Could a Type-1 and Type-2 Superconductor Oscillator Work?

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The proposed device involves a short-circuited type-2 superconducting solenoid with a type-1 superconductor placed inside. As the type-1 superconductor cools and enters a superconducting state, it expels the magnetic field, reducing the solenoid's inductance and increasing current flow. This increase in current raises the magnetic induction to a critical level, causing the type-1 superconductor to lose its superconductivity. Consequently, the inductance returns to its original state, leading to a cyclical oscillation of current through the solenoid. This innovative use of superconductors could have significant applications in various fields.
goran d
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I came up with the following idea of a device:
We have a short circuited type-2 (to allow more current) superconducting solenoid. A current is flowing through the solenoid, and it creates magnetic induction inside, B1. Inside the solenoid we place a piece of type-1 superconductor. B1<critical induction of the type-1 superconductor. When the type-1 superconductor cools down and starts superconducting, it expels the magnetic field from itself, and, therefore, reduces the inductance of the solenoid. Now the coil is superconducting, which means that the voltage drop in the wire is zero. That means that, as the inductance gets reduced, the current through the solenoid is increased. Since the current is increased, the magnetic induction, caused by the coil, also increases, to a value B2. If we arrange the parameters of the device so that B2>critical induction, then the piece of superconductor will lose it's superconductivity. Which means that the inductance of the solenoid is reduced to it's original value. The current decreases, and the induction of the solenoid goes back to B1<critical induction. We are back where we started. So the device will oscillate, changing the current through the solenoid.

What do you think of it?
 
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This is a great idea! It is an interesting concept that could be used in various applications. The concept of using type-1 and type-2 superconductors to create oscillations is very clever and could potentially be very useful.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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