we discuss the effect of saturation we need to define what we mean by saturation.
Put simply, saturation is a state in which the specimen has reached maximum magnetisation.
Now magnetisation can be thought of as the amount of microscopic atomic dipoles
which are aligned with one another. If we apply an external field these dipoles
will tend to align themselves with this field. The stronger the external field
becomes, the more dipoles become aligned. When all the dipoles are aligned the
specimen is said to be saturated. This is a simplified description but it conveys
the general idea. Now we need to ask ourselves what is the cause of the attraction
between the coil and projectile. Ultimately the forces are due to charge motion;
we have the motion of charge in the coil - the coil current, and we have orbital
electron motion in the specimen - the dipoles. If you open any textbook on electromagnetism
you'll find a description of the force between two infinite parallel current carrying
wires. The force between these wires will be attractive if the currents are parallel
and repulsive if the currents are anti-parallel. Now imagine two loops of wire
sitting side by side as shown in fig 1 below.
6.1 Current carrying loops are mutually attracted
the wire currents are in the same direction the force is attractive. Now the force
between these loops will depend on their diameter, their respective current, and
their separation, as well as the medium in which they are placed (e.g. free space).
What is of interest to us is the fact that increasing the current in either loop
will increase the force. Let's think of the coil and projectile. The coil is basically
a large number of wire loops, each carrying the same current. The projectile is
composed of many tiny current loops - the orbital electrons. Now normally in an
unmagnetised ferromagnetic material the current loops are organised into small
groups called domains. These domains are orientated in random directions so that
macroscopically, the material exhibits no magnetisation. Fig 2 illustrates the
randomly aligned loops. When an external field is applied, the loops within the
domains experience a torque force which tries to align them with the field. This
means that domains which are originally more aligned with the field tend to grow
at the expense of the less well aligned domains - the better aligned domains 'hijack'
loops from the surrounding less well aligned ones. The stronger the external field
becomes, the more fully aligned the loops become.
6.2 An unmagnetised material contains randomly ordered magnetic dipoles
3 shows some alignment of the loops as the coil field begins to influence them.
As the coil field is increased, more and more of the loops align until we reach
a point where, for our purposes, all the loops become aligned i.e. the material
is saturated. Think about the two loops in the first diagram again, we'll call
the loop on the left the coil, and the one on the right the projectile. You can
think of the saturation of the projectile as the right hand loop reaching a maximum
current, but the force depends on the current in both loops. Since the current
can be increased in the left hand loop (the coil) the attractive force will increase
even though the projectile is saturated (right hand loop current fixed).
6.3 An external field causes alignment of the dipoles and an attractive force
saturation of the projectile is of limited consequence, insofar as it doesn't
place a limit on the attractive force. I do think that running a coilgun with
a saturated projectile will be less efficient.
is another way to think about this using the pole concept of magnetics. Basically
a projectile can be thought of as one big dipole which has maximum pole strengths
determined by its saturation magnetisation. A magnetic pole (fictitious - nobody
has found an isolated pole, although particle theory predicts their existence)
experiences a force when placed in a magnetic field. Now since the projectile
is a dipole it has two poles of opposite magnitude, so if it is placed in a magnetic
field each pole will experience a force depending on the field strength around
it and the 'sign' of the pole (+north / -south). Since the sign of the pole determines
the direction of the force we find that the front of the projectile is attracted
towards the centre of the coil and the end of the projectile is repelled from
the coil. While this doesn't actually happen in reality, the use of poles is a
valid concept. Here is the important point: the field is stronger towards the
centre of the coil so the front pole experiences an attractive force which is
stronger than the repulsive force generated by the rear pole, resulting in a net
attraction. Now I mentioned earlier that the saturated projectile is a dipole
of fixed maximum strength, however, since the coil field can still be strengthened
by increasing its current the attractive force can still be increased. The strengthening
of the coil field increases the difference in the force on the projectile poles
and so increases the net attractive force. As fig 4 shows, any dipole which is
placed in a field gradient will experience a net force, the larger the gradient
becomes the stronger the resulting force. The forces on the poles can be expressed
P is the pole strength. Since our projectile consists of two opposing poles in
different field strengths, we can write
if we assume that the poles are of equal magnitude this reduces to
6.4. A dipole experiences a net force in a field gradient.
else to bear in mind is that although a material is often quoted with a value
of saturation flux density this doesn't mean that the flux density is limited
to this value. If the field is increased around a saturated material the flux
density will continue to increase with a dB/dH equal to vacuum. The reason for
this is that the material is full of space! - the space still contributes to the
flux with a relative permeability of 1. This is important when using B-H curves
for finite element analyses since the correct dB/dH must be used for large values
of field beyond the materials saturation point.
this simple interpretation of the nature of saturation and the realisation of
the underlying cause of the attractive force, it would appear that the output
from a coilgun can be increased when running with a saturated projectile. The
problem is that although the force becomes proportional to the field ( and hence
current) when the projectile is saturated, the energy required to establish
a given field increases as the square of the current. In order to double
the force it requires four times the energy to be supplied to the coil field.
These diminishing returns make it clear that there will be practical limits to
fields in reluctance coilguns, albeit fuzzy ones.
can find a description of magnetism from the perspective of poles in 'Introduction
to Electromagnetism' by Martin Sibley.