Hazem Mohamed Mahmoud Abdelhafiz <br/><br/>
Resonance Phenomena in Coupled Josephson Junctions 
Hazem Mohamed Mahmoud Abdelhafiz 
 -  2013 
 - p.   ill.   21 cm.  
<br/><br/>Supervisor: Wael Akl 
<br/><br/>Thesis (M.A.)—Nile University, Egypt, 2013 . 
<br/><br/>"Includes bibliographical references" 
<br/><br/>Contents: <br/>2 Theoretical Study 14<br/>2.1 Coupled Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 14<br/>2.2 Electron Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14<br/>2.3 Josephson equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20<br/>2.4 The Josephson critical current Ic . . . . . . . . . . . . . . . . . . . . . . . 22<br/>3 Computational methods 24<br/>3.1 Runge-Kutta Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24<br/>3.1.1 Second-Order method . . . . . . . . . . . . . . . . . . . . . . . . . 24<br/>3.1.2 Fourth-Order Methods . . . . . . . . . . . . . . . . . . . . . . . . . 25<br/>3.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26<br/>3.2.1 Capacitively coupled Josephson junctions (CCJJ) . . . . . . . . . . 26<br/>iii<br/>Contents iv<br/>3.2.2 Capacitively coupled Josephson junctions with diffusion current<br/>(CCJJ+DC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31<br/>3.3 System of equations of IJJ . . . . . . . . . . . . . . . . . . . . . . . . . . . 33<br/>4 Results and Discussion 35<br/>4.1 Charge density wave in IJJ . . . . . . . . . . . . . . . . . . . . . . . . . . 35<br/>4.2 Dynamics of transition LPW → CDW . . . . . . . . . . . . . . . . . . . . 36<br/>4.3 Transformations CDW → CDW . . . . . . . . . . . . . . . . . . . . . . . 37<br/>4.4 Radiation effect on IJJ . . . 
<br/><br/> Abstract:<br/>We demonstrate the creation of a charge density wave (CDW) along a stack of coupled<br/>Josephson junctions in layered superconductors. Electric charge in each superconducting<br/>layer oscillates around some average value, forming a breathing CDW. We show the<br/>transformation of a longitudinal plasma wave to a CDW in the state corresponding to<br/>the outermost branch. Transitions between different types of CDW’s, related to the<br/>inner branches of current voltage characteristics, are demonstrated. We will show the<br/>effect of radiation on the CDW and the appearance of Shapiro steps in the inner branch. 
<br/><br/><br/>Text in English, abstracts in English and Arabic 
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Dissertation, Academic
<br/><br/><label>Dewey Class. No.: </label>620