Apsimon R

Burt G

Doebert S

Fiorito R

Mete O

Welsch C P

Xia G

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MODELING OF AN ELECTRON INJECTOR FOR THE AWAKE PROJECTO. Mete∗, G. Xia, †The University of Manchester, Manchester, UKR. Apsimon, G. Burt, †Lancaster University, Lancaster, UKS. Doebert, CERN, Geneva, SwitzerlandR. Fiorito, C. Welsch, †The University of Liverpool, Liverpool, UKAbstractParticle-in-cell simulations were performed by usingPARMELA to characterise an electron injector with abooster linac for the AWAKE project in order to providethe baseline specifications required by the plasma wakefieldexperiments. Tolerances and errors were investigated. A3GHz travelling wave structure designed by using CST code.Particles were tracked by using the field maps acquired fromthese electromagnetic simulations. These results are pre-sented in comparison with the generic accelerating structuremodel within PARMELA.INTRODUCTIONThe AWAKE project is a proton driven plasma wakefieldacceleration experiment by utilising the driver proton beamfrom CERN’s SPS injector and a custom photo injector forthe witness (trailing) electron beam [1,2].Figure 1 shows the layout of the injector consisting ofan S-band standing wave RF gun (SW), previously used inCERN’s PHIN photo injector [3], followed by laser optics todirect the laser onto the cathode. Beamline continues withbeam current and position monitors and a pepper pot emit-tance measurement system suitable for a beam subject tospace charge effects. A new S-band booster section (acceler-ating travelling wave structure, ATS) was designed by usingCST suite [4] and introduced in the model to boost the beamenergy to a region adjustable between 16 − 20MeV. ATS isfollowed by a quadrupole triplet and a downstream screento perform quadrupole scans for emittance measurement.The tracking studies have been performed by usingPARMELA [5]. For ATS the model provided by PARMELAand field maps extracted from CST were used and compared.Implementation of CST maps into PARMELA are discussedin the following sections.BOOSTER LINACAn S-band booster linac, ATS, was designed as a trav-elling wave structure with constant gradient of 15MV/mthrough the entire structure (Fig.2) . It consists of 30 cellswith 120◦ phase advance and varying radii matched to 1 μmprecision. ATS was optimised for low reflection coefficient∗ oznur.mete@manchester.ac.uk† and The Cockcroft Institute, Sci-Tech Daresbury, Warrington, UKof about 2.5%. The multipole terms [7] due to transverseRF-kicks are 9.4241 × 10−7 mT, 7.8418 × 10−5 mT/m and4.9 × 10−3 mT/m2, respectively, from dipole to sextupleterms.USING CST FIELD MAPS IN PARMELAIn order to use CST field maps in PARMELA trackingsimulations, a MATLAB [6] script was prepared to for-mat the standard CST field maps into the form requiredby PARMELA . The information that PARMELA requireson each line of a field map can be found in Table IV-2 fromthe program manual [5].In PARMELA, two field maps must be provided for a trav-elling wave structure; one produced with Neumann boundarycondition (cosinemap) and the other with Dirichlet boundarycondition (sine map). These fields which are shifted in phaseby 90◦ are fed into PARMELA by using the TRWCFIELDcommand. A single TRWAVE line is used to represent theentire ATS including the bore tubes with lengths equal toa cell length at each end of ATS to account for the fringefields.BASELINE DESIGNIn order to maintain the balance between the emittancegrowth and the energy spread within ATS, a 10◦ off-crestphase was chosen for the baseline design by using the CSTmaps of the current design while the SW is optimised forthe highest energy. In addition, the same beam dynamicsconditions can be met with on-crest RF phase in the case ofthe PARMELA model for a travelling wave structure.The space charge component of the emittance is com-pensated using the field produced by two solenoids locatedaround the SW. Slightly different working points to satisfythe constant envelope condition were determined for the fielddistributions from PARMELA and CST models.The beam dynamics specifications are presented in Table1 in comparison with these two.Table 1: Required specification and values produced withdifferent models.Parameter Required PARMELA Map CST MapE (MeV) 16 16 16ΔE/E (%) 0.5 1.3 1.1ε x,y (mm mrad) 2 1.7,1.8 2.3, 2.5βx,y (m) 5 4, 4 0.8, 0.8αx,y 0 -0.2,-0.2 -1.4, -1.2Figure 1: The layout of the photo injector and the booster linac section to provide a witness beam for the AWAKE plasmawakefield acceleration experiment.Figure 2: A snapshot from CST design of the S-band trav-elling wave structure as the energy booster linac for theelectron injector.RF PHASE ERRORSVariations in the beam dynamics due to the RF phase er-rors induced on SW and ATS were investigated. As they areplanned to be fed by the same klystron, the same phase errorcan be assigned to both structures. A typical phase errorof 300 fs (1σ) was induced over a 500 samples assumingthe RF jitter as the error source. Resulting variations werepresented in Table 2. Especially time of flight errors arecrucial to determine as they affect the synchronisation in theentrance of the plasma cell.Table 2: Implications of the phase errors on various beamdynamics observable.Parameter 1σ Error Error/Degree of the phase jitterE (keV) 1.4 5ΔE/E (ppm) 28 93ε x,n (nm-rad) 2 7Time of flight (fs) 57 190EMITTANCE DIAGNOSTICS UNDERSPACE CHARGEFor a photo injector, the dominant limitation for the emit-tance diagnostics is the effect of space charge. Figure 5shows the ratio of two defocusing terms from the envelopeequation; the space charge and the outward pressure dueto beam emittance. Different curves correspond to differ-ent bunch charges and lengths which are considered withinthe operational range of the injector. Although some cases(a)(b)Figure 3: a) Transverse normalised emittance and b) thebeam size as a function of the distance from the cathode.(Solid and dashed lines are x and y axes, respectively.)are less space charge dominated (> 1) than others, in allcases considered, space charge is the dominating componentof the total beam emittance. In the pre-booster region, apepper-pot measurement system will be implemented as astandard technique to measure the emittance of space chargedominated beams. It is currently being designed at the Cock-croft Institute. For the post-booster region quadrupole scantechnique is planned. The feasibility and reliability of thistechnique was assessed by simulations. Figure 6 comparesthe emittance values calculated from a simulated quadrupolescan and the rms emittance value at the same location. TheFigure 4: Evolution of the beam energy spread as a functionof the distance from the cathode.Figure 5: The ratio of space charge and emittance term ofthe beam envelope as a function of the distance from thecathode.results differ 2% implying that emittance can be reliablymeasured within measurement error by using quadrupolescan in the post-booster region.Figure 6: A simulated quadrupole scan result in the post-booster region.We have also evaluated the Optical Diffraction Radia-tion Dielectric Foil Radiation Interference (ODR-DFRI) tomeasure the rms emittance. This technique which is a modi-fied version of the Optical Transition Radiation Interference(OTRI) [8] technique extends the latter to lower beam en-ergies and has the advantage of single shot operation. TheFigure 7: Beam size, divergence and the correlation termsfor the range of working points of the injector.technique can be used in conjunction with a new algorithmdeveloped to use sparse data from a quad scan to measure therms emittance of space charge dominated beams [9]. Thus,the lower limit of measurable divergence values is 0.3mradfor the injector. Figure 7 shows the beam size, divergenceand the correlations terms for a range of working points forthe injector. As seen in the figure, the divergence valuesrange from 0.5 and upwards implying that the ODR-DFRItechnique could have been implemented for this system as acomplementary technique to the conventional quadrupolescan in case of more severe space charge limitations.CONCLUSIONS AND OUTLOOKThe tracking simulations for the injector were performedby using the field models from both PARMELA and CST.Slight discrepancies in the results are under investigation.Errors due to phase jitter were studied. Emittance diagnos-tics under space charge effect is studied for both low andhigher energies.ACKNOWLEDGEMENTSThis work was supported by the Cockcroft Institute CoreGrant and STFC. Authors would like to express their grati-tude to Janet Susan Smith and Stefano Mazzoni for usefulcommunications on feasibility of beam diagnostics equip-ment during the course of this study.REFERENCES[1] A. Caldwell et al., CERN-SPSC-2013-013 (2013).[2] O. Mete et al., Proc. of IPAC2014, MOPRI50 (2014).[3] R. Roux, et al., CARE Note-2004-034-PHIN (2004).[4] www.cst.com[5] L. M. Young, LA-UR-96-1835 (2005).[6] www.mathworks.co.uk[7] R. G. Olave et al., Proc. of IPAC2013, WEPAC43 (2013).[8] R. Fiorito et al., PRSTAB 9, 052802 (2006).[9] K.Poorrezaie, et al., PRSTAB, 16, 082801 (2013).

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Modeling of an Electron Injector for the AWAKE Project

Modeling of an Electron Injector for the AWAKE Project

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