reproducible from run to run due

to slight variations in the magnetic field of the main dipoles after every switch on.Additionally the optimal steerer setting changes slowly in time because of temperaturedrifts. Especially directly after a setup of the accelerator, correction must be repeatedin time intervals of 1–4 hours. Though this is easy to do with some practice, it isinefficient to adjust the four times 86 steerers manually. A computer program writtenin the interpreter language MOPL [55] accomplishes this task in a few minutes. Buta simultaneous ‘collective’ correction of as many turns as possible based on theirmeasured transverse position deviations would speed up the optimisation routine byabout an order of magnitude. This method has been implemented very successfullyin the RTM cascade [56]. However, it is then necessary to obtain a machine modelwith sufficient predictive power and enough simplicity to be implemented in a fastcomputer algorithm. Since the optics of the HDSM is far more complex than thatof the RTM and the number of free parameters is considerably higher this goal hasnot yet been reached, but encouraging progress has been achieved based on modernnumerical methods such as SVD algorithm [57].

5 Investigations of the longitudinal beam dynamics of the HDSM

The following chapter illustrates the challenges to achieve a reliable routine opera-tion as well as to investigate the beam dynamics of the HDSM. The most importantaspect is to find an appropriate working point that should provide a sufficiently largeacceptance to tolerate beam drifts in position or phase due to thermal drifts.Two fundamentally different approaches can achieve this: either the simulation

is elaborate enough to predict the appropriate setting or different settings have tobe applied and compared to each other. The first approach is challenging because itrequires the most precise knowledge of the behaviour of all the components acting onthe beam while the second one may be time-consuming but should definitely find thebest setting for operation. Both methods are in principle applicable to the longitudi-nal as well as to the transverse dynamics.


Fig. 24. Measured (blue) and simulated (red) phase information for two different injectionenergies and thus different linac rf phases during a scan of the longitudinal phase space.The lower part demonstrates the analysis of the synchrotron oscillation, blue symbols aremeasured data, red symbols illustrate the simulation. Remarkably, the progression of thelongitudinal tune (compare left and right figures) is strongly affected even by different phasesettings alone.

During routine operation the longitudinal beam dynamics of the HDSM emergedto be more critical compared to the transverse dynamics and therefore have been re-searched in detail. The dynamic coherence condition (Eq. (2)) names the main factorsfor the longitudinal dynamics: the magnetic field B, the accelerating rf wavelength λand the energy gain ΔTDSM per turn. As B is fixed to guide the beam through thedispersion beam lines and λDSM is also fixed, the optimal energy gain and thus theappropriate phases and voltages of the rf waves are to be found.

5.1 Examining the longitudinal tune of the HDSM

To investigate the longitudinal dynamics of the HDSM in detail, the behaviour of theaccelerator is analysed and compared with an adequate model. The main comparisoncriteria are the phases of the beam relative to the accelerating wave for each turnbecause this is the most significant quantity to be measured.An important aspect of our HDSM is avoiding the longitudinally instable area

where the phase advance per turn approaches 180◦ (i.e. Q ≈ 0.5). This postulation isgeneral and should be considered for any setting of the accelerator or the model. Asshown in section 2.3 this specially applies to the last 10–15 turns.However, the analysis of the measured synchrotron oscillation is difficult because

the phase migration in both linacs requires to subtract a phase offset curve. That offsetcurve is not even constant: different rf settings lead to different phase migrations.On account of this the offset is calculated by fitting a polynomial to the measuredphase information of both linacs individually. Afterwards the remaining values ofphase deviations of both linacs are combined to a single curve normalised to thefundamental frequency of 4.9GHz. To obtain the longitudinal phase advance, sinecurves are fitted to 4 consecutive turns (i.e. 8 values of phase deviations). A result ofthis procedure is illustrated in Fig. 24. During routine operation it also turned outthat a good longitudinal working point with minimal beam losses is characterised bya tune migration which does not reach the critical value of Q ≈ 0.5.

5.2 Scanning the longitudinal phase space and modelling of the HDSM

Although the phase data acquisition now is very reliable, fitting a model to the mea-sured phase information was not leading to satisfying results from the very beginning.


That results from the strong correlation of both linac amplitudes – i.e. increasing theamplitude of one linac while the other is decreased leads to rather small phase changesat first. For this reason it showed that the fit can result in different linac amplitudes,even if no amplitude was changed: For example the injection energy can be changedby means of the matching section and both linac phases are adjusted to minimise thephase oscillations.Therefore, scanning the longitudinal phase space is the appropriate solution.

5.2.1 Which parameters to scan?

To provide an appropriate energy gain ΔTDSM the rf amplitude and their phases haveto be chosen carefully. The linac rf amplitude is only known to about 5% (→ section3.4.2) but is reproduced very precisely from one machine run to another. More practi-cal parameters are the phases of the rf waves which can be varied very accurately withstep-motor driven waveguide phase shifters yielding a precision of better than 1◦ overa range of up to 500◦. Varying only these should therefore deliver more significantsimulation results concerning the rf amplitudes for example.The longitudinal phase space is scanned within a certain area of the 3 parameter

space formed by injection energy, injection phase and phase shift between linac 1and 2. For each configuration all the rf monitor signals are stored as a data point.Afterwards the best working configuration is chosen – while “best” means least syn-chrotron oscillation amplitude and only small beam losses detected by the ionisationchambers. The extensive data gathered during such scans can later be used offline totest the model.

5.2.2 Modelling the longitudinal dynamics

The model resembles the scanning routine while it considers the energy dependentinterpolated path lengths in the beam dispersion lines with their resulting phasedeviations in the linacs. If the energy deviates between ±1MeV and ±2MeV fromthe reference energy for the beam dispersion line, a beam loss proportional to thedeviation is simulated to emulate the finite apertures of the bending systems. Energylosses due to synchrotron radiation are included as an average energy loss within eachHDSM dipole magnet.To provide a reliable comparison criterion between the measured and simulated

data points the fitting routine at first selects data points where the full energy wasreached and all surrounding data points (the increments of the scan are typicallyabout δEinj. ≈ 50 keV and δφinj. ≈ 2◦) also reached full energy.The fitting routine was based on the Levenberg-Marquardt algorithm (LM) [58,59]

but it turned out that due to the correlation of the two linacs it was not suitable tominimise the deviations between measured and simulated data with the given initialparameters. Another approach was to implement a variant of the Particle-Swarm-Optimisation algorithm [60] which finds the parameters minimising the deviationsvery reliably. These results can be used for a second fit using the LM algorithm again.As the coupling between longitudinal and transversal phase space is influenced

by numerous unknown effects, it has not been implemented to the model. But theroutine weights the data points with the measured transversal beam displacementsto eliminate the falsifications due to betatron motion at best.

5.2.3 Results

The model reproduces the measured phase values at an average phase error of Δφ ∼1◦to 2◦ for the best measurements considering up to ∼ 1500 different phase config-urations. Additionally the tune analysis can be applied to the measured and the


Fig. 25. 3D-plot of measured and of fitted-model longitudinal phase space acceptance of theHDSM for different relative linac phases related to 4.9GHz. The height of each plotted barshows the number of turns completed. From top to bottom the relative phase Δφ betweenboth linacs has been changed. Different colours represent the longitudinal tune reached (fromgreen Q = 0.2 to red Q = 0.5, cf. Fig. 24).

simulated beam phases to further enhance the confidence in the previously foundresults. Figure 25 shows an example of a scan of the longitudinal phase space (right)along with the modelled phase space (left). The colours used result from the longitu-dinal tune analysis. Both the shape of the measured and the simulated phase spaceas well as the progression of the longitudinal tunes appear very similar. The resultingrf voltages for different measurements of this kind are presented in Fig. 15.Altogether, the combination of the validation of the measured phase information

along with the scanning of the longitudinal phase space supplied with an appropriatemodel shows a good agreement between the actual behaviour of the HDSM and thesimulated model, although some discrepancies still have to be examined.

6 Conclusion

The recent decade proved that a complex but innovative accelerator cascade likeMAMI C is able to provide very reliable routine operation for experiments in nuclearand hadron physics while at the same time there is still some considerable margin tothe physical and technical limits of the accelerator. This was confirmed in particularwith the very fast success of demonstrating the maximum beam power of 150 kW butalso with the straight forward energy upgrade running the HDSM at 1.6GeV (i.e.more than 6% above the design parameters).


The success of the MAMI C accelerator also is based on the very experienced crewdeveloping appropriate beam diagnostics. Combined with innovative calibration- andmeasurement procedures reliable working points can be found, even under extremeconditions, like during the energy upgrade.

This work has been supported by the SFB443 of the Deutsche Forschungsgemeinschaft(DFG) and the German Federal State of Rheinland-Pfalz.

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The MAMI C accelerator