Session KI3: Intense Beams

Novel Hamiltonian method for collective dynamics analysis of an intense charged particle beam propagating through a periodic focusing quadrupole lattice

Identifying regimes for quiescent propagation of intense beams over long distances has been a major challenge in accelerator research. In particular, the development of systematic theoretical approaches that are able to treat self-consistently the applied oscillating force and the nonlinear self-field force of the beam simultaneously has been a major challenge of modern beam physics. Recently, a powerful new Hamiltonian averaging technique has been developed, which incorporated both the applied periodic focusing force and the self-field force of the beam. Typically, it is advantageous to eliminate fast oscillations from formalism and describe complex beam particle motion in a new non-oscillating coordinates. Standard Hamiltonian techniques are cumbersome due to use of mixed oscillating and non-oscillating independent variables. Newly developed technique is specially designed to avoid use of oscillating variables. The method is analogous to the Lie transform methods in using only non-oscillating variables. At the same time the new approach retains the advantages of simplicity of Hamiltonian methods. Making use of this new method equations determining the average self-field potential for general boundary conditions has been obtained for the first time by taking into account the average contribution of the charges induced on the boundary. For intense beams the boundary effects can be very important because they strongly affect the average self-fields experienced by the beam particles. For example, it has been shown that in the case of cylindrical conducting boundary the average self-field potential acquires an octupole component, which results in the average motion of some beam particles being non-integrable and their trajectories chaotic. This chaotic behavior of the beam particles may significantly change the nature of Landau damping (growth) of collective excitations supported by an intense charged particle beam.   

Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high intensity beams in coupled transverse focusing lattices

Courant-Snyder (CS) theory gives a complete description of the uncoupled transverse dynamics of charged particles in electromagnetic focusing lattices. In this paper, CS theory is generalized to the case of coupled transverse dynamics with two degree of freedom. The generalized theory has the same structure as the original CS theory for one degree of freedom. The four basic components of the original CS theory, i.e., the envelope equation, phase advance, transfer matrix, and the CS invariant, all have their counterparts in the generalized theory. The envelope function is generalized into an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. The generalized theory gives a new parameterization of the 4D symplectic transfer matrix that has the same structure as the parameterization of the 2D symplectic transfer matrix in the original CS theory. This parameterization can provide a valuable framework for accelerator design and particle simulation studies. For example, it is discovered that the stability of coupled dynamics is completely determined by the generalized phase advance. Two stability criteria are given, which recover the known results about sum and difference resonances in the weakly coupled limit. In an uncoupled lattice, the Kapchinskij-Vladimirskij distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including selffields in a self-consistent manner. The Kapchinskij-Vladimirskij solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.   

Electron self-injection into an evolving plasma bubble: toward a dark current free GeV-scale laser plasma accelerator

A bubble of electron density created by the radiation pressure of a short laser pulse can travel with the driver over many centimeters and accelerate electrons trapped from the ambient plasma to a few GeV. Nonlinear refraction and depletion of the driving pulse cause variations of the bubble shape and potentials; these, in turn, can either stimulate or extinguish electron self-injection and thus directly affect the process of electron beam formation and determine its final characteristics. The new results [1] show that in low-density plasmas relevant to the next generation of GeV-scale laser- plasma accelerators, expansion of the bubble triggers self- injection. The bucket stabilization and contraction stops injection and thus limits electron beam charge and duration. Laser spot size oscillations caused by nonlinear refraction can induce the desired sequence of bubble expansion and shrinkage. Periodic repetition of the sequence, however, can degrade the beam quality [2]. Using dense plasma slabs in the role of nonlinear lenses helps stabilize the bubble pulsations, achieve phase space rotation, and produce a quasi-monoenergetic bunch well before the de-phasing limit [3]. 3D particle-in-cell simulations complemented with the Hamiltonian diagnostics of electron phase space demonstrate robustness of the concept over a broad range of parameters. Modeling also shows that a single- shot non- collinear optical probing (frequency-domain tomography [4]) can facilitate direct observation of bubble evolution and associate it with the observed electron beam characteristics.\\[4pt] [1] S. Kalmykov et al., PRL 103, 135004 (2009).\\[0pt] [2] S. Y. Kalmykov et al., New J. Phys. 12, 045019 (2010).\\[0pt] [3] S. Y. Kalmykov et al., Plasma Phys. Control. Fusion 52(9) (2010) (in press).\\[0pt] [4] P. Dong et al., New J. Phys. 12, 045016 (2010).   

Detuning, wavebreaking, and Landau damping as limiting effects on laser compression by resonant backward Raman scattering

Plasma waves mediate high-power pulse compression, where the persistence of the plasma wave is critical. In this scheme, the plasma wave mediates the energy transfer between long pump and short seed laser pulses through backward Raman scattering. High efficiency of the plasma wave excitation defines both the overall efficiency of the energy transfer and the duration of the amplified pulse. Based on recent extensive experiments, it is possible to deduce that the experimentally realized efficiency of the amplifier is likely constrained by two factors, namely the pump chirp and the plasma wavebreaking [1]. The limits arise because for compression the frequency of the plasma wave should match the bandwidth of the instability and the plasma wave amplitude should be small enough to be sustained by plasma. Both the detuning and the wavebreaking effects can be suppressed by using low pump intensity in plasma having the appropriate density gradient [1]. When these constraints are avoided, Landau damping will be the main limiting factor. However, the Landau damping rate can be significantly reduced in the presence of a strong plasma wave. Currently, nonlinear Landau damping can be described within two recently developed models [2,3]. We show that these two different descriptions result in the same dynamics for the plasma wave amplitude. We use the quasilinear description of nonlinear Landau damping [3] to identify a regime where initially high linear Landau damping can be significantly saturated. Because of the saturation effect, higher temperatures can be tolerated in achieving efficient amplification. Significantly, the plasma temperature can be as much as 50\% larger compared to the case of unsaturated Landau damping.\\[4pt] [1] N.A. Yampolsky et al., Phys. Plasmas 15, 113104 (2008).\\[0pt] [2] D. Benisti et al., Phys. Rev. Lett. 103, 155002 (2009).\\[0pt] [3] N.A. Yampolsky and N.J. Fisch, Phys. Plasmas 16, 072104 (2009).