At the Metrology Light Source  MLS  [1] owned by the Physikalisch Technische Bundesanstalt  PTB  the bunch length can be varied by more than two orders of magnitude  [2]. The bunch length manipulation is achieved by varying different machine parameters, such as RF voltage amplitude up to 500 kV and the momentum compaction factor  amp; 945;  over three orders of magnitude. The subject of this article is the measurement of THz bursting thresholds at the MLS for different bunch length

Feikes, J.

Hoehl, A.

Ries, M.

Schmid, P.

Wüstefeld, G.

HZB Repository

THz BURSTING THRESHOLDS MEASURED AT THEMETROLOGY LIGHT SOURCEM. Ries ∗, J. Feikes, P. Schmid, G. Wu¨stefeld, Helmholtz-Zentrum Berlin, GermanyA. Hoehl, Physikalisch-Technische Bundesanstalt, Berlin, GermanyAbstractAt the Metrology Light Source (MLS) [1] owned by thePhysikalisch-Technische Bundesanstalt (PTB) the bunchlength can be varied by more than two orders of magnitude[2]. The bunch length manipulation is achieved by varyingdifferent machine parameters, such as RF-voltage ampli-tude up to 500 kV and the momentum compaction factor αover three orders of magnitude. The subject of this articleis the measurement of THz bursting thresholds at the MLSfor different bunch lengths.INTRODUCTIONShort bunch operation of electron storage rings is mo-tivated by users interested in short photon pulses as wellas the generation of coherent synchrotron radiation (CSR).The bunch current that is stably storable in short bunches islimited by various storage ring parameters. The transitionfrom stable to bursting CSR was first observed at BESSY II[3]. The transition point is called bursting threshold andwas measured at several light sources by now. The valueof the threshold depends on various properties e.g. beamoptics, RF-parameters and the dimensions of the vacuumchamber. Understanding the bursting process is relevantfor the design of new short pulse storage rings [4] or otherhigh peak current facilities.STORAGE RING PREPARATIONThe first three orders of the momentum compaction fac-tor α(δ) = α0+α1δ+α2δ2 . . . as a function of the momen-tum deviation δ = ∆pp0were set to the desired values [2].α0 was directly measured by Compton backscattering tocheck the scaling of the synchrotron oscillation frequencyfs with RF-voltage V . A measurement of the longitudi-nal tune was then used to calculate α0. The higher ordersα1 and α2 were adjusted as close to zero as possible bydedicated sets of sextupole and octupole magnets eliminat-ing the RF-frequency dependence of the longitudinal tune.Transverse chromaticities were set to small positive val-ues (≈ 0.2). Individually powered quadrupoles were usedto eliminate the dispersion D and its derivative D′ at theposition of the RF-cavity avoiding transverse-longitudinalcoupling predicted by tracking simulations. The currentmeasurement was performed with a diode calibrated by acurrent transformer. Single bunch operation was chosento avoid ion effects, coupled bunch instabilities and fillingpattern inhomogeneities.∗markus.ries@helmholtz-berlin.deTable 1: Selected MLS Machine Parametersparameter valueelectron energy ≤ 629 MeVα0 −3 · 10−2 to 7 · 10−2circumference 48 mRF-frequency fRF 500 MHzRF-voltage V ≤ 500 kVdipole bending radius ρ 1.528 mfull vacuum chamber height h 42 mmTHz BURSTINGMeasurement SetupBursting measurements were carried out at the THzbeam port of the MLS [5]. As a detector an InSb hot elec-tron bolometer was used. Its spectral sensitivity ranges upto 50 cm−1. The detector is only able to resolve frequen-cies of up to 1 MHz and therefore unable to resolve the rev-olution time of a single bunch. However, it is fast enoughto measure fluctuations of the CSR power introduced bybursting, expected to be below 200 kHz. The InSb signalwas recorded using a spectrum analyzer.Figure 1: Temporal fluctuation of the THz power as a func-tion of the single bunch current plotted in the frequencydomain. The measurement was performed using an InSbhot electron bolometer at a the storage ring parametersα0 = 1.3 · 10−4 and V = 330 kV.MeasurementAll measurements discussed here were conducted atan electron beam energy of 629 MeV. Figure 1 showsa measurement where the electron current was changedWEPPR046 Proceedings of IPAC2012, New Orleans, Louisiana, USAISBN 978-3-95450-115-13030Copyrightc ○2012byIEEE–ccCreativeCommonsAttribution3.0(CCBY3.0)—ccCreativeCommonsAttribution3.0(CCBY3.0)05 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, Countermeasuresby about three orders of magnitude with other parametersfixed. Bursting starts at about 5 µA. The variation of theRF-voltage is another way to find the bursting threshold.Thus multiple bursting thresholds can be measured withoutchanging the magnetic properties of the storage ring. Fora given beam optics (α) and single bunch current I theRF-voltage was slowly changed. Measurements show thatthere is no significant difference whether V is increasedor decreased to determine the threshold. The thresholddoes not differ between entering or leaving the burstingregime. Figure 2 shows a selected measurement of abursting threshold using the variation of the RF-voltage.The different appearance compared to Fig. 1 is caused bya different parameter range in terms of I , U and α0.Figure 2: Temporal fluctuation of the THz power as a func-tion of RF-voltage in the frequency domain. The mea-surement was performed at a the storage ring parametersα0 = 5 · 10−4 and I = 300 µA.Periodic fluctuations of the CSR power at the onsetof the instability are observed at characteristic frequenciesin the range up to 50 kHz depending on I , α0 and V .As a criterion for the experimental identification of thebursting threshold a signal of 10 dB above the noisefloor was chosen. This value compromises between anoverestimation of the threshold and the measurement errorand has proven to yield consistent results. The drawbackof this definition is that it means the bunch is alreadybursting. Figure 3 shows a set of spectra near the thresholdaccording to the previous definition.The MLS control system [6] allowed to fully automa-tize measurements resulting in a high resolution and highreproducibility. The algorithm can be outlined as:1. sweep RF-voltage slowly e.g. from 500 kV to 15 kV,2. during sweep:• record Fourier transform of THz bursting signal• record other beam parameters3. at the end of sweep:• restore RF-voltageFigure 3: RF-voltage dependence of the THz power at thebursting threshold. The black line shows the spectrum ofthe fluctuations of the CSR power measured by an InSb hotelectron bolometer. Blue and red lines indicate the spectrabelow and above the threshold.• use automatic scraper procedure to reduce cur-rent e.g. by 5%4. repeat.Offline analysis yields one value for the bursting thresholdper sweep.Figure 4: Examples of bursting threshold measurements at629 MeV with α0 = 0.0005. One bursting threshold (onedata point) corresponds to one RF-voltage sweep as shownin Fig. 2.Figure 4 shows sets of measurements of the current de-pendent bursting threshold at one specific α0. A very char-acteristic feature is a steep change in the voltage neededto reach the bursting threshold in the range from 20 µAto 30 µA single bunch current. This feature is found fordifferent α0 at different RF-voltages, but always at zero-current bunch lengths in the range from 0.8 mm to 1.6 mm.Proceedings of IPAC2012, New Orleans, Louisiana, USA WEPPR04605 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, CountermeasuresISBN 978-3-95450-115-13031 Copyrightc ○2012byIEEE–ccCreativeCommonsAttribution3.0(CCBY3.0)—ccCreativeCommonsAttribution3.0(CCBY3.0)Scaling LawsMeasurements were repeated to check for reproducibil-ity as well as different influences e.g. octupole. Figure 5Figure 5: Results of the measurement of the burstingthreshold. Different symbols correspond to different α0.Colors indicate measurement sets within one α0 set. Dot-ted lines correspond to I/V = constant.shows multiple sets of measurements for different α0. Onemeasurement (cyan box) was taken at a large value of α2(≈ 10), which seems to have an influence in the short bunchlength regime. All measurements show the same structureimplying that there is a scaling law involved allowing toplot the results in scaled units.The calculation of bursting thresholds can be approachedfrom coasting beam theory as well as from the bunchedbeam theory [7, 8]. Both theories yield results, which canbe written in the following form:σ73 =Z0c2qρ138pi2ξthf2RFIV cos (φs), (1)whereas σ is the bunch length, Z0 the free spaceimpedance, q the harmonic number and φs the synchronousphase. For bunched beam theory the scaled threshold cur-rent ξth can be approximated by:ξth = ξth(χ) = 0.5 + 0.34χ− 0.385e−(χ−0.25)22·0.022 , (2)with the shielding parameter χ = σρ 12 /h 32 . ξth(χ) is ex-tracted from [8] and additionally modified by a Gaussiandip to roughly account for a drop of the expected thresholdat χ = 0.25 [7]. From coasting beam theory follows:ξth = 7.456 · 313 /4pi ≈ 0.856. (3)Taking into account the MLS machine parameters fromTab. 1, the dip of Eq. 2 generated by the Gaussian is situ-ated at a bunch length of σdip = 1.7 mm (5.8 ps). Figure 6corresponds to Fig. 5 but uses a scaled view in analogy toEq. 1 to account for different machine parameters [9]. Thebunch length was not measured. Instead the zero currentFigure 6: Scaled values of measured bursting thresholds.Different symbols correspond to different α0. Colors indi-cate measurement series within one α0 set. The small insetis a zoom in the region, where the sets start to spread. Thedotted line marks I/V = 1.4 µA/kV.bunch length σ0 was calculated based on measuring V andfs [8]. The bunch lengths obtained agree well comparedwith streak camera measurements for larger bunch lengths.The scaling agrees with the theory for bunch lengths largerthan 2 mm. At about σdip there is a characteristic feature inthe data (cf. Fig. 4,6). For smaller bunch lengths the mea-surements seem to systematically deviate from the scalinglaw in dependence of α0.ACKNOWLEDGMENTThis work was excellently supported by our HZB andPTB colleagues in particular by R. Mu¨ller (PTB) and P.Kuske (HZB). It is a pleasure to thank C. Evain (formerSOLEIL), V. Judin (ANKA) and I. Martin (DIAMOND)for very interesting cooperative measurements accompa-nied by very fruitful discussions. For ongoing supportand comments we acknowledge the help of A. Jankowiak(HZB) and G. Ulm (PTB).REFERENCES[1] B. Beckhoff et al., Phys. Status Solidi B 246, p. 1415 (2009).[2] J. Feikes et al., Phys. Rev. ST Accel. Beams 14, 030705(2011).[3] M. Abo-Bakr et al., Phys. Rev. Lett. 88, 254801 (2002).[4] G. Wu¨stefeld et al., IPAC 2011, San Sebastia´n, Spain, p.2936-2938 (2011).[5] R. Mu¨ller et al., J. Infrared Milli Terahz Waves 32, 742(2011).[6] J. Feikes et al., IPAC 2011, San Sebastia´n, Spain, p. 2927-2929 (2011).[7] K. L. F. Bane, Y. Cai and G. Stupakov, Phys. Rev. ST Accel.Beams 13, 104402 (2010).[8] Y. Cai, IPAC 2011, San Sebastia´n, Spain, p. 3774 (2011).[9] G. Wu¨stefeld et al., IPAC 2010, Kyoto, Japan, p. 2508 (2010).WEPPR046 Proceedings of IPAC2012, New Orleans, Louisiana, USAISBN 978-3-95450-115-13032Copyrightc ○2012byIEEE–ccCreativeCommonsAttribution3.0(CCBY3.0)—ccCreativeCommonsAttribution3.0(CCBY3.0)05 Beam Dynamics and Electromagnetic FieldsD05 Instabilities - Processes, Impedances, Countermeasures

THz Bursting Thresholds Measured at the Metrology Light Source

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THz Bursting Thresholds Measured at the Metrology Light Source

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