The Metrology Light Source  MLS  is an electron storage ring containing 24 quadrupole magnets which can be powered individually. Fully exploring the capabilities of the machine optics by tracking or experiment would be very time consuming. Therefore the quadrupoles were combined in five families and a numerical brute force approach was used to scan for areas of stable solutions in the scope of linear beam optics. In order to get information on the expected beam lifetimes for each generated optics, a model for the Touschek lifetime was implemented. Simulation results as well as experimental tests of selected optics will be presente

Feikes, J.

Goetsch, T.

Ries, M.

Wüstefeld, G.

HZB Repository

SURVEY OF BEAM OPTICS SOLUTIONS FOR THE MLS LATTICEM. Ries, J. Feikes, T. Goetsch, G. Wu¨stefeld, HZB, Berlin, GermanyAbstractThe Metrology Light Source (MLS) is an electron stor-age ring containing 24 quadrupole magnets which can bepowered individually. Fully exploring the capabilities ofthe machine optics by tracking or experiment would bevery time consuming. Therefore the quadrupoles werecombined in ﬁve families and a numerical brute force ap-proach was used to scan for areas of stable solutions in thescope of linear beam optics. In order to get informationon the expected beam lifetimes for each generated optics, amodel for the Touschek lifetime was implemented. Simula-tion results as well as experimental tests of selected opticswill be presented.INTRODUCTIONThe Metrology Light Source owned by the Physikalisch-Technische Bundesanstalt (PTB) is used as a radiationsource standard from the infrared to the soft X-ray regime[1, 2]. It is a ramped machine with an injection energyof 105 MeV and an operation energy of 630 MeV. Themagnet lattice is characterized by a 4-fold symmetry. Long(LS) and short (SS) straight sections are separated by dou-ble bend achromat (DBA) segments in the setup: SS, DBA,LS, -DBA, SS, DBA, LS, -DBA. The standard operation ofthe machine is to power the quadrupoles in ﬁve differentfamilies as shown in Fig. 1. To study the overall optics ca-Figure 1: DBA segment of the MLS containing dipole (yel-low), quadrupole (red), sextupole (green) magnets and anoctupole magnet (black) in the center. [3].pabilities in this setup, a database containing linearly stablesolutions as well as corresponding performance parameterswas generated.ALGORITHMFollowing the scheme of [4], as a ﬁrst approach a Fortranalgorithm was written to scan for solutions while indepen-dently varying the strengths of the ﬁve quadrupole families:Q1, Q2L, Q2S, Q3L, Q3S (Fig. 1). To save computationtime the model was restricted to a vertically decoupled mo-tion. A sketch of the algorithm with nested loops over allﬁve quadrupole family strengths looks like:1. check vertical transfer matrix for stability criterion2. check horizontal transfer matrix for stability criterion3. apply feasibility ﬁlters• maximum beta functions: βx,y < 20 m• maximum dispersion: |D| < 2 m4. calculate optics quantities of interest5. calculate Touschek lifetimeIn a ﬁrst scan the quadrupole strengths were varied over thefull design range including polarity reversal. A constantstep size for all quadrupoles was used. A total numberof 1012 combinations was checked generating a databaseof approximately 2 · 106 solutions. The runtime of thecode on a 2.66 GHz single core was about 200 h. Figure 2xQ2 3 4 5 6yQ01234normalized solutions-610-510-410Figure 2: Regions of stability for the MLS lattice in thetune diagram [3]. The black cross marks the standard work-ing point, whereas the area marked by the blue box is easilyaccessible and therefore preferred for operation.shows a histogram plot of the 5-dimensional scan into theplane deﬁned by the transverse tunes. The color indicatesthe number of solutions in one bin normalized to the totalnumber of solutions for the scan. The blue box in Fig. 2corresponds to a region easily accessible from the stan-dard working point (black cross). This area can be inves-tigated while keeping the beam stored. Hence, there is noneed to generate new injection states as well as new energyramps. The database generated in the ﬁrst scan was usedto redeﬁne scan ranges of the individual quadrupole familystrengths. In a second run only ranges possibly yielding so-lutions in the blue region were regarded. As a consequencethe step size could be decreased by a factor of four withoutan additional increase in runtime.Proceedings of IPAC2013, Shanghai, China TUPWO00505 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, TransportISBN 978-3-95450-122-91883 Copyrightc ○2013byJACoW—ccCreativeCommonsAttribution3.0(CC-BY-3.0)TOUSCHEK IMPLEMENTATIONAs measurements show, the lifetime at the MLS is Tou-schek limited [5]. To ﬁnd optics with an increased Tou-schek lifetime a Touschek module was implemented intothe Fortran code. The Touschek lifetime depends on theacceptance of the accelerator. Two major effects may limitthe momentum acceptance δacc:• RF-acceptance• geometrical acceptance.The RF-acceptance is calculated following [6]. The geo-metrical acceptance for the MLS can be calculated in a ﬁrstorder approximation asδacc ≈ min[ax(s)2Dx(s)], (1)with ax(s) being the horizontal aperture in each elementand Dx(s) the corresponding horizontal dispersion func-tion. The maximum Touschek lifetime can be expectedwhere RF-acceptance and geometrical acceptance are equal[5].The Touschek lifetime is calculated according to the so-lution presented by [7], including horizontal dispersion:τT =8πσyσs√σ2xβ + σ2xD · γ2δ3accD(ξ)Nr2ec, (2)with the vertical bunch size σy , the bunch length σs andthe Lorentz factor γ. The horizontal bunch size has twocontributions: σxβ =√βxεx being the contribution dueto emittance and σxD =√Dx2σE2 being the contributiondue to dispersion. D(ξ) is a function of acceptance δacc,the optical functions, their derivatives and the electron en-ergy. N is the number of particles in the bunch (calcula-tions for 1 mA at the MLS: N = 1 · 109) and re is theclassical electron radius. For the vertical beam size, it wasassumed that the ratio of vertical to horizontal emittanceequals 1 %. Therefore, the vertical beam size was calcu-lated as σy =√0.01εxβy .The algorithm calculating the Touschek lifetime lookslike:1. Find the minimum of δacc,geom following Eq. 1→ set geometrical acceptance = RF-acceptance toﬁnd optimum cavity voltage corresponding tomaximum achievable acceptance→ calculate bunch length for the optimum cavityvoltage2. Calculate Touschek lifetime with maximum accep-tance following Eq. 2 for each element3. Calculate the total Touschek lifetime by weighting thesingle element Touschek lifetimes with the lengths ofthe elementsThe calculated Touschek lifetimes have been checked forplausibility with the Touschek module offered by MADX.For the settings of the standard user operation in 2012at the MLS the Touschek lifetime was calculated withthe implemented Touschek module of the Fortran code:τT,mod = 12.64 h for a cavity voltage of 408 kV; the Tou-schek module offered by MADX calculates a correspond-ing Touschek lifetime of τT,MADX = 12.47 h.RESULTSBased on the results yielded by the scan, various opticshave been investigated experimentally. Dynamic aperturewas neglected in the ﬁrst runs, as it is not usually a lim-iting parameter at the MLS. Conversion from calculatedk-parameters to quadrupole currents to ﬁt the predictedtransverse tunes was better than 1%. Selected test opticsin the blue region of Fig. 2 were set up by changingthe quadrupole strengths while keeping the beam stored.Afterwards a LOCO characterization of the optics wasconducted [8].At ﬁrst a low emittance (ε) optics was set up as shownin Fig. 3. The emittance in standard user operation isabout 100 nm rad. A tuning of the optics while keepingthe working point ﬁxed promised an emittance reductionby a factor of 2.2, whereas allowing the working point tochange within the blue area yielded a predicted emittancereduction by 3.7. We chose to try the latter concept.xQ2 3 4 5 6yQ01234 / nm radminε10210310Figure 3: Minimum emittance of the MLS [3]. The blackcross marks the standard working point. A recently estab-lished low-ε mode is marked by the white cross.Emittance reduction was measured by two source pointimaging systems yielding a factor of 3.9, which wasreinforced by lifetime measurements. This optics is nowoperational up to 180 mA and was already applied in useroperation.In addition, the correlation between emittance andmomentum compaction factor α has been investigated. Asboth quantities depend on the dispersion in the dipole mag-TUPWO005 Proceedings of IPAC2013, Shanghai, ChinaISBN 978-3-95450-122-91884Copyrightc ○2013byJACoW—ccCreativeCommonsAttribution3.0(CC-BY-3.0)05 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, Transportnets, arbitrary combinations of α and ε are not possible.In the low-α operation mode applied for users at the MLSan increased emittance is observed worsening the userconditions for users interested in short pulsed synchrotronradiation. On the other hand, users interested in coherentsynchrotron radiation in the THz regime would beneﬁtfrom larger emittances as it substantially increases lifetimewithout reducing the brilliance at these wavelengths. Oneemittance / nm rad210 310α-0.1-0.0500.050.10.150.2normalized solutions-710-610-510-410normalized solutionsFigure 4: Momentum compaction - emittance correlation[3]. A global scan (yellow) as well as a subset of stateswithin the currently used tune quadrant (blue) is shown.The black cross marks standard user operation, the redcross marks low-α operation.ﬁnding of the brute force scan is, that there is no opera-tional mode that delivers low-α at the design emittance of100 nm rad as shown in Fig. 4 (blue). However, there areoperational modes for low-α at lower emittances. Theseoptics are all situated outside of the currently used tunequadrant. An optics setup featuring an increased emittanceof 300 nm rad at low-α was experimentally veriﬁed butnot yet tested in user operation.Finding an optics that could provide a larger Touscheklifetime τ at the design emittance of the MLS was the maindriving force to scan for new optics. An analysis of theTouschek lifetime regarding all states featuring an emit-tance smaller than 100 nm rad (Fig. 5) indicated a possibleimprovement of more than 60% at the standard workingpoint and even about 300% when leaving the blue region.However, in the experiments investigating new Touschek-optimized optics inside the blue region, τ has shown an un-expectedly strong dependence on the dispersion at the sep-tum magnet Dsept. Consequently tuning Dsept towards zeroyielded an increase in lifetime of 40% [5]. However, thiswas done by splitting the family Q1 leaving the state spacecovered by the scan.CONCLUSIONThe optics scan has turned out to be a fruitful tool ingenerating new operational modes at the MLS. A user op-xQ2 3 4 5 6yQ01234 / Ahτmax Touschek lifetime: I1234Figure 5: Maximum Touschek lifetime plotted for all so-lutions with ε ≤ 100 nm rad [3]. The black cross marksstandard user operation.erational low-ε mode was set up close to the achievableminimum emittance in the tune quadrant currently used.Trying to increase the Touschek lifetime by changing theoptics led to a better understanding of the limiting effectsand in turn to an increase in lifetime by about 80%. Imple-menting more complex optics by breaking the symmetry ofthe storage ring generates the need to parallelize the code.Assessing the overall distribution of solutions as well ascalculated Touschek lifetimes and emittances, it seems tobe promising to explore other tune quadrants to generatenew optics for standard user operation featuring a largerTouschek lifetime and/or smaller emittance.ACKNOWLEDGMENTWe would like to thank Andreas Jankowiak (HZB) andGerhard Ulm (PTB) for ongoing support as well as MartinRuprecht (HZB) for discussions on this topic.REFERENCES[1] R. Klein et al., Phys. Rev. ST Accel. Beams 11, 110701,(2008).[2] J. Feikes et al., Phys. Rev. ST Accel. Beams 14, 030705,(2011).[3] M. Ries, thesis to be published, “Nonlinear Momentum Com-paction and CSR at the Metrology Light Source”, Humboldt-Universita¨t zu Berlin, Germany, (2013).[4] D. Robin et al., Phys. Rev. ST Accel. Beams 11, 024002,(2008).[5] T. Goetsch et al., “Lifetime Studies at Metrology Light Sourceand ANKA”, Proceedings of IPAC2013, (2013).[6] K. Wille, “The Physics of Particle Accelerators - An Intro-duction”, ISBN 0-19-850549-3. Oxford University Press Inc.,New York, (2005).[7] Joe¨l le Duff, “Single And Multiple Touschek Effects”, CERNAccelerator School, CERN 89-01, (1989).[8] P. Schmid et al., Proceedings of IPAC2010, p. 2505, (2010).Proceedings of IPAC2013, Shanghai, China TUPWO00505 Beam Dynamics and Electromagnetic FieldsD01 Beam Optics - Lattices, Correction Schemes, TransportISBN 978-3-95450-122-91885 Copyrightc ○2013byJACoW—ccCreativeCommonsAttribution3.0(CC-BY-3.0)

Survey of Beam Optics Solutions for the MLS Lattice

http://www.helmholtz-berlin.de/pubbin/oai_publication?VT=1&ID=78887

Survey of Beam Optics Solutions for the MLS Lattice

Abstract

Similar works

Full text

Available Versions

HZB Repository