Akhter, Tahmina (2016) Self-Modulated Dynamics of Relativistic Charged Particle Beams in Plasmas. [Tesi di dottorato]


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Item Type: Tesi di dottorato
Resource language: English
Title: Self-Modulated Dynamics of Relativistic Charged Particle Beams in Plasmas
Akhter, Tahminatahminaphys@gmail.com
Date: 31 March 2016
Number of Pages: 174
Institution: Università degli Studi di Napoli Federico II
Department: Fisica
Scuola di dottorato: Scienze fisiche
Dottorato: Fisica fondamentale ed applicata
Ciclo di dottorato: 28
Coordinatore del Corso di dottorato:
Velotta, Raffaelevelotta@na.infn.it
Date: 31 March 2016
Number of Pages: 174
Keywords: Plasma wake field excitations, Vlasov-Poisson-type pair of equations, virial descriptions, coupling impedance, beam self-modulation
Settori scientifico-disciplinari del MIUR: Area 02 - Scienze fisiche > FIS/03 - Fisica della materia
Date Deposited: 14 Apr 2016 20:51
Last Modified: 16 Nov 2016 08:14
URI: http://www.fedoa.unina.it/id/eprint/10735

Collection description

We carry out a theoretical investigation on the self-modulated dynamics of a relativistic, nonlaminar, charged particle beam travelling through a magnetized plasma due to the plasma wake field excitation mechanism. In this dynamics the beam plays the role of driver, but at the same time it experiences the feedback of the fields produced by the plasma. Driving beam and plasma are strongly coupled by means of the EM fields that they produce: the longer the beam (compared to the plasma wavelength), the stronger the self-consistent beam-plasma interaction. The sources of these EM fields are charges and currents of both plasma and driving beam. While travelling through the plasma, the beam experiences the electro-mechanical actions of the wake fields. They have a 3D character and affects sensitively the beam envelope. To provide a self-consistent description of the driving beam dynamics, we first start from the set of governing equations comprising the Lorentz-Maxwell fluid equations for the beam-plasma system. In the unperturbed particle system (i.e., beam co-moving frame) and in quasi-static approximation, we reduce it to a 3D partial differential equation, called the Poisson-type equation. The latter relates the wake potential to the beam density which is coupled with the 3D Vlasov equation for the beam. Therefore, the Vlasov-Poisson-type pair of equations constitute our set of governing equation for the spatiotemporal evolution of the self-modulated beam dynamics. We divide the analysis in two different cases, purely transverse and purely longitudinal. In the purely transverse dynamics, we investigate the envelope self-modulation of a cylindrically symmetric beam by implementing the Vlasov-Poisson-type system with the corresponding virial equations. This approach allows us to find some constant of motions and some ordinary differential equations, called the \textit{envelope equations} that govern the time evolution of the beam spot size. They are easily integrate-able analytically and/or numerically and therefore facilitate the analysis. Additionally, to approach our analysis also from the qualitative point of view, we make use of the so called \textit{pseudo potential} or \textit{Sagdeev potential}, widely used in nonlinear sciences, that is associated with the envelope equations. We first carry out an analysis in two different regimes, i.e., the local regime (where the beam spot size is much greater than the plasma wavelength) and the strongly nonlocal regime (where the beam spot size is much smaller than the plasma wavelength). In both cases, we find several types of self-modulation, such as focusing, defocusing and betatron-like oscillations, and criteria for instability, such as collapse and self-modulation instability. Then, the analysis is extended to the case where the beam spot size and the plasma wavelength are not necessarily constrained as in the local or strongly nonlocal cases. We carry out a full semi-analytical and numerical investigation for the envelope self-modulation. To this end, criteria for predicting stability and self-modulation instability are suitably provided. In the purely longitudinal dynamics, we specialize the 3D Vlasov-Poisson-type equation to the 1D longitudinal case. Then, the analysis is carried out by perturbing the Vlasov-Poisson-type system up to the first order and taking the Fourier transformation to reduce the Vlasov-Poisson system to a set of algebraic equations in the frequency and wavenumber domain. This allows us to easily get a Landau-type dispersion relation for the beam modes, that is fully similar to the one holding for plasma modes. First, we consider the case of a monochromatic beam (i.e., cold beam) for which we find both a purely growing mode and a simple stability criterion. Moreover, by taking into account a non-monochromatic distribution function with finite small thermal correction, the Landau approach leads to obtain both the dispersion relation for the real and imaginary parts. The former shows all the possible beam modes in the diverse regions of the wave number and the latter shows the stable or unstable character of the beam modes, which suggests a simple stability criterion. Finally, within the framework of the 1D longitudinal Vlasov-Poisson-type system of equations, we introduce the concept of coupling impedance in full analogy with the conventional accelerators. It is shown that also here the coupling impedance is a very useful tool for the Nyquist-type stability analysis.


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