Bulletin of the American Physical Society
56th Annual Meeting of the APS Division of Plasma Physics
Volume 59, Number 15
Monday–Friday, October 27–31, 2014; New Orleans, Louisiana
Session QI2: Particle Beams and Waves |
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Chair: Chuang Ren, University of Rochester Room: Bissonet |
Wednesday, October 29, 2014 3:00PM - 3:30PM |
QI2.00001: Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory Invited Speaker: Hong Qin The dynamics of charged particles in general linear focusing lattices is analyzed using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The general focusing lattices are allowed to include quadrupole, skew-quadrupole, solenoidal, and dipole components, as well as variation of beam energy and torsion of the fiducial orbit. The scalar envelope function is generalized into an envelope matrix, and the scalar envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation. The phase advance is generalized into a 4D symplectic rotation, or an~U(2)~element. Other components of the original CS theory, such as the CS invariant, transfer matrix, and Twiss functions all have their counterparts in the generalized theory with remarkably similar expressions. The gauge group of the generalized theory is analyzed. If the gauge freedom is fixed with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space quantum mechanics and optics has been recently realized. It is shown that the spectral and structural stability properties of a general focusing lattice are uniquely determined by the generalized phase advance. For structural stability, the generalized CS theory developed enables application of the Krein-Moser theory to significantly simplify the theoretical and numerical analysis. The generalized CS theory provides an effective tool to study the coupled dynamics of high-intensity charged particle beams and to discover more optimized lattice designs in the larger parameter space of general focusing lattices. [Preview Abstract] |
Wednesday, October 29, 2014 3:30PM - 4:00PM |
QI2.00002: Optical control of electron trapping: Generation of comb-like electron beams for tunable, pulsed, multi-color radiation sources Invited Speaker: Serge Kalmykov All-optical control over the electron phase space in laser-plasma accelerators enables production of ``designer'' electron beams that can be optimized for specific applications. GeV-scale acceleration with sub-100 TW (rather than PW) laser pulses, at repetition rates orders-of-magnitude higher than permitted by existing PW facilities, in a few-mm (rather than cm) length plasmas, requires maintaining an accelerating gradient as high as 10 GV/cm. This, in turn, dictates acceleration in the blowout regime in a dense plasma ($\sim 10^{19}$ cm$^{-3}$). These highly dispersive plasmas rapidly transform the drive pulse into a relativistic optical shock, causing the plasma wake bucket (electron density bubble) to constantly expand, trapping background electrons, greatly degrading beam quality. We show that these effects can be overcome using a high-bandwidth driver (over 1/2 the carrier frequency) with a negative frequency chirp. Temporally advancing higher frequencies (thus compensating for the plasma-induced nonlinear frequency red-shift) and propagating the pulse in a plasma channel (to suppress diffraction of its leading edge) delays pulse self-steepening through electron dephasing and extends the dephasing length. As a result, continuous injection is suppressed and electron energy is boosted to the GeV level. In addition, periodic self-injection in the channel produces a sequence of femtosecond-length, quasi-monoenergetic bunches. The number of these spectral components, their charge, energy, and energy separation can be controlled by varying the channel radius and length, whereas accumulation of the noise (viz. continuously injected charge) is prevented by the negative chirp of the driver. This level of control is hard to achieve with conventional accelerator techniques. It is demonstrated that these clean, polychromatic, comb-like beams can drive high-brightness, tunable, multi-color gamma-ray sources. [Preview Abstract] |
Wednesday, October 29, 2014 4:00PM - 4:30PM |
QI2.00003: Multi-dimensional Vlasov Simulations and Modeling of Trapped-Electron Sideband and Filamentation Instabilities of Non-Linear Electron Plasma Waves Invited Speaker: Richard Berger Vlasov simulations of large amplitude electron plasma waves (EPWs), which play an essential role in laser-fusion relevant plasmas, have been carried out in 1D and 2D and compared with theoretical models [1]. The electrons trapped in the wave troughs are shown to be well described by an ``adiabatic'' distribution with a corresponding frequency shift of the EPW [2]. Trapped particles play an essential role in the mechanisms underlying sideband instabilities that may affect the EPW, in particular longitudinal instabilities of trapped particle instability (TPI) type, as well as transverse instabilities of kinetic filamentation type. A systematic study of the spectrum of linearly unstable modes in 1D and 2D systems, including their growth rates and wavevectors, has been completed by scanning the amplitude and wavenumber of the initial wave. Simulation results for the TPI are successfully compared with Kruer's reduced model [3] and are also analyzed for the development of the ``negative mass instability'' [4]. In the non-linear phase, both the TPI and filamentation instabilities are shown to lead to a rapid loss of field energy and an associated increase in electron kinetic energy. Saturation of the instabilities is reached in conjunction with the development of significant regions in phase space where trajectories of particles, resonant with the initial wave, become chaotic. \\[4pt] [1] J. W. Banks \textit{et al}, Phys. Plasmas \textbf{18}, 052102(2013); R. L. Berger, \textit{et al}, Phys. Plasmas \textbf{20}, 032107 (2013); B. J. Winjum, \textit{et al}, Phys. Rev. Lett. \textbf{111}, 105002 (2013)\textbf{; }S. Brunner, \textit{et al}, ``Kinetic Simulations and Reduced Modeling of Longitudinal Sideband Instabilities in Non-Linear Electron Plasma Waves,'' submitted to Phys. Plasmas\\[0pt] [2] R. L. Dewar, Phys. Fluids \textbf{15}, 712 (1972)\\[0pt] [3] W. L. Kruer, \textit{et al}, Phys. Rev. Lett. \textbf{23}, 838 (1969)\\[0pt] [4] I. Y. Dodin \textit{et al,} Phys. Rev. Lett. \textbf{110}, 215006 (2013) [Preview Abstract] |
Wednesday, October 29, 2014 4:30PM - 5:00PM |
QI2.00004: Diocotron Mode Damping from a Flux through the Critical Layer Invited Speaker: C. Fred Driscoll Experiments and theory characterize a novel type of spatial Landau damping of diocotron modes which is {\it algebraic} rather than {\it exponential} in time; this damping is caused by a flux of particles through the wave/rotation critical layer.\footnote{A.A. Kabantsev, et al., Phys.~Rev.~Lett. 112, 115003 (2014).} These $k_z = 0$ diocotron (drift) modes with azimuthal mode numbers $m_\theta = 1,2...$ are dominant features in the dynamics of non-neutral plasmas in cylindrical and toroidal traps; and they are directly analogous to Kelvin waves on 2D fluid vortices. Spatial Landau damping is the resonant interaction between a mode at frequency $f_m$ and the plasma rotation $f_E (r)$, at the critical radius $R_c$ where $f_m = m_\theta f_E(R_c)$. This is mathematically analogous to velocity-space Landau damping with $f_k = k v / 2 \pi$. \textbullet Experimentally, diocotron modes on pure electron plasmas exhibit exponential Landau damping when the {\it initial} plasma density is non-zero at $R_c$. Here, we demonstrate that a steady outward {\it flux} of particles through $R_c$ causes diocotron modes to damp algebraically to zero amplitude, as $D(t) = D_0 - \gamma_m t$ . The outward flux is controlled and measured experimentally, and the damping rates $\gamma_m$ are proportional to the flux. In general, any weak non-ideal process which causes outward flux may cause this damping. \textbullet Analytics and simulations have developed a simple model of this damping, treating the transfer of canonical angular momentum from the mode to particles transiting the nonlinear trapping region at $R_c$. The model qualitatively agrees with experiments for $m_\theta = 1$, but nominally predicts a discrepant algebraic exponent for $m_\theta = 2$, perhaps due to the amplitude dependence of the trapping structure. Overall, this novel flux-driven damping is determined by the {\it present} magnitudes of the wave and outward flux, in contrast to the Landau analysis of phase mixing of the {\it initial} density. [Preview Abstract] |
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