Flux line motion

1
Flux line motion
In principlea Type II superconductor should be
better than a Type I for most applications - it
remains superconducting to much higher fields
..but is it?
Flux lines tend to move easily so as to reach
equilibrium.
But if a current flows in a superconductor above
Hc1 there will be a Lorentz force acting between
the current (ie charge carriers) and the flux.
So the flux lines move perpendicular to the
current
v velocity of flux lines
Now, E is parallel to J, so acts like a resistive
voltage, and power is dissipated
1 watt of dissipated power at 4.2K requires 300MW
of refrigerator power!
The solution is to introduce pins by creating
defects within the superconductor
Lecture 8
2
The Bean Model
A Type II superconductor without any pinning is
said to be reversible - flux enters abruptly at
Hc1 and produces a uniform flux density
throughout.
If there are pinning centres within the Type II
superconductor they hold the flux lines back near
the surface creating a gradient of flux lines -
such superconductors are said to be irreversible
surface
Lecture 8
3
The Bean Model
The pins can be thought of as introducing
friction inhibiting the movement of flux lines
into the supercoductor
In this respect the superconductor is a little
like a sandpile with the flux lines behaving like
grains of sand
However big we make the sandpile the sloping
sides always have the same gradient
In an analogous fashion, however large the
magnetic field the gradient of flux lines remains
constant
This is the basis of the Bean Model
Lecture 8
4
The Bean Model
Remember that curl B?oJ So a field gradient
implies that a current is flowing perpendicular
to B
The Bean Model assumes that the effect of pinning
is to
From another viewpoint the Bean model assumes
(a) there exists a maximum current density Jc
(b) any emf, however small induces this current
to flow
The Bean model is therefore also known as the
critical state model only three current states
are allowed - zero current for regions that have
not felt B and Jc (ie the critical current
density) depending upon the sense of the emf
generated by the last field change
Lecture 8
5
Critical state model - increasing field
Lecture 8
6
Critical state model - decreasing field
then reduce B to zero again
Because the flux density gradient must remain
constant, flux is trapped inside the
superconducting sample, even at B0
Lecture 8
7
Predictions of the Bean model
The magnetisation of a sample can be calculated
using the Bean model from diagrams such as the
previous ones, with B as the only free parameter
Lecture 8
8
Calculating the critical current density
From the Bean model the critical current density
is easily calculated from the hysteretic
magnetisation loop
The strength of the pinning force, F, can also be
determined
Lecture 8
9
Magnetic superconductors
Notice that in the 2nd quadrant of the hysteresis
loop the magnetisation of the sample is positive,
ie strongly (or even very strongly) paramagnetic.
2
3
So - depending upon the magnetic history of the
sample - the superconductor can be attracted to a
magnet!
4
1
Lecture 8
10
Critical current densities
Lecture 8
11
Critical current densities
Lecture 8
12
Small Angle Neutron Scattering
Braggs Law ?2dsin? neutron wavelength ?
10Å flux lattice spacing, d 1000Å sin? R/L
1/100
Lecture 9
13
Flux lattice melting
Lecture 9