The advantage of a magnetic mirror machine is that it can hold a plasma ball instead of a plasma torus.
A plasma ball has a better volume to surface ratio which would allow a more efficient explosion,
for the same reason H-bombs aren't doughnut shaped.
One of the fundamental results in magnetic confinement is that you can not form topologically spherical magnetic flux surfaces. This is a direct result of the magnetic divergence constraint \nabla \cdot \vec{B}=0. In practical terms this says that you can not magnetically confine a "plasma ball." (This result only applies to magnetically confined systems. Inertially or gravitationally confined systems can be spherically symmetric because they rely of different principles).
This is why mirrors has end cap losses, but this is also why closed field line systems like tokamaks are toroidal.
Mirrors do a lot of things to "plug" the end and minimize the end losses. In order to maintain magnetic confinement during the compression you would have to both increase the magnetic field everywhere self-similarly and find a way to increase the effect of the end "plugs." This is not practical.
The other way would be to increase the magnetic field so rapidly that the plasma is inertially confined not magnetically confined. The is what the Z-machine does.
If you instead try compressing a toroidal plasma with closed field lines then you don't have to worry about losses at the end. (Note that even though the plasma has to be toroidal, the reactor vessel doesn't have to be). The advantage of this approach is that you maintain magnetic confinement throughout the compression. As a result you don't have to ramp up you magnetic field as rapidly, nor as far. This is why there are a number of people studying FRC merging and compression (FRC=Field Reversed Configuration)
That's why I asked, as I don't see an advantage
Sorry. I didn't click on the "magnetic bottle" link and I didn't realize that it took you to a page about mirrors. I typically associate the magnetic bottle idea with all magnetic confinement concepts not just mirrors.
This produces more induction in the surrounding coils, which is used to produce energy.
Again this does not work. Even if all the energy from fusion where carried in charged particles, their monition is going to be isotropic(in all directions). In-order to capture energy from currents using a coil system you'd want the motion of these particles to be mono-directional.
There are practical ways to directly capture the energy from charged particles.
http://en.wikipedia.org/wiki/Direct_conversion
I wonder how many fusion reactors have already been invented.
I can think of about 2 dozen magnetic confinement concepts off hand. There is a conference dedicated to exploring new Innovative Confinement Concepts(ICC). They recently restructured and now call themselves the ERP(Exploratory Plasma Research).
http://www.iccworkshops.org/
That conference focuses on magnetic confinement. There are a number of alternative approaches to inertial confinement. And then there are the interial-electrostatic folks too.