Download Magnetic Material if the material is linear, i.e, , where is the magnetic

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Magnetic Material
if the material is linear, i.e,
, where
is the magnetic dipole
density due to the spin of electrons.
Diamagnetic:
Paramagnetic:
decreases as
increases as
increases.
increases.
Material with Residual Magnetization
For some material, residue
exist even when the applied
is zero.
Ferromagnetic: neighboring dipoles align in the same direction.
Antiferromagnetic: neighboring dipoles align in the opposite
direction such that cancel each other.
Ferrimagnetic(Ferrites):neighboring dipoles align in the opposite
direction, but due to different types of atoms are present, the dipoles
do not cancel.
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Hysteretic curve
Permeability Matrix of Ferrites
Let
be the angular momentum of an electron, the magnetic
moment is proportional to the angular momentum by a ratio ,
that is,
If
is the torque acting on the electron, we have
Since
If
Since
.
, we have
is the number of electron per unit volume,
.
, we have
.
Consider the applied magnetic field in the form of a sum dc and ac
terms:
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Suppose
is large enough that the ferrite is saturated. Then,
the saturated magnetism and
. Substitute to the above
equation and ignoring higher order terms, we have
Solve for the relationship between
where
in which
is
and
, we have
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TEM Wave Propagation in Ferrites
Assume that direction of the static magnetic field and the propagation
direction of the TEM wave are both in direction. Taking the curl of
Maxwell’s equation, we have
It can be derived that
Let the
. The above equation becomes
dependancy be
, the only possible solution is
: circular polarized waves.
And
The wave impedance becomes
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Faraday Rotation
Let a linearly polarized wave propagate in the
direction with
vector in the direction at the plane
in the ferrite. This field
may be decomposed into circularly polarized modes of propagation
Therefore the total field is
Let the angle of the total field to
be , then
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Thus the wave propagating along the gyrotropic axis has a
propagation constant
and a circularly rotating field. Note that
the direction of the rotation is the same for both
and
propagating waves which is a non-reciprocal behavior.
Faraday rotation: discovered by Michael Faraday around 1845.
Example:
for silica at
.
Ferrite Devices
Gyrator: produce a phase shift of 180 degrees in one direction and no
shift in the opposite direction.
Absorption isolator: attenuate a wave propagating in one direction
while effect only slightly the wave propagating in the other direction.
Circulator: transmit a wave from guide 1 to guide 2, 2 to 3, 3 to 4,
and 4 to 1.
Resonance and field displacement isolators.
Stripline Y-junction circulator.
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Permittivity of a stationary plasma in a magnetic field
Assume:
1. Stationary uniform magnetic field in direction only.
2. Only the electrons are moving. Ions are considered stationary
due to their heavy mass.
3. Thermal velocities and collisions are neglected.
4. Forces due to the magnetic fields of the electromagnetic waves
are ignored.
The DC part of current, charge and electron velocity be
respectively. The AC part of current, charge and electron velocity be
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respectively. Then
Neglecting the second order term, we have
.
From Lorentz equation
where
is the applied steady magnetic field.
Assume a plane wave propagation in an arbitrary direction in the
following form
Then
If the AC velocity is assumed to be small compared with any possible
phase velocities,
Therefore,
We have
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where
is called angular cyclotron frequency.
It is convenient to define an equivalent flux density that includes
the effect of convection currents. In matrix notation, the equivalent
displacement current is
where
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Space-Charge Waves on a Moving Plasma with Infinite Magnetic
Field
Let
and
be the DC and AC parts of the velocity of the space-
charge wave. Then, ignoring second order terms,
From continuity equation,
With infinite magnetic field,
wave form
, then
Also,
Since
or
Finally,
where
Then,
, we have
and all AC quantities having
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From the curl equation,
By assuming
dependancy, then
We find from previous equations,
Then,
Assuming plane wave, then
1.
.
, ordinary TEM with
2.
.
, space-charge waves.
Assume
, then
TEM Waves on a Stationary Plasma with Finite Magnetic Field
Assuming a TEM wave propagating in z-direction
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Similar to ferrites,
and