The 2nd European Advanced Accelerator Concepts Workshop 13-19 September 2015, La Biodola, Isola d'Elba, Italy Dynamics of Electron Bunches at Enhancement of Laser Plasma Wakefield Acceleration by Beam Plasma Wakefield Acceleration O.M. Svystun, V.I.Maslov, I.M.Onishchenko, V.I.Tkachenko NSC “Kharkov Institute of Physics and Technology” svistun_elena@mail.ru Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Outline Introduction Parameters of numerical simulation Dynamics of electron bunches at enhancement of laser plasma wakefield acceleration by beam plasma wakefield acceleration Summary Elena Svystun Outline of talk September 13 - 19, EAAC-2015

Introduction: the advantages of LPA Laser Plasma Accelerators have well-known advantages: LPAs have the ability to sustain accelerating gradients that are several orders of magnitude greater than those obtained in conventional linear accelerators. E. Esarey et al., Rev. Mod. Phys. 81, 1229 (2009); V. Malka et al., Science 298, 1596 (2002) ; W.P. Leemans et al., AIP Conf. Proc. 1299, pp. 3-11 (2010) Cornell's 7-cell superconducting RF cavity RF cavity Electric field < 100 MV/m Plasma cavity Electric field > 100 GV/m Elena Svystun Introduction: the advantages of LPA September 13 - 19, EAAC-2015

Introduction: progress of LPA LPAs have the potential to produce short electron bunches with high energy for various applications [E. Esarey et al., Rev. Mod. Phys. 81, 1229 (2009)]. Over the past decade, due to the rapid development of laser technology LPAs have made significant progress towards producing high quality beams with higher energy of order several GeV. * W.P. Leemans et al., Phys. Rev. Lett. 113, 245002 (2014) Lawrence Berkeley National Laboratory * Multi-GeV electron beams with energy up to 4.2 GeV have been produced from a 9-cm-long capillary discharge waveguide with a plasma density of ≈7·1017 cm−3, powered by laser pulses with peak power up to 0.3 PW. Energy spectrum of a 4.2 GeV electron beam measured using the broadband magnetic spectrometer. The white lines show the angular acceptance of the spectrometer. The two black vertical stripes are areas not covered by the phosphor screen. Elena Svystun Introduction: progress of LPA September 13 - 19, EAAC-2015

S.V. Bulanov et al., Plasma Phys. Rep. 23 (1997) 259 Introduction The main aim of this work is to research the electron bunch dynamics at enhancement of Laser Plasma Wakefield Acceleration by Beam Plasma Wakefield Acceleration. For this purpose, the numerical simulation of the plasma wakefield excitation by a laser pulse in the blowout regime was carried out. Parameters of the numerical simulation Fully relativistic electromagnetic two dimensional particle – in – cell simulation was performed by the UMKA2D3V code (Institute of Computational Technologies) S.V. Bulanov et al., Plasma Phys. Rep. 23 (1997) 259 A computational domain (x, y) has a rectangular shape: 0 < x < 800λ and 0 < y < 50λ, λ is the laser pulse wavelength, λ = 0.8 µm. The computational time interval is τ = 0.05. The number of particles per cell is 8 and the total number of particles is 15.96·106. The simulation was carried out up to 800 laser periods. The period of the laser pulse t0 = 2π/ω0, where ω0 is the laser frequency. Elena Svystun Introduction September 13 - 19, EAAC-2015

Parameters of the numerical simulation The s-polarized laser pulse enters the computation region filled with uniform plasma from the left boundary and is incident normally on the plasma. The plasma density n0 = 0.01016nc= 1.8·1019 cm-3, where the critical plasma density nc = meω02/(4πe2), me is the electron mass, e is the electron charge. The laser pulse is defined with a "cos2" distribution in its spatial longitudinal direction and has a Gaussian profile in the transverse direction. FLHM = 2λ. FWHM = 8λ. The simulation was performed for the peak amplitude of the normalized vector potential of the laser field, a0 = eEx0/mecω0 = 5, where e is the electron charge, Ex0 is the electric field amplitude, me is the electron mass, c is the speed of light. The peak laser intensity: I0 = 5.3·1019 W/cm2. Coordinates x and y, time t, electric field amplitude Ex and electron plasma density n0 are given in dimensionless form in units of λ, 2π/ω0, mecω0/2πe, meω02/16π3e2, respectively. Elena Svystun The parameters of the numerical simulation September 13 - 19, EAAC-2015

Self-injection of three short electron bunches The plasma density: n0 = 0.01016nc= 1.8·1019 cm-3 The peak normalized laser field strength : a0 = 5 The peak laser intensity: I0 = 5.3·1019 W/cm2 FLHM = 2λ and FWHM = 8λ, the laser pulse wavelength: λ = 0.8 µm bunches 3rd 2nd 1st Wake perturbation of plasma electron density excited by one laser pulse at the time t = 105t0 Longitudinal component of the wakefield Ex excited by one laser pulse with intensity at the time t = 105t0 Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Self-injection of three short electron bunches Wake perturbation of plasma electron density and off-axis (y = 25.5) radial wake force Fr (red line) excited by one laser pulse at the time t = 105t0 The 2nd bunch is decelerated and it is close to the area of a strong defocusing field. The 3rd bunch is accelerated. bunches 3rd 2nd 1st Wake perturbation of plasma electron density and longitudinal component of the wakefield Ex (red line) excited by one laser pulse at the time t = 105t0 Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Evolution of the wake perturbation of plasma electron density Wake perturbation of plasma electron density and longitudinal component of the wakefield Ex (red line) excited by one laser pulse time t = 115t0 time t = 125t0 time t = 130t0 bunches 3rd 2nd 1st time t = 135t0 The 2nd self-injected bunch approaches the area of a strong defocusing field. The 2nd bunch continues to decelerate and enhances the field which accelerates the 3rd bunch. Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Defocusing of the 2nd self-injected electron bunch bunches 3rd 2nd 1st Wake perturbation of plasma electron density and longitudinal component of the wakefield Ex (red line) excited by one laser pulse at the time t = 135t0 The 2nd bunch is located in the region of defocusing field and the 2nd bunch approaches the region of defocusing field with higher amplitude. Wake perturbation of plasma electron density and off-axis (y = 25.5) radial wake force Fr (red line) excited by one laser pulse at the time t = 135t0 Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Wake perturbation of the plasma electron density excited by one laser pulse at the time t = 140t0 and longitudinal component of the wakefield Ex off-axis (y = 25.5) radial wake force Fr bunches 3rd 2nd 1st The 2nd bunch is affected by the defocusing field. Therefore, when the 2nd bunch further approaches the 1st wakefield steepening (the 2nd front of the 1st bubble), its self- cleaning becomes faster due to defocusing. The other bunches are in focusing fields and oscillate along the radius. The 1st dense accelerated bunch has been focused to the axial region, so the field of its space charge has exceeded the field of bubble. Hence at the next time the 1st bunch will be periodically expanded. Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Wake perturbation of plasma electron density excited by one laser pulse time t = 145t0 time t = 150t0 time t = 155t0 bunches 3rd 2nd 1st time t = 160t0 The 2nd self-injected electron bunch continues to defocus and self-clean. Thus the 2nd witness bunch becomes driver and transfers its energy to the next witness bunch. Finally this driver bunch is completely self-cleaned due to defocusing by radial fields of the bubble. Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Transformation of the 1st witness bunch to the driver The 1st witness bunch becomes driver together with the partially dissipated laser pulse. They provide further acceleration of witness. time t = 435t0 time t = 490t0 time t = 490t0 1st witness bunch Wake perturbation of plasma electron density and longitudinal component of the wakefield Ex (red line) excited by one laser pulse Elena Svystun The Electron Bunches Dynamics in LPWA September 13 - 19, EAAC-2015

Summary It has been shown that the Laser Plasma Wakefield Acceleration Scheme changes with time into combined Laser Plasma Wakefield Acceleration Scheme and Beam Plasma Wakefield Acceleration Scheme. This leads to the transformation of the 2nd witness bunch behind the laser pulse to the driver. Hence combination of the laser pulse, the 1st and the 2nd bunches behind the laser pulse provide further acceleration of witness (the 3rd bunch behind the laser pulse). Thus the numerical simulation demonstrates that the transition from the laser-wakefield acceleration mechanism to extra beam-plasma-wakefield acceleration mechanism provides additional acceleration of the short electron bunches. Elena Svystun Summary September 13 - 19, EAAC-2015

Thank you for attention ! Elena Svystun Thank you for attention! September 13 - 19, EAAC-2015