Frozen mirror image method (or method of frozen images) is an extension of the
method of images The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which the domain of the sought function is extended by the addition of its mirror image with respect to a symmetry hyperplane. As a resu ...
for
magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nic ...
-
superconductor systems that has been introduced by
Alexander Kordyuk
Alexander A. Kordyuk (born December 9, 1967) is a Ukrainian experimental physicist, known mainly for invention of the Method of frozen images and several experimental techniques based on magnetic levitation, and for contribution to the field of ...
in 1998 to take into account the magnetic
flux pinning phenomenon.
The method gives a simple representation of the
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
distribution generated by a magnet (a system of magnets) outside an infinitely flat surface of a
perfectly hard (with infinite
pinning force)
type-II superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
in more general field cooled (FC) case, i.e. when the superconductor goes into superconducting state been already exposed to the magnetic field. The difference from the mirror image method, which deals with a perfect
type-I superconductor
The interior of a bulk superconductor cannot be penetrated by a weak magnetic field, a phenomenon known as the Meissner effect. When the applied magnetic field becomes too large, superconductivity breaks down. Superconductors can be divided into ...
(that completely expels the magnetic field, see the
Meissner effect), is that the perfectly hard superconductor screens the variation of the external magnetic field rather than the field itself.
Description
The name originates from the replacement of certain elements in the original layout with imaginary magnets, which replicates the boundary conditions of the problem (see
Dirichlet boundary conditions). In a simplest case of the
magnetic dipole
In electromagnetism, a magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric ...
over the flat superconducting surface (see Fig. 1), the magnetic field, generated by a dipole moved from its initial position (at which the superconductor is cooled to the superconducting state) to a final position and by the screening currents at the superconducting surface, is equivalent to the field of three magnetic dipoles: the real one (1), its mirror image (3), and the mirror image of it in initial (FC) position but with the
magnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
vector
Vector most often refers to:
*Euclidean vector, a quantity with a magnitude and a direction
*Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism
Vector may also refer to:
Mathematic ...
inversed (2).
Applications
The method is shown to work for the bulk
high temperature superconductors (HTSC),
which are characterized by strong pinning and used for calculation of the interaction in magnet-HTSC systems such as superconducting
magnetic bearings
A magnetic bearing is a type of bearing that supports a load using magnetic levitation. Magnetic bearings support moving parts without physical contact. For instance, they are able to levitate a rotating shaft and permit relative motion with ve ...
,
superconducting
flywheels,
MAGLEV
Maglev (derived from '' magnetic levitation''), is a system of train transportation that uses two sets of electromagnets: one set to repel and push the train up off the track, and another set to move the elevated train ahead, taking advantag ...
,
for
spacecraft
A spacecraft is a vehicle or machine designed to spaceflight, fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including Telecommunications, communications, Earth observation satellite, Earth ...
applications, as well as a
textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textboo ...
model for
science education
Science education is the teaching and learning of science to school children, college students, or adults within the general public. The field of science education includes work in science content, science process (the scientific method), some ...
.
[{{cite journal , last1 = Saito , first1 = Y. , year = 2009 , title = Observation of magnetic field lines in the vicinity of a superconductor with the naked eye , journal = ]European Journal of Physics
The ''European Journal of Physics'' is a peer-reviewed, scientific journal dedicated to maintaining and improving the standard of physics education in higher education. The journal, published since 1980, is now published by IOP Publishing on beh ...
, volume = 31 , issue = 1 , pages = 229–238 , doi = 10.1088/0143-0807/31/1/020 , bibcode = 2010EJPh...31..229S , arxiv =0805.3990, s2cid = 56360791
See also
*
Method of images The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which the domain of the sought function is extended by the addition of its mirror image with respect to a symmetry hyperplane. As a resu ...
*
Ideally hard superconductor An ideally hard superconductor is a type II superconductor material with an infinite pinning force. In the external magnetic field it behaves like an ideal diamagnet if the field is switched on when the material is in the superconducting state, so-c ...
*
Magnetic levitation
Magnetic levitation (maglev) or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational force and any other forces.
The ...
*
Bean's critical state model
*
High temperature superconductors
References
Demos
Superconducting levitation with strong pinningMagnetic levitation (YouTube)
Electromagnetism
Condensed matter physics
Superconductivity
Applied and interdisciplinary physics