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

L

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)

Theoretical model

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

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.

The main features of single long Josephson junction

The main features of single long Josephson junction

Comparative analysis fo single JJ and Stack of JJs

Comparative analysis of single JJ and Stack of JJs

Comparative analysis of single JJ and Stack of JJs

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