Cinética e dinâmica de feixes de partículas carregadas durante o processo de equipartição

Esta tese analisa a transição de um feixe com perfil isotrópico para um perfil anisotrópico em um canal focalizador linear. Considerando um feixe de íons de alta intensidade no regime dominado pelas forças eletromagnetoestáticas do próprio feixe e com um grande desacasamento (RMS) do envelope do feixe, observa-se um rápido crescimento da anisotropia espacial do feixe. Uma vez que as interações eletromagnetoestáticas do próprio feixe em um acelerador linear de alta intensidade podem levar a equipartição da energia entre os graus de liberdade do feixe, este fenômeno de anisotropização sugere uma espécie de rota para a equipartição. Nesta tese, mostramos que as ressonâncias de partícula-partícula e as ressonâncias entre os modos de oscilação do feixe e as partículas levam a anisotropização do feixe, isto é, tanto a razão do envelope como a razão das emitâncias são diferentes de um. Propomos que esta anisotropia é responsável pelo equiparticionamento do feixe. Os resultados sugerem que quando o feixe permanece equiparticionado ele apresenta uma anisotropia macroscópica, que é caracterizada pelas seguintes propriedades: o desenvolvimento de uma forma elíptica do feixe, com o crescimento do semi-eixo ao longo da direção x, a presença de um acoplamento entre as emitâncias transversais, a formação do anel ao longo de uma direção preferencial, a estacionariedade da temperatura e um crescimento da entropia, sob a forma de cascata. Chamamos o estado caracterizado por estas propriedades como um estado de equartição via anisotropias.This thesis examines the transition from isotropic to anisotropic beam profiles in a linear focusing channel. Considering a high-intensity ion beam in a space-charge dominated regime and with an initially large mismatcaed RMS beam size, we observe a fast increasing spatial anisotropy of the beam. Since space-charge interactions in a high-intensity linear accelerator can lead to energy equip rtition between the degrees of freedom, this anisotropization phenomena suggest a kinc of route to equipartition. In this thesis we show that the particle-particle resonances and mode oscillation of the beam-particle resonances lead to the anisotropization of the beam, that is, both the envelope ratio and the emittance ratio are different from one. We propose that this anisotropy is responsible for the beam's equipartitioning. The results suggest that the beam remains equipartitioned when it exhibits a macroscopic anisotropy, which is characterized by the following properties: the development of an elliptical shape with increasing size along the x-direction, the presence of a coupling between transversal e ittances, halo formation along a preferential direction, stationarity of the temperature and a growth of the entropy in the cascade form. We call the state characterized by these properties as an anisotropic equipartition state

Cinética e dinâmica de feixes de partículas carregadas durante o processo de equipartição

Esta tese analisa a transição de um feixe com perfil isotrópico para um perfil anisotrópico em um canal focalizador linear. Considerando um feixe de íons de alta intensidade no regime dominado pelas forças eletromagnetoestáticas do próprio feixe e com um grande desacasamento (RMS) do envelope do feixe, observa-se um rápido crescimento da anisotropia espacial do feixe. Uma vez que as interações eletromagnetoestáticas do próprio feixe em um acelerador linear de alta intensidade podem levar a equipartição da energia entre os graus de liberdade do feixe, este fenômeno de anisotropização sugere uma espécie de rota para a equipartição. Nesta tese, mostramos que as ressonâncias de partícula-partícula e as ressonâncias entre os modos de oscilação do feixe e as partículas levam a anisotropização do feixe, isto é, tanto a razão do envelope como a razão das emitâncias são diferentes de um. Propomos que esta anisotropia é responsável pelo equiparticionamento do feixe. Os resultados sugerem que quando o feixe permanece equiparticionado ele apresenta uma anisotropia macroscópica, que é caracterizada pelas seguintes propriedades: o desenvolvimento de uma forma elíptica do feixe, com o crescimento do semi-eixo ao longo da direção x, a presença de um acoplamento entre as emitâncias transversais, a formação do anel ao longo de uma direção preferencial, a estacionariedade da temperatura e um crescimento da entropia, sob a forma de cascata. Chamamos o estado caracterizado por estas propriedades como um estado de equartição via anisotropias.This thesis examines the transition from isotropic to anisotropic beam profiles in a linear focusing channel. Considering a high-intensity ion beam in a space-charge dominated regime and with an initially large mismatcaed RMS beam size, we observe a fast increasing spatial anisotropy of the beam. Since space-charge interactions in a high-intensity linear accelerator can lead to energy equip rtition between the degrees of freedom, this anisotropization phenomena suggest a kinc of route to equipartition. In this thesis we show that the particle-particle resonances and mode oscillation of the beam-particle resonances lead to the anisotropization of the beam, that is, both the envelope ratio and the emittance ratio are different from one. We propose that this anisotropy is responsible for the beam's equipartitioning. The results suggest that the beam remains equipartitioned when it exhibits a macroscopic anisotropy, which is characterized by the following properties: the development of an elliptical shape with increasing size along the x-direction, the presence of a coupling between transversal e ittances, halo formation along a preferential direction, stationarity of the temperature and a growth of the entropy in the cascade form. We call the state characterized by these properties as an anisotropic equipartition state

Estabilidade não linear de um feixe de partículas carregadas sujeito a um campo magnético focalizador

Uma análise da estabilidade não-linear de feixes com seção transversal circular considerando perturbações sem simetria axial é executada. Mostra-se que as oscilações simétricas oficialmente circulares de um feixe podem induzir oscilações não-lineares do tipo anti-simétrica(elípticas), com um conseqüente aumento do tamanho do feixe ao logo de uma direção preferencial. O mecanismo da instabilidade e sua relevância às perdas de partícula no feixe são discutidos

Nonlinear coupling between breathing and quadrupole-like oscillations in the transport of mismatched beams in continuous magnetic focusing fields

A nonlinear analysis of the transport of breathing beams considering nonaxisymmetric perturbations is performed. It is shown that large-amplitude breathing oscillations of an initially round beam may couple nonlinearly to quadrupole-like oscillations, such that the excess energy initially constrained to the axisymmetric breathing oscillations is allowed to flow back and forth between breathing and quadrupole-like oscillations. In this case, the beam develops an elliptical shape with a possible increase in its size along one direction as the beam is transported. This is a highly nonlinear phenomenon that occurs for large mismatch amplitudes on the order of 100% and is found to be particularly relevant for space-charge-dominated beams with K k0 , where K is the beam perveance, k0 is the vacuum phase advance per unit axial length, and is the emittance of the beam. A simple model based on mapping techniques is used to clarify the mechanism that leads to the energy exchange between the modes and is tested against results from direct integration of the envelope equations

Nonlinear coupling between breathing and quadrupole-like oscillations in the transport of mismatched beams in continuous magnetic focusing fields

A nonlinear analysis of the transport of breathing beams considering nonaxisymmetric perturbations is performed. It is shown that large-amplitude breathing oscillations of an initially round beam may couple nonlinearly to quadrupole-like oscillations, such that the excess energy initially constrained to the axisymmetric breathing oscillations is allowed to flow back and forth between breathing and quadrupole-like oscillations. In this case, the beam develops an elliptical shape with a possible increase in its size along one direction as the beam is transported. This is a highly nonlinear phenomenon that occurs for large mismatch amplitudes on the order of 100% and is found to be particularly relevant for space-charge-dominated beams with K k0 , where K is the beam perveance, k0 is the vacuum phase advance per unit axial length, and is the emittance of the beam. A simple model based on mapping techniques is used to clarify the mechanism that leads to the energy exchange between the modes and is tested against results from direct integration of the envelope equations

Core-halo issues for a very high intensity beam

The relevance of classical parameters like beam emittance and envelope used to describe a particle beam is questioned in case of a high intensity accelerator. In the presence of strong space charge effects that affect the beam differently following its density, the much less dense halo part behaves differently from the much denser core part. A method for precisely determining the core-halo limit is proposed, that allows characterizing the halo and the core independently. Results in 1D case are given and discussed. Expected developments extending the method to 2D, 4D, or 6D phase spaces are examined

Core-halo issues for a very high intensity beam

The relevance of classical parameters like beam emittance and envelope used to describe a particle beam is questioned in case of a high intensity accelerator. In the presence of strong space charge effects that affect the beam differently following its density, the much less dense halo part behaves differently from the much denser core part. A method for precisely determining the core-halo limit is proposed, that allows characterizing the halo and the core independently. Results in 1D case are given and discussed. Expected developments extending the method to 2D, 4D, or 6D phase spaces are examined