A Superconducting Mechanical Oscillator with a Variable Resonant Frequency
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A Superconducting Mechanical Oscillator with a Variable Resonant Frequency V. L. Tsymbalenko* Kurchatov Institute National Research Center, Moscow, 123182 Russia *e-mail: [email protected] Received March 31, 2020; revised April 7, 2020; accepted April 9, 2020
Abstract—The design of a high-quality mechanical oscillator made of a superconducting material, whose frequency is changed by an external magnetic field, has been proposed and tested. DOI: 10.1134/S002044122005022X
In experiments at low temperatures, an open loop of a superconducting material placed in a magnetic field is used to set the object in motion. Superconductivity ensures that there is no heat from the current that drives the loop. This technique was used to measure the viscosity of liquid 3He [1], on the basis of which a thermometry standard up to ~1 mK was proposed. Crystal propulsion of 4He in experiments on the kinetics of the motion of a quantum crystal was also performed using a superconducting loop [2]. The oscillation frequency of an (open) loop is determined by its mechanical parameters: the dimensions of the superconductor and its elastic constants. Therefore, such a loop can set the studied object in motion only at a fixed frequency. If the loop is closed so that superconductivity is not disturbed in the contact, then when the part of the loop crossing the magnetic field lines is deflected an undamped current is induced in the superconducting circuit, whose interaction with the field creates a non-dissipative restoring force. In this paper, we consider the vibrational regime of an elastic closed superconducting loop in a magnetic field. The effect of a magnetic field on the translational motion of a rigid superconducting rectangular loop was considered in [3, 4]. We consider the simplest U-shaped loop. The bottom of the loop is rigidly embedded in a fixed base. The crossbar length b is perpendicular to the magnetic field B directed along the axis Z. The parts of the loop from the base to the crossbar a are parallel to a magnetic field (see Fig. 1). In such a geometry, additional force is applied only to the crossbar. An object of mass M and moment of inertia J relative to the axis Y is at the free end of the loop. The equation of vibrations of a small rod is as follows [5]
∂ζ ∂ζ = EI y 4 , 2 ∂t ∂z 2
ρS
where ζ is the deviation of the rod profile from the equilibrium position in the direction X, ρ is the density of the material, E is Jung’s module, S is the cross-sectional area of the wire, and Iy is the moment of inertia of the section. The boundary conditions at the base are
ζ(0) = 0,
∂ζ = 0. ∂z z = 0
(2)
The inertia forces of an object of mass M and the interaction of the induced current with an external magnetic field are applied to the free end. The offset of the crossbar by ζ(a) creates a current IB = Bζ(a)b/L, where L is the circuit inductance. The total force when oscillating with a frequency ω is given by the expression
Ftotal = Mω ζ(a) − B b ζ(a)/L = −EI y 2
2 2
∂ζ . (3) 3 ∂z z = a 3
The moment caused by
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