A nonlinear theory for multidimensional relativistic plasma wave wakefields

Abstract

A nonlinear kinetic theory for multidimensional plasma wave wakes with phase velocities near the speed of light is presented. This theory is appropriate for describing plasma wakes excited in the so-called blowout regime by either electron beams or laser pulses where the plasma electrons move predominantly in the transverse direction. The theory assumes that all electrons within a blowout radius are completely expelled. These radially expelled electrons form a narrow sheath just beyond the blowout radius which is surrounded by a region which responds weakly (linearly). This assumption is reasonable when the spot size of the electron beam and laser are substantially less than the blowout radius. By using this theory one can predict the wakefield amplitudes and blowout radius in terms of the electron beam or laser beam parameters, as well as predict the nonlinear modifications to the wake’s wavelength and wave form. For the laser case, the laser spot size must also be properly matched in order for a narrow sheath to form. The requirements for forming a spherical wave form, i.e., “bubble,” are also discussed. The theory is also used to show when linear fluid theory breaks down and how this leads to a saturation of the logarithmic divergence in the linear Green’s function.

Giga-electronvolt electrons due to a transition from laser wakefield acceleration to plasma wakefield acceleration

“…k p σ x ≤ 1 according to the theory developped by Lu et al 16 . As we can see, after more than 2.4 mm of propagation, when the laser is fully depleted, this condition is satisfied.…”

“…Finally, in the past decade, prior to which time most of the experimental accelerated electrons were characterized by an exponential energy distribution 2,3 , high quality monoenergetic electron beams were reported by many groups [4][5][6][7][8][9][10][11][12] . Most of these experiments, were conducted in the so-called blowout regime or "bubble" regime, identified in many simulations and theoretical analyses before [13][14][15][16][17][18][19][20] where the electrons are expelled radially from the beam axis by the transverse ponderomotive force of the laser, which creates a three dimensional (3D) cavity (the "bubble") empty of electrons.…”

Physics of Phase Space Matching for Staging Plasma and Traditional Accelerator Components Using Longitudinally Tailored Plasma Profiles

“…In this Letter, we show through both analytical solutions as well as OSIRIS [19] particle-in-cell (PIC) simulations that using plasmas that have longitudinally tailored density profiles as matching sections it is possible to transport the electron beam to/from the PBA sections without significant emittance growth using ion channel focusing forces which arise in the nonlinear blowout regime [20][21][22]. We investigate several density profiles, how to match the Courant-Snyder (C-S) parameters β and α [23] between the two stages that require beam matching, and exact and adiabatic matching.…”

“…We study the evolution of both β and α, show that perfect matching can be obtained for short sections (non-adiabatic profiles), and show that the adiabatic approximation (for long profiles) misses important physics. Furthermore, we consider nonlinear wakes [21,22] and not linear wakes because linear wakes have nonlinear and axial dependent focusing forces and focusing forces which are altered by beam loading [38] (dephasing would be an issue). We consider four examples where it will be important to achieve beam-matching between two stages where at least one stage is a PBA.…”

Energy Spread Reduction of Electron Beams Produced via Laser Wake

“…There have been several numerical studies of this trapping process [29,30], which predict density thresholds for self-trapping of few-10 18 -10 20 cm −3 for the blowout condition 2<a 0 <4. This thesis will present data indicating that in He plasmas this threshold occurs at 4x10 18 cm −3 for laser powers of 60 TW.…”