Akhter, Tahmina
(2016)
SelfModulated Dynamics of Relativistic Charged Particle Beams in Plasmas.
[Tesi di dottorato]
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Item Type: 
Tesi di dottorato

Lingua: 
English 
Title: 
SelfModulated Dynamics of Relativistic Charged Particle Beams in Plasmas 
Creators: 
Creators  Email 

Akhter, Tahmina  tahminaphys@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: 
nome  email 

Velotta, Raffaele  velotta@na.infn.it 

Tutor: 
nome  email 

Fedele, Renato  UNSPECIFIED 

Date: 
31 March 2016 
Number of Pages: 
174 
Uncontrolled Keywords: 
Plasma wake field excitations, VlasovPoissontype pair of equations, virial descriptions, coupling impedance, beam selfmodulation 
Settori scientificodisciplinari 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 
Abstract
We carry out a theoretical investigation on the selfmodulated 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 selfconsistent beamplasma 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 electromechanical actions of the wake fields. They have a 3D character and affects sensitively the beam
envelope. To provide a selfconsistent description of the driving beam dynamics, we first start from the set of governing equations comprising the LorentzMaxwell fluid equations for the beamplasma system. In the unperturbed particle system (i.e., beam comoving frame) and in quasistatic approximation, we reduce it to a 3D partial differential equation, called the Poissontype equation. The latter relates the wake potential to the beam density which is coupled with the 3D Vlasov equation for the beam. Therefore, the VlasovPoissontype pair of equations constitute our set of governing equation for the spatiotemporal evolution of the selfmodulated beam
dynamics. We divide the analysis in two different cases, purely transverse and purely longitudinal.
In the purely transverse dynamics, we investigate the envelope selfmodulation of a cylindrically symmetric beam by implementing the VlasovPoissontype 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 integrateable 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 selfmodulation, such as focusing, defocusing and betatronlike oscillations, and criteria for instability, such as collapse and selfmodulation 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 semianalytical and numerical investigation for the envelope selfmodulation. To this end, criteria for predicting stability and selfmodulation instability are suitably provided.
In the purely longitudinal dynamics, we specialize the 3D VlasovPoissontype equation to the 1D longitudinal case. Then, the analysis is carried out by perturbing the VlasovPoissontype system up to the first order and taking the Fourier transformation to reduce the VlasovPoisson system to a set of algebraic equations in the frequency and wavenumber domain. This allows us to
easily get a Landautype 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 nonmonochromatic 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 VlasovPoissontype 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 Nyquisttype stability analysis.
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