Post on 12-Apr-2018
The 5th International Workshop on Numerical Modelling of HTS
a Joint Institute for Nuclear Research, Dubna, Russia b Umarov physical and technical institute, Dushanbe, Tajikistan
c Dubna state University, Dubna, Russia d Plovdiv University, Plovdiv, Bulgaria
Bolonga
June 15-17, 2016
Ilhom R. Rahmonov a,b
In collaboration with: Yury M. Shukrinov a,c, Pavlina Atanasova d, Elena V. Zemlyanaya a,c, Oksana I. Streltsova a,c, Maksim I. Zuev a, Maksim V. Bashashin a,c
Outline
Conclusions
I. Introduction
III. The main features of single long Josephson junctions
II. Theoretical model and numerical approach
IV. Stack of long Josephson junctions
Bi2Sr2CaCu2O8+δ
1. Intrinsic Josephson effect was observed in 1992
[R. Kleiner, F. Steinmayer, G. Kunkel P. Müller, Phys. Rev. Lett. 68 (1992) 2394]
Intrinsic Josephson junctions
It was investigated in the several work
[A. A. Yurgens, Super. Science Technol., 13 (2000) R85]
[Xiao Hu, Shi-Zeng Lin] Super. Science Technol., 23 (2010) 053001]
T. M. Benseman, A. E. Koshelev et al. «Tunable terahertz
emission from Bi2Sr2CaCu2O8+δ mesa devices», Phys.
Rev. B 84, 064523 (2011).
Experimental and simulated current voltage characteristics
Yu. M. Shukrinov, I.R. Rahmonov and M.El Demery,
«Phase Dynamics in IJJ: Comparative Study in
Different Models», abstracts book of International
Symposium«PLASMA 2010», p. 2010.(Hirosaki,
Japan)
Theoretical model
M. Machida, S. Sakai, Phys. Rev. B 70 (2004) 144520
S. Sakai, P. Bodin, N. F. Pedersen, J. Appl. Phys. 73 (1993) 2411
I.R. Rahmonov, Yu.M. Shukrinov, A. Irie, JETP Lett. 99, № 11, 735-742 (2014) (russian)
Numerical approach
The left point in coordinate
The middle points in coordinate
The right point in coordinate
Then we solve system of differential equation using fourth order Runge-Kutta method and get the
Parallel numerical approach
The calculation in coordinate nodes xi is distributed between the group of P parallel MPI processes
At each time-step tj, each process with number p calculates the RK coefficients and solutions V(xi, tj), ϕ(xi, tj)
Each process p (p < P−1) sends the RK coefficients and solutions of boundary points to neighbor process.
In order to calculate integral, each p-process calculates the partial sum of elements V(xi, tj) in accordance the Simpson quadrature formula. Then resulting summation is performed in the process p = 0 and averaged in time.
Conclusions
► We demonstrate that the parallel realization of numerical approach of the stack of long JJ leads to the acceleration of calculations 7 times.
► We have shown that in the stack of long Josephson junctions fluxons can coexist with the longitudinal plasma wave and the charge traveling wave.
► Charge traveling wave leads to the decreasing of radiation power
► We have realized the parallel simulation of the phase dynamics of the stack of long JJ using MPI technique.
► When fluxons are synchronized the longitudinal plasma wave brings to the increasing of radiation power