High quality plasma wakefield acceleration experiment in linear regime at SPARC_LAB Stefano Romeo on behalf of SPARC_LAB collaboration stefano.romeo@lnf.infn.it European Advanced Accelerator Concepts, La Biodola 26/09/2017

Blow-out regime 𝜶≫𝟏 𝐸 𝑟 = 𝑛 0 2 𝜀 0 𝑟 There is not a complete analytical solution of the fields inside plasma Ion column model 1 𝑟 𝜕 𝜕𝑟 𝑟( 𝐸 𝑟 −𝑐 𝐵 𝜃 ) = 𝜌 𝜀 0 − 𝜇 0 𝑐 𝐽 𝑧 Since inside bubble there is no current, the transverse field can be derived from electrostatic component only (cylinder with a constant charge density 𝑛 0 ) 𝐸 𝑟 = 𝑛 0 2 𝜀 0 𝑟 Blow out field In the position of the bubble closing there is a spike in the accelerating field Linear dependency of the focusing Accelerating field doesn’t depend on transverse position Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Linear regime 𝒏 𝒃 𝒏 𝟎 =𝜶≪𝟏 𝑊 𝑧,𝑟 =𝑒 𝐸 + 𝑣 × 𝐵 𝑧,𝑟 𝒏 𝒃 𝒏 𝟎 =𝜶≪𝟏 Linear field In linear approximation it is possible to derive an analytical solution for the fields It is possible to inject a beam in the crest region (no focusing) Non linear dependency of the focusing Accelerating field depends on transverse position Lower field 𝑊 𝑧,𝑟 =𝑒 𝐸 + 𝑣 × 𝐵 𝑧,𝑟 𝐸 𝑧 𝑟,𝜉 =𝑅 𝑟 𝑍 ′ 𝜉 𝐸 𝑟 𝑟,𝜉 = 𝑅 ′ 𝑟 𝑍 𝜉 𝑍 𝜉 = 2𝜋 𝑚 𝑒 𝑐 2 𝑒 𝛼 𝑘 𝑝 𝜎 𝑧 𝑒 − 𝑘 𝑝 2 𝜎 𝑧 2 /2 𝑠𝑖𝑛 𝑘 𝑝 𝜉 𝑍 ′ (𝜉)= 2𝜋 𝑚 𝑒 𝑐 2 𝑒 𝛼 𝑘 𝑝 2 𝜎 𝑧 𝑒 − 𝑘 𝑝 2 𝜎 𝑧 2 /2 𝑐𝑜𝑠 𝑘 𝑝 𝜉 𝑅 0 = 𝑘 𝑝 2 𝜎 𝑟 2 2 𝑒 𝑘 𝑝 2 𝜎 𝑧 2 2 𝛤 0, 𝑘 𝑝 2 𝜎 𝑟 2 2 𝑅 𝑟 =𝑅 0 − 𝑘 𝑝 2 4 𝑟 2 + 𝑘 𝑝 2 32 𝑟 4 +… 𝑅 ′ 𝑟 =− 𝑘 𝑝 2 2 𝑟+ 𝑘 𝑝 2 8 𝑟 3 +… 𝑘 𝑝 = 2𝜋 𝜆 𝑝 = 𝑒 2 𝑛 0 𝜀 0 𝑚 𝑒 𝑐 2 Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

High quality acceleration in linear regime Transverse contribution (sliced) 𝐶 𝑆 =− 𝑒 𝑘 𝑝 2 𝑍 𝜉 𝐿 8 𝜎 𝑟,𝐷 2 𝛾 𝑚 𝑒 𝑐 2 Spherical aberration coefficient 𝜎 𝐸,𝑓 = 𝜎 𝐸,𝑖 2 + 1− 𝛾 0 𝛾 2 tan 2 𝜙 0 𝑘 𝑝 2 𝜎 𝑧,𝑤 2 + 3 𝑘 𝑝 4 𝜎 𝑧,𝑤 4 4 + 3 𝑘 𝑝 4 𝜎 𝑟,𝑤 4 16 𝑅 2 (0) − 𝑘 𝑝 4 𝜎 𝑟,𝑤 2 𝜎 𝑧,𝑤 2 4𝑅 (0) Bunch length LT correlation Chirp Energy spread growth High quality requires: 𝜎 𝑟,𝑤 ≪ 𝜎 𝑟,𝐷 𝑘 𝑝 𝜎 𝑧,𝑤 ≪1 In many realistic cases, beam loading is not negligible Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

BLAST scheme 𝛽 𝑥 = 2 𝛾 𝑘 𝑝 𝜎 𝑥 = 4 𝛾Λ𝒵 𝜀 𝑛 𝜎 𝑥 = 4 1 𝛾 2 𝜀 𝑛 𝑘 𝑝 The driver generates a linear field Witness can be injected on crest The field generated by the witness is non linear Focusing is guaranteed by a beam loading effect 𝜎 𝑥 = 4 𝛾Λ𝒵 𝜀 𝑛 𝜎 𝑥 = 4 1 𝛾 2 𝜀 𝑛 𝑘 𝑝 𝛽 𝑥 = 2 𝛾 𝑘 𝑝 Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Energy spread growth 𝜕 𝐸 𝑧 𝜕𝜉 =0 Beam loading compensation The longitudinal field generated by a low charge high density bunch can be described by linear equations Barov, Nick, et al. "Energy loss of a high-charge bunched electron beam in plasma: Analysis." Physical Review Special Topics-Accelerators and Beams 7.6 (2004): 061301. The beam loading compensation occurs when the first derivative of the accelerating field in the center of the witness is 0 Chiou, T. C., and T. Katsouleas. "High beam quality and efficiency in plasma-based accelerators." Physical review letters 81.16 (1998): 3411. From the analytical model of field it is possible to evaluate the energy spread LCLS, CDR, ch07. SLAC 𝜕 𝐸 𝑧 𝜕𝜉 =0 sin 𝜙 0 =− 𝑘 𝑝 𝑍 𝑤 0 𝑅 𝑤 0 𝐸 0 Beam loading compensation For any witness in a great range of parameters it’s possible to find a bunch separation that guarantees beam loading compensation 𝜎 𝐸,𝑓 = 𝜎 𝐸,𝑖 2 + 1− 𝛾 0 𝛾 2 3 𝑘 𝑝 4 𝜎 𝑧,𝑤 4 4 Energy spread growth depends only on witness length Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

BLAST scheme transverse matching A correlated focusing on longitudinal dimension causes emittance growth 𝜀 𝑛,𝑐 = 𝑘 2 𝜎 𝑥 2 𝐿 𝑐 𝑓 2 𝜉 Hypotesis of energy spread compensation using beam loading (NO BUNCH SHAPING) 𝜕 𝐸 𝑧 𝜕𝜉 =0 𝜕( 𝐸 𝑟 −𝑐 𝐵 𝜃 ) 𝜕𝜉 =0 Hypotesis of quasi-linearity 𝐽 𝑧 =0 Lu, W., et al. "A nonlinear theory for multidimensional relativistic plasma wave wakefields a." Physics of Plasmas 13.5 (2006): 056709. 𝜕𝜌 𝜕𝑟,𝜉 =0 𝜕( 𝐸 𝑟 −𝑐 𝐵 𝜃 ) 𝜕𝜉 =0 Consequences 𝐽 𝑟 =0 𝜎 𝑚 = 4 1 𝛾 2𝜀 𝑛 𝑘 𝑝 𝑛= 𝑛 0 2 Ion column model can be applied Stupakov, G., et al. "Wake excited in plasma by an ultrarelativistic pointlike bunch." Physical Review Accelerators and Beams 19.10 (2016): 101302. Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Working point parameters SPARC_LAB Working Point Driver Injection Witness 200 10.3 1.26 37.2 3 0.1 17 0.3 10 0.68 0.42 1.2 0.06 2⋅ 10 16 2 5 𝛾 𝜎 𝑟 [μm] 𝜎 𝑧 [μm] 𝜎 𝐸 [%] 𝜀 𝑛 [μm] 𝑄[pC] 𝐼[kA] 𝑄 𝑛 0 [ cm −3 ] 𝐸 𝑧 [GV/m] Δ𝑠[cm] 𝝀 𝒑 ≈𝟐𝟑𝟓 𝛍𝐦 Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Hybrid Tool: Architect Bunch(es) are treated kinetically background plasma as a fluid cylindrical symmetry assumed run time figure of merit: 1cm/h no-Quasi Static Approximation Code reliability respect to full PIC code showed both for linear and quasi-linear regimes Massimo, F., S. Atzeni, and A. Marocchino. "Comparisons of time explicit hybrid kinetic-fluid code Architect for Plasma Wakefield Acceleration with a full PIC code. " Journal of Computational Physics 327 (2016): 841-850. Marocchino, A., et al. "Efficient modeling of plasma wakefield acceleration in quasi-non-linear-regimes with the hybrid code Architect.“ Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 829 (2016): 386-391. Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Bunch separation scan Optimal injection distance 𝟎.𝟓𝟎𝟓 𝝀 𝒑 The model developed for BLAST scheme doesn’t forsee the driver head erosion effects A simulation scan is required in order to evaluate 𝑬 𝟎 and 𝝓 𝟎 sin 𝜙 0 =− 𝑘 𝑝 𝑍 𝑤 0 𝑅 𝑤 0 𝐸 0 Optimal injection distance 𝟎.𝟓𝟎𝟓 𝝀 𝒑 Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Witness longitudinal phase space Unoptimized injection phase Optimized injection phase Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Energy spread evolution and accelerating gradient 𝜎 𝐸,𝑓 = 𝜎 𝐸,𝑖 2 + 1− 𝛾 0 𝛾 2 3 𝑘 𝑝 4 𝜎 𝑧,𝑤 4 4 Energy spread growth depends only on witness length Final accelerating gradient 1.07 GV/m 𝑬 𝟎 is not constant for the first cm Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Witness envelope Envelope doesn’t follow the prevision for the first cm After the first cm the simulated background approaches the theoretical one Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

SPARC_LAB layout for beam driven PWFA experiments Incoming witness Outcoming witness 𝛾=200 𝛾=300 𝜀 𝑛 =0.3 𝑚𝑚 𝑚𝑟𝑎𝑑 𝜀 𝑛 =0.308 𝑚𝑚 𝑚𝑟𝑎𝑑 𝜎 𝐸 =0.1% 𝜎 𝐸 =0.22% Acceleration parameters Δ𝑠=5𝑐𝑚 𝐸 𝑧 =1.07𝐺𝑉/𝑚 𝑬≅𝟏𝟎𝟎−𝟏𝟓𝟎 𝐌𝐞𝐕 𝜺≅𝟎.𝟑−𝟒 𝐦𝐦 𝐦𝐫𝐚𝐝 𝝈 𝑬 <𝟎.𝟏% 𝝈 𝒛 =𝟒−𝟕𝟓 𝛍𝐦 High quality PWFA Beam diagnostic Photoinjector that allows to create trains of high quality electron bunches 2 S band accelerating cavities (velocity bunching) C band accelerating cavity FEL Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Stability analysis 𝜎 𝐸 =0.4±0.2% 𝛾=306±14 A scan of 30 simulation was performed using the latin hypercube sample in order to analyze the working point robustness The chosen parameter range of the scan is consistent with measurements performed at SPARC_LAB injector (worst results) 𝜎 𝑟 ±15% 𝜎 𝑧 ±8% 𝑄±10% Δ𝑧±8% 𝜎 𝐸 =0.4±0.2% 𝜀 𝑛 =0.307±0.005 mm mrad 𝛾=306±14 Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Conclusions Results Theoretical basis for working point design Low energy working point fullfilled First working point stability test performed with promising results Future perspectives Start to end simulation of a BLAST working point at SPARC_LAB Stability analysis in the context of a S2E simulation Stefano Romeo EAAC 2017, La Biodola – 26/09/2017

Thanks for the attention Acknowledgements: SPARC_LAB GROUP EAAC organizing committee Old and new friends here Stefano Romeo PhD defense La Sapienza, University of Rome 2017/09/20

Half density ion column 𝜕 𝐸 𝑧 𝜕𝜉 =0 𝜕 𝐸 𝑧 𝜕𝑟 = 𝜇 0 𝑐 𝐽 𝑟 𝜕 𝐽 𝑟 𝜕𝜉 =0 𝐽 𝑟 =0 𝐽 z =0 𝜌= 𝑛 0 2 𝜕 (𝐸 𝑟 −𝑐 𝐵 𝜃 ) 𝜕𝜉 = 𝜇 0 𝑐 𝐽 𝑟 =0 𝜕𝜌 𝜕𝜉 =0 1 𝑟 𝜕 𝜕𝑟 𝑟( 𝐸 𝑟 −𝑐 𝐵 𝜃 ) = 𝜌 𝜖 0 − 𝜇 0 𝑐 𝐽 𝑧 Stefano Romeo PhD defense La Sapienza, University of Rome 2017/09/20