Cooper pairs are assumed to be paired due to phonon-electron interaction. In Josephson junction a critical current is developed with zero voltage. In a recent work I have found that there associated with this critical current a critical force that is associated with critical pow P_c=mu_0 c (I_0^2). This power can be seen as the ordinary electric power dissipated by a vacuum resistance, Z_0=mu_0c. I wonder whether this critical force could be related to force between two Cooper-pairs in the two sides of the junctions or not. Its value for a microampere current is 10^(-10) N which amounts to a force between two pairs at a distance of a few nanometer....Can any one help me what this force could represent?
Thank you in advance!
Arbab, is this experimental data or a calculation where you found the force? I specialize in finding very small exotic forces and unusual boundary condition effects.
Dear Chafin,
Thank you for your response.
The current density is along/opposite the direction of the magnetic field, depending on the sign of the charge.
Dear Remi
Thank you for your notice.
The force that result from my work relates to a critical power that is $P_c=mu_0 c I_0^2 and a critical force F_=\sqrt (6pi) mu_0 I_0^2. This current result from the magnetic field applied on the system (junction). It seems that this power is electric and is associated with a vacuum resistance Z_0=mu_0 c.
Dear Remi
Thank you once again. The formula was missing a term mu_0. It should read F_0=sqrt{6 pi) mu_0 I_0^2. This can be checked from the force between two straight long wires that is F=mu_0 (I_1) (I_2) L) /(2 pi r). Moreover, power is force X velocity.
Good luck for your careful reading.
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You quoted:
- "a critical force that is associated with critical pow P_c=mu_0 c (I_0^2)"
And I see what you have done now, P = Force x Velocity and you formula is dimensionally correct. I misread the P and thought you meant force.
You then equate the mu0.c term with resistance (characteristic impedance of free space) and draw an analogy with I^2R.
Most intriguing as it appears that power is being dissipated, yet we are talking about superconductors.
Where is your paper on this subject so that we can see the experimental and theoretical justifications for this, please?
3rd Mar, 2015
Arbab I. Arbab
Qassim University
Dears
You may look at my work related to this question in the attached file
3rd Mar, 2015
Patrick Das Gupta
University of Delhi
How thick was the slice of the insulator sandwiched between the two superconductors in your experiment involving the Josephson junction? Could the dissipation be due to taking a thicker slice so that (apart from the quantum tunneling of the Cooper pair from one superconductor to the other) the impedance of the insulator makes its presence felt?
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3rd Mar, 2015
Arbab I. Arbab
Qassim University
Dear Gupta
The thickness of the insulator is some a few nanometers.
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I have had a quick look at Arbab's paper and have found it very scholarly and convincing in its argument. It's definitely worth printing out for closer inspection.
What he is doing is reconstructing Maxwell's equations by analogy to Cooper pairs as massive bosons. He derives some very interesting results and one wonders as to their generality outside of a superconducting medium - or whether it forms an analogue for the study of massive spin 1 particles.
I see now also that the contentious stuff about radiation resistance and critical power is really to do with the radiation resistance to the propagation of massive spin 1 waves. I will give pages 5 onwards a more detailed reading to see what his thesis is and where this is going.
It's an interesting original read.
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