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@MastersThesis{InostrozaLara:2020:MoPaCa,
               author = "Inostroza Lara, Ana Mar{\'{\i}}a",
                title = "Movimento de part{\'{\i}}culas carregadas, com velocidades 
                         relativ{\'{\i}}sticas, sob a{\c{c}}{\~a}o de campo 
                         geomagn{\'e}tico perturbado",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
                 year = "2020",
              address = "S{\~a}o Jos{\'e} dos Campos",
                month = "2020-03-26",
             keywords = "el{\'e}trons relativ{\'{\i}}sticos, cintur{\~o}es de 
                         radia{\c{c}}{\~a}o, ondas chorus, campo geomagn{\'e}tico 
                         perturbado, relativistic electrons, radiation belts, chorus waves, 
                         perturbed magnetic field.",
             abstract = "O campo magn{\'e}tico da Terra varia dependendo das 
                         condi{\c{c}}{\~o}es da magnetosfera e a din{\^a}mica das 
                         part{\'{\i}}culas presentes. Quando as part{\'{\i}}culas 
                         est{\~a}o no campo magn{\'e}tico descrevem tr{\^e}s movimentos 
                         principais: giro ao redor da linha de campo; repique entre os 
                         pontos de espelhamento nos hemisf{\'e}rios e a deriva em torno da 
                         Terra, e a cada um destes movimentos est{\'a} associado uma 
                         quantidade f{\'{\i}}sica denominada invariante adiab{\'a}tico. 
                         Se n{\~a}o existe uma perturba{\c{c}}{\~a}o no campo, a 
                         part{\'{\i}}cula permanecer{\'a} aprisionada. No entanto, na 
                         aus{\^e}ncia de perturba{\c{c}}{\~o}es externas, existem certos 
                         limites nos quais os invariantes adiab{\'a}ticos s{\~a}o 
                         quebrados. Neste trabalho, conseguiu-se obter que, para 
                         part{\'{\i}}culas teste com energias entre 2 e 5 MeV, que 
                         iniciam sua trajet{\'o}ria na posi{\c{c}}{\~a}o maior a 7RE, 
                         pode existir perdas de part{\'{\i}}culas, dependendo de sua 
                         energia. Existem certos mecanismos que podem gerar perdas de 
                         part{\'{\i}}culas, sendo um deles a intera{\c{c}}{\~a}o com 
                         ondas chorus. As ondas chorus s{\~a}o um tipo de ondas whistler 
                         com polariza{\c{c}}{\~a}o RCP (Right-hand Circularly Polarized) 
                         que se propagam em dire{\c{c}}{\~a}o paralela ao campo 
                         magn{\'e}tico da Terra com frequ{\^e}ncias entre centenas de Hz 
                         at{\'e} alguns kHz. Enquanto se propagam, podem interagir com 
                         el{\'e}trons energ{\'e}ticos relativ{\'{\i}}sticos do 
                         cintur{\~a}o de radia{\c{c}}{\~a}o Van Allen, quando se cumpre 
                         a condi{\c{c}}{\~a}o de resson{\^a}ncia, o que pode causar 
                         perdas dos el{\'e}trons. Este trabalho tem como objetivo avaliar 
                         a varia{\c{c}}{\~a}o do pitch angle de um el{\'e}tron com 
                         energia relativ{\'{\i}}stica em um campo magn{\'e}tico dipolar, 
                         perturbado pela ocorr{\^e}ncia de ondas chorus. A 
                         solu{\c{c}}{\~a}o da equa{\c{c}}{\~a}o do movimento foi obtida 
                         numericamente. Em uma primeira etapa, realizou-se a 
                         valida{\c{c}}{\~a}o do c{\'o}digo desenvolvido utilizando o 
                         m{\'o}dulo Scipy de Python, comparando com os resultados obtidos 
                         por Bortnik et al. (2008). Uma vez validado o c{\'o}digo, este 
                         foi utilizado para calcular a varia{\c{c}}{\~a}o do pitch angle 
                         do el{\'e}tron para a intera{\c{c}}{\~a}o 
                         onda-part{\'{\i}}cula em um evento de perda de el{\'e}trons 
                         ocorrido em 12 de setembro de 2014 (ALVES et al., 2016). Os dados 
                         dos campos eletromagn{\'e}ticos da onda foram obtidos a partir 
                         das sondas Van Allen Probes para el{\'e}trons de energia 2 e 5 
                         MeV na zona equatorial e par{\^a}metro L = 5, 5 e 6. A 
                         varia{\c{c}}{\~a}o do pitch angle {\'e} contabilizada 
                         atrav{\'e}s do valor quadr{\'a}tico m{\'e}dio rms. Na 
                         an{\'a}lise do evento obteve-se o menor valor de 
                         [Delta][Alpha]rms = 0,25o, para dois casos diferentes quando L = 6 
                         e L = 5,5, ambos com frequ{\^e}ncia de 1 kHz, energia de 5 MeV. O 
                         valor m{\'a}ximo foi de [Delta][Alpha]rms = 0,44o para a onda de 
                         0,5 kHz e o el{\'e}tron de 2 MeV posicionado inicialmente em L = 
                         5,5. ABSTRACT: The Earths magnetic field varies depending on the 
                         conditions of the magnetosphere, as well as on the dynamics of the 
                         particles present in it. When charged particles are in the 
                         magnetic field, they describe three main movements: gyro motion 
                         around the field lines; bounce motion between the mirroring points 
                         in the northern and southern hemispheres and drift motion around 
                         the Earth, and each of these movements is associated with a 
                         physical quantity called adiabatic invariant. If there is no 
                         disturbance in the field, particles will remain trapped inside the 
                         magnetosphere. However, in the presence of external disturbances, 
                         there are certain limits at which adiabatic invariants are broken. 
                         In this work, it is found that for particles with energies between 
                         2 and 5 MeV with an initial position greater than 7RE there may be 
                         loss of the particle, depending on its energy. Certain mechanisms 
                         can generate particle loss, one of which is the interaction with 
                         chorus waves. Chorus waves are a type of whistler waves with RCP 
                         (Right-hand Circularly Polarized) polarization that propagate 
                         parallel to the Earths magnetic field with frequencies between 
                         hundreds of Hz to a few kHz. As they propagate, they can interact 
                         with relativistic energetic electrons in the Van Allen radiation 
                         belt. When the gyro-resonance condition is reached, the 
                         interaction can cause electron loss. This work aims to evaluate 
                         the pitch angle variation of an electron with relativistic energy 
                         in a dipolar magnetic field, disturbed by the occurrence of chorus 
                         waves. The motion equations solution is obtained numerically. In 
                         the first step, the code developed using the Python Scipy module 
                         was validated, comparing with the results obtained by (BORTNIK et 
                         al., 2008). Once the code was validated, it was used to calculate 
                         the electron pitch angle variation for the wave-particle 
                         interaction in an electron loss event that occurred on September 
                         12, 2014 (ALVES et al., 2016). The waves eletromagnetic fields 
                         data were obtained from the Van Allen Probes for electrons 
                         energies of 2 and 5 MeV in the equatorial zone and at L-shell 
                         values of L = 5,5 and 6. The variation of the pitch angle is 
                         accounted for by using the average square value of rms. In the 
                         event analysis, the lowest value of [Delta][Alpha]rms = 0,25o was 
                         obtained for two different cases when L = 6 and L = 5,5, both with 
                         a frequency of 1 kHz, energy of 5 MeV. The maximum value of 
                         [Delta][Alpha]rms was 0,44o for the wave with frequency 0,5 kHz 
                         and for the 2 MeV electron initially positioned at L = 5,5.",
            committee = "Alves, Maria Virg{\'{\i}}nia (presidente) and Alves, 
                         L{\'{\i}}via Ribeiro (orientadora) and Silva Souza, Vitor Moura 
                         Cardoso e and Lucas, Aline de",
         englishtitle = "Movement of charged particles, with relativistic velocity, under 
                         action of disturbed geomagnetic field",
             language = "pt",
                pages = "88",
                  ibi = "8JMKD3MGP3W34R/42EJHLP",
                  url = "http://urlib.net/rep/8JMKD3MGP3W34R/42EJHLP",
           targetfile = "publicacao.pdf",
        urlaccessdate = "05 mar. 2021"
}


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